Merge branch 'develop' into feature/gpu-port

Grid/DisableWarnings.h

@@ -0,0 +1,63 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/DisableWarnings.h
+
+Copyright (C) 2016
+
+Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#ifndef DISABLE_WARNINGS_H
+#define DISABLE_WARNINGS_H
+
+
+
+#if defined __GNUC__ && __GNUC__>=6
+#pragma GCC diagnostic ignored "-Wignored-attributes"
+#endif
+
+ //disables and intel compiler specific warning (in json.hpp)
+#pragma warning disable 488  
+
+#ifdef __NVCC__
+ //disables nvcc specific warning in json.hpp
+#pragma clang diagnostic ignored "-Wdeprecated-register"
+#pragma diag_suppress unsigned_compare_with_zero
+#pragma diag_suppress cast_to_qualified_type
+
+ //disables nvcc specific warning in many files
+#pragma diag_suppress esa_on_defaulted_function_ignored
+#pragma diag_suppress extra_semicolon
+
+//Eigen only
+#endif
+
+// Disable vectorisation in Eigen on the Power8/9 and PowerPC
+#ifdef  __ALTIVEC__
+#define  EIGEN_DONT_VECTORIZE
+#endif
+#ifdef  __VSX__
+#define  EIGEN_DONT_VECTORIZE
+#endif
+
+#endif

Grid/Grid.h

@@ -0,0 +1,51 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Grid.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: azusayamaguchi <ayamaguc@YAMAKAZE.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+//
+//  Grid.h
+//  simd
+//
+//  Created by Peter Boyle on 09/05/2014.
+//  Copyright (c) 2014 University of Edinburgh. All rights reserved.
+//
+
+#ifndef GRID_H
+#define GRID_H
+
+#include <Grid/GridCore.h>
+#include <Grid/GridQCDcore.h>
+#include <Grid/qcd/action/Action.h>
+#include <Grid/qcd/utils/GaugeFix.h>
+NAMESPACE_CHECK(GaugeFix);
+#include <Grid/qcd/smearing/Smearing.h>
+NAMESPACE_CHECK(Smearing);
+#include <Grid/parallelIO/MetaData.h>
+#include <Grid/qcd/hmc/HMC_aggregate.h>
+
+#endif

Grid/GridCore.h

@@ -0,0 +1,66 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Grid.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: azusayamaguchi <ayamaguc@YAMAKAZE.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+//
+//  Grid.h
+//  simd
+//
+//  Created by Peter Boyle on 09/05/2014.
+//  Copyright (c) 2014 University of Edinburgh. All rights reserved.
+//
+
+#ifndef GRID_BASE_H
+#define GRID_BASE_H
+
+
+
+#include <Grid/DisableWarnings.h>
+#include <Grid/Namespace.h>
+#include <Grid/GridStd.h>
+#include <Grid/threads/Pragmas.h>
+#include <Grid/perfmon/Timer.h>
+#include <Grid/perfmon/PerfCount.h>
+#include <Grid/util/Util.h>
+#include <Grid/log/Log.h>
+#include <Grid/allocator/AlignedAllocator.h>
+#include <Grid/simd/Simd.h>
+#include <Grid/threads/Threads.h>
+#include <Grid/serialisation/Serialisation.h>
+#include <Grid/util/Sha.h>
+#include <Grid/communicator/Communicator.h> 
+#include <Grid/cartesian/Cartesian.h>    
+#include <Grid/tensors/Tensors.h>      
+#include <Grid/lattice/Lattice.h>      
+#include <Grid/cshift/Cshift.h>       
+#include <Grid/stencil/Stencil.h>      
+#include <Grid/parallelIO/BinaryIO.h>
+#include <Grid/algorithms/Algorithms.h>   
+NAMESPACE_CHECK(GridCore)
+
+#endif

Grid/GridQCDcore.h

@@ -0,0 +1,43 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Grid.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: azusayamaguchi <ayamaguc@YAMAKAZE.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_QCD_CORE_H
+#define GRID_QCD_CORE_H
+
+/////////////////////////
+// Core Grid QCD headers
+/////////////////////////
+#include <Grid/GridCore.h>
+#include <Grid/qcd/QCD.h>
+#include <Grid/qcd/spin/Spin.h>
+#include <Grid/qcd/utils/Utils.h>
+#include <Grid/qcd/representations/Representations.h>
+NAMESPACE_CHECK(GridQCDCore);
+
+#endif

Grid/GridStd.h

@@ -0,0 +1,29 @@
+#ifndef GRID_STD_H
+#define GRID_STD_H
+
+///////////////////
+// Std C++ dependencies
+///////////////////
+#include <cassert>
+#include <complex>
+#include <vector>
+#include <string>
+#include <iostream>
+#include <iomanip>
+#include <random>
+#include <functional>
+#include <stdio.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <signal.h>
+#include <ctime>
+#include <sys/time.h>
+#include <chrono>
+#include <zlib.h>
+
+///////////////////
+// Grid config
+///////////////////
+#include "Config.h"
+
+#endif /* GRID_STD_H */

Grid/Grid_Eigen_Dense.h

@@ -0,0 +1,52 @@
+#include <Grid/GridCore.h>
+#pragma once
+// Force Eigen to use MKL if Grid has been configured with --enable-mkl
+#ifdef USE_MKL
+#define EIGEN_USE_MKL_ALL
+#endif
+
+#if defined __GNUC__
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+#endif
+
+#ifdef __NVCC__
+
+#pragma push
+#pragma diag_suppress code_is_unreachable
+
+#define __NVCC__REDEFINE__
+
+#undef __NVCC__
+#undef __CUDACC__
+
+#ifdef __CUDA_ARCH__
+
+#define __CUDA_ARCH__REDEFINE__ 1
+#define __CUDA_ARCH_SAVE__ __CUDA_ARCH__
+
+#undef __CUDA_ARCH__
+
+#endif
+
+#endif
+
+#include <Grid/Eigen/Dense>
+
+#ifdef __NVCC__REDEFINE__
+
+#pragma pop
+
+#define __NVCC__
+#define __CUDACC__
+
+#ifdef __CUDA_ARCH__REDEFINE__
+
+#define __CUDA_ARCH__ __CUDA_ARCH_SAVE__
+
+#endif
+#endif
+
+#if defined __GNUC__
+#pragma GCC diagnostic pop
+#endif

Grid/Makefile.am

@@ -0,0 +1,63 @@
+extra_sources=
+extra_headers=
+
+if BUILD_COMMS_MPI3
+  extra_sources+=communicator/Communicator_mpi3.cc
+  extra_sources+=communicator/Communicator_base.cc
+  extra_sources+=communicator/SharedMemoryMPI.cc
+  extra_sources+=communicator/SharedMemory.cc
+endif
+
+if BUILD_COMMS_NONE
+  extra_sources+=communicator/Communicator_none.cc
+  extra_sources+=communicator/Communicator_base.cc
+  extra_sources+=communicator/SharedMemoryNone.cc
+  extra_sources+=communicator/SharedMemory.cc
+endif
+
+if BUILD_HDF5
+  extra_sources+=serialisation/Hdf5IO.cc 
+  extra_headers+=serialisation/Hdf5IO.h
+  extra_headers+=serialisation/Hdf5Type.h
+endif
+
+all: version-cache
+
+version-cache:
+	@if [ `git status --porcelain | grep -v '??' | wc -l` -gt 0 ]; then\
+		a="uncommited changes";\
+	else\
+		a="clean";\
+	fi;\
+	echo "`git log -n 1 --format=format:"#define GITHASH \\"%H:%d $$a\\"%n" HEAD`" > vertmp;\
+	if [ -e version-cache ]; then\
+		d=`diff vertmp version-cache`;\
+		if [ "$${d}" != "" ]; then\
+			mv vertmp version-cache;\
+			rm -f Version.h;\
+		fi;\
+	else\
+		mv vertmp version-cache;\
+		rm -f Version.h;\
+	fi;\
+	rm -f vertmp
+
+Version.h:
+	cp version-cache Version.h
+
+.PHONY: version-cache
+
+#
+# Libraries
+#
+include Make.inc
+include Eigen.inc
+
+lib_LIBRARIES = libGrid.a
+
+CCFILES += $(extra_sources)
+HFILES  += $(extra_headers) Config.h Version.h
+
+libGrid_a_SOURCES              = $(CCFILES)
+libGrid_adir                   = $(includedir)/Grid
+nobase_dist_pkginclude_HEADERS = $(HFILES) $(eigen_files) $(eigen_unsupp_files)

Grid/Namespace.h

@@ -0,0 +1,38 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/Namespace.h
+
+Copyright (C) 2016
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#include <type_traits>
+#include <cassert>
+
+#define NAMESPACE_BEGIN(A) namespace A {
+#define NAMESPACE_END(A)   }
+#define GRID_NAMESPACE_BEGIN NAMESPACE_BEGIN(Grid)
+#define GRID_NAMESPACE_END   NAMESPACE_END(Grid)
+#define NAMESPACE_CHECK(x) struct namespaceTEST##x {};  static_assert(std::is_same<namespaceTEST##x, ::namespaceTEST##x>::value,"Not in :: at"  ); 

Grid/algorithms/Algorithms.h

@@ -0,0 +1,61 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: ./lib/Algorithms.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_ALGORITHMS_H
+#define GRID_ALGORITHMS_H
+
+#include <Grid/algorithms/SparseMatrix.h>
+#include <Grid/algorithms/LinearOperator.h>
+#include <Grid/algorithms/Preconditioner.h>
+
+#include <Grid/algorithms/approx/Zolotarev.h>
+#include <Grid/algorithms/approx/Chebyshev.h>
+#include <Grid/algorithms/approx/Remez.h>
+#include <Grid/algorithms/approx/MultiShiftFunction.h>
+#include <Grid/algorithms/approx/Forecast.h>
+
+#include <Grid/algorithms/iterative/Deflation.h>
+#include <Grid/algorithms/iterative/ConjugateGradient.h>
+#include <Grid/algorithms/iterative/ConjugateResidual.h>
+#include <Grid/algorithms/iterative/NormalEquations.h>
+#include <Grid/algorithms/iterative/SchurRedBlack.h>
+#include <Grid/algorithms/iterative/ConjugateGradientMultiShift.h>
+#include <Grid/algorithms/iterative/ConjugateGradientMixedPrec.h>
+#include <Grid/algorithms/iterative/BlockConjugateGradient.h>
+#include <Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h>
+#include <Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h>
+#include <Grid/algorithms/CoarsenedMatrix.h>
+#include <Grid/algorithms/FFT.h>
+
+// EigCg
+// Pcg
+// Hdcg
+// GCR
+// etc..
+
+#endif

Grid/algorithms/CoarsenedMatrix.h

@@ -0,0 +1,486 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/CoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef  GRID_ALGORITHM_COARSENED_MATRIX_H
+#define  GRID_ALGORITHM_COARSENED_MATRIX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+class Geometry {
+  //    int dimension;
+public:
+  int npoint;
+  std::vector<int> directions   ;
+  std::vector<int> displacements;
+
+  Geometry(int _d)  {
+  
+    int base = (_d==5) ? 1:0;
+
+    // make coarse grid stencil for 4d , not 5d
+    if ( _d==5 ) _d=4;
+
+    npoint = 2*_d+1;
+    directions.resize(npoint);
+    displacements.resize(npoint);
+    for(int d=0;d<_d;d++){
+      directions[2*d  ] = d+base;
+      directions[2*d+1] = d+base;
+      displacements[2*d  ] = +1;
+      displacements[2*d+1] = -1;
+    }
+    directions   [2*_d]=0;
+    displacements[2*_d]=0;
+      
+    //// report back
+    std::cout<<GridLogMessage<<"directions    :";
+    for(int d=0;d<npoint;d++) std::cout<< directions[d]<< " ";
+    std::cout <<std::endl;
+    std::cout<<GridLogMessage<<"displacements :";
+    for(int d=0;d<npoint;d++) std::cout<< displacements[d]<< " ";
+    std::cout<<std::endl;
+  }
+  
+  /*
+  // Original cleaner code
+  Geometry(int _d) : dimension(_d), npoint(2*_d+1), directions(npoint), displacements(npoint) {
+  for(int d=0;d<dimension;d++){
+  directions[2*d  ] = d;
+  directions[2*d+1] = d;
+  displacements[2*d  ] = +1;
+  displacements[2*d+1] = -1;
+  }
+  directions   [2*dimension]=0;
+  displacements[2*dimension]=0;
+  }
+  std::vector<int> GetDelta(int point) {
+  std::vector<int> delta(dimension,0);
+  delta[directions[point]] = displacements[point];
+  return delta;
+  };
+  */    
+
+};
+  
+template<class Fobj,class CComplex,int nbasis>
+class Aggregation   {
+public:
+  typedef iVector<CComplex,nbasis >             siteVector;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  GridBase *CoarseGrid;
+  GridBase *FineGrid;
+  std::vector<Lattice<Fobj> > subspace;
+  int checkerboard;
+  int Checkerboard(void){return checkerboard;}
+  Aggregation(GridBase *_CoarseGrid,GridBase *_FineGrid,int _checkerboard) : 
+    CoarseGrid(_CoarseGrid),
+    FineGrid(_FineGrid),
+    subspace(nbasis,_FineGrid),
+    checkerboard(_checkerboard)
+  {
+  };
+  
+  void Orthogonalise(void){
+    CoarseScalar InnerProd(CoarseGrid); 
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 2"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+    //      std::cout << GridLogMessage <<" Gramm-Schmidt checking orthogonality"<<std::endl;
+    //      CheckOrthogonal();
+  } 
+  void CheckOrthogonal(void){
+    CoarseVector iProj(CoarseGrid); 
+    CoarseVector eProj(CoarseGrid); 
+    for(int i=0;i<nbasis;i++){
+      blockProject(iProj,subspace[i],subspace);
+      eProj=Zero(); 
+      thread_loop( (int ss=0;ss<CoarseGrid->oSites();ss++),{
+	eProj[ss](i)=CComplex(1.0);
+      });
+      eProj=eProj - iProj;
+      std::cout<<GridLogMessage<<"Orthog check error "<<i<<" " << norm2(eProj)<<std::endl;
+    }
+    std::cout<<GridLogMessage <<"CheckOrthog done"<<std::endl;
+  }
+  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+    blockProject(CoarseVec,FineVec,subspace);
+  }
+  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+    FineVec.Checkerboard() = subspace[0].Checkerboard();
+    blockPromote(CoarseVec,FineVec,subspace);
+  }
+  void CreateSubspaceRandom(GridParallelRNG &RNG){
+    for(int i=0;i<nbasis;i++){
+      random(RNG,subspace[i]);
+      std::cout<<GridLogMessage<<" norm subspace["<<i<<"] "<<norm2(subspace[i])<<std::endl;
+    }
+    Orthogonalise();
+  }
+
+  /*
+    virtual void CreateSubspaceLanczos(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) 
+    {
+    // Run a Lanczos with sloppy convergence
+    const int Nstop = nn;
+    const int Nk = nn+20;
+    const int Np = nn+20;
+    const int Nm = Nk+Np;
+    const int MaxIt= 10000;
+    RealD resid = 1.0e-3;
+
+    Chebyshev<FineField> Cheb(0.5,64.0,21);
+    ImplicitlyRestartedLanczos<FineField> IRL(hermop,Cheb,Nstop,Nk,Nm,resid,MaxIt);
+    //	IRL.lock = 1;
+
+    FineField noise(FineGrid); gaussian(RNG,noise);
+    FineField tmp(FineGrid); 
+    std::vector<RealD>     eval(Nm);
+    std::vector<FineField> evec(Nm,FineGrid);
+
+    int Nconv;
+    IRL.calc(eval,evec,
+    noise,
+    Nconv);
+
+    // pull back nn vectors
+    for(int b=0;b<nn;b++){
+
+    subspace[b]   = evec[b];
+
+    std::cout << GridLogMessage <<"subspace["<<b<<"] = "<<norm2(subspace[b])<<std::endl;
+
+    hermop.Op(subspace[b],tmp); 
+    std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(tmp)<<std::endl;
+
+    noise = tmp -  sqrt(eval[b])*subspace[b] ;
+
+    std::cout<<GridLogMessage << " lambda_"<<b<<" = "<< eval[b] <<"  ;  [ M - Lambda ]_"<<b<<" vec_"<<b<<"  = " <<norm2(noise)<<std::endl;
+
+    noise = tmp +  eval[b]*subspace[b] ;
+
+    std::cout<<GridLogMessage << " lambda_"<<b<<" = "<< eval[b] <<"  ;  [ M - Lambda ]_"<<b<<" vec_"<<b<<"  = " <<norm2(noise)<<std::endl;
+
+    }
+    Orthogonalise();
+    for(int b=0;b<nn;b++){
+    std::cout << GridLogMessage <<"subspace["<<b<<"] = "<<norm2(subspace[b])<<std::endl;
+    }
+    }
+  */
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) {
+
+    RealD scale;
+
+    ConjugateGradient<FineField> CG(1.0e-2,10000);
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+
+    for(int b=0;b<nn;b++){
+	
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      for(int i=0;i<1;i++){
+
+	CG(hermop,noise,subspace[b]);
+
+	noise = subspace[b];
+	scale = std::pow(norm2(noise),-0.5); 
+	noise=noise*scale;
+
+      }
+
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
+      subspace[b]   = noise;
+
+    }
+
+    Orthogonalise();
+
+  }
+};
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class CoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+    
+  typedef iVector<CComplex,nbasis >             siteVector;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  Geometry         geom;
+  GridBase *       _grid; 
+  CartesianStencil<siteVector,siteVector> Stencil; 
+
+  std::vector<CoarseMatrix> A;
+
+      
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase * Grid(void)         { return _grid; };   // this is all the linalg routines need to know
+
+  RealD M (const CoarseVector &in, CoarseVector &out){
+
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+
+    SimpleCompressor<siteVector> compressor;
+    Stencil.HaloExchange(in,compressor);
+    auto in_v = in.View();
+    auto out_v = in.View();
+    thread_loop( (int ss=0;ss<Grid()->oSites();ss++),{
+      siteVector res = Zero();
+      siteVector nbr;
+      int ptype;
+      StencilEntry *SE;
+      for(int point=0;point<geom.npoint;point++){
+
+	SE=Stencil.GetEntry(ptype,point,ss);
+	  
+	if(SE->_is_local&&SE->_permute) { 
+	  permute(nbr,in_v[SE->_offset],ptype);
+	} else if(SE->_is_local) { 
+	  nbr = in_v[SE->_offset];
+	} else {
+	  nbr = Stencil.CommBuf()[SE->_offset];
+	}
+	auto A_point = A[point].View();
+	res = res + A_point[ss]*nbr;
+      }
+      vstream(out_v[ss],res);
+    });
+    return norm2(out);
+  };
+
+  RealD Mdag (const CoarseVector &in, CoarseVector &out){ 
+    return M(in,out);
+  };
+
+  // Defer support for further coarsening for now
+  void Mdiag    (const CoarseVector &in,  CoarseVector &out){};
+  void Mdir     (const CoarseVector &in,  CoarseVector &out,int dir, int disp){};
+
+  CoarsenedMatrix(GridCartesian &CoarseGrid) 	: 
+
+    _grid(&CoarseGrid),
+    geom(CoarseGrid._ndimension),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    A(geom.npoint,&CoarseGrid)
+  {
+  };
+
+  void CoarsenOperator(GridBase *FineGrid,LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace){
+
+    FineField iblock(FineGrid); // contributions from within this block
+    FineField oblock(FineGrid); // contributions from outwith this block
+
+    FineField     phi(FineGrid);
+    FineField     tmp(FineGrid);
+    FineField     zz(FineGrid); zz=Zero();
+    FineField    Mphi(FineGrid);
+
+    Lattice<iScalar<vInteger> > coor(FineGrid);
+
+    CoarseVector iProj(Grid()); 
+    CoarseVector oProj(Grid()); 
+    CoarseScalar InnerProd(Grid()); 
+
+    // Orthogonalise the subblocks over the basis
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    // Compute the matrix elements of linop between this orthonormal
+    // set of vectors.
+    int self_stencil=-1;
+    for(int p=0;p<geom.npoint;p++){ 
+      A[p]=Zero();
+      if( geom.displacements[p]==0){
+	self_stencil=p;
+      }
+    }
+    assert(self_stencil!=-1);
+
+    for(int i=0;i<nbasis;i++){
+      phi=Subspace.subspace[i];
+	
+      std::cout<<GridLogMessage<<"("<<i<<").."<<std::endl;
+
+      for(int p=0;p<geom.npoint;p++){ 
+
+	int dir   = geom.directions[p];
+	int disp  = geom.displacements[p];
+
+	Integer block=(FineGrid->_rdimensions[dir])/(Grid()->_rdimensions[dir]);
+
+	LatticeCoordinate(coor,dir);
+
+	if ( disp==0 ){
+	  linop.OpDiag(phi,Mphi);
+	}
+	else  {
+	  linop.OpDir(phi,Mphi,dir,disp); 
+	}
+
+	////////////////////////////////////////////////////////////////////////
+	// Pick out contributions coming from this cell and neighbour cell
+	////////////////////////////////////////////////////////////////////////
+	if ( disp==0 ) {
+	  iblock = Mphi;
+	  oblock = Zero();
+	} else if ( disp==1 ) {
+	  oblock = where(mod(coor,block)==(block-1),Mphi,zz);
+	  iblock = where(mod(coor,block)!=(block-1),Mphi,zz);
+	} else if ( disp==-1 ) {
+	  oblock = where(mod(coor,block)==(Integer)0,Mphi,zz);
+	  iblock = where(mod(coor,block)!=(Integer)0,Mphi,zz);
+	} else {
+	  assert(0);
+	}
+
+	Subspace.ProjectToSubspace(iProj,iblock);
+	Subspace.ProjectToSubspace(oProj,oblock);
+	//	  blockProject(iProj,iblock,Subspace.subspace);
+	//	  blockProject(oProj,oblock,Subspace.subspace);
+	auto iProj_v = iProj.View() ;
+	auto oProj_v = oProj.View() ;
+	auto A_p     =  A[p].View();
+	auto A_self  = A[self_stencil].View();
+	thread_loop( (int ss=0;ss<Grid()->oSites();ss++),{
+	  for(int j=0;j<nbasis;j++){
+	    if( disp!= 0 ) {
+	      A_p[ss](j,i) = oProj_v[ss](j);
+	    }
+	    A_self[ss](j,i) =	A_self[ss](j,i) + iProj_v[ss](j);
+	  }
+	});
+      }
+    }
+
+#if 0
+    ///////////////////////////
+    // test code worth preserving in if block
+    ///////////////////////////
+    std::cout<<GridLogMessage<< " Computed matrix elements "<< self_stencil <<std::endl;
+    for(int p=0;p<geom.npoint;p++){
+      std::cout<<GridLogMessage<< "A["<<p<<"]" << std::endl;
+      std::cout<<GridLogMessage<< A[p] << std::endl;
+    }
+    std::cout<<GridLogMessage<< " picking by block0 "<< self_stencil <<std::endl;
+
+    phi=Subspace.subspace[0];
+    std::vector<int> bc(FineGrid->_ndimension,0);
+
+    blockPick(Grid(),phi,tmp,bc);      // Pick out a block
+    linop.Op(tmp,Mphi);                // Apply big dop
+    blockProject(iProj,Mphi,Subspace.subspace); // project it and print it
+    std::cout<<GridLogMessage<< " Computed matrix elements from block zero only "<<std::endl;
+    std::cout<<GridLogMessage<< iProj <<std::endl;
+    std::cout<<GridLogMessage<<"Computed Coarse Operator"<<std::endl;
+#endif
+    //      ForceHermitian();
+    AssertHermitian();
+    // ForceDiagonal();
+  }
+  void ForceDiagonal(void) {
+
+
+    std::cout<<GridLogMessage<<"**************************************************"<<std::endl;
+    std::cout<<GridLogMessage<<"****   Forcing coarse operator to be diagonal ****"<<std::endl;
+    std::cout<<GridLogMessage<<"**************************************************"<<std::endl;
+    for(int p=0;p<8;p++){
+      A[p]=Zero();
+    }
+
+    GridParallelRNG  RNG(Grid()); RNG.SeedFixedIntegers(std::vector<int>({55,72,19,17,34}));
+    Lattice<iScalar<CComplex> > val(Grid()); random(RNG,val);
+
+    Complex one(1.0);
+
+    iMatrix<CComplex,nbasis> ident;  ident=one;
+
+    val = val*adj(val);
+    val = val + 1.0;
+
+    A[8] = val*ident;
+
+    //      for(int s=0;s<Grid()->oSites();s++) {
+    //	A[8][s]=val[s];
+    //      }
+  }
+  void ForceHermitian(void) {
+    for(int d=0;d<4;d++){
+      int dd=d+1;
+      A[2*d] = adj(Cshift(A[2*d+1],dd,1));
+    }
+    //      A[8] = 0.5*(A[8] + adj(A[8]));
+  }
+  void AssertHermitian(void) {
+    CoarseMatrix AA    (Grid());
+    CoarseMatrix AAc   (Grid());
+    CoarseMatrix Diff  (Grid());
+    for(int d=0;d<4;d++){
+	
+      int dd=d+1;
+      AAc = Cshift(A[2*d+1],dd,1);
+      AA  = A[2*d];
+	
+      Diff = AA - adj(AAc);
+
+      std::cout<<GridLogMessage<<"Norm diff dim "<<d<<" "<< norm2(Diff)<<std::endl;
+      std::cout<<GridLogMessage<<"Norm dim "<<d<<" "<< norm2(AA)<<std::endl;
+	  
+    }
+    Diff = A[8] - adj(A[8]);
+    std::cout<<GridLogMessage<<"Norm diff local "<< norm2(Diff)<<std::endl;
+    std::cout<<GridLogMessage<<"Norm local "<< norm2(A[8])<<std::endl;
+  }
+    
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/FFT.h

@@ -0,0 +1,291 @@
+
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Cshift.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_FFT_H_
+#define _GRID_FFT_H_
+
+#ifdef HAVE_FFTW
+#ifdef USE_MKL
+#include <fftw/fftw3.h>
+#else
+#include <fftw3.h>
+#endif
+#endif
+
+
+NAMESPACE_BEGIN(Grid);
+
+template<class scalar> struct FFTW { };
+
+#ifdef HAVE_FFTW	
+template<> struct FFTW<ComplexD> {
+public:
+
+  typedef fftw_complex FFTW_scalar;
+  typedef fftw_plan    FFTW_plan;
+
+  static FFTW_plan fftw_plan_many_dft(int rank, const int *n,int howmany,
+				      FFTW_scalar *in, const int *inembed,		
+				      int istride, int idist,		
+				      FFTW_scalar *out, const int *onembed,		
+				      int ostride, int odist,		
+				      int sign, unsigned flags) {
+    return ::fftw_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
+  }	  
+    
+  static void fftw_flops(const FFTW_plan p,double *add, double *mul, double *fmas){
+    ::fftw_flops(p,add,mul,fmas);
+  }
+
+  inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out) {
+    ::fftw_execute_dft(p,in,out);
+  }
+  inline static void fftw_destroy_plan(const FFTW_plan p) {
+    ::fftw_destroy_plan(p);
+  }
+};
+
+template<> struct FFTW<ComplexF> {
+public:
+
+  typedef fftwf_complex FFTW_scalar;
+  typedef fftwf_plan    FFTW_plan;
+
+  static FFTW_plan fftw_plan_many_dft(int rank, const int *n,int howmany,
+				      FFTW_scalar *in, const int *inembed,		
+				      int istride, int idist,		
+				      FFTW_scalar *out, const int *onembed,		
+				      int ostride, int odist,		
+				      int sign, unsigned flags) {
+    return ::fftwf_plan_many_dft(rank,n,howmany,in,inembed,istride,idist,out,onembed,ostride,odist,sign,flags);
+  }	  
+    
+  static void fftw_flops(const FFTW_plan p,double *add, double *mul, double *fmas){
+    ::fftwf_flops(p,add,mul,fmas);
+  }
+
+  inline static void fftw_execute_dft(const FFTW_plan p,FFTW_scalar *in,FFTW_scalar *out) {
+    ::fftwf_execute_dft(p,in,out);
+  }
+  inline static void fftw_destroy_plan(const FFTW_plan p) {
+    ::fftwf_destroy_plan(p);
+  }
+};
+
+#endif
+
+#ifndef FFTW_FORWARD
+#define FFTW_FORWARD (-1)
+#define FFTW_BACKWARD (+1)
+#endif
+
+class FFT {
+private:
+    
+  GridCartesian *vgrid;
+  GridCartesian *sgrid;
+    
+  int Nd;
+  double flops;
+  double flops_call;
+  uint64_t usec;
+    
+  Coordinate dimensions;
+  Coordinate processors;
+  Coordinate processor_coor;
+    
+public:
+    
+  static const int forward=FFTW_FORWARD;
+  static const int backward=FFTW_BACKWARD;
+    
+  double Flops(void) {return flops;}
+  double MFlops(void) {return flops/usec;}
+  double USec(void)   {return (double)usec;}    
+
+  FFT ( GridCartesian * grid ) :
+    vgrid(grid),
+    Nd(grid->_ndimension),
+    dimensions(grid->_fdimensions),
+    processors(grid->_processors),
+    processor_coor(grid->_processor_coor)
+  {
+    flops=0;
+    usec =0;
+    Coordinate layout(Nd,1);
+    sgrid = new GridCartesian(dimensions,layout,processors);
+  };
+    
+  ~FFT ( void)  {
+    delete sgrid;
+  }
+    
+  template<class vobj>
+  void FFT_dim_mask(Lattice<vobj> &result,const Lattice<vobj> &source,Coordinate mask,int sign){
+
+    conformable(result.Grid(),vgrid);
+    conformable(source.Grid(),vgrid);
+    Lattice<vobj> tmp(vgrid);
+    tmp = source;
+    for(int d=0;d<Nd;d++){
+      if( mask[d] ) {
+	FFT_dim(result,tmp,d,sign);
+	tmp=result;
+      }
+    }
+  }
+
+  template<class vobj>
+  void FFT_all_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int sign){
+    Coordinate mask(Nd,1);
+    FFT_dim_mask(result,source,mask,sign);
+  }
+
+
+  template<class vobj>
+  void FFT_dim(Lattice<vobj> &result,const Lattice<vobj> &source,int dim, int sign){
+#ifndef HAVE_FFTW
+    assert(0);
+#else
+    conformable(result.Grid(),vgrid);
+    conformable(source.Grid(),vgrid);
+
+    int L = vgrid->_ldimensions[dim];
+    int G = vgrid->_fdimensions[dim];
+      
+    Coordinate layout(Nd,1);
+    Coordinate pencil_gd(vgrid->_fdimensions);
+      
+    pencil_gd[dim] = G*processors[dim];
+      
+    // Pencil global vol LxLxGxLxL per node
+    GridCartesian pencil_g(pencil_gd,layout,processors);
+      
+    // Construct pencils
+    typedef typename vobj::scalar_object sobj;
+    typedef typename sobj::scalar_type   scalar;
+      
+    Lattice<sobj> pgbuf(&pencil_g);
+    auto pgbuf_v = pgbuf.View();
+
+    typedef typename FFTW<scalar>::FFTW_scalar FFTW_scalar;
+    typedef typename FFTW<scalar>::FFTW_plan   FFTW_plan;
+      
+    int Ncomp = sizeof(sobj)/sizeof(scalar);
+    int Nlow  = 1;
+    for(int d=0;d<dim;d++){
+      Nlow*=vgrid->_ldimensions[d];
+    }
+      
+    int rank = 1;  /* 1d transforms */
+    int n[] = {G}; /* 1d transforms of length G */
+    int howmany = Ncomp;
+    int odist,idist,istride,ostride;
+    idist   = odist   = 1;          /* Distance between consecutive FT's */
+    istride = ostride = Ncomp*Nlow; /* distance between two elements in the same FT */
+    int *inembed = n, *onembed = n;
+      
+    scalar div;
+    if ( sign == backward ) div = 1.0/G;
+    else if ( sign == forward ) div = 1.0;
+    else assert(0);
+      
+    FFTW_plan p;
+    {
+      FFTW_scalar *in = (FFTW_scalar *)&pgbuf_v[0];
+      FFTW_scalar *out= (FFTW_scalar *)&pgbuf_v[0];
+      p = FFTW<scalar>::fftw_plan_many_dft(rank,n,howmany,
+					   in,inembed,
+					   istride,idist,
+					   out,onembed,
+					   ostride, odist,
+					   sign,FFTW_ESTIMATE);
+    }
+      
+    // Barrel shift and collect global pencil
+    Coordinate lcoor(Nd), gcoor(Nd);
+    result = source;
+    int pc = processor_coor[dim];
+    for(int p=0;p<processors[dim];p++) {
+      thread_loop( (int idx=0;idx<sgrid->lSites();idx++), {
+          Coordinate cbuf(Nd);
+          sobj s;
+	  sgrid->LocalIndexToLocalCoor(idx,cbuf);
+	  peekLocalSite(s,result,cbuf);
+	  cbuf[dim]+=((pc+p) % processors[dim])*L;
+	  //            cbuf[dim]+=p*L;
+	  pokeLocalSite(s,pgbuf,cbuf);
+      });
+      if (p != processors[dim] - 1) {
+	result = Cshift(result,dim,L);
+      }
+    }
+      
+    // Loop over orthog coords
+    int NN=pencil_g.lSites();
+    GridStopWatch timer;
+    timer.Start();
+    thread_loop( (int idx=0;idx<NN;idx++), {
+        Coordinate cbuf(Nd);
+	pencil_g.LocalIndexToLocalCoor(idx, cbuf);
+	if ( cbuf[dim] == 0 ) {  // restricts loop to plane at lcoor[dim]==0
+	  FFTW_scalar *in = (FFTW_scalar *)&pgbuf_v[idx];
+	  FFTW_scalar *out= (FFTW_scalar *)&pgbuf_v[idx];
+	  FFTW<scalar>::fftw_execute_dft(p,in,out);
+	}
+    });
+    timer.Stop();
+      
+    // performance counting
+    double add,mul,fma;
+    FFTW<scalar>::fftw_flops(p,&add,&mul,&fma);
+    flops_call = add+mul+2.0*fma;
+    usec += timer.useconds();
+    flops+= flops_call*NN;
+      
+    // writing out result
+    thread_loop( (int idx=0;idx<sgrid->lSites();idx++), {
+	Coordinate clbuf(Nd), cgbuf(Nd);
+	sobj s;
+	sgrid->LocalIndexToLocalCoor(idx,clbuf);
+	cgbuf = clbuf;
+	cgbuf[dim] = clbuf[dim]+L*pc;
+	peekLocalSite(s,pgbuf,cgbuf);
+	pokeLocalSite(s,result,clbuf);
+    });
+    result = result*div;
+      
+    // destroying plan
+    FFTW<scalar>::fftw_destroy_plan(p);
+#endif
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/LinearOperator.h

@@ -0,0 +1,498 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/LinearOperator.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef  GRID_ALGORITHM_LINEAR_OP_H
+#define  GRID_ALGORITHM_LINEAR_OP_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// LinearOperators Take a something and return a something.
+/////////////////////////////////////////////////////////////////////////////////////////////
+//
+// Hopefully linearity is satisfied and the AdjOp is indeed the Hermitian Conjugateugate (transpose if real):
+//SBase
+//   i)  F(a x + b y) = aF(x) + b F(y).
+//  ii)  <x|Op|y> = <y|AdjOp|x>^\ast
+//
+// Would be fun to have a test linearity & Herm Conj function!
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class LinearOperatorBase {
+public:
+
+  // Support for coarsening to a multigrid
+  virtual void OpDiag (const Field &in, Field &out) = 0; // Abstract base
+  virtual void OpDir  (const Field &in, Field &out,int dir,int disp) = 0; // Abstract base
+
+  virtual void Op     (const Field &in, Field &out) = 0; // Abstract base
+  virtual void AdjOp  (const Field &in, Field &out) = 0; // Abstract base
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2)=0;
+  virtual void HermOp(const Field &in, Field &out)=0;
+};
+
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// By sharing the class for Sparse Matrix across multiple operator wrappers, we can share code
+// between RB and non-RB variants. Sparse matrix is like the fermion action def, and then
+// the wrappers implement the specialisation of "Op" and "AdjOp" to the cases minimising
+// replication of code.
+//
+// I'm not entirely happy with implementation; to share the Schur code between herm and non-herm
+// while still having a "OpAndNorm" in the abstract base I had to implement it in both cases
+// with an assert trap in the non-herm. This isn't right; there must be a better C++ way to
+// do it, but I fear it required multiple inheritance and mixed in abstract base classes
+/////////////////////////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////
+// Construct herm op from non-herm matrix
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class MdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  MdagMLinearOperator(Matrix &Mat): _Mat(Mat){};
+
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+  }
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.Mdag(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    _Mat.MdagM(in,out,n1,n2);
+  }
+  void HermOp(const Field &in, Field &out){
+    RealD n1,n2;
+    HermOpAndNorm(in,out,n1,n2);
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// Construct herm op and shift it for mgrid smoother
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class ShiftedMdagMLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+  RealD _shift;
+public:
+  ShiftedMdagMLinearOperator(Matrix &Mat,RealD shift): _Mat(Mat), _shift(shift){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+    assert(0);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+    assert(0);
+  }
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+    assert(0);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.Mdag(in,out);
+    assert(0);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    _Mat.MdagM(in,out,n1,n2);
+    out = out + _shift*in;
+
+    ComplexD dot;	
+    dot= innerProduct(in,out);
+    n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    RealD n1,n2;
+    HermOpAndNorm(in,out,n1,n2);
+  }
+};
+
+////////////////////////////////////////////////////////////////////
+// Wrap an already herm matrix
+////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class HermitianLinearOperator : public LinearOperatorBase<Field> {
+  Matrix &_Mat;
+public:
+  HermitianLinearOperator(Matrix &Mat): _Mat(Mat){};
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    _Mat.Mdiag(in,out);
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    _Mat.Mdir(in,out,dir,disp);
+  }
+  void Op     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    _Mat.M(in,out);
+	
+    ComplexD dot= innerProduct(in,out); n1=real(dot);
+    n2=norm2(out);
+  }
+  void HermOp(const Field &in, Field &out){
+    _Mat.M(in,out);
+  }
+};
+
+//////////////////////////////////////////////////////////
+// Even Odd Schur decomp operators; there are several
+// ways to introduce the even odd checkerboarding
+//////////////////////////////////////////////////////////
+
+template<class Field>
+class SchurOperatorBase :  public LinearOperatorBase<Field> {
+public:
+  virtual  RealD Mpc      (const Field &in, Field &out) =0;
+  virtual  RealD MpcDag   (const Field &in, Field &out) =0;
+  virtual void MpcDagMpc(const Field &in, Field &out,RealD &ni,RealD &no) 
+  {
+    Field tmp(in.Grid());
+    tmp.Checkerboard() = in.Checkerboard();
+    ni=Mpc(in,tmp);
+    no=MpcDag(tmp,out);
+  }
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+    out.Checkerboard() = in.Checkerboard();
+    MpcDagMpc(in,out,n1,n2);
+  }
+  virtual void HermOp(const Field &in, Field &out){
+    RealD n1,n2;
+    HermOpAndNorm(in,out,n1,n2);
+  }
+  void Op     (const Field &in, Field &out){
+    Mpc(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){ 
+    MpcDag(in,out);
+  }
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {
+    assert(0); // must coarsen the unpreconditioned system
+  }
+  void OpDir  (const Field &in, Field &out,int dir,int disp) {
+    assert(0);
+  }
+};
+template<class Matrix,class Field>
+class SchurDiagMooeeOperator :  public SchurOperatorBase<Field> {
+protected:
+  Matrix &_Mat;
+public:
+  SchurDiagMooeeOperator (Matrix &Mat): _Mat(Mat){};
+  virtual  RealD Mpc      (const Field &in, Field &out) {
+    Field tmp(in.Grid());
+    //	std::cout <<"grid pointers: in.Grid()="<< in.Grid() << " out.Grid()=" << out.Grid() << "  _Mat.Grid=" << _Mat.Grid() << " _Mat.RedBlackGrid=" << _Mat.RedBlackGrid() << std::endl;
+    tmp.Checkerboard() = !in.Checkerboard();
+
+    _Mat.Meooe(in,tmp);
+    _Mat.MooeeInv(tmp,out);
+    _Mat.Meooe(out,tmp);
+
+      //std::cout << "cb in " << in.Checkerboard() << "  cb out " << out.Checkerboard() << std::endl;
+    _Mat.Mooee(in,out);
+    return axpy_norm(out,-1.0,tmp,out);
+  }
+  virtual  RealD MpcDag   (const Field &in, Field &out){
+    Field tmp(in.Grid());
+
+    _Mat.MeooeDag(in,tmp);
+    _Mat.MooeeInvDag(tmp,out);
+    _Mat.MeooeDag(out,tmp);
+
+    _Mat.MooeeDag(in,out);
+    return axpy_norm(out,-1.0,tmp,out);
+  }
+};
+template<class Matrix,class Field>
+class SchurDiagOneOperator :  public SchurOperatorBase<Field> {
+protected:
+  Matrix &_Mat;
+public:
+  SchurDiagOneOperator (Matrix &Mat): _Mat(Mat){};
+
+  virtual  RealD Mpc      (const Field &in, Field &out) {
+    Field tmp(in.Grid());
+
+    _Mat.Meooe(in,out);
+    _Mat.MooeeInv(out,tmp);
+    _Mat.Meooe(tmp,out);
+    _Mat.MooeeInv(out,tmp);
+
+    return axpy_norm(out,-1.0,tmp,in);
+  }
+  virtual  RealD MpcDag   (const Field &in, Field &out){
+    Field tmp(in.Grid());
+
+    _Mat.MooeeInvDag(in,out);
+    _Mat.MeooeDag(out,tmp);
+    _Mat.MooeeInvDag(tmp,out);
+    _Mat.MeooeDag(out,tmp);
+
+    return axpy_norm(out,-1.0,tmp,in);
+  }
+};
+template<class Matrix,class Field>
+class SchurDiagTwoOperator :  public SchurOperatorBase<Field> {
+protected:
+  Matrix &_Mat;
+public:
+  SchurDiagTwoOperator (Matrix &Mat): _Mat(Mat){};
+
+  virtual  RealD Mpc      (const Field &in, Field &out) {
+    Field tmp(in.Grid());
+
+    _Mat.MooeeInv(in,out);
+    _Mat.Meooe(out,tmp);
+    _Mat.MooeeInv(tmp,out);
+    _Mat.Meooe(out,tmp);
+
+    return axpy_norm(out,-1.0,tmp,in);
+  }
+  virtual  RealD MpcDag   (const Field &in, Field &out){
+    Field tmp(in.Grid());
+
+    _Mat.MeooeDag(in,out);
+    _Mat.MooeeInvDag(out,tmp);
+    _Mat.MeooeDag(tmp,out);
+    _Mat.MooeeInvDag(out,tmp);
+
+    return axpy_norm(out,-1.0,tmp,in);
+  }
+};
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Left  handed Moo^-1 ; (Moo - Moe Mee^-1 Meo) psi = eta  -->  ( 1 - Moo^-1 Moe Mee^-1 Meo ) psi = Moo^-1 eta
+// Right handed Moo^-1 ; (Moo - Moe Mee^-1 Meo) Moo^-1 Moo psi = eta  -->  ( 1 - Moe Mee^-1 Meo ) Moo^-1 phi=eta ; psi = Moo^-1 phi
+///////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field> using SchurDiagOneRH = SchurDiagTwoOperator<Matrix,Field> ;
+template<class Matrix,class Field> using SchurDiagOneLH = SchurDiagOneOperator<Matrix,Field> ;
+///////////////////////////////////////////////////////////////////////////////////////////////////
+//  Staggered use
+///////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Matrix,class Field>
+class SchurStaggeredOperator :  public SchurOperatorBase<Field> {
+protected:
+  Matrix &_Mat;
+      Field tmp;
+      RealD mass;
+      double tMpc;
+      double tIP;
+      double tMeo;
+      double taxpby_norm;
+      uint64_t ncall;
+public:
+      void Report(void)
+      {
+	std::cout << GridLogMessage << " HermOpAndNorm.Mpc "<< tMpc/ncall<<" usec "<<std::endl;
+	std::cout << GridLogMessage << " HermOpAndNorm.IP  "<< tIP /ncall<<" usec "<<std::endl;
+	std::cout << GridLogMessage << " Mpc.MeoMoe        "<< tMeo/ncall<<" usec "<<std::endl;
+	std::cout << GridLogMessage << " Mpc.axpby_norm    "<< taxpby_norm/ncall<<" usec "<<std::endl;
+      }
+      SchurStaggeredOperator (Matrix &Mat): _Mat(Mat), tmp(_Mat.RedBlackGrid()) 
+      { 
+	assert( _Mat.isTrivialEE() );
+	mass = _Mat.Mass();
+	tMpc=0;
+	tIP =0;
+        tMeo=0;
+        taxpby_norm=0;
+	ncall=0;
+      }
+  virtual void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){
+	ncall++;
+	tMpc-=usecond();
+    n2 = Mpc(in,out);
+	tMpc+=usecond();
+	tIP-=usecond();
+    ComplexD dot= innerProduct(in,out);
+	tIP+=usecond();
+    n1 = real(dot);
+  }
+  virtual void HermOp(const Field &in, Field &out){
+	ncall++;
+	tMpc-=usecond();
+	_Mat.Meooe(in,out);
+	_Mat.Meooe(out,tmp);
+	tMpc+=usecond();
+	taxpby_norm-=usecond();
+	axpby(out,-1.0,mass*mass,tmp,in);
+	taxpby_norm+=usecond();
+  }
+  virtual  RealD Mpc      (const Field &in, Field &out) 
+  {
+
+    Field tmp(in.Grid());
+    Field tmp2(in.Grid());
+
+    //    std::cout << GridLogIterative << " HermOp.Mpc "<<std::endl;
+    _Mat.Mooee(in,out);
+    _Mat.Mooee(out,tmp);
+    //    std::cout << GridLogIterative << " HermOp.MooeeMooee "<<std::endl;
+
+    tMeo-=usecond();
+    _Mat.Meooe(in,out);
+    _Mat.Meooe(out,tmp);
+    tMeo+=usecond();
+    taxpby_norm-=usecond();
+    RealD nn=axpby_norm(out,-1.0,mass*mass,tmp,in);
+    taxpby_norm+=usecond();
+    return nn;
+  }
+  virtual  RealD MpcDag   (const Field &in, Field &out){
+    return Mpc(in,out);
+  }
+  virtual void MpcDagMpc(const Field &in, Field &out,RealD &ni,RealD &no) {
+    assert(0);// Never need with staggered
+  }
+};
+template<class Matrix,class Field> using SchurStagOperator = SchurStaggeredOperator<Matrix,Field>;
+
+
+/////////////////////////////////////////////////////////////
+// Base classes for functions of operators
+/////////////////////////////////////////////////////////////
+template<class Field> class OperatorFunction {
+public:
+  virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) = 0;
+      virtual void operator() (LinearOperatorBase<Field> &Linop, const std::vector<Field> &in,std::vector<Field> &out) {
+	assert(in.size()==out.size());
+	for(int k=0;k<in.size();k++){
+	  (*this)(Linop,in[k],out[k]);
+	}
+      };
+};
+
+template<class Field> class LinearFunction {
+public:
+  virtual void operator() (const Field &in, Field &out) = 0;
+};
+
+template<class Field> class IdentityLinearFunction : public LinearFunction<Field> {
+public:
+  void operator() (const Field &in, Field &out){
+    out = in;
+  };
+};
+
+
+/////////////////////////////////////////////////////////////
+// Base classes for Multishift solvers for operators
+/////////////////////////////////////////////////////////////
+template<class Field> class OperatorMultiFunction {
+public:
+  virtual void operator() (LinearOperatorBase<Field> &Linop, const Field &in, std::vector<Field> &out) = 0;
+};
+
+// FIXME : To think about
+
+// Chroma functionality list defining LinearOperator
+/*
+  virtual void operator() (T& chi, const T& psi, enum PlusMinus isign) const = 0;
+  virtual void operator() (T& chi, const T& psi, enum PlusMinus isign, Real epsilon) const
+  virtual const Subset& subset() const = 0;
+  virtual unsigned long nFlops() const { return 0; }
+  virtual void deriv(P& ds_u, const T& chi, const T& psi, enum PlusMinus isign) const
+  class UnprecLinearOperator : public DiffLinearOperator<T,P,Q>
+  const Subset& subset() const {return all;}
+  };
+*/
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Hermitian operator Linear function and operator function
+////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class HermOpOperatorFunction : public OperatorFunction<Field> {
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+    Linop.HermOp(in,out);
+  };
+};
+
+template<typename Field>
+class PlainHermOp : public LinearFunction<Field> {
+public:
+  LinearOperatorBase<Field> &_Linop;
+      
+  PlainHermOp(LinearOperatorBase<Field>& linop) : _Linop(linop) 
+  {}
+      
+  void operator()(const Field& in, Field& out) {
+    _Linop.HermOp(in,out);
+  }
+};
+
+template<typename Field>
+class FunctionHermOp : public LinearFunction<Field> {
+public:
+  OperatorFunction<Field>   & _poly;
+  LinearOperatorBase<Field> &_Linop;
+      
+  FunctionHermOp(OperatorFunction<Field> & poly,LinearOperatorBase<Field>& linop) 
+    : _poly(poly), _Linop(linop) {};
+      
+  void operator()(const Field& in, Field& out) {
+    _poly(_Linop,in,out);
+  }
+};
+
+template<class Field>
+class Polynomial : public OperatorFunction<Field> {
+private:
+  std::vector<RealD> Coeffs;
+public:
+  Polynomial(std::vector<RealD> &_Coeffs) : Coeffs(_Coeffs) { };
+
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    Field AtoN(in.Grid());
+    Field Mtmp(in.Grid());
+    AtoN = in;
+    out = AtoN*Coeffs[0];
+    for(int n=1;n<Coeffs.size();n++){
+      Mtmp = AtoN;
+      Linop.HermOp(Mtmp,AtoN);
+      out=out+AtoN*Coeffs[n];
+    }
+  };
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/Preconditioner.h

@@ -0,0 +1,46 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/Preconditioner.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PRECONDITIONER_H
+#define GRID_PRECONDITIONER_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Field> class Preconditioner :  public LinearFunction<Field> { 
+  virtual void operator()(const Field &src, Field & psi)=0;
+};
+
+template<class Field> class TrivialPrecon :  public Preconditioner<Field> { 
+public:
+  void operator()(const Field &src, Field & psi){
+    psi = src;
+  }
+  TrivialPrecon(void){};
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/SparseMatrix.h

@@ -0,0 +1,79 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/SparseMatrix.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef  GRID_ALGORITHM_SPARSE_MATRIX_H
+#define  GRID_ALGORITHM_SPARSE_MATRIX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// Interface defining what I expect of a general sparse matrix, such as a Fermion action
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class SparseMatrixBase {
+public:
+  virtual GridBase *Grid(void) =0;
+  // Full checkerboar operations
+  virtual RealD M    (const Field &in, Field &out)=0;
+  virtual RealD Mdag (const Field &in, Field &out)=0;
+  virtual void  MdagM(const Field &in, Field &out,RealD &ni,RealD &no) {
+    Field tmp (in.Grid());
+    ni=M(in,tmp);
+    no=Mdag(tmp,out);
+  }
+  virtual  void Mdiag    (const Field &in, Field &out)=0;
+  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp)=0;
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////////
+// Interface augmented by a red black sparse matrix, such as a Fermion action
+/////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class CheckerBoardedSparseMatrixBase : public SparseMatrixBase<Field> {
+public:
+  virtual GridBase *RedBlackGrid(void)=0;
+
+      //////////////////////////////////////////////////////////////////////
+      // Query the even even properties to make algorithmic decisions
+      //////////////////////////////////////////////////////////////////////
+      virtual RealD  Mass(void)        { return 0.0; };
+      virtual int    ConstEE(void)     { return 0; }; // Disable assumptions unless overridden
+      virtual int    isTrivialEE(void) { return 0; }; // by a derived class that knows better
+
+  // half checkerboard operaions
+  virtual  void Meooe    (const Field &in, Field &out)=0;
+  virtual  void Mooee    (const Field &in, Field &out)=0;
+  virtual  void MooeeInv (const Field &in, Field &out)=0;
+
+  virtual  void MeooeDag    (const Field &in, Field &out)=0;
+  virtual  void MooeeDag    (const Field &in, Field &out)=0;
+  virtual  void MooeeInvDag (const Field &in, Field &out)=0;
+
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/Chebyshev.h

@@ -0,0 +1,377 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/Chebyshev.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Christoph Lehner <clehner@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CHEBYSHEV_H
+#define GRID_CHEBYSHEV_H
+
+#include <Grid/algorithms/LinearOperator.h>
+
+NAMESPACE_BEGIN(Grid);
+
+struct ChebyParams : Serializable {
+  GRID_SERIALIZABLE_CLASS_MEMBERS(ChebyParams,
+				  RealD, alpha,  
+				  RealD, beta,   
+				  int, Npoly);
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Generic Chebyshev approximations
+////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field>
+class Chebyshev : public OperatorFunction<Field> {
+private:
+  std::vector<RealD> Coeffs;
+  int order;
+  RealD hi;
+  RealD lo;
+
+public:
+  void csv(std::ostream &out){
+    RealD diff = hi-lo;
+    RealD delta = diff*1.0e-9;
+    for (RealD x=lo; x<hi; x+=delta) {
+      delta*=1.1;
+      RealD f = approx(x);
+      out<< x<<" "<<f<<std::endl;
+    }
+    return;
+  }
+
+  // Convenience for plotting the approximation
+  void   PlotApprox(std::ostream &out) {
+    out<<"Polynomial approx ["<<lo<<","<<hi<<"]"<<std::endl;
+    for(RealD x=lo;x<hi;x+=(hi-lo)/50.0){
+      out <<x<<"\t"<<approx(x)<<std::endl;
+    }
+  };
+
+  Chebyshev(){};
+  Chebyshev(ChebyParams p){ Init(p.alpha,p.beta,p.Npoly);};
+  Chebyshev(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD) ) {Init(_lo,_hi,_order,func);};
+  Chebyshev(RealD _lo,RealD _hi,int _order) {Init(_lo,_hi,_order);};
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // c.f. numerical recipes "chebft"/"chebev". This is sec 5.8 "Chebyshev approximation".
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // CJ: the one we need for Lanczos
+  void Init(RealD _lo,RealD _hi,int _order)
+  {
+    lo=_lo;
+    hi=_hi;
+    order=_order;
+      
+    if(order < 2) exit(-1);
+    Coeffs.resize(order);
+    Coeffs.assign(0.,order);
+    Coeffs[order-1] = 1.;
+  };
+
+  void Init(RealD _lo,RealD _hi,int _order, RealD (* func)(RealD))
+  {
+    lo=_lo;
+    hi=_hi;
+    order=_order;
+      
+    if(order < 2) exit(-1);
+    Coeffs.resize(order);
+    for(int j=0;j<order;j++){
+      RealD s=0;
+      for(int k=0;k<order;k++){
+	RealD y=std::cos(M_PI*(k+0.5)/order);
+	RealD x=0.5*(y*(hi-lo)+(hi+lo));
+	RealD f=func(x);
+	s=s+f*std::cos( j*M_PI*(k+0.5)/order );
+      }
+      Coeffs[j] = s * 2.0/order;
+    }
+  };
+
+    
+  void JacksonSmooth(void){
+    RealD M=order;
+    RealD alpha = M_PI/(M+2);
+    RealD lmax = std::cos(alpha);
+    RealD sumUsq =0;
+    std::vector<RealD> U(M);
+    std::vector<RealD> a(M);
+    std::vector<RealD> g(M);
+    for(int n=0;n<=M;n++){
+      U[n] = std::sin((n+1)*std::acos(lmax))/std::sin(std::acos(lmax));
+      sumUsq += U[n]*U[n];
+    }      
+    sumUsq = std::sqrt(sumUsq);
+
+    for(int i=1;i<=M;i++){
+      a[i] = U[i]/sumUsq;
+    }
+    g[0] = 1.0;
+    for(int m=1;m<=M;m++){
+      g[m] = 0;
+      for(int i=0;i<=M-m;i++){
+	g[m]+= a[i]*a[m+i];
+      }
+    }
+    for(int m=1;m<=M;m++){
+      Coeffs[m]*=g[m];
+    }
+  }
+  RealD approx(RealD x) // Convenience for plotting the approximation
+  {
+    RealD Tn;
+    RealD Tnm;
+    RealD Tnp;
+      
+    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
+      
+    RealD T0=1;
+    RealD T1=y;
+      
+    RealD sum;
+    sum = 0.5*Coeffs[0]*T0;
+    sum+= Coeffs[1]*T1;
+      
+    Tn =T1;
+    Tnm=T0;
+    for(int i=2;i<order;i++){
+      Tnp=2*y*Tn-Tnm;
+      Tnm=Tn;
+      Tn =Tnp;
+      sum+= Tn*Coeffs[i];
+    }
+    return sum;
+  };
+
+  RealD approxD(RealD x)
+  {
+    RealD Un;
+    RealD Unm;
+    RealD Unp;
+      
+    RealD y=( x-0.5*(hi+lo))/(0.5*(hi-lo));
+      
+    RealD U0=1;
+    RealD U1=2*y;
+      
+    RealD sum;
+    sum = Coeffs[1]*U0;
+    sum+= Coeffs[2]*U1*2.0;
+      
+    Un =U1;
+    Unm=U0;
+    for(int i=2;i<order-1;i++){
+      Unp=2*y*Un-Unm;
+      Unm=Un;
+      Un =Unp;
+      sum+= Un*Coeffs[i+1]*(i+1.0);
+    }
+    return sum/(0.5*(hi-lo));
+  };
+    
+  RealD approxInv(RealD z, RealD x0, int maxiter, RealD resid) {
+    RealD x = x0;
+    RealD eps;
+      
+    int i;
+    for (i=0;i<maxiter;i++) {
+      eps = approx(x) - z;
+      if (fabs(eps / z) < resid)
+	return x;
+      x = x - eps / approxD(x);
+    }
+      
+    return std::numeric_limits<double>::quiet_NaN();
+  }
+    
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    GridBase *grid=in.Grid();
+
+    // std::cout << "Chevyshef(): in.Grid()="<<in.Grid()<<std::endl;
+    //std::cout <<" Linop.Grid()="<<Linop.Grid()<<"Linop.RedBlackGrid()="<<Linop.RedBlackGrid()<<std::endl;
+
+    int vol=grid->gSites();
+
+    Field T0(grid); T0 = in;  
+    Field T1(grid); 
+    Field T2(grid);
+    Field y(grid);
+      
+    Field *Tnm = &T0;
+    Field *Tn  = &T1;
+    Field *Tnp = &T2;
+
+    // Tn=T1 = (xscale M + mscale)in
+    RealD xscale = 2.0/(hi-lo);
+    RealD mscale = -(hi+lo)/(hi-lo);
+    Linop.HermOp(T0,y);
+    T1=y*xscale+in*mscale;
+
+    // sum = .5 c[0] T0 + c[1] T1
+    out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
+    for(int n=2;n<order;n++){
+	
+      Linop.HermOp(*Tn,y);
+
+      y=xscale*y+mscale*(*Tn);
+
+      *Tnp=2.0*y-(*Tnm);
+
+      out=out+Coeffs[n]* (*Tnp);
+
+      // Cycle pointers to avoid copies
+      Field *swizzle = Tnm;
+      Tnm    =Tn;
+      Tn     =Tnp;
+      Tnp    =swizzle;
+	  
+    }
+  }
+};
+
+
+template<class Field>
+class ChebyshevLanczos : public Chebyshev<Field> {
+private:
+  std::vector<RealD> Coeffs;
+  int order;
+  RealD alpha;
+  RealD beta;
+  RealD mu;
+
+public:
+  ChebyshevLanczos(RealD _alpha,RealD _beta,RealD _mu,int _order) :
+    alpha(_alpha),
+    beta(_beta),
+    mu(_mu)
+  {
+    order=_order;
+    Coeffs.resize(order);
+    for(int i=0;i<_order;i++){
+      Coeffs[i] = 0.0;
+    }
+    Coeffs[order-1]=1.0;
+  };
+
+  void csv(std::ostream &out){
+    for (RealD x=-1.2*alpha; x<1.2*alpha; x+=(2.0*alpha)/10000) {
+      RealD f = approx(x);
+      out<< x<<" "<<f<<std::endl;
+    }
+    return;
+  }
+
+  RealD approx(RealD xx) // Convenience for plotting the approximation
+  {
+    RealD Tn;
+    RealD Tnm;
+    RealD Tnp;
+    Real aa = alpha * alpha;
+    Real bb = beta  *  beta;
+      
+    RealD x = ( 2.0 * (xx-mu)*(xx-mu) - (aa+bb) ) / (aa-bb);
+
+    RealD y= x;
+      
+    RealD T0=1;
+    RealD T1=y;
+      
+    RealD sum;
+    sum = 0.5*Coeffs[0]*T0;
+    sum+= Coeffs[1]*T1;
+      
+    Tn =T1;
+    Tnm=T0;
+    for(int i=2;i<order;i++){
+      Tnp=2*y*Tn-Tnm;
+      Tnm=Tn;
+      Tn =Tnp;
+      sum+= Tn*Coeffs[i];
+    }
+    return sum;
+  };
+
+  // shift_Multiply in Rudy's code
+  void AminusMuSq(LinearOperatorBase<Field> &Linop, const Field &in, Field &out) 
+  {
+    GridBase *grid=in.Grid();
+    Field tmp(grid);
+
+    RealD aa= alpha*alpha;
+    RealD bb= beta * beta;
+
+    Linop.HermOp(in,out);
+    out = out - mu*in;
+
+    Linop.HermOp(out,tmp);
+    tmp = tmp - mu * out;
+
+    out = (2.0/ (aa-bb) ) * tmp -  ((aa+bb)/(aa-bb))*in;
+  };
+  // Implement the required interface
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &in, Field &out) {
+
+    GridBase *grid=in.Grid();
+
+    int vol=grid->gSites();
+
+    Field T0(grid); T0 = in;  
+    Field T1(grid); 
+    Field T2(grid);
+    Field  y(grid);
+      
+    Field *Tnm = &T0;
+    Field *Tn  = &T1;
+    Field *Tnp = &T2;
+
+    // Tn=T1 = (xscale M )*in
+    AminusMuSq(Linop,T0,T1);
+
+    // sum = .5 c[0] T0 + c[1] T1
+    out = (0.5*Coeffs[0])*T0 + Coeffs[1]*T1;
+    for(int n=2;n<order;n++){
+	
+      AminusMuSq(Linop,*Tn,y);
+
+      *Tnp=2.0*y-(*Tnm);
+
+      out=out+Coeffs[n]* (*Tnp);
+
+      // Cycle pointers to avoid copies
+      Field *swizzle = Tnm;
+      Tnm    =Tn;
+      Tn     =Tnp;
+      Tnp    =swizzle;
+	  
+    }
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/approx/Forecast.h

@@ -0,0 +1,152 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/approx/Forecast.h
+
+Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: David Murphy <dmurphy@phys.columbia.edu>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+			   /*  END LEGAL */
+
+#ifndef INCLUDED_FORECAST_H
+#define INCLUDED_FORECAST_H
+
+NAMESPACE_BEGIN(Grid);
+
+// Abstract base class.
+// Takes a matrix (Mat), a source (phi), and a vector of Fields (chi)
+// and returns a forecasted solution to the system D*psi = phi (psi).
+template<class Matrix, class Field>
+class Forecast
+{
+public:
+  virtual Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& chi) = 0;
+};
+
+// Implementation of Brower et al.'s chronological inverter (arXiv:hep-lat/9509012),
+// used to forecast solutions across poles of the EOFA heatbath.
+//
+// Modified from CPS (cps_pp/src/util/dirac_op/d_op_base/comsrc/minresext.C)
+template<class Matrix, class Field>
+class ChronoForecast : public Forecast<Matrix,Field>
+{
+public:
+  Field operator()(Matrix &Mat, const Field& phi, const std::vector<Field>& prev_solns)
+  {
+    int degree = prev_solns.size();
+    Field chi(phi); // forecasted solution
+
+    // Trivial cases
+    if(degree == 0){ chi = Zero(); return chi; }
+    else if(degree == 1){ return prev_solns[0]; }
+
+    //    RealD dot;
+    ComplexD xp;
+    Field r(phi); // residual
+    Field Mv(phi);
+    std::vector<Field> v(prev_solns); // orthonormalized previous solutions
+    std::vector<Field> MdagMv(degree,phi);
+
+    // Array to hold the matrix elements
+    std::vector<std::vector<ComplexD>> G(degree, std::vector<ComplexD>(degree));
+
+    // Solution and source vectors
+    std::vector<ComplexD> a(degree);
+    std::vector<ComplexD> b(degree);
+
+    // Orthonormalize the vector basis
+    for(int i=0; i<degree; i++){
+      v[i] *= 1.0/std::sqrt(norm2(v[i]));
+      for(int j=i+1; j<degree; j++){ v[j] -= innerProduct(v[i],v[j]) * v[i]; }
+    }
+
+    // Perform sparse matrix multiplication and construct rhs
+    for(int i=0; i<degree; i++){
+      b[i] = innerProduct(v[i],phi);
+      Mat.M(v[i],Mv);
+      Mat.Mdag(Mv,MdagMv[i]);
+      G[i][i] = innerProduct(v[i],MdagMv[i]);
+    }
+
+    // Construct the matrix
+    for(int j=0; j<degree; j++){
+      for(int k=j+1; k<degree; k++){
+	G[j][k] = innerProduct(v[j],MdagMv[k]);
+	G[k][j] = conjugate(G[j][k]);
+      }}
+
+    // Gauss-Jordan elimination with partial pivoting
+    for(int i=0; i<degree; i++){
+
+      // Perform partial pivoting
+      int k = i;
+      for(int j=i+1; j<degree; j++){ if(abs(G[j][j]) > abs(G[k][k])){ k = j; } }
+      if(k != i){
+	xp = b[k];
+	b[k] = b[i];
+	b[i] = xp;
+	for(int j=0; j<degree; j++){
+	  xp = G[k][j];
+	  G[k][j] = G[i][j];
+	  G[i][j] = xp;
+	}
+      }
+
+      // Convert matrix to upper triangular form
+      for(int j=i+1; j<degree; j++){
+	xp = G[j][i]/G[i][i];
+	b[j] -= xp * b[i];
+	for(int k=0; k<degree; k++){ G[j][k] -= xp*G[i][k]; }
+      }
+    }
+
+    // Use Gaussian elimination to solve equations and calculate initial guess
+    chi = Zero();
+    r = phi;
+    for(int i=degree-1; i>=0; i--){
+      a[i] = 0.0;
+      for(int j=i+1; j<degree; j++){ a[i] += G[i][j] * a[j]; }
+      a[i] = (b[i]-a[i])/G[i][i];
+      chi += a[i]*v[i];
+      r -= a[i]*MdagMv[i];
+    }
+
+    RealD true_r(0.0);
+    ComplexD tmp;
+    for(int i=0; i<degree; i++){
+      tmp = -b[i];
+      for(int j=0; j<degree; j++){ tmp += G[i][j]*a[j]; }
+      tmp = conjugate(tmp)*tmp;
+      true_r += std::sqrt(tmp.real());
+    }
+
+    RealD error = std::sqrt(norm2(r)/norm2(phi));
+    std::cout << GridLogMessage << "ChronoForecast: |res|/|src| = " << error << std::endl;
+
+    return chi;
+  };
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/approx/LICENSE

@@ -0,0 +1,21 @@
+
+Copyright (c) 2011 Michael Clark
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+

Grid/algorithms/approx/MultiShiftFunction.cc

@@ -0,0 +1,57 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/MultiShiftFunction.cc
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid);
+
+double MultiShiftFunction::approx(double x)
+{
+  double a = norm;
+  for(int n=0;n<poles.size();n++){
+    a = a + residues[n]/(x+poles[n]);
+  }
+  return a;
+}
+void MultiShiftFunction::gnuplot(std::ostream &out)
+{
+  out<<"f(x) = "<<norm<<"";
+  for(int n=0;n<poles.size();n++){
+    out<<"+("<<residues[n]<<"/(x+"<<poles[n]<<"))";
+  }
+  out<<";"<<std::endl;
+}
+void MultiShiftFunction::csv(std::ostream &out)
+{
+  for (double x=lo; x<hi; x*=1.05) {
+    double f = approx(x);
+    double r = sqrt(x);
+    out<< x<<","<<r<<","<<f<<","<<r-f<<std::endl;
+  }
+  return;
+}
+NAMESPACE_END(Grid);

Grid/algorithms/approx/MultiShiftFunction.h

@@ -0,0 +1,67 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/MultiShiftFunction.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef MULTI_SHIFT_FUNCTION
+#define MULTI_SHIFT_FUNCTION
+
+NAMESPACE_BEGIN(Grid);
+
+class MultiShiftFunction {
+public:
+  int order;
+  std::vector<RealD> poles;
+  std::vector<RealD> residues;
+  std::vector<RealD> tolerances;
+  RealD norm;
+  RealD lo,hi;
+
+  MultiShiftFunction(int n,RealD _lo,RealD _hi): poles(n), residues(n), lo(_lo), hi(_hi) {;};
+  RealD approx(RealD x);
+  void csv(std::ostream &out);
+  void gnuplot(std::ostream &out);
+
+  void Init(AlgRemez & remez,double tol,bool inverse) 
+  {
+    order=remez.getDegree();
+    tolerances.resize(remez.getDegree(),tol);
+    poles.resize(remez.getDegree());
+    residues.resize(remez.getDegree());
+    remez.getBounds(lo,hi);
+    if ( inverse ) remez.getIPFE (&residues[0],&poles[0],&norm);
+    else           remez.getPFE (&residues[0],&poles[0],&norm);
+  }
+  // Allow deferred initialisation
+  MultiShiftFunction(void){};
+  MultiShiftFunction(AlgRemez & remez,double tol,bool inverse)
+  {
+    Init(remez,tol,inverse);
+  }
+
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/approx/README

@@ -0,0 +1,80 @@
+-----------------------------------------------------------------------------------
+
+PAB. Took Mike Clark's AlgRemez from GitHub and (modified a little) include.
+This is open source and license and readme and comments are preserved consistent
+with the license. Mike, thankyou!
+-----------------------------------------------------------------------------------
+-----------------------------------------------------------------------------------
+AlgRemez
+
+The archive downloadable here contains an implementation of the Remez
+algorithm which calculates optimal rational (and polynomial)
+approximations to the nth root over a given spectral range.  The Remez
+algorithm, although in principle is extremely straightforward to
+program, is quite difficult to get completely correct, e.g., the Maple
+implementation of the algorithm does not always converge to the
+correct answer.
+
+To use this algorithm you need to install GMP, the GNU Multiple
+Precision Library, and when configuring the install, you must include
+the --enable-mpfr option (see the GMP manual for more details).  You
+also have to edit the Makefile for AlgRemez appropriately for your
+system, namely to point corrrectly to the location of the GMP library.
+
+The simple main program included with this archive invokes the
+AlgRemez class to calculate an approximation given by command line
+arguments.  It is invoked by the following
+
+./test y z n d lambda_low lambda_high precision,
+
+where the function to be approximated is f(x) = x^(y/z), with degree
+(n,d) over the spectral range [lambda_low, lambda_high], using
+precision digits of precision in the arithmetic.  So an example would
+be
+
+./test 1 2 5 5 0.0004 64 40
+
+which corresponds to constructing a rational approximation to the
+square root function, with degree (5,5) over the range [0.0004,64]
+with 40 digits of precision used for the arithmetic.  The parameters y
+and z must be positive, the approximation to f(x) = x^(-y/z) is simply
+the inverse of the approximation to f(x) = x^(y/z).  After the
+approximation has been constructed, the roots and poles of the
+rational function are found, and then the partial fraction expansion
+of both the rational function and it's inverse are found, the results
+of which are output to a file called "approx.dat".  In addition, the
+error function of the approximation is output to "error.dat", where it
+can be checked that the resultant approximation satisfies Chebychev's
+criterion, namely all error maxima are equal in magnitude, and
+adjacent maxima are oppostie in sign.  There are some caveats here
+however, the optimal polynomial approximation has complex roots, and
+the root finding implemented here cannot (yet) handle complex roots.
+In addition, the partial fraction expansion of rational approximations
+is only found for the case n = d, i.e., the degree of numerator
+polynomial equals that of the denominator polynomial.  The convention
+for the partial fraction expansion is that polar shifts are always
+written added to x, not subtracted.
+
+To do list
+
+1.  Include an exponential dampening factor in the function to be
+approximated.  This may sound trivial to implement, but for some
+parameters, the algorithm seems to breakdown.  Also, the roots in the
+rational approximation sometimes become complex, which currently
+breaks the stupidly simple root finding code.
+
+2. Make the algorithm faster - it's too slow when running on qcdoc.
+
+3. Add complex root finding.
+
+4. Add more options for error minimisation - currently the code
+minimises the relative error, should add options for absolute error,
+and other norms.
+
+There will be a forthcoming publication concerning the results
+generated by this software, but in the meantime, if you use this
+software, please cite it as
+"M.A. Clark and A.D. Kennedy, https://github.com/mikeaclark/AlgRemez, 2005".
+
+If you have any problems using the software, then please email scientist.mike@gmail.com.
+

Grid/algorithms/approx/Remez.cc

@@ -0,0 +1,759 @@
+/*
+
+  Mike Clark - 25th May 2005
+
+  alg_remez.C
+
+  AlgRemez is an implementation of the Remez algorithm, which in this
+  case is used for generating the optimal nth root rational
+  approximation.
+
+  Note this class requires the gnu multiprecision (GNU MP) library.
+
+*/
+
+#include<math.h>
+#include<stdio.h>
+#include<stdlib.h>
+#include<string>
+#include<iostream>
+#include<iomanip>
+#include<cassert>
+
+#include<Grid/algorithms/approx/Remez.h>
+
+// Constructor
+AlgRemez::AlgRemez(double lower, double upper, long precision) 
+{
+  prec = precision;
+  bigfloat::setDefaultPrecision(prec);
+
+  apstrt = lower;
+  apend = upper;
+  apwidt = apend - apstrt;
+
+  std::cout<<"Approximation bounds are ["<<apstrt<<","<<apend<<"]\n";
+  std::cout<<"Precision of arithmetic is "<<precision<<std::endl;
+
+  alloc = 0;
+  n = 0;
+  d = 0;
+
+  foundRoots = 0;
+
+  // Only require the approximation spread to be less than 1 ulp
+  tolerance = 1e-15;
+}
+
+// Destructor
+AlgRemez::~AlgRemez()
+{
+  if (alloc) {
+    delete [] param;
+    delete [] roots;
+    delete [] poles;
+    delete [] xx;
+    delete [] mm;
+    delete [] a_power;
+    delete [] a;
+  }
+}
+
+// Free memory and reallocate as necessary
+void AlgRemez::allocate(int num_degree, int den_degree)
+{
+  // Arrays have previously been allocated, deallocate first, then allocate
+  if (alloc) {
+    delete [] param;
+    delete [] roots;
+    delete [] poles;
+    delete [] xx;
+    delete [] mm;
+  }
+
+  // Note use of new and delete in memory allocation - cannot run on qcdsp
+  param = new bigfloat[num_degree+den_degree+1];
+  roots = new bigfloat[num_degree];
+  poles = new bigfloat[den_degree];
+  xx = new bigfloat[num_degree+den_degree+3];
+  mm = new bigfloat[num_degree+den_degree+2];
+
+  if (!alloc) {
+    // The coefficients of the sum in the exponential
+    a = new bigfloat[SUM_MAX];
+    a_power = new int[SUM_MAX];
+  }
+
+  alloc = 1;
+}
+
+// Reset the bounds of the approximation
+void AlgRemez::setBounds(double lower, double upper)
+{
+  apstrt = lower;
+  apend = upper;
+  apwidt = apend - apstrt;
+}
+
+// Generate the rational approximation x^(pnum/pden)
+double AlgRemez::generateApprox(int degree, unsigned long pnum, 
+				unsigned long pden)
+{
+  return generateApprox(degree, degree, pnum, pden);
+}
+
+double AlgRemez::generateApprox(int num_degree, int den_degree, 
+				unsigned long pnum, unsigned long pden)
+{
+  double *a_param = 0;
+  int *a_pow = 0;
+  return generateApprox(num_degree, den_degree, pnum, pden, 0, a_param, a_pow);
+}
+
+// Generate the rational approximation x^(pnum/pden)
+double AlgRemez::generateApprox(int num_degree, int den_degree, 
+				unsigned long pnum, unsigned long pden,
+				int a_len, double *a_param, int *a_pow)
+{
+  std::cout<<"Degree of the approximation is ("<<num_degree<<","<<den_degree<<")\n";
+  std::cout<<"Approximating the function x^("<<pnum<<"/"<<pden<<")\n";
+
+  // Reallocate arrays, since degree has changed
+  if (num_degree != n || den_degree != d) allocate(num_degree,den_degree);
+
+  assert(a_len<=SUM_MAX);
+
+  step = new bigfloat[num_degree+den_degree+2];
+
+  a_length = a_len;
+  for (int j=0; j<a_len; j++) {
+    a[j]= a_param[j];
+    a_power[j] = a_pow[j];
+  }
+
+  power_num = pnum;
+  power_den = pden;
+  spread = 1.0e37;
+  iter = 0;
+
+  n = num_degree;
+  d = den_degree;
+  neq = n + d + 1;
+
+  initialGuess();
+  stpini(step);
+
+  while (spread > tolerance) { //iterate until convergance
+
+    if (iter++%100==0) 
+      std::cout<<"Iteration " <<iter-1<<" spread "<<(double)spread<<" delta "<<(double)delta<<std::endl; 
+
+    equations();
+    if (delta < tolerance) {
+      std::cout<<"Delta too small, try increasing precision\n";
+      assert(0);
+    };    
+    assert( delta>= tolerance);
+
+    search(step);
+  }
+
+  int sign;
+  double error = (double)getErr(mm[0],&sign);
+  std::cout<<"Converged at "<<iter<<" iterations; error = "<<error<<std::endl;
+
+  // Once the approximation has been generated, calculate the roots
+  if(!root()) {
+    std::cout<<"Root finding failed\n";
+  } else {
+    foundRoots = 1;
+  }
+  
+  delete [] step;
+
+  // Return the maximum error in the approximation
+  return error;
+}
+
+// Return the partial fraction expansion of the approximation x^(pnum/pden)
+int AlgRemez::getPFE(double *Res, double *Pole, double *Norm) {
+
+  if (n!=d) {
+    std::cout<<"Cannot handle case: Numerator degree neq Denominator degree\n";
+    return 0;
+  }
+
+  if (!alloc) {
+    std::cout<<"Approximation not yet generated\n";
+    return 0;
+  }
+
+  if (!foundRoots) {
+    std::cout<<"Roots not found, so PFE cannot be taken\n";
+    return 0;
+  }
+
+  bigfloat *r = new bigfloat[n];
+  bigfloat *p = new bigfloat[d];
+  
+  for (int i=0; i<n; i++) r[i] = roots[i];
+  for (int i=0; i<d; i++) p[i] = poles[i];
+  
+  // Perform a partial fraction expansion
+  pfe(r, p, norm);
+
+  // Convert to double and return
+  *Norm = (double)norm;
+  for (int i=0; i<n; i++) Res[i] = (double)r[i];
+  for (int i=0; i<d; i++) Pole[i] = (double)p[i];
+
+  delete [] r;
+  delete [] p;
+
+  // Where the smallest shift is located
+  return 0;
+}
+
+// Return the partial fraction expansion of the approximation x^(-pnum/pden)
+int AlgRemez::getIPFE(double *Res, double *Pole, double *Norm) {
+
+  if (n!=d) {
+    std::cout<<"Cannot handle case: Numerator degree neq Denominator degree\n";
+    return 0;
+  }
+
+  if (!alloc) {
+    std::cout<<"Approximation not yet generated\n";
+    return 0;
+  }
+
+  if (!foundRoots) {
+    std::cout<<"Roots not found, so PFE cannot be taken\n";
+    return 0;
+  }
+
+  bigfloat *r = new bigfloat[d];
+  bigfloat *p = new bigfloat[n];
+  
+  // Want the inverse function
+  for (int i=0; i<n; i++) {
+    r[i] = poles[i];
+    p[i] = roots[i];
+  }
+
+  // Perform a partial fraction expansion
+  pfe(r, p, (bigfloat)1l/norm);
+
+  // Convert to double and return
+  *Norm = (double)((bigfloat)1l/(norm));
+  for (int i=0; i<n; i++) {
+    Res[i] = (double)r[i];
+    Pole[i] = (double)p[i];
+  }
+
+  delete [] r;
+  delete [] p;
+
+  // Where the smallest shift is located
+  return 0;
+}
+
+// Initial values of maximal and minimal errors
+void AlgRemez::initialGuess() {
+
+  // Supply initial guesses for solution points
+  long ncheb = neq;			// Degree of Chebyshev error estimate
+  bigfloat a, r;
+
+  // Find ncheb+1 extrema of Chebyshev polynomial
+
+  a = ncheb;
+  mm[0] = apstrt;
+  for (long i = 1; i < ncheb; i++) {
+    r = 0.5 * (1 - cos((M_PI * i)/(double) a));
+    //r *= sqrt_bf(r);
+    r = (exp((double)r)-1.0)/(exp(1.0)-1.0);
+    mm[i] = apstrt + r * apwidt;
+  }
+  mm[ncheb] = apend;
+
+  a = 2.0 * ncheb;
+  for (long i = 0; i <= ncheb; i++) {
+    r = 0.5 * (1 - cos(M_PI * (2*i+1)/(double) a));
+    //r *= sqrt_bf(r); // Squeeze to low end of interval
+    r = (exp((double)r)-1.0)/(exp(1.0)-1.0);
+    xx[i] = apstrt + r * apwidt;
+  }
+}
+
+// Initialise step sizes
+void AlgRemez::stpini(bigfloat *step) {
+  xx[neq+1] = apend;
+  delta = 0.25;
+  step[0] = xx[0] - apstrt;
+  for (int i = 1; i < neq; i++) step[i] = xx[i] - xx[i-1];
+  step[neq] = step[neq-1];
+}
+
+// Search for error maxima and minima
+void AlgRemez::search(bigfloat *step) {
+  bigfloat a, q, xm, ym, xn, yn, xx0, xx1;
+  int i, meq, emsign, ensign, steps;
+
+  meq = neq + 1;
+  bigfloat *yy = new bigfloat[meq];
+
+  bigfloat eclose = 1.0e30;
+  bigfloat farther = 0l;
+
+  xx0 = apstrt;
+
+  for (i = 0; i < meq; i++) {
+    steps = 0;
+    xx1 = xx[i]; // Next zero
+    if (i == meq-1) xx1 = apend;
+    xm = mm[i];
+    ym = getErr(xm,&emsign);
+    q = step[i];
+    xn = xm + q;
+    if (xn < xx0 || xn >= xx1) {	// Cannot skip over adjacent boundaries
+      q = -q;
+      xn = xm;
+      yn = ym;
+      ensign = emsign;
+    } else {
+      yn = getErr(xn,&ensign);
+      if (yn < ym) {
+	q = -q;
+	xn = xm;
+	yn = ym;
+	ensign = emsign;
+      }
+    }
+  
+    while(yn >= ym) {		// March until error becomes smaller.
+      if (++steps > 10) break;
+      ym = yn;
+      xm = xn;
+      emsign = ensign;
+      a = xm + q;
+      if (a == xm || a <= xx0 || a >= xx1) break;// Must not skip over the zeros either side.
+      xn = a;
+      yn = getErr(xn,&ensign);
+    }
+
+    mm[i] = xm;			// Position of maximum
+    yy[i] = ym;			// Value of maximum
+
+    if (eclose > ym) eclose = ym;
+    if (farther < ym) farther = ym;
+
+    xx0 = xx1; // Walk to next zero.
+  } // end of search loop
+
+  q = (farther - eclose);	// Decrease step size if error spread increased
+  if (eclose != 0.0) q /= eclose; // Relative error spread
+  if (q >= spread) delta *= 0.5; // Spread is increasing; decrease step size
+  spread = q;
+
+  for (i = 0; i < neq; i++) {
+    q = yy[i+1];
+    if (q != 0.0) q = yy[i] / q  - (bigfloat)1l;
+    else q = 0.0625;
+    if (q > (bigfloat)0.25) q = 0.25;
+    q *= mm[i+1] - mm[i];
+    step[i] = q * delta;
+  }
+  step[neq] = step[neq-1];
+  
+  for (i = 0; i < neq; i++) {	// Insert new locations for the zeros.
+    xm = xx[i] - step[i];
+    if (xm <= apstrt) continue;
+    if (xm >= apend) continue;
+    if (xm <= mm[i]) xm = (bigfloat)0.5 * (mm[i] + xx[i]);
+    if (xm >= mm[i+1]) xm = (bigfloat)0.5 * (mm[i+1] + xx[i]);
+    xx[i] = xm;
+  }
+
+  delete [] yy;
+}
+
+// Solve the equations
+void AlgRemez::equations(void) {
+  bigfloat x, y, z;
+  int i, j, ip;
+  bigfloat *aa;
+
+  bigfloat *AA = new bigfloat[(neq)*(neq)];
+  bigfloat *BB = new bigfloat[neq];
+  
+  for (i = 0; i < neq; i++) {	// set up the equations for solution by simq()
+    ip = neq * i;		// offset to 1st element of this row of matrix
+    x = xx[i];			// the guess for this row
+    y = func(x);		// right-hand-side vector
+
+    z = (bigfloat)1l;
+    aa = AA+ip;
+    for (j = 0; j <= n; j++) {
+      *aa++ = z;
+      z *= x;
+    }
+
+    z = (bigfloat)1l;
+    for (j = 0; j < d; j++) {
+      *aa++ = -y * z;
+      z *= x;
+    }
+    BB[i] = y * z;		// Right hand side vector
+  }
+
+  // Solve the simultaneous linear equations.
+  if (simq(AA, BB, param, neq)) {
+    std::cout<<"simq failed\n";
+    exit(0);
+  }
+
+  delete [] AA;
+  delete [] BB;
+
+}
+
+// Evaluate the rational form P(x)/Q(x) using coefficients
+// from the solution vector param
+bigfloat AlgRemez::approx(const bigfloat x) {
+  bigfloat yn, yd;
+  int i;
+
+  // Work backwards toward the constant term.
+  yn = param[n];		// Highest order numerator coefficient
+  for (i = n-1; i >= 0; i--) yn = x * yn  +  param[i]; 
+  yd = x + param[n+d];	// Highest degree coefficient = 1.0
+  for (i = n+d-1; i > n; i--) yd = x * yd  +  param[i];
+
+  return(yn/yd);
+}
+
+// Compute size and sign of the approximation error at x
+bigfloat AlgRemez::getErr(bigfloat x, int *sign) {
+  bigfloat e, f;
+
+  f = func(x);
+  e = approx(x) - f;
+  if (f != 0) e /= f;
+  if (e < (bigfloat)0.0) {
+    *sign = -1;
+    e = -e;
+  }
+  else *sign = 1;
+  
+  return(e);
+}
+
+// Calculate function required for the approximation.
+bigfloat AlgRemez::func(const bigfloat x) {
+
+  bigfloat z = (bigfloat)power_num / (bigfloat)power_den;
+  bigfloat y;
+
+  if (x == (bigfloat)1.0) y = (bigfloat)1.0;
+  else y = pow_bf(x,z);
+
+  if (a_length > 0) {
+    bigfloat sum = 0l;
+    for (int j=0; j<a_length; j++) sum += a[j]*pow_bf(x,a_power[j]);
+    return y * exp_bf(sum);
+  } else {
+    return y;
+  }
+
+}
+
+// Solve the system AX=B
+int AlgRemez::simq(bigfloat A[], bigfloat B[], bigfloat X[], int n) {
+
+  int i, j, ij, ip, ipj, ipk, ipn;
+  int idxpiv, iback;
+  int k, kp, kp1, kpk, kpn;
+  int nip, nkp, nm1;
+  bigfloat em, q, rownrm, big, size, pivot, sum;
+  bigfloat *aa;
+
+  // simq() work vector
+  int *IPS = new int[(neq) * sizeof(int)];
+
+  nm1 = n - 1;
+  // Initialize IPS and X
+  
+  ij = 0;
+  for (i = 0; i < n; i++) {
+    IPS[i] = i;
+    rownrm = 0.0;
+    for(j = 0; j < n; j++) {
+      q = abs_bf(A[ij]);
+      if(rownrm < q) rownrm = q;
+      ++ij;
+    }
+    if (rownrm == (bigfloat)0l) {
+      std::cout<<"simq rownrm=0\n";
+      delete [] IPS;
+      return(1);
+    }
+    X[i] = (bigfloat)1.0 / rownrm;
+  }
+  
+  for (k = 0; k < nm1; k++) {
+    big = 0.0;
+    idxpiv = 0;
+    
+    for (i = k; i < n; i++) {
+      ip = IPS[i];
+      ipk = n*ip + k;
+      size = abs_bf(A[ipk]) * X[ip];
+      if (size > big) {
+	big = size;
+	idxpiv = i;
+      }
+    }
+    
+    if (big == (bigfloat)0l) {
+      std::cout<<"simq big=0\n";
+      delete [] IPS;
+      return(2);
+    }
+    if (idxpiv != k) {
+      j = IPS[k];
+      IPS[k] = IPS[idxpiv];
+      IPS[idxpiv] = j;
+    }
+    kp = IPS[k];
+    kpk = n*kp + k;
+    pivot = A[kpk];
+    kp1 = k+1;
+    for (i = kp1; i < n; i++) {
+      ip = IPS[i];
+      ipk = n*ip + k;
+      em = -A[ipk] / pivot;
+      A[ipk] = -em;
+      nip = n*ip;
+      nkp = n*kp;
+      aa = A+nkp+kp1;
+      for (j = kp1; j < n; j++) {
+	ipj = nip + j;
+	A[ipj] = A[ipj] + em * *aa++;
+      }
+    }
+  }
+  kpn = n * IPS[n-1] + n - 1;	// last element of IPS[n] th row
+  if (A[kpn] == (bigfloat)0l) {
+    std::cout<<"simq A[kpn]=0\n";
+    delete [] IPS;
+    return(3);
+  }
+
+  
+  ip = IPS[0];
+  X[0] = B[ip];
+  for (i = 1; i < n; i++) {
+    ip = IPS[i];
+    ipj = n * ip;
+    sum = 0.0;
+    for (j = 0; j < i; j++) {
+      sum += A[ipj] * X[j];
+      ++ipj;
+    }
+    X[i] = B[ip] - sum;
+  }
+  
+  ipn = n * IPS[n-1] + n - 1;
+  X[n-1] = X[n-1] / A[ipn];
+  
+  for (iback = 1; iback < n; iback++) {
+    //i goes (n-1),...,1
+    i = nm1 - iback;
+    ip = IPS[i];
+    nip = n*ip;
+    sum = 0.0;
+    aa = A+nip+i+1;
+    for (j= i + 1; j < n; j++) 
+      sum += *aa++ * X[j];
+    X[i] = (X[i] - sum) / A[nip+i];
+  }
+  
+  delete [] IPS;
+  return(0);
+}
+
+// Calculate the roots of the approximation
+int AlgRemez::root() {
+
+  long i,j;
+  bigfloat x,dx=0.05;
+  bigfloat upper=1, lower=-100000;
+  bigfloat tol = 1e-20;
+
+  bigfloat *poly = new bigfloat[neq+1];
+
+  // First find the numerator roots
+  for (i=0; i<=n; i++) poly[i] = param[i];
+
+  for (i=n-1; i>=0; i--) {
+    roots[i] = rtnewt(poly,i+1,lower,upper,tol);
+    if (roots[i] == 0.0) {
+      std::cout<<"Failure to converge on root "<<i+1<<"/"<<n<<"\n";
+      return 0;
+    }
+    poly[0] = -poly[0]/roots[i];
+    for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/roots[i];
+  }
+  
+ // Now find the denominator roots
+  poly[d] = 1l;
+  for (i=0; i<d; i++) poly[i] = param[n+1+i];
+
+  for (i=d-1; i>=0; i--) {
+    poles[i]=rtnewt(poly,i+1,lower,upper,tol);
+    if (poles[i] == 0.0) {
+      std::cout<<"Failure to converge on pole "<<i+1<<"/"<<d<<"\n";
+      return 0;
+    }
+    poly[0] = -poly[0]/poles[i];
+    for (j=1; j<=i; j++) poly[j] = (poly[j-1] - poly[j])/poles[i];
+  }
+
+  norm = param[n];
+
+  delete [] poly;
+
+  return 1;
+}
+
+// Evaluate the polynomial
+bigfloat AlgRemez::polyEval(bigfloat x, bigfloat *poly, long size) {
+  bigfloat f = poly[size];
+  for (int i=size-1; i>=0; i--) f = f*x + poly[i];
+  return f;
+}
+
+// Evaluate the differential of the polynomial
+bigfloat AlgRemez::polyDiff(bigfloat x, bigfloat *poly, long size) {
+  bigfloat df = (bigfloat)size*poly[size];
+  for (int i=size-1; i>0; i--) df = df*x + (bigfloat)i*poly[i];
+  return df;
+}
+
+
+// Newton's method to calculate roots
+bigfloat AlgRemez::rtnewt(bigfloat *poly, long i, bigfloat x1, 
+			  bigfloat x2, bigfloat xacc) {
+  int j;
+  bigfloat df, dx, f, rtn;
+
+  rtn=(bigfloat)0.5*(x1+x2);
+  for (j=1; j<=JMAX;j++) {
+    f = polyEval(rtn, poly, i);
+    df = polyDiff(rtn, poly, i);
+    dx = f/df;
+    rtn -= dx;
+    if (abs_bf(dx) < xacc) return rtn;
+  }
+  std::cout<<"Maximum number of iterations exceeded in rtnewt\n";
+  return 0.0;
+}
+
+// Evaluate the partial fraction expansion of the rational function
+// with res roots and poles poles.  Result is overwritten on input
+// arrays.
+void AlgRemez::pfe(bigfloat *res, bigfloat *poles, bigfloat norm) {
+  int i,j,small;
+  bigfloat temp;
+  bigfloat *numerator = new bigfloat[n];
+  bigfloat *denominator = new bigfloat[d];
+
+  // Construct the polynomials explicitly 
+  for (i=1; i<n; i++) {
+    numerator[i] = 0l;
+    denominator[i] = 0l;
+  }
+  numerator[0]=1l;
+  denominator[0]=1l;
+
+  for (j=0; j<n; j++) {
+    for (i=n-1; i>=0; i--) {
+      numerator[i] *= -res[j];
+      denominator[i] *= -poles[j];
+      if (i>0) {
+	numerator[i] += numerator[i-1];
+	denominator[i] += denominator[i-1];
+      }
+    }
+  }
+
+  // Convert to proper fraction form.
+  // Fraction is now in the form 1 + n/d, where O(n)+1=O(d)
+  for (i=0; i<n; i++) numerator[i] -= denominator[i];
+
+  // Find the residues of the partial fraction expansion and absorb the
+  // coefficients.
+  for (i=0; i<n; i++) {
+    res[i] = 0l;
+    for (j=n-1; j>=0; j--) {
+      res[i] = poles[i]*res[i]+numerator[j];
+    }
+    for (j=n-1; j>=0; j--) {
+      if (i!=j) res[i] /= poles[i]-poles[j];
+    }
+    res[i] *= norm;
+  }  
+
+  // res now holds the residues
+  j = 0;
+  for (i=0; i<n; i++) poles[i] = -poles[i];
+
+  // Move the ordering of the poles from smallest to largest
+  for (j=0; j<n; j++) {
+    small = j;
+    for (i=j+1; i<n; i++) {
+      if (poles[i] < poles[small]) small = i;
+    }
+    if (small != j) {
+      temp = poles[small];
+      poles[small] = poles[j];
+      poles[j] = temp;
+      temp = res[small];
+      res[small] = res[j];
+      res[j] = temp;
+    }
+  }
+
+  delete [] numerator;
+  delete [] denominator;
+}
+
+double AlgRemez::evaluateApprox(double x) {
+  return (double)approx((bigfloat)x);
+}
+
+double AlgRemez::evaluateInverseApprox(double x) {
+  return 1.0/(double)approx((bigfloat)x);
+}
+
+double AlgRemez::evaluateFunc(double x) {
+  return (double)func((bigfloat)x);
+}
+
+double AlgRemez::evaluateInverseFunc(double x) {
+  return 1.0/(double)func((bigfloat)x);
+}
+
+void AlgRemez::csv(std::ostream & os)
+{
+  double lambda_low = apstrt;
+  double lambda_high= apend;
+  for (double x=lambda_low; x<lambda_high; x*=1.05) {
+    double f = evaluateFunc(x);
+    double r = evaluateApprox(x);
+    os<< x<<","<<r<<","<<f<<","<<r-f<<std::endl;
+  }
+  return;
+}
+

Grid/algorithms/approx/Remez.h

@@ -0,0 +1,184 @@
+/*
+
+  Mike Clark - 25th May 2005
+
+  alg_remez.h
+
+  AlgRemez is an implementation of the Remez algorithm, which in this
+  case is used for generating the optimal nth root rational
+  approximation.
+
+  Note this class requires the gnu multiprecision (GNU MP) library.
+
+*/
+
+#ifndef INCLUDED_ALG_REMEZ_H
+#define INCLUDED_ALG_REMEZ_H
+
+#include <stddef.h>
+#include <Grid/GridStd.h>
+
+#ifdef HAVE_LIBGMP
+#include "bigfloat.h"
+#else
+#include "bigfloat_double.h"
+#endif
+
+#define JMAX 10000 //Maximum number of iterations of Newton's approximation
+#define SUM_MAX 10 // Maximum number of terms in exponential
+
+/*
+ *Usage examples
+  AlgRemez remez(lambda_low,lambda_high,precision);
+  error = remez.generateApprox(n,d,y,z);
+  remez.getPFE(res,pole,&norm);
+  remez.getIPFE(res,pole,&norm);
+  remez.csv(ostream &os);
+ */
+
+class AlgRemez
+{
+ private:
+  char *cname;
+
+  // The approximation parameters
+  bigfloat *param, *roots, *poles;
+  bigfloat norm;
+
+  // The numerator and denominator degree (n=d)
+  int n, d;
+  
+  // The bounds of the approximation
+  bigfloat apstrt, apwidt, apend;
+
+  // the numerator and denominator of the power we are approximating
+  unsigned long power_num; 
+  unsigned long power_den;
+
+  // Flag to determine whether the arrays have been allocated
+  int alloc;
+
+  // Flag to determine whether the roots have been found
+  int foundRoots;
+
+  // Variables used to calculate the approximation
+  int nd1, iter;
+  bigfloat *xx, *mm, *step;
+  bigfloat delta, spread, tolerance;
+
+  // The exponential summation coefficients
+  bigfloat *a;
+  int *a_power;
+  int a_length;
+
+  // The number of equations we must solve at each iteration (n+d+1)
+  int neq;
+
+  // The precision of the GNU MP library
+  long prec;
+
+  // Initial values of maximal and minmal errors
+  void initialGuess();
+
+  // Solve the equations
+  void equations();
+
+  // Search for error maxima and minima
+  void search(bigfloat *step); 
+
+  // Initialise step sizes
+  void stpini(bigfloat *step);
+
+  // Calculate the roots of the approximation
+  int root();
+
+  // Evaluate the polynomial
+  bigfloat polyEval(bigfloat x, bigfloat *poly, long size);
+  //complex_bf polyEval(complex_bf x, complex_bf *poly, long size);
+
+  // Evaluate the differential of the polynomial
+  bigfloat polyDiff(bigfloat x, bigfloat *poly, long size);
+  //complex_bf polyDiff(complex_bf x, complex_bf *poly, long size);
+
+  // Newton's method to calculate roots
+  bigfloat rtnewt(bigfloat *poly, long i, bigfloat x1, bigfloat x2, bigfloat xacc);
+  //complex_bf rtnewt(complex_bf *poly, long i, bigfloat x1, bigfloat x2, bigfloat xacc);
+
+  // Evaluate the partial fraction expansion of the rational function
+  // with res roots and poles poles.  Result is overwritten on input
+  // arrays.
+  void pfe(bigfloat *res, bigfloat* poles, bigfloat norm);
+
+  // Calculate function required for the approximation
+  bigfloat func(bigfloat x);
+
+  // Compute size and sign of the approximation error at x
+  bigfloat getErr(bigfloat x, int *sign);
+
+  // Solve the system AX=B
+  int simq(bigfloat *A, bigfloat *B, bigfloat *X, int n);
+
+  // Free memory and reallocate as necessary
+  void allocate(int num_degree, int den_degree);
+
+  // Evaluate the rational form P(x)/Q(x) using coefficients from the
+  // solution vector param
+  bigfloat approx(bigfloat x);
+
+ public:
+  
+  // Constructor
+  AlgRemez(double lower, double upper, long prec);
+
+  // Destructor
+  virtual ~AlgRemez();
+
+  int getDegree(void){ 
+    assert(n==d);
+    return n;
+  }
+  // Reset the bounds of the approximation
+  void setBounds(double lower, double upper);
+  // Reset the bounds of the approximation
+  void getBounds(double &lower, double &upper) { 
+    lower=(double)apstrt;
+    upper=(double)apend;
+  }
+
+  // Generate the rational approximation x^(pnum/pden)
+  double generateApprox(int num_degree, int den_degree, 
+			unsigned long power_num, unsigned long power_den, 
+			int a_len, double* a_param, int* a_pow);
+  double generateApprox(int num_degree, int den_degree, 
+			unsigned long power_num, unsigned long power_den);
+  double generateApprox(int degree, unsigned long power_num, 
+			unsigned long power_den);
+
+  // Return the partial fraction expansion of the approximation x^(pnum/pden)
+  int getPFE(double *res, double *pole, double *norm);
+
+  // Return the partial fraction expansion of the approximation x^(-pnum/pden)
+  int getIPFE(double *res, double *pole, double *norm);
+
+  // Evaluate the rational form P(x)/Q(x) using coefficients from the
+  // solution vector param
+  double evaluateApprox(double x);
+
+  // Evaluate the rational form Q(x)/P(x) using coefficients from the
+  // solution vector param
+  double evaluateInverseApprox(double x);
+
+  // Calculate function required for the approximation
+  double evaluateFunc(double x);
+
+  // Calculate inverse function required for the approximation
+  double evaluateInverseFunc(double x);
+  
+  // Dump csv of function, approx and error
+  void csv(std::ostream &os);
+};
+
+#endif  // Include guard
+
+
+

Grid/algorithms/approx/Zolotarev.cc

@@ -0,0 +1,730 @@
+/* -*- Mode: C; comment-column: 22; fill-column: 79; compile-command: "gcc -o zolotarev zolotarev.c -ansi -pedantic -lm -DTEST"; -*- */
+#define VERSION Source Time-stamp: <2015-05-18 16:32:08 neo>
+
+/* These C routines evalute the optimal rational approximation to the signum
+ * function for epsilon < |x| < 1 using Zolotarev's theorem.
+ *
+ * To obtain reliable results for high degree approximations (large n) it is
+ * necessary to compute using sufficiently high precision arithmetic. To this
+ * end the code has been parameterised to work with the preprocessor names
+ * INTERNAL_PRECISION and PRECISION set to float, double, or long double as
+ * appropriate. INTERNAL_PRECISION is used in computing the Zolotarev
+ * coefficients, which are converted to PRECISION before being returned to the
+ * caller. Presumably even higher precision could be obtained using GMP or
+ * similar package, but bear in mind that rounding errors might also be
+ * significant in evaluating the resulting polynomial. The convergence criteria
+ * have been written in a precision-independent form. */
+
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+
+#define MAX(a,b) ((a) > (b) ? (a) : (b))
+#define MIN(a,b) ((a) < (b) ? (a) : (b))
+
+#ifndef INTERNAL_PRECISION
+#define INTERNAL_PRECISION double
+#endif
+
+#include "Zolotarev.h"
+#define ZOLOTAREV_INTERNAL
+#undef ZOLOTAREV_DATA
+#define ZOLOTAREV_DATA izd
+#undef ZPRECISION
+#define ZPRECISION INTERNAL_PRECISION
+#include "Zolotarev.h"
+#undef ZOLOTAREV_INTERNAL
+
+/* The ANSI standard appears not to know what pi is */
+
+#ifndef M_PI
+#define M_PI ((INTERNAL_PRECISION) 3.141592653589793238462643383279502884197\
+169399375105820974944592307816406286208998628034825342117068)
+#endif
+
+#define ZERO ((INTERNAL_PRECISION) 0)
+#define ONE ((INTERNAL_PRECISION) 1)
+#define TWO ((INTERNAL_PRECISION) 2)
+#define THREE ((INTERNAL_PRECISION) 3)
+#define FOUR ((INTERNAL_PRECISION) 4)
+#define HALF (ONE/TWO)
+
+/* The following obscenity seems to be the simplest (?) way to coerce the C
+ * preprocessor to convert the value of a preprocessor token into a string. */
+
+#define PP2(x) #x
+#define PP1(a,b,c) a ## b(c)
+#define STRINGIFY(name) PP1(PP,2,name)
+
+/* Compute the partial fraction expansion coefficients (alpha) from the
+ * factored form */
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
+
+static void construct_partfrac(izd *z) {
+  int dn = z -> dn, dd = z -> dd, type = z -> type;
+  int j, k, da = dd + 1 + type;
+  INTERNAL_PRECISION A = z -> A, *a = z -> a, *ap = z -> ap, *alpha;
+  alpha = (INTERNAL_PRECISION*) malloc(da * sizeof(INTERNAL_PRECISION));
+  for (j = 0; j < dd; j++)
+    for (k = 0, alpha[j] = A; k < dd; k++)
+      alpha[j] *=
+	(k < dn ? ap[j] - a[k] : ONE) / (k == j ? ONE : ap[j] - ap[k]);
+  if(type == 1)	      /* implicit pole at zero? */
+    for (k = 0, alpha[dd] = A * (dn > dd ? - a[dd] : ONE); k < dd; k++) {
+      alpha[dd] *= a[k] / ap[k];
+      alpha[k] *= (dn > dd ? ap[k] - a[dd] : ONE) / ap[k];
+    }
+  alpha[da-1] = dn == da - 1 ? A : ZERO;
+  z -> alpha = alpha;
+  z -> da = da;
+  return;
+}
+
+/* Convert factored polynomial into dense polynomial. The input is the overall
+ * factor A and the roots a[i], such that p = A product(x - a[i], i = 1..d) */
+
+static INTERNAL_PRECISION *poly_factored_to_dense(INTERNAL_PRECISION A, 
+						  INTERNAL_PRECISION *a,
+						  int d) {
+  INTERNAL_PRECISION *p;
+  int i, j;
+  p = (INTERNAL_PRECISION *) malloc((d + 2) * sizeof(INTERNAL_PRECISION));
+  p[0] = A;
+  for (i = 0; i < d; i++) {
+    p[i+1] = p[i];
+    for (j = i; j > 0; j--) p[j] = p[j-1] - a[i]*p[j];
+    p[0] *= - a[i];
+  }
+  return p;
+}
+
+/* Convert a rational function of the form R0(x) = x p(x^2)/q(x^2) (type 0) or
+ * R1(x) = p(x^2)/[x q(x^2)] (type 1) into its continued fraction
+ * representation. We assume that 0 <= deg(q) - deg(p) <= 1 for type 0 and 0 <=
+ * deg(p) - deg(q) <= 1 for type 1. On input p and q are in factored form, and
+ * deg(q) = dq, deg(p) = dp.  The output is the continued fraction coefficients
+ * beta, where R(x) = beta[0] x + 1/(beta[1] x + 1/(...)).
+ *
+ * The method used is as follows. There are four cases to consider:
+ *
+ * 0.i.  Type 0, deg p = deg q
+ *
+ * 0.ii. Type 0, deg p = deg q - 1
+ *
+ * 1.i.  Type 1, deg p = deg q
+ *
+ * 1.ii. Type 1, deg p = deg q + 1
+ *
+ * and these are connected by two transformations:
+ *
+ * A. To obtain a continued fraction expansion of type 1 we use a single-step
+ * polynomial division we find beta and r(x) such that p(x) = beta x q(x) +
+ * r(x), with deg(r) = deg(q). This implies that p(x^2) = beta x^2 q(x^2) +
+ * r(x^2), and thus R1(x) = x beta + r(x^2)/(x q(x^2)) = x beta + 1/R0(x)
+ * with R0(x) = x q(x^2)/r(x^2).
+ *
+ * B. A continued fraction expansion of type 0 is obtained in a similar, but
+ * not identical, manner. We use the polynomial division algorithm to compute
+ * the quotient beta and the remainder r that satisfy p(x) = beta q(x) + r(x)
+ * with deg(r) = deg(q) - 1. We thus have x p(x^2) = x beta q(x^2) + x r(x^2),
+ * so R0(x) = x beta + x r(x^2)/q(x^2) = x beta + 1/R1(x) with R1(x) = q(x^2) /
+ * (x r(x^2)).
+ *
+ * Note that the deg(r) must be exactly deg(q) for (A) and deg(q) - 1 for (B)
+ * because p and q have disjoint roots all of multiplicity 1. This means that
+ * the division algorithm requires only a single polynomial subtraction step.
+ *
+ * The transformations between the cases form the following finite state
+ * automaton:
+ *
+ * +------+            +------+            +------+            +------+
+ * |      |            |      | ---(A)---> |      |            |      |
+ * | 0.ii | ---(B)---> | 1.ii |            | 0.i  | <---(A)--- | 1.i  |
+ * |      |            |      | <---(B)--- |      |            |      |
+ * +------+            +------+            +------+            +------+
+ */
+
+static INTERNAL_PRECISION *contfrac_A(INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *, int, int);
+
+static INTERNAL_PRECISION *contfrac_B(INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *,
+				      INTERNAL_PRECISION *, int, int);
+
+static void construct_contfrac(izd *z){
+  INTERNAL_PRECISION *r, A = z -> A, *p = z -> a, *q = z -> ap;
+  int dp = z -> dn, dq = z -> dd, type = z -> type;
+
+  z -> db = 2 * dq + 1 + type;
+  z -> beta = (INTERNAL_PRECISION *)
+    malloc(z -> db * sizeof(INTERNAL_PRECISION));
+  p = poly_factored_to_dense(A, p, dp);
+  q = poly_factored_to_dense(ONE, q, dq);
+  r = (INTERNAL_PRECISION *) malloc((MAX(dp,dq) + 1) *
+				    sizeof(INTERNAL_PRECISION));
+  if (type == 0) (void) contfrac_B(z -> beta, p, q, r, dp, dq);
+  else (void) contfrac_A(z -> beta, p, q, r, dp, dq);
+  free(p); free(q); free(r);
+  return;
+}
+
+static INTERNAL_PRECISION *contfrac_A(INTERNAL_PRECISION *beta,
+				      INTERNAL_PRECISION *p,
+				      INTERNAL_PRECISION *q,
+				      INTERNAL_PRECISION *r, int dp, int dq) {
+  INTERNAL_PRECISION quot, *rb;
+  int j;
+
+  /* p(x) = x beta q(x) + r(x); dp = dq or dp = dq + 1 */
+
+  quot = dp == dq ? ZERO : p[dp] / q[dq];
+  r[0] = p[0];
+  for (j = 1; j <= dp; j++) r[j] = p[j] - quot * q[j-1];
+#ifdef DEBUG
+  printf("%s: Continued Fraction form: deg p = %2d, deg q = %2d, beta = %g\n",
+	 __FUNCTION__, dp, dq, (float) quot);
+  for (j = 0; j <= dq + 1; j++)
+    printf("\tp[%2d] = %14.6g\tq[%2d] = %14.6g\tr[%2d] = %14.6g\n",
+	   j, (float) (j > dp ? ZERO : p[j]),
+	   j, (float) (j == 0 ? ZERO : q[j-1]),
+	   j, (float) (j == dp ? ZERO : r[j]));
+#endif /* DEBUG */
+  *(rb = contfrac_B(beta, q, r, p, dq, dq)) = quot;
+  return rb + 1;
+}
+
+static INTERNAL_PRECISION *contfrac_B(INTERNAL_PRECISION *beta,
+				      INTERNAL_PRECISION *p,
+				      INTERNAL_PRECISION *q,
+				      INTERNAL_PRECISION *r, int dp, int dq) {
+  INTERNAL_PRECISION quot, *rb;
+  int j;
+
+  /* p(x) = beta q(x) + r(x); dp = dq or dp = dq - 1 */
+
+  quot = dp == dq ? p[dp] / q[dq] : ZERO;
+  for (j = 0; j < dq; j++) r[j] = p[j] - quot * q[j];
+#ifdef DEBUG
+  printf("%s: Continued Fraction form: deg p = %2d, deg q = %2d, beta = %g\n",
+	 __FUNCTION__, dp, dq, (float) quot);
+  for (j = 0; j <= dq; j++)
+    printf("\tp[%2d] = %14.6g\tq[%2d] = %14.6g\tr[%2d] = %14.6g\n",
+	   j, (float) (j > dp ? ZERO : p[j]),
+	   j, (float) q[j],
+	   j, (float) (j == dq ? ZERO : r[j]));
+#endif /* DEBUG */
+  *(rb = dq > 0 ? contfrac_A(beta, q, r, p, dq, dq-1) : beta) = quot;
+  return rb + 1;
+}
+
+/* The global variable U is used to hold the argument u throughout the AGM
+ * recursion. The global variables F and K are set in the innermost
+ * instantiation of the recursive function AGM to the values of the elliptic
+ * integrals F(u,k) and K(k) respectively. They must be made thread local to
+ * make this code thread-safe in a multithreaded environment. */
+
+static INTERNAL_PRECISION U, F, K;	/* THREAD LOCAL */
+
+/* Recursive implementation of Gauss' arithmetico-geometric mean, which is the
+ * kernel of the method used to compute the Jacobian elliptic functions
+ * sn(u,k), cn(u,k), and dn(u,k) with parameter k (where 0 < k < 1), as well
+ * as the elliptic integral F(s,k) satisfying F(sn(u,k)) = u and the complete
+ * elliptic integral K(k).
+ *
+ * The algorithm used is a recursive implementation of the Gauss (Landen)
+ * transformation.
+ *
+ * The function returns the value of sn(u,k'), where k' is the dual parameter,
+ * and also sets the values of the global variables F and K.  The latter is
+ * used to determine the sign of cn(u,k').
+ *
+ * The algorithm is deemed to have converged when b ceases to increase. This
+ * works whatever INTERNAL_PRECISION is specified. */
+
+static INTERNAL_PRECISION AGM(INTERNAL_PRECISION a,
+			      INTERNAL_PRECISION b,
+			      INTERNAL_PRECISION s) {
+  static INTERNAL_PRECISION pb = -ONE;
+  INTERNAL_PRECISION c, d, xi;
+
+  if (b <= pb) {
+    pb = -ONE;
+    F = asin(s) / a;		/* Here, a is the AGM */
+    K = M_PI / (TWO * a);
+    return sin(U * a);
+  }
+  pb = b;
+  c = a - b;
+  d = a + b;
+  xi = AGM(HALF*d, sqrt(a*b), ONE + c*c == ONE ?
+	   HALF*s*d/a : (a - sqrt(a*a - s*s*c*d))/(c*s));
+  return 2*a*xi / (d + c*xi*xi);
+}
+
+/* Computes sn(u,k), cn(u,k), dn(u,k), F(u,k), and K(k). It is essentially a
+ * wrapper for the routine AGM. The sign of cn(u,k) is defined to be -1 if
+ * K(k) < u < 3*K(k) and +1 otherwise, and thus sign is computed by some quite
+ * unnecessarily obfuscated bit manipulations. */
+
+static void sncndnFK(INTERNAL_PRECISION u, INTERNAL_PRECISION k,
+		     INTERNAL_PRECISION* sn, INTERNAL_PRECISION* cn,
+		     INTERNAL_PRECISION* dn, INTERNAL_PRECISION* elF,
+		     INTERNAL_PRECISION* elK) {
+  int sgn;
+  U = u;
+  *sn = AGM(ONE, sqrt(ONE - k*k), u);
+  sgn = ((int) (fabs(u) / K)) % 4; /* sgn = 0, 1, 2, 3 */
+  sgn ^= sgn >> 1;    /* (sgn & 1) = 0, 1, 1, 0 */
+  sgn = 1 - ((sgn & 1) << 1);	/* sgn = 1, -1, -1, 1 */
+  *cn = ((INTERNAL_PRECISION) sgn) * sqrt(ONE - *sn * *sn);
+  *dn = sqrt(ONE - k*k* *sn * *sn);
+  *elF = F;
+  *elK = K;
+}
+
+/* Compute the coefficients for the optimal rational approximation R(x) to
+ * sgn(x) of degree n over the interval epsilon < |x| < 1 using Zolotarev's
+ * formula. 
+ *
+ * Set type = 0 for the Zolotarev approximation, which is zero at x = 0, and
+ * type = 1 for the approximation which is infinite at x = 0. */
+
+zolotarev_data* zolotarev(PRECISION epsilon, int n, int type) {
+  INTERNAL_PRECISION A, c, cp, kp, ksq, sn, cn, dn, Kp, Kj, z, z0, t, M, F,
+    l, invlambda, xi, xisq, *tv, s, opl;
+  int m, czero, ts;
+  zolotarev_data *zd;
+  izd *d = (izd*) malloc(sizeof(izd));
+
+  d -> type = type;
+  d -> epsilon = (INTERNAL_PRECISION) epsilon;
+  d -> n = n;
+  d -> dd = n / 2;
+  d -> dn = d -> dd - 1 + n % 2; /* n even: dn = dd - 1, n odd: dn = dd */
+  d -> deg_denom = 2 * d -> dd;
+  d -> deg_num = 2 * d -> dn + 1;
+
+  d -> a = (INTERNAL_PRECISION*) malloc((1 + d -> dn) *
+					sizeof(INTERNAL_PRECISION));
+  d -> ap = (INTERNAL_PRECISION*) malloc(d -> dd *
+					 sizeof(INTERNAL_PRECISION));
+  ksq = d -> epsilon * d -> epsilon;
+  kp = sqrt(ONE - ksq);
+  sncndnFK(ZERO, kp, &sn, &cn, &dn, &F, &Kp); /* compute Kp = K(kp) */
+  z0 = TWO * Kp / (INTERNAL_PRECISION) n;
+  M = ONE;
+  A = ONE / d -> epsilon;
+
+  sncndnFK(HALF * z0, kp, &sn, &cn, &dn, &F, &Kj); /* compute xi */
+  xi = ONE / dn;
+  xisq = xi * xi;
+  invlambda = xi;
+
+  for (m = 0; m < d -> dd; m++) {
+    czero = 2 * (m + 1) == n; /* n even and m = dd -1 */
+
+    z = z0 * ((INTERNAL_PRECISION) m + ONE);
+    sncndnFK(z, kp, &sn, &cn, &dn, &F, &Kj);
+    t = cn / sn;
+    c = - t*t;
+    if (!czero) (d -> a)[d -> dn - 1 - m] = ksq / c;
+
+    z = z0 * ((INTERNAL_PRECISION) m + HALF);
+    sncndnFK(z, kp, &sn, &cn, &dn, &F, &Kj);
+    t = cn / sn;
+    cp = - t*t;
+    (d -> ap)[d -> dd - 1 - m] = ksq / cp;
+
+    M *= (ONE - c) / (ONE - cp);
+    A *= (czero ? -ksq : c) * (ONE - cp) / (cp * (ONE - c));
+    invlambda *= (ONE - c*xisq) / (ONE - cp*xisq);
+  }
+  invlambda /= M;
+  d -> A = TWO / (ONE + invlambda) * A;
+  d -> Delta = (invlambda - ONE) / (invlambda + ONE);
+
+  d -> gamma = (INTERNAL_PRECISION*) malloc((1 + d -> n) *
+					    sizeof(INTERNAL_PRECISION));
+  l = ONE / invlambda;
+  opl = ONE + l;
+  sncndnFK(sqrt( d -> type == 1
+		   ? (THREE + l) / (FOUR * opl)
+		   : (ONE + THREE*l) / (opl*opl*opl)
+	       ), sqrt(ONE - l*l), &sn, &cn, &dn, &F, &Kj);
+  s = M * F;
+  for (m = 0; m < d -> n; m++) {
+    sncndnFK(s + TWO*Kp*m/n, kp, &sn, &cn, &dn, &F, &Kj);
+    d -> gamma[m] = d -> epsilon / dn;
+  }
+
+  /* If R(x) is a Zolotarev rational approximation of degree (n,m) with maximum
+   * error Delta, then (1 - Delta^2) / R(x) is also an optimal Chebyshev
+   * approximation of degree (m,n) */
+
+  if (d -> type == 1) {
+    d -> A = (ONE - d -> Delta * d -> Delta) / d -> A;
+    tv = d -> a; d -> a = d -> ap; d -> ap = tv;
+    ts = d -> dn; d -> dn = d -> dd; d -> dd = ts;
+    ts = d -> deg_num; d -> deg_num = d -> deg_denom; d -> deg_denom = ts;
+  }
+
+  construct_partfrac(d);
+  construct_contfrac(d);
+
+  /* Converting everything to PRECISION for external use only */
+
+  zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
+  zd -> A = (PRECISION) d -> A;
+  zd -> Delta = (PRECISION) d -> Delta;
+  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> n = d -> n;
+  zd -> type = d -> type;
+  zd -> dn = d -> dn;
+  zd -> dd = d -> dd;
+  zd -> da = d -> da;
+  zd -> db = d -> db;
+  zd -> deg_num = d -> deg_num;
+  zd -> deg_denom = d -> deg_denom;
+
+  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  free(d -> a);
+
+  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  free(d -> ap);
+
+  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  free(d -> alpha);
+
+  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  free(d -> beta);
+
+  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  free(d -> gamma);
+
+  free(d);
+  return zd;
+}
+
+
+void zolotarev_free(zolotarev_data *zdata)
+{
+    free(zdata -> a);
+    free(zdata -> ap);
+    free(zdata -> alpha);
+    free(zdata -> beta);
+    free(zdata -> gamma);
+    free(zdata);
+}
+
+
+zolotarev_data* higham(PRECISION epsilon, int n) {
+  INTERNAL_PRECISION A, M, c, cp, z, z0, t, epssq;
+  int m, czero;
+  zolotarev_data *zd;
+  izd *d = (izd*) malloc(sizeof(izd));
+
+  d -> type = 0;
+  d -> epsilon = (INTERNAL_PRECISION) epsilon;
+  d -> n = n;
+  d -> dd = n / 2;
+  d -> dn = d -> dd - 1 + n % 2; /* n even: dn = dd - 1, n odd: dn = dd */
+  d -> deg_denom = 2 * d -> dd;
+  d -> deg_num = 2 * d -> dn + 1;
+
+  d -> a = (INTERNAL_PRECISION*) malloc((1 + d -> dn) *
+					sizeof(INTERNAL_PRECISION));
+  d -> ap = (INTERNAL_PRECISION*) malloc(d -> dd *
+					 sizeof(INTERNAL_PRECISION));
+  A = (INTERNAL_PRECISION) n;
+  z0 = M_PI / A;
+  A = n % 2 == 0 ? A : ONE / A;
+  M = d -> epsilon * A;
+  epssq = d -> epsilon * d -> epsilon;
+
+  for (m = 0; m < d -> dd; m++) {
+    czero = 2 * (m + 1) == n; /* n even and m = dd - 1*/
+
+    if (!czero) {
+      z = z0 * ((INTERNAL_PRECISION) m + ONE);
+      t = tan(z);
+      c = - t*t;
+      (d -> a)[d -> dn - 1 - m] = c;
+      M *= epssq - c;
+    }
+
+    z = z0 * ((INTERNAL_PRECISION) m + HALF);
+    t = tan(z);
+    cp = - t*t;
+    (d -> ap)[d -> dd - 1 - m] = cp;
+    M /= epssq - cp;
+  }
+
+  d -> gamma = (INTERNAL_PRECISION*) malloc((1 + d -> n) *
+					    sizeof(INTERNAL_PRECISION));
+  for (m = 0; m < d -> n; m++) d -> gamma[m] = ONE;
+
+  d -> A = A;
+  d -> Delta = ONE - M;
+
+  construct_partfrac(d);
+  construct_contfrac(d);
+
+  /* Converting everything to PRECISION for external use only */
+
+  zd = (zolotarev_data*) malloc(sizeof(zolotarev_data));
+  zd -> A = (PRECISION) d -> A;
+  zd -> Delta = (PRECISION) d -> Delta;
+  zd -> epsilon = (PRECISION) d -> epsilon;
+  zd -> n = d -> n;
+  zd -> type = d -> type;
+  zd -> dn = d -> dn;
+  zd -> dd = d -> dd;
+  zd -> da = d -> da;
+  zd -> db = d -> db;
+  zd -> deg_num = d -> deg_num;
+  zd -> deg_denom = d -> deg_denom;
+
+  zd -> a = (PRECISION*) malloc(zd -> dn * sizeof(PRECISION));
+  for (m = 0; m < zd -> dn; m++) zd -> a[m] = (PRECISION) d -> a[m];
+  free(d -> a);
+
+  zd -> ap = (PRECISION*) malloc(zd -> dd * sizeof(PRECISION));
+  for (m = 0; m < zd -> dd; m++) zd -> ap[m] = (PRECISION) d -> ap[m];
+  free(d -> ap);
+
+  zd -> alpha = (PRECISION*) malloc(zd -> da * sizeof(PRECISION));
+  for (m = 0; m < zd -> da; m++) zd -> alpha[m] = (PRECISION) d -> alpha[m];
+  free(d -> alpha);
+
+  zd -> beta = (PRECISION*) malloc(zd -> db * sizeof(PRECISION));
+  for (m = 0; m < zd -> db; m++) zd -> beta[m] = (PRECISION) d -> beta[m];
+  free(d -> beta);
+
+  zd -> gamma = (PRECISION*) malloc(zd -> n * sizeof(PRECISION));
+  for (m = 0; m < zd -> n; m++) zd -> gamma[m] = (PRECISION) d -> gamma[m];
+  free(d -> gamma);
+
+  free(d);
+  return zd;
+}
+
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
+
+#ifdef TEST
+
+#undef ZERO
+#define ZERO ((PRECISION) 0)
+#undef ONE
+#define ONE ((PRECISION) 1)
+#undef TWO
+#define TWO ((PRECISION) 2)
+
+/* Evaluate the rational approximation R(x) using the factored form */
+
+static PRECISION zolotarev_eval(PRECISION x, zolotarev_data* rdata) {
+  int m;
+  PRECISION R;
+
+  if (rdata -> type == 0) {
+    R = rdata -> A * x;
+    for (m = 0; m < rdata -> deg_denom/2; m++)
+      R *= (2*(m+1) > rdata -> deg_num ? ONE : x*x - rdata -> a[m]) /
+	(x*x - rdata -> ap[m]);
+  } else {
+    R = rdata -> A / x;
+    for (m = 0; m < rdata -> deg_num/2; m++)
+      R *= (x*x - rdata -> a[m]) /
+	(2*(m+1) > rdata -> deg_denom ? ONE : x*x - rdata -> ap[m]);
+  }
+  return R;
+}
+
+/* Evaluate the rational approximation R(x) using the partial fraction form */
+
+static PRECISION zolotarev_partfrac_eval(PRECISION x, zolotarev_data* rdata) {
+  int m;
+  PRECISION R = rdata -> alpha[rdata -> da - 1];
+  for (m = 0; m < rdata -> dd; m++)
+    R += rdata -> alpha[m] / (x * x - rdata -> ap[m]);
+  if (rdata -> type == 1) R += rdata -> alpha[rdata -> dd] / (x * x);
+  return R * x;
+}    
+
+/* Evaluate the rational approximation R(x) using continued fraction form. 
+ *
+ * If x = 0 and type = 1 then the result should be INF, whereas if x = 0 and
+ * type = 0 then the result should be 0, but division by zero will occur at
+ * intermediate stages of the evaluation. For IEEE implementations with
+ * non-signalling overflow this will work correctly since 1/(1/0) = 1/INF = 0,
+ * but with signalling overflow you will get an error message. */
+
+static PRECISION zolotarev_contfrac_eval(PRECISION x, zolotarev_data* rdata) {
+  int m;
+  PRECISION R = rdata -> beta[0] * x;
+  for (m = 1; m < rdata -> db; m++) R = rdata -> beta[m] * x + ONE / R;
+  return R;
+}    
+
+/* Evaluate the rational approximation R(x) using Cayley form */
+
+static PRECISION zolotarev_cayley_eval(PRECISION x, zolotarev_data* rdata) {
+  int m;
+  PRECISION T;
+
+  T = rdata -> type == 0 ? ONE : -ONE;
+  for (m = 0; m < rdata -> n; m++)
+    T *= (rdata -> gamma[m] - x) / (rdata -> gamma[m] + x);
+  return (ONE - T) / (ONE + T);
+}
+
+
+/* Test program. Apart from printing out the parameters for R(x) it produces
+ * the following data files for plotting (unless NPLOT is defined):
+ *
+ * zolotarev-fn is a plot of R(x) for |x| < 1.2. This should look like sgn(x).
+ *
+ * zolotarev-err is a plot of the error |R(x) - sgn(x)| scaled by 1/Delta. This
+ * should oscillate deg_num + deg_denom + 2 times between +1 and -1 over the
+ * domain epsilon <= |x| <= 1.
+ *
+ * If ALLPLOTS is defined then zolotarev-partfrac (zolotarev-contfrac) is a
+ * plot of the difference between the values of R(x) computed using the
+ * factored form and the partial fraction (continued fraction) form, scaled by
+ * 1/Delta. It should be zero everywhere. */
+
+int main(int argc, char** argv) {
+  
+  int m, n, plotpts = 5000, type = 0;
+  float eps, x, ypferr, ycferr, ycaylerr, maxypferr, maxycferr, maxycaylerr;
+  zolotarev_data *rdata;
+  PRECISION y;
+  FILE *plot_function, *plot_error, 
+    *plot_partfrac, *plot_contfrac, *plot_cayley;
+
+  if (argc < 3 || argc > 4) {
+    fprintf(stderr, "Usage: %s epsilon n [type]\n", *argv);
+    exit(EXIT_FAILURE);
+  }
+  sscanf(argv[1], "%g", &eps);	/* First argument is epsilon */
+  sscanf(argv[2], "%d", &n);	/* Second argument is n */
+  if (argc == 4) sscanf(argv[3], "%d", &type); /* Third argument is type */
+
+  if (type < 0 || type > 2) {
+    fprintf(stderr, "%s: type must be 0 (Zolotarev R(0) = 0),\n"
+	    "\t\t1 (Zolotarev R(0) = Inf, or 2 (Higham)\n", *argv);
+    exit(EXIT_FAILURE);
+  }
+
+  rdata = type == 2 
+    ? higham((PRECISION) eps, n) 
+    : zolotarev((PRECISION) eps, n, type);
+
+  printf("Zolotarev Test: R(epsilon = %g, n = %d, type = %d)\n\t" 
+	 STRINGIFY(VERSION) "\n\t" STRINGIFY(HVERSION)
+	 "\n\tINTERNAL_PRECISION = " STRINGIFY(INTERNAL_PRECISION)
+	 "\tPRECISION = " STRINGIFY(PRECISION)
+	 "\n\n\tRational approximation of degree (%d,%d), %s at x = 0\n"
+	 "\tDelta = %g (maximum error)\n\n"
+	 "\tA = %g (overall factor)\n",
+	 (float) rdata -> epsilon, rdata -> n, type,
+	 rdata -> deg_num, rdata -> deg_denom,
+	 rdata -> type == 1 ? "infinite" : "zero",
+	 (float) rdata -> Delta, (float) rdata -> A);
+  for (m = 0; m < MIN(rdata -> dd, rdata -> dn); m++)
+    printf("\ta[%2d] = %14.8g\t\ta'[%2d] = %14.8g\n",
+	   m + 1, (float) rdata -> a[m], m + 1, (float) rdata -> ap[m]);
+  if (rdata -> dd > rdata -> dn)
+    printf("\t\t\t\t\ta'[%2d] = %14.8g\n",
+	   rdata -> dn + 1, (float) rdata -> ap[rdata -> dn]);
+  if (rdata -> dd < rdata -> dn)
+    printf("\ta[%2d] = %14.8g\n",
+	   rdata -> dd + 1, (float) rdata -> a[rdata -> dd]);
+
+  printf("\n\tPartial fraction coefficients\n");
+  printf("\talpha[ 0] = %14.8g\n",
+	 (float) rdata -> alpha[rdata -> da - 1]);
+  for (m = 0; m < rdata -> dd; m++)
+    printf("\talpha[%2d] = %14.8g\ta'[%2d] = %14.8g\n",
+	   m + 1, (float) rdata -> alpha[m], m + 1, (float) rdata -> ap[m]);
+  if (rdata -> type == 1)
+    printf("\talpha[%2d] = %14.8g\ta'[%2d] = %14.8g\n",
+	   rdata -> dd + 1, (float) rdata -> alpha[rdata -> dd],
+	   rdata -> dd + 1, (float) ZERO);
+
+  printf("\n\tContinued fraction coefficients\n");
+  for (m = 0; m < rdata -> db; m++)
+    printf("\tbeta[%2d] = %14.8g\n", m, (float) rdata -> beta[m]);
+
+  printf("\n\tCayley transform coefficients\n");
+  for (m = 0; m < rdata -> n; m++)
+    printf("\tgamma[%2d] = %14.8g\n", m, (float) rdata -> gamma[m]);
+
+#ifndef NPLOT
+  plot_function = fopen("zolotarev-fn.dat", "w");
+  plot_error = fopen("zolotarev-err.dat", "w");
+#ifdef ALLPLOTS
+  plot_partfrac = fopen("zolotarev-partfrac.dat", "w");
+  plot_contfrac = fopen("zolotarev-contfrac.dat", "w");
+  plot_cayley = fopen("zolotarev-cayley.dat", "w");
+#endif /* ALLPLOTS */
+  for (m = 0, maxypferr = maxycferr = maxycaylerr = 0.0; m <= plotpts; m++) {
+    x = 2.4 * (float) m / plotpts - 1.2;
+    if (rdata -> type == 0 || fabs(x) * (float) plotpts > 1.0) {
+      /* skip x = 0 for type 1, as R(0) is singular */
+      y = zolotarev_eval((PRECISION) x, rdata);
+      fprintf(plot_function, "%g %g\n", x, (float) y);
+      fprintf(plot_error, "%g %g\n",
+	      x, (float)((y - ((x > 0.0 ? ONE : -ONE))) / rdata -> Delta));
+      ypferr = (float)((zolotarev_partfrac_eval((PRECISION) x, rdata) - y)
+		       / rdata -> Delta);
+      ycferr = (float)((zolotarev_contfrac_eval((PRECISION) x, rdata) - y)
+		       / rdata -> Delta);
+      ycaylerr = (float)((zolotarev_cayley_eval((PRECISION) x, rdata) - y)
+		       / rdata -> Delta);
+      if (fabs(x) < 1.0 && fabs(x) > rdata -> epsilon) {
+	maxypferr = MAX(maxypferr, fabs(ypferr));
+	maxycferr = MAX(maxycferr, fabs(ycferr));
+	maxycaylerr = MAX(maxycaylerr, fabs(ycaylerr));
+      }
+#ifdef ALLPLOTS
+      fprintf(plot_partfrac, "%g %g\n", x, ypferr);
+      fprintf(plot_contfrac, "%g %g\n", x, ycferr);
+      fprintf(plot_cayley, "%g %g\n", x, ycaylerr);
+#endif /* ALLPLOTS */
+    }
+  }
+#ifdef ALLPLOTS
+  fclose(plot_cayley);
+  fclose(plot_contfrac);
+  fclose(plot_partfrac);
+#endif /* ALLPLOTS */
+  fclose(plot_error);
+  fclose(plot_function);
+
+  printf("\n\tMaximum PF error = %g (relative to Delta)\n", maxypferr);
+  printf("\tMaximum CF error = %g (relative to Delta)\n", maxycferr);
+  printf("\tMaximum Cayley error = %g (relative to Delta)\n", maxycaylerr);
+#endif /* NPLOT */
+
+  free(rdata -> a);
+  free(rdata -> ap);
+  free(rdata -> alpha);
+  free(rdata -> beta);
+  free(rdata -> gamma);
+  free(rdata);
+
+  return EXIT_SUCCESS;
+}
+
+#endif /* TEST */
+

Grid/algorithms/approx/Zolotarev.h

@@ -0,0 +1,88 @@
+/* -*- Mode: C; comment-column: 22; fill-column: 79; -*- */
+
+#ifdef __cplusplus
+#include <Grid/Namespace.h>
+NAMESPACE_BEGIN(Grid);
+NAMESPACE_BEGIN(Approx);
+#endif
+
+#define HVERSION Header Time-stamp: <14-OCT-2004 09:26:51.00 adk@MISSCONTRARY>
+
+#ifndef ZOLOTAREV_INTERNAL
+#ifndef PRECISION
+#define PRECISION double
+#endif
+#define ZPRECISION PRECISION
+#define ZOLOTAREV_DATA zolotarev_data
+#endif
+
+/* This struct contains the coefficients which parameterise an optimal rational
+ * approximation to the signum function.
+ *
+ * The parameterisations used are:
+ *
+ * Factored form for type 0 (R0(0) = 0)
+ *
+ * R0(x) = A * x * prod(x^2 - a[j], j = 0 .. dn-1) / prod(x^2 - ap[j], j = 0
+ * .. dd-1),
+ *
+ * where deg_num = 2*dn + 1 and deg_denom = 2*dd.
+ *
+ * Factored form for type 1 (R1(0) = infinity)
+ *
+ * R1(x) = (A / x) * prod(x^2 - a[j], j = 0 .. dn-1) / prod(x^2 - ap[j], j = 0
+ * .. dd-1),
+ *
+ * where deg_num = 2*dn and deg_denom = 2*dd + 1. 
+ *
+ * Partial fraction form
+ *
+ * R(x) = alpha[da] * x + sum(alpha[j] * x / (x^2 - ap[j]), j = 0 .. da-1)
+ *
+ * where da = dd for type 0 and da = dd + 1 with ap[dd] = 0 for type 1.
+ *
+ * Continued fraction form 
+ *
+ * R(x) = beta[db-1] * x + 1 / (beta[db-2] * x + 1 / (beta[db-3] * x + ...))
+ *
+ * with the final coefficient being beta[0], with d' = 2 * dd + 1 for type 0
+ * and db = 2 * dd + 2 for type 1.
+ *
+ * Cayley form (Chiu's domain wall formulation)
+ *
+ * R(x) = (1 - T(x)) / (1 + T(x))
+ *
+ * where T(x) = prod((x - gamma[j]) / (x + gamma[j]), j = 0 .. n-1)
+ */
+
+typedef struct {
+  ZPRECISION *a,      /* zeros of numerator, a[0 .. dn-1] */
+    *ap,	      /* poles (zeros of denominator), ap[0 .. dd-1] */
+    A,		      /* overall factor */
+    *alpha,	      /* coefficients of partial fraction, alpha[0 .. da-1] */
+    *beta,	      /* coefficients of continued fraction, beta[0 .. db-1] */
+    *gamma,	      /* zeros of numerator of T in Cayley form */
+    Delta,	      /* maximum error, |R(x) - sgn(x)| <= Delta */
+    epsilon;	      /* minimum x value, epsilon < |x| < 1 */
+  int n,	      /* approximation degree */
+    type,	      /* 0: R(0) = 0, 1: R(0) = infinity */
+    dn, dd, da, db,   /* number of elements of a, ap, alpha, and beta */
+    deg_num,	      /* degree of numerator = deg_denom +/- 1 */
+    deg_denom;	      /* degree of denominator */
+} ZOLOTAREV_DATA;
+
+#ifndef ZOLOTAREV_INTERNAL
+
+/* zolotarev(epsilon, n, type) returns a pointer to an initialised
+ * zolotarev_data structure. The arguments must satisfy the constraints that
+ * epsilon > 0, n > 0, and type = 0 or 1. */
+
+ZOLOTAREV_DATA* higham(PRECISION epsilon, int n) ;
+ZOLOTAREV_DATA* zolotarev(PRECISION epsilon, int n, int type);
+void zolotarev_free(zolotarev_data *zdata);
+#endif
+
+#ifdef __cplusplus
+NAMESPACE_END(Approx);
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/approx/bigfloat.h

@@ -0,0 +1,206 @@
+/*
+  Mike Clark - 25th May 2005
+
+  bigfloat.h
+
+  Simple C++ wrapper for multiprecision datatype used by AlgRemez
+  algorithm
+*/
+
+#ifndef INCLUDED_BIGFLOAT_H
+#define INCLUDED_BIGFLOAT_H
+
+
+#include <gmp.h>
+#include <mpf2mpfr.h>
+#include <mpfr.h>
+class bigfloat {
+
+private:
+
+  mpf_t x;
+
+public:
+
+  bigfloat() { mpf_init(x); }
+  bigfloat(const bigfloat& y) { mpf_init_set(x, y.x); }
+  bigfloat(const unsigned long u) { mpf_init_set_ui(x, u); }
+  bigfloat(const long i) { mpf_init_set_si(x, i); }
+  bigfloat(const int i) {mpf_init_set_si(x,(long)i);}
+  bigfloat(const float d) { mpf_init_set_d(x, (double)d); }
+  bigfloat(const double d) { mpf_init_set_d(x, d); }  
+  bigfloat(const char *str) { mpf_init_set_str(x, (char*)str, 10); }
+  ~bigfloat(void) { mpf_clear(x); }
+  operator double (void) const { return (double)mpf_get_d(x); }
+  static void setDefaultPrecision(unsigned long dprec) {
+    unsigned long bprec =  (unsigned long)(3.321928094 * (double)dprec);
+    mpf_set_default_prec(bprec);
+  }
+
+  void setPrecision(unsigned long dprec) {
+    unsigned long bprec =  (unsigned long)(3.321928094 * (double)dprec);
+    mpf_set_prec(x,bprec);
+  }
+  
+  unsigned long getPrecision(void) const { return mpf_get_prec(x); }
+
+  unsigned long getDefaultPrecision(void) const { return mpf_get_default_prec(); }
+
+  bigfloat& operator=(const bigfloat& y) {
+    mpf_set(x, y.x); 
+    return *this;
+  }
+
+  bigfloat& operator=(const unsigned long y) { 
+    mpf_set_ui(x, y);
+    return *this; 
+  }
+  
+  bigfloat& operator=(const signed long y) {
+    mpf_set_si(x, y); 
+    return *this;
+  }
+  
+  bigfloat& operator=(const float y) {
+    mpf_set_d(x, (double)y); 
+    return *this;
+  }
+
+  bigfloat& operator=(const double y) {
+    mpf_set_d(x, y); 
+    return *this;
+  }
+
+  size_t write(void);
+  size_t read(void);
+
+  /* Arithmetic Functions */
+
+  bigfloat& operator+=(const bigfloat& y) { return *this = *this + y; }
+  bigfloat& operator-=(const bigfloat& y) { return *this = *this - y; }
+  bigfloat& operator*=(const bigfloat& y) { return *this = *this * y; }
+  bigfloat& operator/=(const bigfloat& y) { return *this = *this / y; }
+
+  friend bigfloat operator+(const bigfloat& x, const bigfloat& y) {
+    bigfloat a;
+    mpf_add(a.x,x.x,y.x);
+    return a;
+  }
+
+  friend bigfloat operator+(const bigfloat& x, const unsigned long y) {
+    bigfloat a;
+    mpf_add_ui(a.x,x.x,y);
+    return a;
+  }
+
+  friend bigfloat operator-(const bigfloat& x, const bigfloat& y) {
+    bigfloat a;
+    mpf_sub(a.x,x.x,y.x);
+    return a;
+  }
+  
+  friend bigfloat operator-(const unsigned long x, const bigfloat& y) {
+    bigfloat a;
+    mpf_ui_sub(a.x,x,y.x);
+    return a;
+  }
+  
+  friend bigfloat operator-(const bigfloat& x, const unsigned long y) {
+    bigfloat a;
+    mpf_sub_ui(a.x,x.x,y);
+    return a;
+  }
+
+  friend bigfloat operator-(const bigfloat& x) {
+    bigfloat a;
+    mpf_neg(a.x,x.x);
+    return a;
+  }
+
+  friend bigfloat operator*(const bigfloat& x, const bigfloat& y) {
+    bigfloat a;
+    mpf_mul(a.x,x.x,y.x);
+    return a;
+  }
+
+  friend bigfloat operator*(const bigfloat& x, const unsigned long y) {
+    bigfloat a;
+    mpf_mul_ui(a.x,x.x,y);
+    return a;
+  }
+
+  friend bigfloat operator/(const bigfloat& x, const bigfloat& y){
+    bigfloat a;
+    mpf_div(a.x,x.x,y.x);
+    return a;
+  }
+
+  friend bigfloat operator/(const unsigned long x, const bigfloat& y){
+    bigfloat a;
+    mpf_ui_div(a.x,x,y.x);
+    return a;
+  }
+
+  friend bigfloat operator/(const bigfloat& x, const unsigned long y){
+    bigfloat a;
+    mpf_div_ui(a.x,x.x,y);
+    return a;
+  }
+
+  friend bigfloat sqrt_bf(const bigfloat& x){
+    bigfloat a;
+    mpf_sqrt(a.x,x.x);
+    return a;
+  }
+
+  friend bigfloat sqrt_bf(const unsigned long x){
+    bigfloat a;
+    mpf_sqrt_ui(a.x,x);
+    return a;
+  }
+
+  friend bigfloat abs_bf(const bigfloat& x){
+    bigfloat a;
+    mpf_abs(a.x,x.x);
+    return a;
+  }
+
+  friend bigfloat pow_bf(const bigfloat& a, long power) {
+    bigfloat b;
+    mpf_pow_ui(b.x,a.x,power);
+    return b;
+  }
+
+  friend bigfloat pow_bf(const bigfloat& a, bigfloat &power) {
+    bigfloat b;
+    mpfr_pow(b.x,a.x,power.x,GMP_RNDN);
+    return b;
+  }
+
+  friend bigfloat exp_bf(const bigfloat& a) {
+    bigfloat b;
+    mpfr_exp(b.x,a.x,GMP_RNDN);
+    return b;
+  }
+
+  /* Comparison Functions */
+
+  friend int operator>(const bigfloat& x, const bigfloat& y) {
+    int test;
+    test = mpf_cmp(x.x,y.x);
+    if (test > 0) return 1;
+    else return 0;
+  }
+
+  friend int operator<(const bigfloat& x, const bigfloat& y) {
+    int test;
+    test = mpf_cmp(x.x,y.x);
+    if (test < 0) return 1;
+    else return 0;
+  }
+
+  friend int sgn(const bigfloat&);
+
+};
+
+#endif

Grid/algorithms/approx/bigfloat_double.h

@@ -0,0 +1,189 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/approx/bigfloat_double.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <math.h>
+
+typedef double mfloat; 
+class bigfloat {
+private:
+
+  mfloat x;
+
+public:
+
+  bigfloat() { }
+  bigfloat(const bigfloat& y) { x=y.x; }
+  bigfloat(const unsigned long u) { x=u; }
+  bigfloat(const long i) { x=i; }
+  bigfloat(const int i) { x=i;}
+  bigfloat(const float d) { x=d;}
+  bigfloat(const double d) {  x=d;}
+  bigfloat(const char *str) { x=std::stod(std::string(str));}
+  ~bigfloat(void) { }
+  operator double (void) const { return (double)x; }
+  static void setDefaultPrecision(unsigned long dprec) {
+  }
+
+  void setPrecision(unsigned long dprec) {
+  }
+  
+  unsigned long getPrecision(void) const { return 64; }
+  unsigned long getDefaultPrecision(void) const { return 64; }
+
+  bigfloat& operator=(const bigfloat& y)     { x=y.x;    return *this;  }
+  bigfloat& operator=(const unsigned long y) { x=y; return *this; }
+  bigfloat& operator=(const signed long y)   { x=y; return *this; }
+  bigfloat& operator=(const float y)    { x=y; return *this; }
+  bigfloat& operator=(const double y)   { x=y; return *this; }
+
+  size_t write(void);
+  size_t read(void);
+
+  /* Arithmetic Functions */
+
+  bigfloat& operator+=(const bigfloat& y) { return *this = *this + y; }
+  bigfloat& operator-=(const bigfloat& y) { return *this = *this - y; }
+  bigfloat& operator*=(const bigfloat& y) { return *this = *this * y; }
+  bigfloat& operator/=(const bigfloat& y) { return *this = *this / y; }
+
+  friend bigfloat operator+(const bigfloat& x, const bigfloat& y) { 
+    bigfloat a;
+    a.x=x.x+y.x;
+    return a;
+  }
+
+  friend bigfloat operator+(const bigfloat& x, const unsigned long y) {
+    bigfloat a;
+    a.x=x.x+y;
+    return a;
+  }
+
+  friend bigfloat operator-(const bigfloat& x, const bigfloat& y) {
+    bigfloat a;
+    a.x=x.x-y.x;
+    return a;
+  }
+  
+  friend bigfloat operator-(const unsigned long x, const bigfloat& y) {
+    bigfloat bx(x);
+    return bx-y;
+  }
+  
+  friend bigfloat operator-(const bigfloat& x, const unsigned long y) {
+    bigfloat by(y);
+    return x-by;
+  }
+
+  friend bigfloat operator-(const bigfloat& x) {
+    bigfloat a;
+    a.x=-x.x;
+    return a;
+  }
+
+  friend bigfloat operator*(const bigfloat& x, const bigfloat& y) {
+    bigfloat a;
+    a.x=x.x*y.x;
+    return a;
+  }
+
+  friend bigfloat operator*(const bigfloat& x, const unsigned long y) {
+    bigfloat a;
+    a.x=x.x*y;
+    return a;
+  }
+
+  friend bigfloat operator/(const bigfloat& x, const bigfloat& y){
+    bigfloat a;
+    a.x=x.x/y.x;
+    return a;
+  }
+
+  friend bigfloat operator/(const unsigned long x, const bigfloat& y){
+    bigfloat bx(x);
+    return bx/y;
+  }
+
+  friend bigfloat operator/(const bigfloat& x, const unsigned long y){
+    bigfloat by(y);
+    return x/by;
+  }
+
+  friend bigfloat sqrt_bf(const bigfloat& x){
+    bigfloat a;
+    a.x= sqrt(x.x);
+    return a;
+  }
+
+  friend bigfloat sqrt_bf(const unsigned long x){
+    bigfloat a(x);
+    return sqrt_bf(a);
+  }
+
+  friend bigfloat abs_bf(const bigfloat& x){
+    bigfloat a;
+    a.x=fabs(x.x);
+    return a;
+  }
+
+  friend bigfloat pow_bf(const bigfloat& a, long power) {
+    bigfloat b;
+    b.x=pow(a.x,power);
+    return b;
+  }
+
+  friend bigfloat pow_bf(const bigfloat& a, bigfloat &power) {
+    bigfloat b;
+    b.x=pow(a.x,power.x);
+    return b;
+  }
+
+  friend bigfloat exp_bf(const bigfloat& a) {
+    bigfloat b;
+    b.x=exp(a.x);
+    return b;
+  }
+
+  /* Comparison Functions */
+  friend int operator>(const bigfloat& x, const bigfloat& y) {
+    return x.x>y.x;
+  }
+
+  friend int operator<(const bigfloat& x, const bigfloat& y) {
+    return x.x<y.x;
+  }
+
+  friend int sgn(const bigfloat& x) {
+    if ( x.x>=0 )  return 1;   
+    else return 0;
+  }
+
+  /* Miscellaneous Functions */
+
+  //  friend bigfloat& random(void);
+};
+
+

Grid/algorithms/iterative/AdefGeneric.h

@@ -0,0 +1,397 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/AdefGeneric.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_ALGORITHMS_ITERATIVE_GENERIC_PCG
+#define GRID_ALGORITHMS_ITERATIVE_GENERIC_PCG
+
+  /*
+   * Compared to Tang-2009:  P=Pleft. P^T = PRight Q=MssInv. 
+   * Script A = SolverMatrix 
+   * Script P = Preconditioner
+   *
+   * Deflation methods considered
+   *      -- Solve P A x = P b        [ like Luscher ]
+   * DEF-1        M P A x = M P b     [i.e. left precon]
+   * DEF-2        P^T M A x = P^T M b
+   * ADEF-1       Preconditioner = M P + Q      [ Q + M + M A Q]
+   * ADEF-2       Preconditioner = P^T M + Q
+   * BNN          Preconditioner = P^T M P + Q
+   * BNN2         Preconditioner = M P + P^TM +Q - M P A M 
+   * 
+   * Implement ADEF-2
+   *
+   * Vstart = P^Tx + Qb
+   * M1 = P^TM + Q
+   * M2=M3=1
+   * Vout = x
+   */
+
+// abstract base
+template<class Field, class CoarseField>
+class TwoLevelFlexiblePcg : public LinearFunction<Field>
+{
+ public:
+  int verbose;
+  RealD   Tolerance;
+  Integer MaxIterations;
+  const int mmax = 5;
+  GridBase *grid;
+  GridBase *coarsegrid;
+
+  LinearOperatorBase<Field>   *_Linop
+  OperatorFunction<Field>     *_Smoother,
+  LinearFunction<CoarseField> *_CoarseSolver;
+
+  // Need somthing that knows how to get from Coarse to fine and back again
+  
+  // more most opertor functions
+  TwoLevelFlexiblePcg(RealD tol,
+		     Integer maxit,
+		     LinearOperatorBase<Field> *Linop,
+		     LinearOperatorBase<Field> *SmootherLinop,
+		     OperatorFunction<Field>   *Smoother,
+		     OperatorFunction<CoarseField>  CoarseLinop
+		     ) : 
+      Tolerance(tol), 
+      MaxIterations(maxit),
+      _Linop(Linop),
+      _PreconditionerLinop(PrecLinop),
+      _Preconditioner(Preconditioner)
+  { 
+    verbose=0;
+  };
+
+  // The Pcg routine is common to all, but the various matrices differ from derived 
+  // implementation to derived implmentation
+  void operator() (const Field &src, Field &psi){
+  void operator() (const Field &src, Field &psi){
+
+    psi.Checkerboard() = src.Checkerboard();
+    grid             = src.Grid();
+
+    RealD f;
+    RealD rtzp,rtz,a,d,b;
+    RealD rptzp;
+    RealD tn;
+    RealD guess = norm2(psi);
+    RealD ssq   = norm2(src);
+    RealD rsq   = ssq*Tolerance*Tolerance;
+    
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    std::vector<Field> p  (mmax,grid);
+    std::vector<Field> mmp(mmax,grid);
+    std::vector<RealD> pAp(mmax);
+
+    Field x  (grid); x = psi;
+    Field z  (grid);
+    Field tmp(grid);
+    Field r  (grid);
+    Field mu (grid);
+  
+    //////////////////////////
+    // x0 = Vstart -- possibly modify guess
+    //////////////////////////
+    x=src;
+    Vstart(x,src);
+
+    // r0 = b -A x0
+    HermOp(x,mmp); // Shouldn't this be something else?
+    axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
+
+    //////////////////////////////////
+    // Compute z = M1 x
+    //////////////////////////////////
+    M1(r,z,tmp,mp,SmootherMirs);
+    rtzp =real(innerProduct(r,z));
+
+    ///////////////////////////////////////
+    // Solve for Mss mu = P A z and set p = z-mu
+    // Def2: p = 1 - Q Az = Pright z 
+    // Other algos M2 is trivial
+    ///////////////////////////////////////
+    M2(z,p[0]);
+
+    for (int k=0;k<=MaxIterations;k++){
+    
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
+
+      rtz=rtzp;
+      d= M3(p[peri_k],mp,mmp[peri_k],tmp);
+      a = rtz/d;
+    
+      // Memorise this
+      pAp[peri_k] = d;
+
+      axpy(x,a,p[peri_k],x);
+      RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
+
+      // Compute z = M x
+      M1(r,z,tmp,mp);
+
+      rtzp =real(innerProduct(r,z));
+
+      M2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+
+      p[peri_kp]=p[peri_k];
+
+      // Standard search direction  p -> z + b p    ; b = 
+      b = (rtzp)/rtz;
+
+      int northog;
+      //    northog     = (peri_kp==0)?1:peri_kp; // This is the fCG(mmax) algorithm
+      northog     = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
+    
+      for(int back=0; back < northog; back++){
+	int peri_back = (k-back)%mmax;
+	RealD pbApk= real(innerProduct(mmp[peri_back],p[peri_kp]));
+	RealD beta = -pbApk/pAp[peri_back];
+	axpy(p[peri_kp],beta,p[peri_back],p[peri_kp]);
+      }
+
+      RealD rrn=sqrt(rn/ssq);
+      std::cout<<GridLogMessage<<"TwoLevelfPcg: k= "<<k<<" residual = "<<rrn<<std::endl;
+
+      // Stopping condition
+      if ( rn <= rsq ) { 
+
+	HermOp(x,mmp); // Shouldn't this be something else?
+	axpy(tmp,-1.0,src,mmp[0]);
+	
+	RealD psinorm = sqrt(norm2(x));
+	RealD srcnorm = sqrt(norm2(src));
+	RealD tmpnorm = sqrt(norm2(tmp));
+	RealD true_residual = tmpnorm/srcnorm;
+	std::cout<<GridLogMessage<<"TwoLevelfPcg:   true residual is "<<true_residual<<std::endl;
+	std::cout<<GridLogMessage<<"TwoLevelfPcg: target residual was"<<Tolerance<<std::endl;
+	return k;
+      }
+    }
+    // Non-convergence
+    assert(0);
+  }
+
+ public:
+
+  virtual void M(Field & in,Field & out,Field & tmp) {
+
+  }
+
+  virtual void M1(Field & in, Field & out) {// the smoother
+
+    // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
+    Field tmp(grid);
+    Field Min(grid);
+
+    PcgM(in,Min); // Smoother call
+
+    HermOp(Min,out);
+    axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
+
+    ProjectToSubspace(tmp,PleftProj);     
+    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    axpy(out,1.0,Min,tmp); // Min+tmp
+  }
+
+  virtual void M2(const Field & in, Field & out) {
+    out=in;
+    // Must override for Def2 only
+    //  case PcgDef2:
+    //    Pright(in,out);
+    //    break;
+  }
+
+  virtual RealD M3(const Field & p, Field & mmp){
+    double d,dd;
+    HermOpAndNorm(p,mmp,d,dd);
+    return dd;
+    // Must override for Def1 only
+    //  case PcgDef1:
+    //    d=linop_d->Mprec(p,mmp,tmp,0,1);// Dag no
+    //      linop_d->Mprec(mmp,mp,tmp,1);// Dag yes
+    //    Pleft(mp,mmp);
+    //    d=real(linop_d->inner(p,mmp));
+  }
+
+  virtual void VstartDef2(Field & xconst Field & src){
+    //case PcgDef2:
+    //case PcgAdef2: 
+    //case PcgAdef2f:
+    //case PcgV11f:
+    ///////////////////////////////////
+    // Choose x_0 such that 
+    // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
+    //                               = [1 - Ass_inv A] Guess + Assinv src
+    //                               = P^T guess + Assinv src 
+    //                               = Vstart  [Tang notation]
+    // This gives:
+    // W^T (src - A x_0) = src_s - A guess_s - r_s
+    //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
+    //                   = 0 
+    ///////////////////////////////////
+    Field r(grid);
+    Field mmp(grid);
+    
+    HermOp(x,mmp);
+    axpy (r, -1.0, mmp, src);        // r_{-1} = src - A x
+    ProjectToSubspace(r,PleftProj);     
+    ApplyInverseCG(PleftProj,PleftMss_proj); // Ass^{-1} r_s
+    PromoteFromSubspace(PleftMss_proj,mmp);  
+    x=x+mmp;
+
+  }
+
+  virtual void Vstart(Field & x,const Field & src){
+    return;
+  }
+
+  /////////////////////////////////////////////////////////////////////
+  // Only Def1 has non-trivial Vout. Override in Def1
+  /////////////////////////////////////////////////////////////////////
+  virtual void   Vout  (Field & in, Field & out,Field & src){
+    out = in;
+    //case PcgDef1:
+    //    //Qb + PT x
+    //    ProjectToSubspace(src,PleftProj);     
+    //    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} r_s
+    //    PromoteFromSubspace(PleftMss_proj,tmp);  
+    //    
+    //    Pright(in,out);
+    //    
+    //    linop_d->axpy(out,tmp,out,1.0);
+    //    break;
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // Pright and Pleft are common to all implementations
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  virtual void Pright(Field & in,Field & out){
+    // P_R  = [ 1              0 ] 
+    //        [ -Mss^-1 Msb    0 ] 
+    Field in_sbar(grid);
+
+    ProjectToSubspace(in,PleftProj);     
+    PromoteFromSubspace(PleftProj,out);  
+    axpy(in_sbar,-1.0,out,in);       // in_sbar = in - in_s 
+
+    HermOp(in_sbar,out);
+    ProjectToSubspace(out,PleftProj);           // Mssbar in_sbar  (project)
+
+    ApplyInverse     (PleftProj,PleftMss_proj); // Mss^{-1} Mssbar 
+    PromoteFromSubspace(PleftMss_proj,out);     // 
+
+    axpy(out,-1.0,out,in_sbar);     // in_sbar - Mss^{-1} Mssbar in_sbar
+  }
+  virtual void Pleft (Field & in,Field & out){
+    // P_L  = [ 1  -Mbs Mss^-1] 
+    //        [ 0   0         ] 
+    Field in_sbar(grid);
+    Field    tmp2(grid);
+    Field    Mtmp(grid);
+
+    ProjectToSubspace(in,PleftProj);     
+    PromoteFromSubspace(PleftProj,out);  
+    axpy(in_sbar,-1.0,out,in);      // in_sbar = in - in_s
+
+    ApplyInverse(PleftProj,PleftMss_proj); // Mss^{-1} in_s
+    PromoteFromSubspace(PleftMss_proj,out);
+
+    HermOp(out,Mtmp);
+
+    ProjectToSubspace(Mtmp,PleftProj);      // Msbar s Mss^{-1}
+    PromoteFromSubspace(PleftProj,tmp2);
+
+    axpy(out,-1.0,tmp2,Mtmp);
+    axpy(out,-1.0,out,in_sbar);     // in_sbar - Msbars Mss^{-1} in_s
+  }
+}
+
+template<class Field>
+class TwoLevelFlexiblePcgADef2 : public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp){
+
+  } 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp){
+
+  }
+  virtual void M2(Field & in, Field & out){
+
+  }
+  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp){
+
+  }
+  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp){
+
+  }
+}
+/*
+template<class Field>
+class TwoLevelFlexiblePcgAD : public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp); 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
+  virtual void M2(Field & in, Field & out);
+  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
+  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
+}
+
+template<class Field>
+class TwoLevelFlexiblePcgDef1 : public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp); 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
+  virtual void M2(Field & in, Field & out);
+  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
+  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
+  virtual void   Vout  (Field & in, Field & out,Field & src,Field & tmp);
+}
+
+template<class Field>
+class TwoLevelFlexiblePcgDef2 : public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp); 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
+  virtual void M2(Field & in, Field & out);
+  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
+  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
+}
+
+template<class Field>
+class TwoLevelFlexiblePcgV11: public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp); 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
+  virtual void M2(Field & in, Field & out);
+  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
+  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
+}
+*/
+#endif

Grid/algorithms/iterative/BlockConjugateGradient.h

@@ -0,0 +1,694 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/BlockConjugateGradient.h
+
+Copyright (C) 2017
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+enum BlockCGtype { BlockCG, BlockCGrQ, CGmultiRHS, BlockCGVec, BlockCGrQVec };
+
+//////////////////////////////////////////////////////////////////////////
+// Block conjugate gradient. Dimension zero should be the block direction
+//////////////////////////////////////////////////////////////////////////
+template <class Field>
+class BlockConjugateGradient : public OperatorFunction<Field> {
+ public:
+
+  typedef typename Field::scalar_type scomplex;
+
+  int blockDim ;
+  int Nblock;
+
+  BlockCGtype CGtype;
+  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+                           // Defaults true.
+  RealD Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  Integer PrintInterval; //GridLogMessages or Iterative
+  
+  BlockConjugateGradient(BlockCGtype cgtype,int _Orthog,RealD tol, Integer maxit, bool err_on_no_conv = true)
+    : Tolerance(tol), CGtype(cgtype),   blockDim(_Orthog),  MaxIterations(maxit), ErrorOnNoConverge(err_on_no_conv),PrintInterval(100)
+  {};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Thin QR factorisation (google it)
+////////////////////////////////////////////////////////////////////////////////////////////////////
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  //Dimensions
+  // R_{ferm x Nblock} =  Q_{ferm x Nblock} x  C_{Nblock x Nblock} -> ferm x Nblock
+  //
+  // Rdag R = m_rr = Herm = L L^dag        <-- Cholesky decomposition (LLT routine in Eigen)
+  //
+  //   Q  C = R => Q = R C^{-1}
+  //
+  // Want  Ident = Q^dag Q = C^{-dag} R^dag R C^{-1} = C^{-dag} L L^dag C^{-1} = 1_{Nblock x Nblock} 
+  //
+  // Set C = L^{dag}, and then Q^dag Q = ident 
+  //
+  // Checks:
+  // Cdag C = Rdag R ; passes.
+  // QdagQ  = 1      ; passes
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+void ThinQRfact (Eigen::MatrixXcd &m_rr,
+		 Eigen::MatrixXcd &C,
+		 Eigen::MatrixXcd &Cinv,
+		 Field & Q,
+		 const Field & R)
+{
+  int Orthog = blockDim; // First dimension is block dim; this is an assumption
+  sliceInnerProductMatrix(m_rr,R,R,Orthog);
+
+  // Force manifest hermitian to avoid rounding related
+  m_rr = 0.5*(m_rr+m_rr.adjoint());
+
+  Eigen::MatrixXcd L    = m_rr.llt().matrixL(); 
+
+  C    = L.adjoint();
+  Cinv = C.inverse();
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Q = R C^{-1}
+  //
+  // Q_j  = R_i Cinv(i,j) 
+  //
+  // NB maddMatrix conventions are Right multiplication X[j] a[j,i] already
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  sliceMulMatrix(Q,Cinv,R,Orthog);
+}
+// see comments above
+void ThinQRfact (Eigen::MatrixXcd &m_rr,
+		 Eigen::MatrixXcd &C,
+		 Eigen::MatrixXcd &Cinv,
+		 std::vector<Field> & Q,
+		 const std::vector<Field> & R)
+{
+  InnerProductMatrix(m_rr,R,R);
+
+  m_rr = 0.5*(m_rr+m_rr.adjoint());
+
+  Eigen::MatrixXcd L    = m_rr.llt().matrixL(); 
+
+  C    = L.adjoint();
+  Cinv = C.inverse();
+
+  MulMatrix(Q,Cinv,R);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Call one of several implementations
+////////////////////////////////////////////////////////////////////////////////////////////////////
+void operator()(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi) 
+{
+  if ( CGtype == BlockCGrQ ) {
+    BlockCGrQsolve(Linop,Src,Psi);
+  } else if (CGtype == CGmultiRHS ) {
+    CGmultiRHSsolve(Linop,Src,Psi);
+  } else {
+    assert(0);
+  }
+}
+virtual void operator()(LinearOperatorBase<Field> &Linop, const std::vector<Field> &Src, std::vector<Field> &Psi) 
+{
+  if ( CGtype == BlockCGrQVec ) {
+    BlockCGrQsolveVec(Linop,Src,Psi);
+  } else {
+    assert(0);
+  }
+}
+
+////////////////////////////////////////////////////////////////////////////
+// BlockCGrQ implementation:
+//--------------------------
+// X is guess/Solution
+// B is RHS
+// Solve A X_i = B_i    ;        i refers to Nblock index
+////////////////////////////////////////////////////////////////////////////
+void BlockCGrQsolve(LinearOperatorBase<Field> &Linop, const Field &B, Field &X) 
+{
+  int Orthog = blockDim; // First dimension is block dim; this is an assumption
+  Nblock = B.Grid()->_fdimensions[Orthog];
+/* FAKE */
+  Nblock=8;
+  std::cout<<GridLogMessage<<" Block Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
+
+  X.checkerboard = B.checkerboard;
+  conformable(X, B);
+
+  Field tmp(B);
+  Field Q(B);
+  Field D(B);
+  Field Z(B);
+  Field AD(B);
+
+  Eigen::MatrixXcd m_DZ     = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_M      = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_rr     = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_C      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Cinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_S      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Sinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_tmp    = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_tmp1   = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+
+  // Initial residual computation & set up
+  std::vector<RealD> residuals(Nblock);
+  std::vector<RealD> ssq(Nblock);
+
+  sliceNorm(ssq,B,Orthog);
+  RealD sssum=0;
+  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
+
+  sliceNorm(residuals,B,Orthog);
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  sliceNorm(residuals,X,Orthog);
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  /************************************************************************
+   * Block conjugate gradient rQ (Sebastien Birk Thesis, after Dubrulle 2001)
+   ************************************************************************
+   * Dimensions:
+   *
+   *   X,B==(Nferm x Nblock)
+   *   A==(Nferm x Nferm)
+   *  
+   * Nferm = Nspin x Ncolour x Ncomplex x Nlattice_site
+   * 
+   * QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+   * for k: 
+   *   Z  = AD
+   *   M  = [D^dag Z]^{-1}
+   *   X  = X + D MC
+   *   QS = Q - ZM
+   *   D  = Q + D S^dag
+   *   C  = S C
+   */
+  ///////////////////////////////////////
+  // Initial block: initial search dir is guess
+  ///////////////////////////////////////
+  std::cout << GridLogMessage<<"BlockCGrQ algorithm initialisation " <<std::endl;
+
+  //1.  QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+  Linop.HermOp(X, AD);
+  tmp = B - AD;  
+
+  ThinQRfact (m_rr, m_C, m_Cinv, Q, tmp);
+  D=Q;
+
+  std::cout << GridLogMessage<<"BlockCGrQ computed initial residual and QR fact " <<std::endl;
+
+  ///////////////////////////////////////
+  // Timers
+  ///////////////////////////////////////
+  GridStopWatch sliceInnerTimer;
+  GridStopWatch sliceMaddTimer;
+  GridStopWatch QRTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+  SolverTimer.Start();
+
+  int k;
+  for (k = 1; k <= MaxIterations; k++) {
+
+    //3. Z  = AD
+    MatrixTimer.Start();
+    Linop.HermOp(D, Z);      
+    MatrixTimer.Stop();
+
+    //4. M  = [D^dag Z]^{-1}
+    sliceInnerTimer.Start();
+    sliceInnerProductMatrix(m_DZ,D,Z,Orthog);
+    sliceInnerTimer.Stop();
+    m_M       = m_DZ.inverse();
+    
+    //5. X  = X + D MC
+    m_tmp     = m_M * m_C;
+    sliceMaddTimer.Start();
+    sliceMaddMatrix(X,m_tmp, D,X,Orthog);     
+    sliceMaddTimer.Stop();
+
+    //6. QS = Q - ZM
+    sliceMaddTimer.Start();
+    sliceMaddMatrix(tmp,m_M,Z,Q,Orthog,-1.0);
+    sliceMaddTimer.Stop();
+    QRTimer.Start();
+    ThinQRfact (m_rr, m_S, m_Sinv, Q, tmp);
+    QRTimer.Stop();
+    
+    //7. D  = Q + D S^dag
+    m_tmp = m_S.adjoint();
+
+    sliceMaddTimer.Start();
+    sliceMaddMatrix(D,m_tmp,D,Q,Orthog);
+    sliceMaddTimer.Stop();
+
+    //8. C  = S C
+    m_C = m_S*m_C;
+    
+    /*********************
+     * convergence monitor
+     *********************
+     */
+    m_rr = m_C.adjoint() * m_C;
+
+    RealD max_resid=0;
+    RealD rrsum=0;
+    RealD rr;
+
+    for(int b=0;b<Nblock;b++) {
+      rrsum+=real(m_rr(b,b));
+      rr = real(m_rr(b,b))/ssq[b];
+      if ( rr > max_resid ) max_resid = rr;
+    }
+
+    std::cout << GridLogIterative << "\titeration "<<k<<" rr_sum "<<rrsum<<" ssq_sum "<< sssum
+	      <<" ave "<<std::sqrt(rrsum/sssum) << " max "<< max_resid <<std::endl;
+
+    if ( max_resid < Tolerance*Tolerance ) { 
+
+      SolverTimer.Stop();
+
+      std::cout << GridLogMessage<<"BlockCGrQ converged in "<<k<<" iterations"<<std::endl;
+
+      for(int b=0;b<Nblock;b++){
+	std::cout << GridLogMessage<< "\t\tblock "<<b<<" computed resid "
+		  << std::sqrt(real(m_rr(b,b))/ssq[b])<<std::endl;
+      }
+      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
+
+      Linop.HermOp(X, AD);
+      AD = AD-B;
+      std::cout << GridLogMessage <<"\t True residual is " << std::sqrt(norm2(AD)/norm2(B)) <<std::endl;
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
+      std::cout << GridLogMessage << "\tThinQRfact " << QRTimer.Elapsed()  <<std::endl;
+	    
+      IterationsToComplete = k;
+      return;
+    }
+
+  }
+  std::cout << GridLogMessage << "BlockConjugateGradient(rQ) did NOT converge" << std::endl;
+
+  if (ErrorOnNoConverge) assert(0);
+  IterationsToComplete = k;
+}
+//////////////////////////////////////////////////////////////////////////
+// multiRHS conjugate gradient. Dimension zero should be the block direction
+// Use this for spread out across nodes
+//////////////////////////////////////////////////////////////////////////
+void CGmultiRHSsolve(LinearOperatorBase<Field> &Linop, const Field &Src, Field &Psi) 
+{
+  int Orthog = blockDim; // First dimension is block dim
+  Nblock = Src.Grid()->_fdimensions[Orthog];
+
+  std::cout<<GridLogMessage<<"MultiRHS Conjugate Gradient : Orthog "<<Orthog<<" Nblock "<<Nblock<<std::endl;
+
+  Psi.checkerboard = Src.checkerboard;
+  conformable(Psi, Src);
+
+  Field P(Src);
+  Field AP(Src);
+  Field R(Src);
+  
+  std::vector<ComplexD> v_pAp(Nblock);
+  std::vector<RealD> v_rr (Nblock);
+  std::vector<RealD> v_rr_inv(Nblock);
+  std::vector<RealD> v_alpha(Nblock);
+  std::vector<RealD> v_beta(Nblock);
+
+  // Initial residual computation & set up
+  std::vector<RealD> residuals(Nblock);
+  std::vector<RealD> ssq(Nblock);
+
+  sliceNorm(ssq,Src,Orthog);
+  RealD sssum=0;
+  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
+
+  sliceNorm(residuals,Src,Orthog);
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  sliceNorm(residuals,Psi,Orthog);
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  // Initial search dir is guess
+  Linop.HermOp(Psi, AP);
+
+  R = Src - AP;  
+  P = R;
+  sliceNorm(v_rr,R,Orthog);
+
+  GridStopWatch sliceInnerTimer;
+  GridStopWatch sliceMaddTimer;
+  GridStopWatch sliceNormTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+
+  SolverTimer.Start();
+  int k;
+  for (k = 1; k <= MaxIterations; k++) {
+
+    RealD rrsum=0;
+    for(int b=0;b<Nblock;b++) rrsum+=real(v_rr[b]);
+
+    std::cout << GridLogIterative << "\titeration "<<k<<" rr_sum "<<rrsum<<" ssq_sum "<< sssum
+	      <<" / "<<std::sqrt(rrsum/sssum) <<std::endl;
+
+    MatrixTimer.Start();
+    Linop.HermOp(P, AP);
+    MatrixTimer.Stop();
+
+    // Alpha
+    sliceInnerTimer.Start();
+    sliceInnerProductVector(v_pAp,P,AP,Orthog);
+    sliceInnerTimer.Stop();
+    for(int b=0;b<Nblock;b++){
+      v_alpha[b] = v_rr[b]/real(v_pAp[b]);
+    }
+
+    // Psi, R update
+    sliceMaddTimer.Start();
+    sliceMaddVector(Psi,v_alpha, P,Psi,Orthog);     // add alpha *  P to psi
+    sliceMaddVector(R  ,v_alpha,AP,  R,Orthog,-1.0);// sub alpha * AP to resid
+    sliceMaddTimer.Stop();
+
+    // Beta
+    for(int b=0;b<Nblock;b++){
+      v_rr_inv[b] = 1.0/v_rr[b];
+    }
+    sliceNormTimer.Start();
+    sliceNorm(v_rr,R,Orthog);
+    sliceNormTimer.Stop();
+    for(int b=0;b<Nblock;b++){
+      v_beta[b] = v_rr_inv[b] *v_rr[b];
+    }
+
+    // Search update
+    sliceMaddTimer.Start();
+    sliceMaddVector(P,v_beta,P,R,Orthog);
+    sliceMaddTimer.Stop();
+
+    /*********************
+     * convergence monitor
+     *********************
+     */
+    RealD max_resid=0;
+    for(int b=0;b<Nblock;b++){
+      RealD rr = v_rr[b]/ssq[b];
+      if ( rr > max_resid ) max_resid = rr;
+    }
+    
+    if ( max_resid < Tolerance*Tolerance ) { 
+
+      SolverTimer.Stop();
+
+      std::cout << GridLogMessage<<"MultiRHS solver converged in " <<k<<" iterations"<<std::endl;
+      for(int b=0;b<Nblock;b++){
+	std::cout << GridLogMessage<< "\t\tBlock "<<b<<" computed resid "<< std::sqrt(v_rr[b]/ssq[b])<<std::endl;
+      }
+      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
+
+      Linop.HermOp(Psi, AP);
+      AP = AP-Src;
+      std::cout <<GridLogMessage << "\tTrue residual is " << std::sqrt(norm2(AP)/norm2(Src)) <<std::endl;
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tNorm       " << sliceNormTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
+
+
+      IterationsToComplete = k;
+      return;
+    }
+
+  }
+  std::cout << GridLogMessage << "MultiRHSConjugateGradient did NOT converge" << std::endl;
+
+  if (ErrorOnNoConverge) assert(0);
+  IterationsToComplete = k;
+}
+
+void InnerProductMatrix(Eigen::MatrixXcd &m , const std::vector<Field> &X, const std::vector<Field> &Y){
+  for(int b=0;b<Nblock;b++){
+  for(int bp=0;bp<Nblock;bp++) {
+    m(b,bp) = innerProduct(X[b],Y[bp]);  
+  }}
+}
+void MaddMatrix(std::vector<Field> &AP, Eigen::MatrixXcd &m , const std::vector<Field> &X,const std::vector<Field> &Y,RealD scale=1.0){
+  // Should make this cache friendly with site outermost, parallel_for
+  // Deal with case AP aliases with either Y or X
+  std::vector<Field> tmp(Nblock,X[0]);
+  for(int b=0;b<Nblock;b++){
+    tmp[b]   = Y[b];
+    for(int bp=0;bp<Nblock;bp++) {
+      tmp[b] = tmp[b] + (scale*m(bp,b))*X[bp]; 
+    }
+  }
+  for(int b=0;b<Nblock;b++){
+    AP[b] = tmp[b];
+  }
+}
+void MulMatrix(std::vector<Field> &AP, Eigen::MatrixXcd &m , const std::vector<Field> &X){
+  // Should make this cache friendly with site outermost, parallel_for
+  for(int b=0;b<Nblock;b++){
+    AP[b] = Zero();
+    for(int bp=0;bp<Nblock;bp++) {
+      AP[b] += (m(bp,b))*X[bp]; 
+    }
+  }
+}
+double normv(const std::vector<Field> &P){
+  double nn = 0.0;
+  for(int b=0;b<Nblock;b++) {
+    nn+=norm2(P[b]);
+  }
+  return nn;
+}
+
+////////////////////////////////////////////////////////////////////////////
+// BlockCGrQvec implementation:
+//--------------------------
+// X is guess/Solution
+// B is RHS
+// Solve A X_i = B_i    ;        i refers to Nblock index
+////////////////////////////////////////////////////////////////////////////
+void BlockCGrQsolveVec(LinearOperatorBase<Field> &Linop, const std::vector<Field> &B, std::vector<Field> &X) 
+{
+  Nblock = B.size();
+  assert(Nblock == X.size());
+
+  std::cout<<GridLogMessage<<" Block Conjugate Gradient Vec rQ : Nblock "<<Nblock<<std::endl;
+
+  for(int b=0;b<Nblock;b++){ 
+    X[b].checkerboard = B[b].checkerboard;
+    conformable(X[b], B[b]);
+    conformable(X[b], X[0]); 
+  }
+
+  Field Fake(B[0]);
+
+  std::vector<Field> tmp(Nblock,Fake);
+  std::vector<Field>   Q(Nblock,Fake);
+  std::vector<Field>   D(Nblock,Fake);
+  std::vector<Field>   Z(Nblock,Fake);
+  std::vector<Field>  AD(Nblock,Fake);
+
+  Eigen::MatrixXcd m_DZ     = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_M      = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_rr     = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_C      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Cinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_S      = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+  Eigen::MatrixXcd m_Sinv   = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  Eigen::MatrixXcd m_tmp    = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+  Eigen::MatrixXcd m_tmp1   = Eigen::MatrixXcd::Identity(Nblock,Nblock);
+
+  // Initial residual computation & set up
+  std::vector<RealD> residuals(Nblock);
+  std::vector<RealD> ssq(Nblock);
+
+  RealD sssum=0;
+  for(int b=0;b<Nblock;b++){ ssq[b] = norm2(B[b]);}
+  for(int b=0;b<Nblock;b++) sssum+=ssq[b];
+
+  for(int b=0;b<Nblock;b++){ residuals[b] = norm2(B[b]);}
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  for(int b=0;b<Nblock;b++){ residuals[b] = norm2(X[b]);}
+  for(int b=0;b<Nblock;b++){ assert(std::isnan(residuals[b])==0); }
+
+  /************************************************************************
+   * Block conjugate gradient rQ (Sebastien Birk Thesis, after Dubrulle 2001)
+   ************************************************************************
+   * Dimensions:
+   *
+   *   X,B==(Nferm x Nblock)
+   *   A==(Nferm x Nferm)
+   *  
+   * Nferm = Nspin x Ncolour x Ncomplex x Nlattice_site
+   * 
+   * QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+   * for k: 
+   *   Z  = AD
+   *   M  = [D^dag Z]^{-1}
+   *   X  = X + D MC
+   *   QS = Q - ZM
+   *   D  = Q + D S^dag
+   *   C  = S C
+   */
+  ///////////////////////////////////////
+  // Initial block: initial search dir is guess
+  ///////////////////////////////////////
+  std::cout << GridLogMessage<<"BlockCGrQvec algorithm initialisation " <<std::endl;
+
+  //1.  QC = R = B-AX, D = Q     ; QC => Thin QR factorisation (google it)
+  for(int b=0;b<Nblock;b++) {
+    Linop.HermOp(X[b], AD[b]);
+    tmp[b] = B[b] - AD[b];  
+  }
+
+  ThinQRfact (m_rr, m_C, m_Cinv, Q, tmp);
+
+  for(int b=0;b<Nblock;b++) D[b]=Q[b];
+
+  std::cout << GridLogMessage<<"BlockCGrQ vec computed initial residual and QR fact " <<std::endl;
+
+  ///////////////////////////////////////
+  // Timers
+  ///////////////////////////////////////
+  GridStopWatch sliceInnerTimer;
+  GridStopWatch sliceMaddTimer;
+  GridStopWatch QRTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+  SolverTimer.Start();
+
+  int k;
+  for (k = 1; k <= MaxIterations; k++) {
+
+    //3. Z  = AD
+    MatrixTimer.Start();
+    for(int b=0;b<Nblock;b++) Linop.HermOp(D[b], Z[b]);      
+    MatrixTimer.Stop();
+
+    //4. M  = [D^dag Z]^{-1}
+    sliceInnerTimer.Start();
+    InnerProductMatrix(m_DZ,D,Z);
+    sliceInnerTimer.Stop();
+    m_M       = m_DZ.inverse();
+    
+    //5. X  = X + D MC
+    m_tmp     = m_M * m_C;
+    sliceMaddTimer.Start();
+    MaddMatrix(X,m_tmp, D,X);     
+    sliceMaddTimer.Stop();
+
+    //6. QS = Q - ZM
+    sliceMaddTimer.Start();
+    MaddMatrix(tmp,m_M,Z,Q,-1.0);
+    sliceMaddTimer.Stop();
+    QRTimer.Start();
+    ThinQRfact (m_rr, m_S, m_Sinv, Q, tmp);
+    QRTimer.Stop();
+    
+    //7. D  = Q + D S^dag
+    m_tmp = m_S.adjoint();
+    sliceMaddTimer.Start();
+    MaddMatrix(D,m_tmp,D,Q);
+    sliceMaddTimer.Stop();
+
+    //8. C  = S C
+    m_C = m_S*m_C;
+    
+    /*********************
+     * convergence monitor
+     *********************
+     */
+    m_rr = m_C.adjoint() * m_C;
+
+    RealD max_resid=0;
+    RealD rrsum=0;
+    RealD rr;
+
+    for(int b=0;b<Nblock;b++) {
+      rrsum+=real(m_rr(b,b));
+      rr = real(m_rr(b,b))/ssq[b];
+      if ( rr > max_resid ) max_resid = rr;
+    }
+
+    std::cout << GridLogIterative << "\t Block Iteration "<<k<<" ave resid "<< sqrt(rrsum/sssum) << " max "<< sqrt(max_resid) <<std::endl;
+
+    if ( max_resid < Tolerance*Tolerance ) { 
+
+      SolverTimer.Stop();
+
+      std::cout << GridLogMessage<<"BlockCGrQ converged in "<<k<<" iterations"<<std::endl;
+
+      for(int b=0;b<Nblock;b++){
+	std::cout << GridLogMessage<< "\t\tblock "<<b<<" computed resid "<< std::sqrt(real(m_rr(b,b))/ssq[b])<<std::endl;
+      }
+      std::cout << GridLogMessage<<"\tMax residual is "<<std::sqrt(max_resid)<<std::endl;
+
+      for(int b=0;b<Nblock;b++) Linop.HermOp(X[b], AD[b]);
+      for(int b=0;b<Nblock;b++) AD[b] = AD[b]-B[b];
+      std::cout << GridLogMessage <<"\t True residual is " << std::sqrt(normv(AD)/normv(B)) <<std::endl;
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tInnerProd  " << sliceInnerTimer.Elapsed() <<std::endl;
+      std::cout << GridLogMessage << "\tMaddMatrix " << sliceMaddTimer.Elapsed()  <<std::endl;
+      std::cout << GridLogMessage << "\tThinQRfact " << QRTimer.Elapsed()  <<std::endl;
+	    
+      IterationsToComplete = k;
+      return;
+    }
+
+  }
+  std::cout << GridLogMessage << "BlockConjugateGradient(rQ) did NOT converge" << std::endl;
+
+  if (ErrorOnNoConverge) assert(0);
+  IterationsToComplete = k;
+}
+
+};
+
+NAMESPACE_END(Grid);
+

Grid/algorithms/iterative/ConjugateGradient.h

@@ -0,0 +1,180 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/algorithms/iterative/ConjugateGradient.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_H
+#define GRID_CONJUGATE_GRADIENT_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template <class Field>
+class ConjugateGradient : public OperatorFunction<Field> {
+public:
+  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+                           // Defaults true.
+  RealD Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  
+  ConjugateGradient(RealD tol, Integer maxit, bool err_on_no_conv = true)
+    : Tolerance(tol),
+      MaxIterations(maxit),
+      ErrorOnNoConverge(err_on_no_conv){};
+
+  void operator()(LinearOperatorBase<Field> &Linop, const Field &src, Field &psi) {
+
+    psi.Checkerboard() = src.Checkerboard();
+
+    conformable(psi, src);
+
+    RealD cp, c, a, d, b, ssq, qq, b_pred;
+
+    Field p(src);
+    Field mmp(src);
+    Field r(src);
+
+    // Initial residual computation & set up
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+
+    
+    Linop.HermOpAndNorm(psi, mmp, d, b);
+    
+    r = src - mmp;
+    p = r;
+
+    a = norm2(p);
+    cp = a;
+    ssq = norm2(src);
+
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient: guess " << guess << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   src " << ssq << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:    mp " << d << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:   mmp " << b << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:  cp,r " << cp << std::endl;
+    std::cout << GridLogIterative << std::setprecision(8) << "ConjugateGradient:     p " << a << std::endl;
+
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    // Check if guess is really REALLY good :)
+    if (cp <= rsq) {
+      return;
+    }
+
+    std::cout << GridLogIterative << std::setprecision(8)
+              << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
+
+    GridStopWatch LinalgTimer;
+    GridStopWatch InnerTimer;
+    GridStopWatch AxpyNormTimer;
+    GridStopWatch LinearCombTimer;
+    GridStopWatch MatrixTimer;
+    GridStopWatch SolverTimer;
+
+    SolverTimer.Start();
+    int k;
+    for (k = 1; k <= MaxIterations*1000; k++) {
+      c = cp;
+
+      MatrixTimer.Start();
+      Linop.HermOp(p, mmp);
+      MatrixTimer.Stop();
+
+      LinalgTimer.Start();
+
+      InnerTimer.Start();
+      ComplexD dc  = innerProduct(p,mmp);
+      InnerTimer.Stop();
+      d = dc.real();
+      a = c / d;
+
+      AxpyNormTimer.Start();
+      cp = axpy_norm(r, -a, mmp, r);
+      AxpyNormTimer.Stop();
+      b = cp / c;
+
+      LinearCombTimer.Start();
+      auto psi_v = psi.View();
+      auto p_v   = p.View();
+      auto r_v   = r.View();
+      parallel_for(int ss=0;ss<src.Grid()->oSites();ss++){
+	vstream(psi_v[ss], a      *  p_v[ss] + psi_v[ss]);
+	vstream(p_v  [ss], b      *  p_v[ss] + r_v[ss]);
+      }
+      LinearCombTimer.Stop();
+      LinalgTimer.Stop();
+
+      std::cout << GridLogIterative << "ConjugateGradient: Iteration " << k
+                << " residual^2 " << sqrt(cp/ssq) << " target " << Tolerance << std::endl;
+
+      // Stopping condition
+      if (cp <= rsq) {
+        SolverTimer.Stop();
+        Linop.HermOpAndNorm(psi, mmp, d, qq);
+        p = mmp - src;
+
+        RealD srcnorm = std::sqrt(norm2(src));
+        RealD resnorm = std::sqrt(norm2(p));
+        RealD true_residual = resnorm / srcnorm;
+
+        std::cout << GridLogMessage << "ConjugateGradient Converged on iteration " << k << std::endl;
+        std::cout << GridLogMessage << "\tComputed residual " << std::sqrt(cp / ssq)<<std::endl;
+	std::cout << GridLogMessage << "\tTrue residual " << true_residual<<std::endl;
+	std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
+
+        std::cout << GridLogMessage << "Time breakdown "<<std::endl;
+	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+
+        if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
+
+	IterationsToComplete = k;	
+
+        return;
+      }
+    }
+    std::cout << GridLogMessage << "ConjugateGradient did NOT converge"
+              << std::endl;
+
+    if (ErrorOnNoConverge) assert(0);
+    IterationsToComplete = k;
+
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/ConjugateGradientMixedPrec.h

@@ -0,0 +1,156 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientMixedPrec.h
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_MIXED_PREC_H
+#define GRID_CONJUGATE_GRADIENT_MIXED_PREC_H
+
+NAMESPACE_BEGIN(Grid);
+
+//Mixed precision restarted defect correction CG
+template<class FieldD,class FieldF, 
+	 typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0,
+	 typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0> 
+class MixedPrecisionConjugateGradient : public LinearFunction<FieldD> {
+public:                                                
+  RealD   Tolerance;
+  RealD   InnerTolerance; //Initial tolerance for inner CG. Defaults to Tolerance but can be changed
+  Integer MaxInnerIterations;
+  Integer MaxOuterIterations;
+  GridBase* SinglePrecGrid; //Grid for single-precision fields
+  RealD OuterLoopNormMult; //Stop the outer loop and move to a final double prec solve when the residual is OuterLoopNormMult * Tolerance
+  LinearOperatorBase<FieldF> &Linop_f;
+  LinearOperatorBase<FieldD> &Linop_d;
+
+  Integer TotalInnerIterations; //Number of inner CG iterations
+  Integer TotalOuterIterations; //Number of restarts
+  Integer TotalFinalStepIterations; //Number of CG iterations in final patch-up step
+
+  //Option to speed up *inner single precision* solves using a LinearFunction that produces a guess
+  LinearFunction<FieldF> *guesser;
+    
+  MixedPrecisionConjugateGradient(RealD tol, Integer maxinnerit, Integer maxouterit, GridBase* _sp_grid, LinearOperatorBase<FieldF> &_Linop_f, LinearOperatorBase<FieldD> &_Linop_d) :
+    Linop_f(_Linop_f), Linop_d(_Linop_d),
+    Tolerance(tol), InnerTolerance(tol), MaxInnerIterations(maxinnerit), MaxOuterIterations(maxouterit), SinglePrecGrid(_sp_grid),
+    OuterLoopNormMult(100.), guesser(NULL){ };
+
+  void useGuesser(LinearFunction<FieldF> &g){
+    guesser = &g;
+  }
+  
+  void operator() (const FieldD &src_d_in, FieldD &sol_d){
+    TotalInnerIterations = 0;
+	
+    GridStopWatch TotalTimer;
+    TotalTimer.Start();
+    
+    int cb = src_d_in.Checkerboard();
+    sol_d.Checkerboard() = cb;
+    
+    RealD src_norm = norm2(src_d_in);
+    RealD stop = src_norm * Tolerance*Tolerance;
+
+    GridBase* DoublePrecGrid = src_d_in.Grid();
+    FieldD tmp_d(DoublePrecGrid);
+    tmp_d.Checkerboard() = cb;
+    
+    FieldD tmp2_d(DoublePrecGrid);
+    tmp2_d.Checkerboard() = cb;
+    
+    FieldD src_d(DoublePrecGrid);
+    src_d = src_d_in; //source for next inner iteration, computed from residual during operation
+    
+    RealD inner_tol = InnerTolerance;
+    
+    FieldF src_f(SinglePrecGrid);
+    src_f.Checkerboard() = cb;
+    
+    FieldF sol_f(SinglePrecGrid);
+    sol_f.Checkerboard() = cb;
+    
+    ConjugateGradient<FieldF> CG_f(inner_tol, MaxInnerIterations);
+    CG_f.ErrorOnNoConverge = false;
+
+    GridStopWatch InnerCGtimer;
+
+    GridStopWatch PrecChangeTimer;
+    
+    Integer &outer_iter = TotalOuterIterations; //so it will be equal to the final iteration count
+      
+    for(outer_iter = 0; outer_iter < MaxOuterIterations; outer_iter++){
+      //Compute double precision rsd and also new RHS vector.
+      Linop_d.HermOp(sol_d, tmp_d);
+      RealD norm = axpy_norm(src_d, -1., tmp_d, src_d_in); //src_d is residual vector
+      
+      std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Outer iteration " <<outer_iter<<" residual "<< norm<< " target "<< stop<<std::endl;
+
+      if(norm < OuterLoopNormMult * stop){
+	std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Outer iteration converged on iteration " <<outer_iter <<std::endl;
+	break;
+      }
+      while(norm * inner_tol * inner_tol < stop) inner_tol *= 2;  // inner_tol = sqrt(stop/norm) ??
+
+      PrecChangeTimer.Start();
+      precisionChange(src_f, src_d);
+      PrecChangeTimer.Stop();
+      
+      sol_f = Zero();
+
+      //Optionally improve inner solver guess (eg using known eigenvectors)
+      if(guesser != NULL)
+	(*guesser)(src_f, sol_f);
+
+      //Inner CG
+      CG_f.Tolerance = inner_tol;
+      InnerCGtimer.Start();
+      CG_f(Linop_f, src_f, sol_f);
+      InnerCGtimer.Stop();
+      TotalInnerIterations += CG_f.IterationsToComplete;
+      
+      //Convert sol back to double and add to double prec solution
+      PrecChangeTimer.Start();
+      precisionChange(tmp_d, sol_f);
+      PrecChangeTimer.Stop();
+      
+      axpy(sol_d, 1.0, tmp_d, sol_d);
+    }
+    
+    //Final trial CG
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Starting final patch-up double-precision solve"<<std::endl;
+    
+    ConjugateGradient<FieldD> CG_d(Tolerance, MaxInnerIterations);
+    CG_d(Linop_d, src_d_in, sol_d);
+    TotalFinalStepIterations = CG_d.IterationsToComplete;
+
+    TotalTimer.Stop();
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Inner CG iterations " << TotalInnerIterations << " Restarts " << TotalOuterIterations << " Final CG iterations " << TotalFinalStepIterations << std::endl;
+    std::cout<<GridLogMessage<<"MixedPrecisionConjugateGradient: Total time " << TotalTimer.Elapsed() << " Precision change " << PrecChangeTimer.Elapsed() << " Inner CG total " << InnerCGtimer.Elapsed() << std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/algorithms/iterative/ConjugateGradientMultiShift.h

@@ -0,0 +1,322 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientMultiShift.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
+#define GRID_CONJUGATE_MULTI_SHIFT_GRADIENT_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class ConjugateGradientMultiShift : public OperatorMultiFunction<Field>,
+				    public OperatorFunction<Field>
+{
+public:                                                
+  RealD   Tolerance;
+  Integer MaxIterations;
+    Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  int verbose;
+  MultiShiftFunction shifts;
+
+  ConjugateGradientMultiShift(Integer maxit,MultiShiftFunction &_shifts) : 
+    MaxIterations(maxit),
+    shifts(_shifts)
+  { 
+    verbose=1;
+  }
+
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, Field &psi)
+  {
+    GridBase *grid = src.Grid();
+    int nshift = shifts.order;
+    std::vector<Field> results(nshift,grid);
+    (*this)(Linop,src,results,psi);
+  }
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, std::vector<Field> &results, Field &psi)
+  {
+    int nshift = shifts.order;
+
+    (*this)(Linop,src,results);
+  
+    psi = shifts.norm*src;
+    for(int i=0;i<nshift;i++){
+      psi = psi + shifts.residues[i]*results[i];
+    }
+
+    return;
+  }
+
+  void operator() (LinearOperatorBase<Field> &Linop, const Field &src, std::vector<Field> &psi)
+  {
+  
+    GridBase *grid = src.Grid();
+  
+    ////////////////////////////////////////////////////////////////////////
+    // Convenience references to the info stored in "MultiShiftFunction"
+    ////////////////////////////////////////////////////////////////////////
+    int nshift = shifts.order;
+
+    std::vector<RealD> &mass(shifts.poles); // Make references to array in "shifts"
+    std::vector<RealD> &mresidual(shifts.tolerances);
+    std::vector<RealD> alpha(nshift,1.0);
+    std::vector<Field>   ps(nshift,grid);// Search directions
+
+    assert(psi.size()==nshift);
+    assert(mass.size()==nshift);
+    assert(mresidual.size()==nshift);
+  
+    // dynamic sized arrays on stack; 2d is a pain with vector
+    RealD  bs[nshift];
+    RealD  rsq[nshift];
+    RealD  z[nshift][2];
+    int     converged[nshift];
+  
+    const int       primary =0;
+  
+    //Primary shift fields CG iteration
+    RealD a,b,c,d;
+    RealD cp,bp,qq; //prev
+  
+    // Matrix mult fields
+    Field r(grid);
+    Field p(grid);
+    Field tmp(grid);
+    Field mmp(grid);
+  
+    // Check lightest mass
+    for(int s=0;s<nshift;s++){
+      assert( mass[s]>= mass[primary] );
+      converged[s]=0;
+    }
+  
+    // Wire guess to zero
+    // Residuals "r" are src
+    // First search direction "p" is also src
+    cp = norm2(src);
+    for(int s=0;s<nshift;s++){
+      rsq[s] = cp * mresidual[s] * mresidual[s];
+      std::cout<<GridLogMessage<<"ConjugateGradientMultiShift: shift "<<s
+	       <<" target resid "<<rsq[s]<<std::endl;
+      ps[s] = src;
+    }
+    // r and p for primary
+    r=src;
+    p=src;
+  
+    //MdagM+m[0]
+    Linop.HermOpAndNorm(p,mmp,d,qq);
+    axpy(mmp,mass[0],p,mmp);
+    RealD rn = norm2(p);
+    d += rn*mass[0];
+  
+    // have verified that inner product of 
+    // p and mmp is equal to d after this since
+    // the d computation is tricky
+    //  qq = real(innerProduct(p,mmp));
+    //  std::cout<<GridLogMessage << "debug equal ?  qq "<<qq<<" d "<< d<<std::endl;
+  
+    b = -cp /d;
+  
+    // Set up the various shift variables
+    int       iz=0;
+    z[0][1-iz] = 1.0;
+    z[0][iz]   = 1.0;
+    bs[0]      = b;
+    for(int s=1;s<nshift;s++){
+      z[s][1-iz] = 1.0;
+      z[s][iz]   = 1.0/( 1.0 - b*(mass[s]-mass[0]));
+      bs[s]      = b*z[s][iz]; 
+    }
+  
+    // r += b[0] A.p[0]
+    // c= norm(r)
+    c=axpy_norm(r,b,mmp,r);
+  
+    for(int s=0;s<nshift;s++) {
+      axpby(psi[s],0.,-bs[s]*alpha[s],src,src);
+    }
+  
+  ///////////////////////////////////////
+  // Timers
+  ///////////////////////////////////////
+  GridStopWatch AXPYTimer;
+  GridStopWatch ShiftTimer;
+  GridStopWatch QRTimer;
+  GridStopWatch MatrixTimer;
+  GridStopWatch SolverTimer;
+  SolverTimer.Start();
+  
+    // Iteration loop
+    int k;
+  
+    for (k=1;k<=MaxIterations;k++){
+    
+      a = c /cp;
+    AXPYTimer.Start();
+      axpy(p,a,p,r);
+    AXPYTimer.Stop();
+    
+      // Note to self - direction ps is iterated seperately
+      // for each shift. Does not appear to have any scope
+      // for avoiding linear algebra in "single" case.
+      // 
+      // However SAME r is used. Could load "r" and update
+      // ALL ps[s]. 2/3 Bandwidth saving
+      // New Kernel: Load r, vector of coeffs, vector of pointers ps
+    AXPYTimer.Start();
+      for(int s=0;s<nshift;s++){
+	if ( ! converged[s] ) { 
+	  if (s==0){
+	    axpy(ps[s],a,ps[s],r);
+	  } else{
+	    RealD as =a *z[s][iz]*bs[s] /(z[s][1-iz]*b);
+	    axpby(ps[s],z[s][iz],as,r,ps[s]);
+	  }
+	}
+      }
+    AXPYTimer.Stop();
+    
+      cp=c;
+    MatrixTimer.Start();  
+    //Linop.HermOpAndNorm(p,mmp,d,qq); // d is used
+    // The below is faster on KNL
+    Linop.HermOp(p,mmp); 
+    d=real(innerProduct(p,mmp));
+    
+    MatrixTimer.Stop();  
+
+    AXPYTimer.Start();
+      axpy(mmp,mass[0],p,mmp);
+    AXPYTimer.Stop();
+      RealD rn = norm2(p);
+      d += rn*mass[0];
+    
+      bp=b;
+      b=-cp/d;
+    
+    AXPYTimer.Start();
+      c=axpy_norm(r,b,mmp,r);
+    AXPYTimer.Stop();
+
+      // Toggle the recurrence history
+      bs[0] = b;
+      iz = 1-iz;
+    ShiftTimer.Start();
+      for(int s=1;s<nshift;s++){
+	if((!converged[s])){
+	  RealD z0 = z[s][1-iz];
+	  RealD z1 = z[s][iz];
+	  z[s][iz] = z0*z1*bp
+	    / (b*a*(z1-z0) + z1*bp*(1- (mass[s]-mass[0])*b)); 
+	  bs[s] = b*z[s][iz]/z0; // NB sign  rel to Mike
+	}
+      }
+    ShiftTimer.Stop();
+    
+      for(int s=0;s<nshift;s++){
+	int ss = s;
+	// Scope for optimisation here in case of "single".
+	// Could load psi[0] and pull all ps[s] in.
+	//      if ( single ) ss=primary;
+	// Bandwith saving in single case is Ls * 3 -> 2+Ls, so ~ 3x saving
+	// Pipelined CG gain:
+	//
+	// New Kernel: Load r, vector of coeffs, vector of pointers ps
+	// New Kernel: Load psi[0], vector of coeffs, vector of pointers ps
+	// If can predict the coefficient bs then we can fuse these and avoid write reread cyce
+	//  on ps[s].
+	// Before:  3 x npole  + 3 x npole
+	// After :  2 x npole (ps[s])        => 3x speed up of multishift CG.
+      
+	if( (!converged[s]) ) { 
+	  axpy(psi[ss],-bs[s]*alpha[s],ps[s],psi[ss]);
+	}
+      }
+    
+      // Convergence checks
+      int all_converged = 1;
+      for(int s=0;s<nshift;s++){
+      
+	if ( (!converged[s]) ){
+	
+	  RealD css  = c * z[s][iz]* z[s][iz];
+	
+	  if(css<rsq[s]){
+	    if ( ! converged[s] )
+	      std::cout<<GridLogMessage<<"ConjugateGradientMultiShift k="<<k<<" Shift "<<s<<" has converged"<<std::endl;
+	    converged[s]=1;
+	  } else {
+	    all_converged=0;
+	  }
+
+	}
+      }
+    
+      if ( all_converged ){
+
+    SolverTimer.Stop();
+
+
+	std::cout<<GridLogMessage<< "CGMultiShift: All shifts have converged iteration "<<k<<std::endl;
+	std::cout<<GridLogMessage<< "CGMultiShift: Checking solutions"<<std::endl;
+      
+	// Check answers 
+	for(int s=0; s < nshift; s++) { 
+	  Linop.HermOpAndNorm(psi[s],mmp,d,qq);
+	  axpy(tmp,mass[s],psi[s],mmp);
+	  axpy(r,-alpha[s],src,tmp);
+	  RealD rn = norm2(r);
+	  RealD cn = norm2(src);
+	  std::cout<<GridLogMessage<<"CGMultiShift: shift["<<s<<"] true residual "<<std::sqrt(rn/cn)<<std::endl;
+	}
+
+      std::cout << GridLogMessage << "Time Breakdown "<<std::endl;
+      std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tAXPY    " << AXPYTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tMarix    " << MatrixTimer.Elapsed()     <<std::endl;
+      std::cout << GridLogMessage << "\tShift    " << ShiftTimer.Elapsed()     <<std::endl;
+
+      IterationsToComplete = k;	
+
+	return;
+      }
+
+   
+    }
+    // ugly hack
+    std::cout<<GridLogMessage<<"CG multi shift did not converge"<<std::endl;
+    //  assert(0);
+  }
+
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/ConjugateGradientReliableUpdate.h

@@ -0,0 +1,258 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateGradientReliableUpdate.h
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@phys.columbia.edu>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_GRADIENT_RELIABLE_UPDATE_H
+#define GRID_CONJUGATE_GRADIENT_RELIABLE_UPDATE_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class FieldD,class FieldF, 
+	 typename std::enable_if< getPrecision<FieldD>::value == 2, int>::type = 0,
+	 typename std::enable_if< getPrecision<FieldF>::value == 1, int>::type = 0> 
+class ConjugateGradientReliableUpdate : public LinearFunction<FieldD> {
+public:
+  bool ErrorOnNoConverge;  // throw an assert when the CG fails to converge.
+  // Defaults true.
+  RealD Tolerance;
+  Integer MaxIterations;
+  Integer IterationsToComplete; //Number of iterations the CG took to finish. Filled in upon completion
+  Integer ReliableUpdatesPerformed;
+
+  bool DoFinalCleanup; //Final DP cleanup, defaults to true
+  Integer IterationsToCleanup; //Final DP cleanup step iterations
+    
+  LinearOperatorBase<FieldF> &Linop_f;
+  LinearOperatorBase<FieldD> &Linop_d;
+  GridBase* SinglePrecGrid;
+  RealD Delta; //reliable update parameter
+
+  //Optional ability to switch to a different linear operator once the tolerance reaches a certain point. Useful for single/half -> single/single
+  LinearOperatorBase<FieldF> *Linop_fallback;
+  RealD fallback_transition_tol;
+
+    
+  ConjugateGradientReliableUpdate(RealD tol, Integer maxit, RealD _delta, GridBase* _sp_grid, LinearOperatorBase<FieldF> &_Linop_f, LinearOperatorBase<FieldD> &_Linop_d, bool err_on_no_conv = true)
+    : Tolerance(tol),
+      MaxIterations(maxit),
+      Delta(_delta),
+      Linop_f(_Linop_f),
+      Linop_d(_Linop_d),
+      SinglePrecGrid(_sp_grid),
+      ErrorOnNoConverge(err_on_no_conv),
+      DoFinalCleanup(true),
+      Linop_fallback(NULL)
+  {};
+
+  void setFallbackLinop(LinearOperatorBase<FieldF> &_Linop_fallback, const RealD _fallback_transition_tol){
+    Linop_fallback = &_Linop_fallback;
+    fallback_transition_tol = _fallback_transition_tol;      
+  }
+    
+  void operator()(const FieldD &src, FieldD &psi) {
+    LinearOperatorBase<FieldF> *Linop_f_use = &Linop_f;
+    bool using_fallback = false;
+      
+    psi.Checkerboard() = src.Checkerboard();
+    conformable(psi, src);
+
+    RealD cp, c, a, d, b, ssq, qq, b_pred;
+
+    FieldD p(src);
+    FieldD mmp(src);
+    FieldD r(src);
+
+    // Initial residual computation & set up
+    RealD guess = norm2(psi);
+    assert(std::isnan(guess) == 0);
+    
+    Linop_d.HermOpAndNorm(psi, mmp, d, b);
+    
+    r = src - mmp;
+    p = r;
+
+    a = norm2(p);
+    cp = a;
+    ssq = norm2(src);
+
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate: guess " << guess << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:   src " << ssq << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:    mp " << d << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:   mmp " << b << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:  cp,r " << cp << std::endl;
+    std::cout << GridLogIterative << std::setprecision(4) << "ConjugateGradientReliableUpdate:     p " << a << std::endl;
+
+    RealD rsq = Tolerance * Tolerance * ssq;
+
+    // Check if guess is really REALLY good :)
+    if (cp <= rsq) {
+      std::cout << GridLogMessage << "ConjugateGradientReliableUpdate guess was REALLY good\n";
+      std::cout << GridLogMessage << "\tComputed residual " << std::sqrt(cp / ssq)<<std::endl;
+      return;
+    }
+
+    //Single prec initialization
+    FieldF r_f(SinglePrecGrid);
+    r_f.Checkerboard() = r.Checkerboard();
+    precisionChange(r_f, r);
+
+    FieldF psi_f(r_f);
+    psi_f = Zero();
+
+    FieldF p_f(r_f);
+    FieldF mmp_f(r_f);
+
+    RealD MaxResidSinceLastRelUp = cp; //initial residual    
+    
+    std::cout << GridLogIterative << std::setprecision(4)
+	      << "ConjugateGradient: k=0 residual " << cp << " target " << rsq << std::endl;
+
+    GridStopWatch LinalgTimer;
+    GridStopWatch MatrixTimer;
+    GridStopWatch SolverTimer;
+
+    SolverTimer.Start();
+    int k = 0;
+    int l = 0;
+    
+    for (k = 1; k <= MaxIterations; k++) {
+      c = cp;
+
+      MatrixTimer.Start();
+      Linop_f_use->HermOpAndNorm(p_f, mmp_f, d, qq);
+      MatrixTimer.Stop();
+
+      LinalgTimer.Start();
+
+      a = c / d;
+      b_pred = a * (a * qq - d) / c;
+
+      cp = axpy_norm(r_f, -a, mmp_f, r_f);
+      b = cp / c;
+
+      // Fuse these loops ; should be really easy
+      psi_f = a * p_f + psi_f;
+      //p_f = p_f * b + r_f;
+
+      LinalgTimer.Stop();
+
+      std::cout << GridLogIterative << "ConjugateGradientReliableUpdate: Iteration " << k
+		<< " residual " << cp << " target " << rsq << std::endl;
+      std::cout << GridLogDebug << "a = "<< a << " b_pred = "<< b_pred << "  b = "<< b << std::endl;
+      std::cout << GridLogDebug << "qq = "<< qq << " d = "<< d << "  c = "<< c << std::endl;
+
+      if(cp > MaxResidSinceLastRelUp){
+	std::cout << GridLogIterative << "ConjugateGradientReliableUpdate: updating MaxResidSinceLastRelUp : " << MaxResidSinceLastRelUp << " -> " << cp << std::endl;
+	MaxResidSinceLastRelUp = cp;
+      }
+	  
+      // Stopping condition
+      if (cp <= rsq) {
+	//Although not written in the paper, I assume that I have to add on the final solution
+	precisionChange(mmp, psi_f);
+	psi = psi + mmp;
+	
+	
+	SolverTimer.Stop();
+	Linop_d.HermOpAndNorm(psi, mmp, d, qq);
+	p = mmp - src;
+
+	RealD srcnorm = std::sqrt(norm2(src));
+	RealD resnorm = std::sqrt(norm2(p));
+	RealD true_residual = resnorm / srcnorm;
+
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate Converged on iteration " << k << " after " << l << " reliable updates" << std::endl;
+	std::cout << GridLogMessage << "\tComputed residual " << std::sqrt(cp / ssq)<<std::endl;
+	std::cout << GridLogMessage << "\tTrue residual " << true_residual<<std::endl;
+	std::cout << GridLogMessage << "\tTarget " << Tolerance << std::endl;
+
+	std::cout << GridLogMessage << "Time breakdown "<<std::endl;
+	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+
+	IterationsToComplete = k;	
+	ReliableUpdatesPerformed = l;
+	  
+	if(DoFinalCleanup){
+	  //Do a final CG to cleanup
+	  std::cout << GridLogMessage << "ConjugateGradientReliableUpdate performing final cleanup.\n";
+	  ConjugateGradient<FieldD> CG(Tolerance,MaxIterations);
+	  CG.ErrorOnNoConverge = ErrorOnNoConverge;
+	  CG(Linop_d,src,psi);
+	  IterationsToCleanup = CG.IterationsToComplete;
+	}
+	else if (ErrorOnNoConverge) assert(true_residual / Tolerance < 10000.0);
+
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate complete.\n";
+	return;
+      }
+      else if(cp < Delta * MaxResidSinceLastRelUp) { //reliable update
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate "
+		  << cp << "(residual) < " << Delta << "(Delta) * " << MaxResidSinceLastRelUp << "(MaxResidSinceLastRelUp) on iteration " << k << " : performing reliable update\n";
+	precisionChange(mmp, psi_f);
+	psi = psi + mmp;
+
+	Linop_d.HermOpAndNorm(psi, mmp, d, qq);
+	r = src - mmp;
+
+	psi_f = Zero();
+	precisionChange(r_f, r);
+	cp = norm2(r);
+	MaxResidSinceLastRelUp = cp;
+
+	b = cp/c;
+	  
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate new residual " << cp << std::endl;
+	  
+	l = l+1;
+      }
+
+      p_f = p_f * b + r_f; //update search vector after reliable update appears to help convergence
+
+      if(!using_fallback && Linop_fallback != NULL && cp < fallback_transition_tol){
+	std::cout << GridLogMessage << "ConjugateGradientReliableUpdate switching to fallback linear operator on iteration " << k << " at residual " << cp << std::endl;
+	Linop_f_use = Linop_fallback;
+	using_fallback = true;
+      }
+
+	
+    }
+    std::cout << GridLogMessage << "ConjugateGradientReliableUpdate did NOT converge"
+	      << std::endl;
+      
+    if (ErrorOnNoConverge) assert(0);
+    IterationsToComplete = k;
+    ReliableUpdatesPerformed = l;      
+  }    
+};
+
+
+NAMESPACE_END(Grid);
+
+
+
+#endif

Grid/algorithms/iterative/ConjugateResidual.h

@@ -0,0 +1,111 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CONJUGATE_RESIDUAL_H
+#define GRID_CONJUGATE_RESIDUAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class ConjugateResidual : public OperatorFunction<Field> {
+public:                                                
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+
+  ConjugateResidual(RealD tol,Integer maxit) : Tolerance(tol), MaxIterations(maxit) { 
+    verbose=0;
+  };
+
+  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
+
+    RealD a, b; // c, d;
+    RealD cp, ssq,rsq;
+      
+    RealD rAr, rAAr, rArp;
+    RealD pAp, pAAp;
+
+    GridBase *grid = src.Grid();
+    psi=Zero();
+    Field r(grid),  p(grid), Ap(grid), Ar(grid);
+      
+    r=src;
+    p=src;
+
+    Linop.HermOpAndNorm(p,Ap,pAp,pAAp);
+    Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+    cp =norm2(r);
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+
+    if (verbose) std::cout<<GridLogMessage<<"ConjugateResidual: iteration " <<0<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+    for(int k=1;k<MaxIterations;k++){
+
+      a = rAr/pAAp;
+
+      axpy(psi,a,p,psi);
+
+      cp = axpy_norm(r,-a,Ap,r);
+
+      rArp=rAr;
+
+      Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+      b   =rAr/rArp;
+ 
+      axpy(p,b,p,r);
+      pAAp=axpy_norm(Ap,b,Ap,Ar);
+	
+      if(verbose) std::cout<<GridLogMessage<<"ConjugateResidual: iteration " <<k<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+      if(cp<rsq) {
+	Linop.HermOp(psi,Ap);
+	axpy(r,-1.0,src,Ap);
+	RealD true_resid = norm2(r)/ssq;
+	std::cout<<GridLogMessage<<"ConjugateResidual: Converged on iteration " <<k
+		 << " computed residual "<<std::sqrt(cp/ssq)
+		 << " true residual "<<std::sqrt(true_resid)
+		 << " target "       <<Tolerance <<std::endl;
+	return;
+      }
+
+    }
+
+    std::cout<<GridLogMessage<<"ConjugateResidual did NOT converge"<<std::endl;
+    assert(0);
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/Deflation.h

@@ -0,0 +1,104 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_DEFLATION_H
+#define GRID_DEFLATION_H
+
+namespace Grid { 
+
+template<class Field>
+class ZeroGuesser: public LinearFunction<Field> {
+public:
+    virtual void operator()(const Field &src, Field &guess) { guess = Zero(); };
+};
+
+template<class Field>
+class SourceGuesser: public LinearFunction<Field> {
+public:
+  virtual void operator()(const Field &src, Field &guess) { guess = src; };
+};
+
+////////////////////////////////
+// Fine grid deflation
+////////////////////////////////
+template<class Field>
+class DeflatedGuesser: public LinearFunction<Field> {
+private:
+  const std::vector<Field> &evec;
+  const std::vector<RealD> &eval;
+
+public:
+
+  DeflatedGuesser(const std::vector<Field> & _evec,const std::vector<RealD> & _eval) : evec(_evec), eval(_eval) {};
+
+  virtual void operator()(const Field &src,Field &guess) {
+    guess = Zero();
+    assert(evec.size()==eval.size());
+    auto N = evec.size();
+    for (int i=0;i<N;i++) {
+      const Field& tmp = evec[i];
+      axpy(guess,TensorRemove(innerProduct(tmp,src)) / eval[i],tmp,guess);
+    }
+    guess.Checkerboard() = src.Checkerboard();
+  }
+};
+
+template<class FineField, class CoarseField>
+class LocalCoherenceDeflatedGuesser: public LinearFunction<FineField> {
+private:
+  const std::vector<FineField>   &subspace;
+  const std::vector<CoarseField> &evec_coarse;
+  const std::vector<RealD>       &eval_coarse;
+public:
+  
+  LocalCoherenceDeflatedGuesser(const std::vector<FineField>   &_subspace,
+				const std::vector<CoarseField> &_evec_coarse,
+				const std::vector<RealD>       &_eval_coarse)
+    : subspace(_subspace), 
+      evec_coarse(_evec_coarse), 
+      eval_coarse(_eval_coarse)  
+  {
+  }
+  
+  void operator()(const FineField &src,FineField &guess) { 
+    int N = (int)evec_coarse.size();
+    CoarseField src_coarse(evec_coarse[0].Grid());
+    CoarseField guess_coarse(evec_coarse[0].Grid());    guess_coarse = Zero();
+    blockProject(src_coarse,src,subspace);    
+    for (int i=0;i<N;i++) {
+      const CoarseField & tmp = evec_coarse[i];
+      axpy(guess_coarse,TensorRemove(innerProduct(tmp,src_coarse)) / eval_coarse[i],tmp,guess_coarse);
+    }
+    blockPromote(guess_coarse,guess,subspace);
+    guess.Checkerboard() = src.Checkerboard();
+  };
+};
+
+
+
+}
+#endif

Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -0,0 +1,863 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/ImplicitlyRestartedLanczos.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+Author: Chulwoo Jung <chulwoo@bnl.gov>
+Author: Christoph Lehner <clehner@bnl.gov>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_BIRL_H
+#define GRID_BIRL_H
+
+#include <string.h> //memset
+//#include <zlib.h>
+#include <sys/stat.h>
+
+NAMESPACE_BEGIN(Grid); 
+
+  ////////////////////////////////////////////////////////
+  // Move following 100 LOC to lattice/Lattice_basis.h
+  ////////////////////////////////////////////////////////
+template<class Field>
+void basisOrthogonalize(std::vector<Field> &basis,Field &w,int k) 
+{
+  for(int j=0; j<k; ++j){
+    auto ip = innerProduct(basis[j],w);
+    w = w - ip*basis[j];
+  }
+}
+
+template<class Field>
+void basisRotate(std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j0, int j1, int k0,int k1,int Nm) 
+{
+  typedef decltype(basis[0].View()) View;
+  auto tmp_v = basis[0].View();
+  std::vector<View> basis_v(basis.size(),tmp_v);
+  typedef typename Field::vector_object vobj;
+  GridBase* grid = basis[0].Grid();
+      
+  for(int k=0;k<basis.size();k++){
+    basis_v[k] = basis[k].View();
+  }
+
+  thread_region
+  {
+    std::vector < vobj , commAllocator<vobj> > B(Nm); // Thread private
+    thread_loop_in_region( (int ss=0;ss < grid->oSites();ss++),{
+      for(int j=j0; j<j1; ++j) B[j]=0.;
+      
+      for(int j=j0; j<j1; ++j){
+	for(int k=k0; k<k1; ++k){
+	  B[j] +=Qt(j,k) * basis_v[k][ss];
+	}
+      }
+      for(int j=j0; j<j1; ++j){
+	basis_v[j][ss] = B[j];
+      }
+    });
+  }
+}
+
+// Extract a single rotated vector
+template<class Field>
+void basisRotateJ(Field &result,std::vector<Field> &basis,Eigen::MatrixXd& Qt,int j, int k0,int k1,int Nm) 
+{
+  typedef typename Field::vector_object vobj;
+  GridBase* grid = basis[0].Grid();
+
+  result.Checkerboard() = basis[0].Checkerboard();
+  auto result_v=result.View();
+  thread_loop( (int ss=0;ss < grid->oSites();ss++),{
+    vobj B = Zero();
+    for(int k=k0; k<k1; ++k){
+      auto basis_k = basis[k].View();
+      B +=Qt(j,k) * basis_k[ss];
+    }
+    result_v[ss] = B;
+  });
+}
+
+template<class Field>
+void basisReorderInPlace(std::vector<Field> &_v,std::vector<RealD>& sort_vals, std::vector<int>& idx) 
+{
+  int vlen = idx.size();
+
+  assert(vlen>=1);
+  assert(vlen<=sort_vals.size());
+  assert(vlen<=_v.size());
+
+  for (size_t i=0;i<vlen;i++) {
+
+    if (idx[i] != i) {
+
+      //////////////////////////////////////
+      // idx[i] is a table of desired sources giving a permutation.
+      // Swap v[i] with v[idx[i]].
+      // Find  j>i for which _vnew[j] = _vold[i],
+      // track the move idx[j] => idx[i]
+      // track the move idx[i] => i
+      //////////////////////////////////////
+      size_t j;
+      for (j=i;j<idx.size();j++)
+	if (idx[j]==i)
+	  break;
+
+      assert(idx[i] > i);     assert(j!=idx.size());      assert(idx[j]==i);
+
+      swap(_v[i],_v[idx[i]]); // should use vector move constructor, no data copy
+      std::swap(sort_vals[i],sort_vals[idx[i]]);
+
+      idx[j] = idx[i];
+      idx[i] = i;
+    }
+  }
+}
+
+inline std::vector<int> basisSortGetIndex(std::vector<RealD>& sort_vals) 
+{
+  std::vector<int> idx(sort_vals.size());
+  std::iota(idx.begin(), idx.end(), 0);
+
+  // sort indexes based on comparing values in v
+  std::sort(idx.begin(), idx.end(), [&sort_vals](int i1, int i2) {
+    return ::fabs(sort_vals[i1]) < ::fabs(sort_vals[i2]);
+  });
+  return idx;
+}
+
+template<class Field>
+void basisSortInPlace(std::vector<Field> & _v,std::vector<RealD>& sort_vals, bool reverse) 
+{
+  std::vector<int> idx = basisSortGetIndex(sort_vals);
+  if (reverse)
+    std::reverse(idx.begin(), idx.end());
+  
+  basisReorderInPlace(_v,sort_vals,idx);
+}
+
+// PAB: faster to compute the inner products first then fuse loops.
+// If performance critical can improve.
+template<class Field>
+void basisDeflate(const std::vector<Field> &_v,const std::vector<RealD>& eval,const Field& src_orig,Field& result) {
+  result = Zero();
+  assert(_v.size()==eval.size());
+  int N = (int)_v.size();
+  for (int i=0;i<N;i++) {
+    Field& tmp = _v[i];
+    axpy(result,TensorRemove(innerProduct(tmp,src_orig)) / eval[i],tmp,result);
+  }
+}
+
+/////////////////////////////////////////////////////////////
+// Implicitly restarted lanczos
+/////////////////////////////////////////////////////////////
+template<class Field> class ImplicitlyRestartedLanczosTester 
+{
+ public:
+  virtual int TestConvergence(int j,RealD resid,Field &evec, RealD &eval,RealD evalMaxApprox)=0;
+  virtual int ReconstructEval(int j,RealD resid,Field &evec, RealD &eval,RealD evalMaxApprox)=0;
+};
+
+enum IRLdiagonalisation { 
+  IRLdiagonaliseWithDSTEGR,
+  IRLdiagonaliseWithQR,
+  IRLdiagonaliseWithEigen
+};
+
+template<class Field> class ImplicitlyRestartedLanczosHermOpTester  : public ImplicitlyRestartedLanczosTester<Field>
+{
+ public:
+
+  LinearFunction<Field>       &_HermOp;
+  ImplicitlyRestartedLanczosHermOpTester(LinearFunction<Field> &HermOp) : _HermOp(HermOp)  {  };
+  int ReconstructEval(int j,RealD resid,Field &B, RealD &eval,RealD evalMaxApprox)
+  {
+    return TestConvergence(j,resid,B,eval,evalMaxApprox);
+  }
+  int TestConvergence(int j,RealD eresid,Field &B, RealD &eval,RealD evalMaxApprox)
+  {
+    Field v(B);
+    RealD eval_poly = eval;
+    // Apply operator
+    _HermOp(B,v);
+
+    RealD vnum = real(innerProduct(B,v)); // HermOp.
+    RealD vden = norm2(B);
+    RealD vv0  = norm2(v);
+    eval   = vnum/vden;
+    v -= eval*B;
+
+    RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
+
+    std::cout.precision(13);
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<std::endl;
+
+    int conv=0;
+    if( (vv<eresid*eresid) ) conv = 1;
+
+    return conv;
+  }
+};
+
+template<class Field> 
+class ImplicitlyRestartedLanczos {
+ private:
+  const RealD small = 1.0e-8;
+  int MaxIter;
+  int MinRestart; // Minimum number of restarts; only check for convergence after
+  int Nstop;   // Number of evecs checked for convergence
+  int Nk;      // Number of converged sought
+  //  int Np;      // Np -- Number of spare vecs in krylov space //  == Nm - Nk
+  int Nm;      // Nm -- total number of vectors
+  IRLdiagonalisation diagonalisation;
+  int orth_period;
+    
+  RealD OrthoTime;
+  RealD eresid, betastp;
+  ////////////////////////////////
+  // Embedded objects
+  ////////////////////////////////
+  LinearFunction<Field>       &_PolyOp;
+  LinearFunction<Field>       &_HermOp;
+  ImplicitlyRestartedLanczosTester<Field> &_Tester;
+  // Default tester provided (we need a ref to something in default case)
+  ImplicitlyRestartedLanczosHermOpTester<Field> SimpleTester;
+  /////////////////////////
+  // Constructor
+  /////////////////////////
+  
+public:       
+
+  //////////////////////////////////////////////////////////////////
+  // PAB:
+  //////////////////////////////////////////////////////////////////
+  // Too many options  & knobs. 
+  // Eliminate:
+  //   orth_period
+  //   betastp
+  //   MinRestart
+  //
+  // Do we really need orth_period
+  // What is the theoretical basis & guarantees of betastp ?
+  // Nstop=Nk viable?
+  // MinRestart avoidable with new convergence test?
+  // Could cut to PolyOp, HermOp, Tester, Nk, Nm, resid, maxiter (+diagonalisation)
+  // HermOp could be eliminated if we dropped the Power method for max eval.
+  // -- also: The eval, eval2, eval2_copy stuff is still unnecessarily unclear
+  //////////////////////////////////////////////////////////////////
+ ImplicitlyRestartedLanczos(LinearFunction<Field> & PolyOp,
+			    LinearFunction<Field> & HermOp,
+			    ImplicitlyRestartedLanczosTester<Field> & Tester,
+			    int _Nstop, // sought vecs
+			    int _Nk, // sought vecs
+			    int _Nm, // spare vecs
+			    RealD _eresid, // resid in lmdue deficit 
+			    int _MaxIter, // Max iterations
+			    RealD _betastp=0.0, // if beta(k) < betastp: converged
+			    int _MinRestart=1, int _orth_period = 1,
+			    IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
+    SimpleTester(HermOp), _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(Tester),
+    Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
+    eresid(_eresid),      betastp(_betastp),
+    MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
+    orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
+
+    ImplicitlyRestartedLanczos(LinearFunction<Field> & PolyOp,
+			       LinearFunction<Field> & HermOp,
+			       int _Nstop, // sought vecs
+			       int _Nk, // sought vecs
+			       int _Nm, // spare vecs
+			       RealD _eresid, // resid in lmdue deficit 
+			       int _MaxIter, // Max iterations
+			       RealD _betastp=0.0, // if beta(k) < betastp: converged
+			       int _MinRestart=1, int _orth_period = 1,
+			       IRLdiagonalisation _diagonalisation= IRLdiagonaliseWithEigen) :
+    SimpleTester(HermOp),  _PolyOp(PolyOp),      _HermOp(HermOp), _Tester(SimpleTester),
+    Nstop(_Nstop)  ,      Nk(_Nk),      Nm(_Nm),
+    eresid(_eresid),      betastp(_betastp),
+    MaxIter(_MaxIter)  ,      MinRestart(_MinRestart),
+    orth_period(_orth_period), diagonalisation(_diagonalisation)  { };
+
+  ////////////////////////////////
+  // Helpers
+  ////////////////////////////////
+  template<typename T>  static RealD normalise(T& v) 
+  {
+    RealD nn = norm2(v);
+    nn = std::sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+
+  void orthogonalize(Field& w, std::vector<Field>& evec,int k)
+  {
+    OrthoTime-=usecond()/1e6;
+    basisOrthogonalize(evec,w,k);
+    normalise(w);
+    OrthoTime+=usecond()/1e6;
+  }
+
+/* Rudy Arthur's thesis pp.137
+------------------------
+Require: M > K P = M − K †
+Compute the factorization AVM = VM HM + fM eM 
+repeat
+  Q=I
+  for i = 1,...,P do
+    QiRi =HM −θiI Q = QQi
+    H M = Q †i H M Q i
+  end for
+  βK =HM(K+1,K) σK =Q(M,K)
+  r=vK+1βK +rσK
+  VK =VM(1:M)Q(1:M,1:K)
+  HK =HM(1:K,1:K)
+  →AVK =VKHK +fKe†K † Extend to an M = K + P step factorization AVM = VMHM + fMeM
+until convergence
+*/
+  void calc(std::vector<RealD>& eval, std::vector<Field>& evec,  const Field& src, int& Nconv, bool reverse=false)
+  {
+    GridBase *grid = src.Grid();
+    assert(grid == evec[0].Grid());
+    
+    GridLogIRL.TimingMode(1);
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL <<" ImplicitlyRestartedLanczos::calc() starting iteration 0 /  "<< MaxIter<< std::endl;
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL <<" -- seek   Nk    = " << Nk    <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- accept Nstop = " << Nstop <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- total  Nm    = " << Nm    <<" vectors"<< std::endl;
+    std::cout << GridLogIRL <<" -- size of eval = " << eval.size() << std::endl;
+    std::cout << GridLogIRL <<" -- size of evec = " << evec.size() << std::endl;
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      std::cout << GridLogIRL << "Diagonalisation is DSTEGR "<<std::endl;
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      std::cout << GridLogIRL << "Diagonalisation is QR "<<std::endl;
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      std::cout << GridLogIRL << "Diagonalisation is Eigen "<<std::endl;
+    }
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+	
+    assert(Nm <= evec.size() && Nm <= eval.size());
+    
+    // quickly get an idea of the largest eigenvalue to more properly normalize the residuum
+    RealD evalMaxApprox = 0.0;
+    {
+      auto src_n = src;
+      auto tmp = src;
+      const int _MAX_ITER_IRL_MEVAPP_ = 50;
+      for (int i=0;i<_MAX_ITER_IRL_MEVAPP_;i++) {
+	normalise(src_n);
+	_HermOp(src_n,tmp);
+	RealD vnum = real(innerProduct(src_n,tmp)); // HermOp.
+	RealD vden = norm2(src_n);
+	RealD na = vnum/vden;
+	if (fabs(evalMaxApprox/na - 1.0) < 0.05)
+	  i=_MAX_ITER_IRL_MEVAPP_;
+	evalMaxApprox = na;
+	std::cout << GridLogIRL << " Approximation of largest eigenvalue: " << evalMaxApprox << std::endl;
+	src_n = tmp;
+      }
+    }
+	
+    std::vector<RealD> lme(Nm);  
+    std::vector<RealD> lme2(Nm);
+    std::vector<RealD> eval2(Nm);
+    std::vector<RealD> eval2_copy(Nm);
+    Eigen::MatrixXd Qt = Eigen::MatrixXd::Zero(Nm,Nm);
+
+    Field f(grid);
+    Field v(grid);
+    int k1 = 1;
+    int k2 = Nk;
+    RealD beta_k;
+
+    Nconv = 0;
+  
+    // Set initial vector
+    evec[0] = src;
+    normalise(evec[0]);
+	
+    // Initial Nk steps
+    OrthoTime=0.;
+    for(int k=0; k<Nk; ++k) step(eval,lme,evec,f,Nm,k);
+    std::cout<<GridLogIRL <<"Initial "<< Nk <<"steps done "<<std::endl;
+    std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
+
+    //////////////////////////////////
+    // Restarting loop begins
+    //////////////////////////////////
+    int iter;
+    for(iter = 0; iter<MaxIter; ++iter){
+      
+      OrthoTime=0.;
+
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+      std::cout<< GridLogMessage <<" Restart iteration = "<< iter << std::endl;
+      std::cout<< GridLogMessage <<" **********************"<< std::endl;
+
+      std::cout<<GridLogIRL <<" running "<<Nm-Nk <<" steps: "<<std::endl;
+      for(int k=Nk; k<Nm; ++k) step(eval,lme,evec,f,Nm,k);
+      f *= lme[Nm-1];
+
+      std::cout<<GridLogIRL <<" "<<Nm-Nk <<" steps done "<<std::endl;
+      std::cout<<GridLogIRL <<"Initial steps:OrthoTime "<<OrthoTime<< "seconds"<<std::endl;
+	  
+      //////////////////////////////////
+      // getting eigenvalues
+      //////////////////////////////////
+      for(int k=0; k<Nm; ++k){
+	eval2[k] = eval[k+k1-1];
+	lme2[k] = lme[k+k1-1];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nm,Nm,Qt,grid);
+      std::cout<<GridLogIRL <<" diagonalized "<<std::endl;
+
+      //////////////////////////////////
+      // sorting
+      //////////////////////////////////
+      eval2_copy = eval2;
+      std::partial_sort(eval2.begin(),eval2.begin()+Nm,eval2.end(),std::greater<RealD>());
+      std::cout<<GridLogIRL <<" evals sorted "<<std::endl;
+      const int chunk=8;
+      for(int io=0; io<k2;io+=chunk){
+	std::cout<<GridLogIRL << "eval "<< std::setw(3) << io ;
+	for(int ii=0;ii<chunk;ii++){
+	  if ( (io+ii)<k2 )
+	    std::cout<< " "<< std::setw(12)<< eval2[io+ii];
+	}
+	std::cout << std::endl;
+      }
+
+      //////////////////////////////////
+      // Implicitly shifted QR transformations
+      //////////////////////////////////
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      for(int ip=k2; ip<Nm; ++ip){ 
+	QR_decomp(eval,lme,Nm,Nm,Qt,eval2[ip],k1,Nm);
+      }
+      std::cout<<GridLogIRL <<"QR decomposed "<<std::endl;
+
+      assert(k2<Nm);      assert(k2<Nm);      assert(k1>0);
+
+      basisRotate(evec,Qt,k1-1,k2+1,0,Nm,Nm); /// big constraint on the basis
+      std::cout<<GridLogIRL <<"basisRotated  by Qt *"<<k1-1<<","<<k2+1<<")"<<std::endl;
+      
+      ////////////////////////////////////////////////////
+      // Compressed vector f and beta(k2)
+      ////////////////////////////////////////////////////
+      f *= Qt(k2-1,Nm-1);
+      f += lme[k2-1] * evec[k2];
+      beta_k = norm2(f);
+      beta_k = std::sqrt(beta_k);
+      std::cout<<GridLogIRL<<" beta(k) = "<<beta_k<<std::endl;
+	  
+      RealD betar = 1.0/beta_k;
+      evec[k2] = betar * f;
+      lme[k2-1] = beta_k;
+	  
+      ////////////////////////////////////////////////////
+      // Convergence test
+      ////////////////////////////////////////////////////
+      for(int k=0; k<Nm; ++k){    
+	eval2[k] = eval[k];
+	lme2[k] = lme[k];
+      }
+      Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+      diagonalize(eval2,lme2,Nk,Nm,Qt,grid);
+      std::cout<<GridLogIRL <<" Diagonalized "<<std::endl;
+	  
+      Nconv = 0;
+      if (iter >= MinRestart) {
+
+	std::cout << GridLogIRL << "Test convergence: rotate subset of vectors to test convergence " << std::endl;
+
+	Field B(grid); B.Checkerboard() = evec[0].Checkerboard();
+
+	//  power of two search pattern;  not every evalue in eval2 is assessed.
+	int allconv =1;
+	for(int jj = 1; jj<=Nstop; jj*=2){
+	  int j = Nstop-jj;
+	  RealD e = eval2_copy[j]; // Discard the evalue
+	  basisRotateJ(B,evec,Qt,j,0,Nk,Nm);	    
+	  if( !_Tester.TestConvergence(j,eresid,B,e,evalMaxApprox) ) {
+	    allconv=0;
+	  }
+	}
+	// Do evec[0] for good measure
+	{ 
+	  int j=0;
+	  RealD e = eval2_copy[0]; 
+	  basisRotateJ(B,evec,Qt,j,0,Nk,Nm);	    
+	  if( !_Tester.TestConvergence(j,eresid,B,e,evalMaxApprox) ) allconv=0;
+	}
+	if ( allconv ) Nconv = Nstop;
+
+	// test if we converged, if so, terminate
+	std::cout<<GridLogIRL<<" #modes converged: >= "<<Nconv<<"/"<<Nstop<<std::endl;
+	//	if( Nconv>=Nstop || beta_k < betastp){
+	if( Nconv>=Nstop){
+	  goto converged;
+	}
+	  
+      } else {
+	std::cout << GridLogIRL << "iter < MinRestart: do not yet test for convergence\n";
+      } // end of iter loop
+    }
+
+    std::cout<<GridLogError<<"\n NOT converged.\n";
+    abort();
+	
+  converged:
+    {
+      Field B(grid); B.Checkerboard() = evec[0].Checkerboard();
+      basisRotate(evec,Qt,0,Nk,0,Nk,Nm);	    
+      std::cout << GridLogIRL << " Rotated basis"<<std::endl;
+      Nconv=0;
+      //////////////////////////////////////////////////////////////////////
+      // Full final convergence test; unconditionally applied
+      //////////////////////////////////////////////////////////////////////
+      for(int j = 0; j<=Nk; j++){
+	B=evec[j];
+	if( _Tester.ReconstructEval(j,eresid,B,eval2[j],evalMaxApprox) ) {
+	  Nconv++;
+	}
+      }
+
+      if ( Nconv < Nstop )
+	std::cout << GridLogIRL << "Nconv ("<<Nconv<<") < Nstop ("<<Nstop<<")"<<std::endl;
+
+      eval=eval2;
+      
+      //Keep only converged
+      eval.resize(Nconv);// Nstop?
+      evec.resize(Nconv,grid);// Nstop?
+      basisSortInPlace(evec,eval,reverse);
+      
+    }
+       
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL << "ImplicitlyRestartedLanczos CONVERGED ; Summary :\n";
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+    std::cout << GridLogIRL << " -- Iterations  = "<< iter   << "\n";
+    std::cout << GridLogIRL << " -- beta(k)     = "<< beta_k << "\n";
+    std::cout << GridLogIRL << " -- Nconv       = "<< Nconv  << "\n";
+    std::cout << GridLogIRL <<"**************************************************************************"<< std::endl;
+  }
+
+ private:
+/* Saad PP. 195
+1. Choose an initial vector v1 of 2-norm unity. Set β1 ≡ 0, v0 ≡ 0
+2. For k = 1,2,...,m Do:
+3. wk:=Avk−βkv_{k−1}      
+4. αk:=(wk,vk)       // 
+5. wk:=wk−αkvk       // wk orthog vk 
+6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
+7. vk+1 := wk/βk+1
+8. EndDo
+ */
+  void step(std::vector<RealD>& lmd,
+	    std::vector<RealD>& lme, 
+	    std::vector<Field>& evec,
+	    Field& w,int Nm,int k)
+  {
+    const RealD tiny = 1.0e-20;
+    assert( k< Nm );
+
+    GridStopWatch gsw_op,gsw_o;
+
+    Field& evec_k = evec[k];
+
+    _PolyOp(evec_k,w);    std::cout<<GridLogIRL << "PolyOp" <<std::endl;
+
+    if(k>0) w -= lme[k-1] * evec[k-1];
+
+    ComplexD zalph = innerProduct(evec_k,w); // 4. αk:=(wk,vk)
+    RealD     alph = real(zalph);
+
+    w = w - alph * evec_k;// 5. wk:=wk−αkvk
+
+    RealD beta = normalise(w); // 6. βk+1 := ∥wk∥2. If βk+1 = 0 then Stop
+    // 7. vk+1 := wk/βk+1
+
+    lmd[k] = alph;
+    lme[k] = beta;
+
+    if (k>0 && k % orth_period == 0) {
+      orthogonalize(w,evec,k); // orthonormalise
+      std::cout<<GridLogIRL << "Orthogonalised " <<std::endl;
+    }
+
+    if(k < Nm-1) evec[k+1] = w;
+
+    std::cout<<GridLogIRL << "alpha[" << k << "] = " << zalph << " beta[" << k << "] = "<<beta<<std::endl;
+    if ( beta < tiny ) 
+      std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
+  }
+
+  void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+			 int Nk, int Nm,  
+			 Eigen::MatrixXd & Qt, // Nm x Nm
+			 GridBase *grid)
+  {
+    Eigen::MatrixXd TriDiag = Eigen::MatrixXd::Zero(Nk,Nk);
+
+    for(int i=0;i<Nk;i++)   TriDiag(i,i)   = lmd[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i,i+1) = lme[i];
+    for(int i=0;i<Nk-1;i++) TriDiag(i+1,i) = lme[i];
+    
+    Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> eigensolver(TriDiag);
+
+    for (int i = 0; i < Nk; i++) {
+      lmd[Nk-1-i] = eigensolver.eigenvalues()(i);
+    }
+    for (int i = 0; i < Nk; i++) {
+      for (int j = 0; j < Nk; j++) {
+	Qt(Nk-1-i,j) = eigensolver.eigenvectors()(j,i);
+      }
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////
+  // File could end here if settle on Eigen ??? !!!
+  ///////////////////////////////////////////////////////////////////////////
+  void QR_decomp(std::vector<RealD>& lmd,   // Nm 
+		 std::vector<RealD>& lme,   // Nm 
+		 int Nk, int Nm,            // Nk, Nm
+		 Eigen::MatrixXd& Qt,       // Nm x Nm matrix
+		 RealD Dsh, int kmin, int kmax)
+  {
+    int k = kmin-1;
+    RealD x;
+    
+    RealD Fden = 1.0/hypot(lmd[k]-Dsh,lme[k]);
+    RealD c = ( lmd[k] -Dsh) *Fden;
+    RealD s = -lme[k] *Fden;
+      
+    RealD tmpa1 = lmd[k];
+    RealD tmpa2 = lmd[k+1];
+    RealD tmpb  = lme[k];
+
+    lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+    lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+    lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+    x        =-s*lme[k+1];
+    lme[k+1] = c*lme[k+1];
+      
+    for(int i=0; i<Nk; ++i){
+      RealD Qtmp1 = Qt(k,i);
+      RealD Qtmp2 = Qt(k+1,i);
+      Qt(k,i)  = c*Qtmp1 - s*Qtmp2;
+      Qt(k+1,i)= s*Qtmp1 + c*Qtmp2; 
+    }
+
+    // Givens transformations
+    for(int k = kmin; k < kmax-1; ++k){
+      
+      RealD Fden = 1.0/hypot(x,lme[k-1]);
+      RealD c = lme[k-1]*Fden;
+      RealD s = - x*Fden;
+	
+      RealD tmpa1 = lmd[k];
+      RealD tmpa2 = lmd[k+1];
+      RealD tmpb  = lme[k];
+
+      lmd[k]   = c*c*tmpa1 +s*s*tmpa2 -2.0*c*s*tmpb;
+      lmd[k+1] = s*s*tmpa1 +c*c*tmpa2 +2.0*c*s*tmpb;
+      lme[k]   = c*s*(tmpa1-tmpa2) +(c*c-s*s)*tmpb;
+      lme[k-1] = c*lme[k-1] -s*x;
+
+      if(k != kmax-2){
+	x = -s*lme[k+1];
+	lme[k+1] = c*lme[k+1];
+      }
+
+      for(int i=0; i<Nk; ++i){
+	RealD Qtmp1 = Qt(k,i);
+	RealD Qtmp2 = Qt(k+1,i);
+	Qt(k,i)     = c*Qtmp1 -s*Qtmp2;
+	Qt(k+1,i)   = s*Qtmp1 +c*Qtmp2;
+      }
+    }
+  }
+
+  void diagonalize(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		   int Nk, int Nm,   
+		   Eigen::MatrixXd & Qt,
+		   GridBase *grid)
+  {
+    Qt = Eigen::MatrixXd::Identity(Nm,Nm);
+    if ( diagonalisation == IRLdiagonaliseWithDSTEGR ) {
+      diagonalize_lapack(lmd,lme,Nk,Nm,Qt,grid);
+    } else if ( diagonalisation == IRLdiagonaliseWithQR ) { 
+      diagonalize_QR(lmd,lme,Nk,Nm,Qt,grid);
+    }  else if ( diagonalisation == IRLdiagonaliseWithEigen ) { 
+      diagonalize_Eigen(lmd,lme,Nk,Nm,Qt,grid);
+    } else { 
+      assert(0);
+    }
+  }
+
+#ifdef USE_LAPACK
+void LAPACK_dstegr(char *jobz, char *range, int *n, double *d, double *e,
+                   double *vl, double *vu, int *il, int *iu, double *abstol,
+                   int *m, double *w, double *z, int *ldz, int *isuppz,
+                   double *work, int *lwork, int *iwork, int *liwork,
+                   int *info);
+#endif
+
+void diagonalize_lapack(std::vector<RealD>& lmd,
+			std::vector<RealD>& lme, 
+			int Nk, int Nm,  
+			Eigen::MatrixXd& Qt,
+			GridBase *grid)
+{
+#ifdef USE_LAPACK
+  const int size = Nm;
+  int NN = Nk;
+  double evals_tmp[NN];
+  double evec_tmp[NN][NN];
+  memset(evec_tmp[0],0,sizeof(double)*NN*NN);
+  double DD[NN];
+  double EE[NN];
+  for (int i = 0; i< NN; i++) {
+    for (int j = i - 1; j <= i + 1; j++) {
+      if ( j < NN && j >= 0 ) {
+	if (i==j) DD[i] = lmd[i];
+	if (i==j) evals_tmp[i] = lmd[i];
+	if (j==(i-1)) EE[j] = lme[j];
+      }
+    }
+  }
+  int evals_found;
+  int lwork = ( (18*NN) > (1+4*NN+NN*NN)? (18*NN):(1+4*NN+NN*NN)) ;
+  int liwork =  3+NN*10 ;
+  int iwork[liwork];
+  double work[lwork];
+  int isuppz[2*NN];
+  char jobz = 'V'; // calculate evals & evecs
+  char range = 'I'; // calculate all evals
+  //    char range = 'A'; // calculate all evals
+  char uplo = 'U'; // refer to upper half of original matrix
+  char compz = 'I'; // Compute eigenvectors of tridiagonal matrix
+  int ifail[NN];
+  int info;
+  int total = grid->_Nprocessors;
+  int node  = grid->_processor;
+  int interval = (NN/total)+1;
+  double vl = 0.0, vu = 0.0;
+  int il = interval*node+1 , iu = interval*(node+1);
+  if (iu > NN)  iu=NN;
+  double tol = 0.0;
+  if (1) {
+    memset(evals_tmp,0,sizeof(double)*NN);
+    if ( il <= NN){
+      LAPACK_dstegr(&jobz, &range, &NN,
+		    (double*)DD, (double*)EE,
+		    &vl, &vu, &il, &iu, // these four are ignored if second parameteris 'A'
+		    &tol, // tolerance
+		    &evals_found, evals_tmp, (double*)evec_tmp, &NN,
+		    isuppz,
+		    work, &lwork, iwork, &liwork,
+		    &info);
+      for (int i = iu-1; i>= il-1; i--){
+	evals_tmp[i] = evals_tmp[i - (il-1)];
+	if (il>1) evals_tmp[i-(il-1)]=0.;
+	for (int j = 0; j< NN; j++){
+	  evec_tmp[i][j] = evec_tmp[i - (il-1)][j];
+	  if (il>1) evec_tmp[i-(il-1)][j]=0.;
+	}
+      }
+    }
+    {
+      grid->GlobalSumVector(evals_tmp,NN);
+      grid->GlobalSumVector((double*)evec_tmp,NN*NN);
+    }
+  } 
+  // Safer to sort instead of just reversing it, 
+  // but the document of the routine says evals are sorted in increasing order. 
+  // qr gives evals in decreasing order.
+  for(int i=0;i<NN;i++){
+    lmd [NN-1-i]=evals_tmp[i];
+    for(int j=0;j<NN;j++){
+      Qt((NN-1-i),j)=evec_tmp[i][j];
+    }
+  }
+#else 
+  assert(0);
+#endif
+}
+
+void diagonalize_QR(std::vector<RealD>& lmd, std::vector<RealD>& lme, 
+		    int Nk, int Nm,   
+		    Eigen::MatrixXd & Qt,
+		    GridBase *grid)
+{
+  int QRiter = 100*Nm;
+  int kmin = 1;
+  int kmax = Nk;
+  
+  // (this should be more sophisticated)
+  for(int iter=0; iter<QRiter; ++iter){
+    
+    // determination of 2x2 leading submatrix
+    RealD dsub = lmd[kmax-1]-lmd[kmax-2];
+    RealD dd = std::sqrt(dsub*dsub + 4.0*lme[kmax-2]*lme[kmax-2]);
+    RealD Dsh = 0.5*(lmd[kmax-2]+lmd[kmax-1] +dd*(dsub/fabs(dsub)));
+    // (Dsh: shift)
+    
+    // transformation
+    QR_decomp(lmd,lme,Nk,Nm,Qt,Dsh,kmin,kmax); // Nk, Nm
+    
+    // Convergence criterion (redef of kmin and kamx)
+    for(int j=kmax-1; j>= kmin; --j){
+      RealD dds = fabs(lmd[j-1])+fabs(lmd[j]);
+      if(fabs(lme[j-1])+dds > dds){
+	kmax = j+1;
+	goto continued;
+      }
+    }
+    QRiter = iter;
+    return;
+    
+  continued:
+    for(int j=0; j<kmax-1; ++j){
+      RealD dds = fabs(lmd[j])+fabs(lmd[j+1]);
+      if(fabs(lme[j])+dds > dds){
+	kmin = j+1;
+	break;
+      }
+    }
+  }
+  std::cout << GridLogError << "[QL method] Error - Too many iteration: "<<QRiter<<"\n";
+  abort();
+}
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/LocalCoherenceLanczos.h

@@ -0,0 +1,405 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/LocalCoherenceLanczos.h
+
+    Copyright (C) 2015
+
+Author: Christoph Lehner <clehner@bnl.gov>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LOCAL_COHERENCE_IRL_H
+#define GRID_LOCAL_COHERENCE_IRL_H
+
+NAMESPACE_BEGIN(Grid); 
+
+struct LanczosParams : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(LanczosParams,
+				  ChebyParams, Cheby,/*Chebyshev*/
+				  int, Nstop,    /*Vecs in Lanczos must converge Nstop < Nk < Nm*/
+				  int, Nk,       /*Vecs in Lanczos seek converge*/
+				  int, Nm,       /*Total vecs in Lanczos include restart*/
+				  RealD, resid,  /*residual*/
+ 				  int, MaxIt, 
+				  RealD, betastp,  /* ? */
+				  int, MinRes);    // Must restart
+};
+
+struct LocalCoherenceLanczosParams : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(LocalCoherenceLanczosParams,
+				  bool, saveEvecs,
+				  bool, doFine,
+				  bool, doFineRead,
+				  bool, doCoarse,
+	       			  bool, doCoarseRead,
+				  LanczosParams, FineParams,
+				  LanczosParams, CoarseParams,
+				  ChebyParams,   Smoother,
+				  RealD        , coarse_relax_tol,
+				  std::vector<int>, blockSize,
+				  std::string, config,
+				  std::vector < ComplexD  >, omega,
+				  RealD, mass,
+				  RealD, M5);
+};
+
+// Duplicate functionality; ProjectedFunctionHermOp could be used with the trivial function
+template<class Fobj,class CComplex,int nbasis>
+class ProjectedHermOp : public LinearFunction<Lattice<iVector<CComplex,nbasis > > > {
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+  LinearOperatorBase<FineField> &_Linop;
+  std::vector<FineField>        &subspace;
+
+  ProjectedHermOp(LinearOperatorBase<FineField>& linop, std::vector<FineField> & _subspace) : 
+    _Linop(linop), subspace(_subspace)
+  {  
+    assert(subspace.size() >0);
+  };
+
+  void operator()(const CoarseField& in, CoarseField& out) {
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].Checkerboard();
+
+    FineField fin (FineGrid);     fin.Checkerboard()= checkerboard;
+    FineField fout(FineGrid);   fout.Checkerboard() = checkerboard;
+
+    blockPromote(in,fin,subspace);       std::cout<<GridLogIRL<<"ProjectedHermop : Promote to fine"<<std::endl;
+    _Linop.HermOp(fin,fout);                   std::cout<<GridLogIRL<<"ProjectedHermop : HermOp (fine) "<<std::endl;
+    blockProject(out,fout,subspace);     std::cout<<GridLogIRL<<"ProjectedHermop : Project to coarse "<<std::endl;
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class ProjectedFunctionHermOp : public LinearFunction<Lattice<iVector<CComplex,nbasis > > > {
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+
+  OperatorFunction<FineField>   & _poly;
+  LinearOperatorBase<FineField> &_Linop;
+  std::vector<FineField>        &subspace;
+
+  ProjectedFunctionHermOp(OperatorFunction<FineField> & poly,
+			  LinearOperatorBase<FineField>& linop, 
+			  std::vector<FineField> & _subspace) :
+    _poly(poly),
+    _Linop(linop),
+    subspace(_subspace)
+  {  };
+
+  void operator()(const CoarseField& in, CoarseField& out) {
+
+    GridBase *FineGrid = subspace[0].Grid();    
+    int   checkerboard = subspace[0].Checkerboard();
+
+    FineField fin (FineGrid); fin.Checkerboard() =checkerboard;
+    FineField fout(FineGrid);fout.Checkerboard() =checkerboard;
+    
+    blockPromote(in,fin,subspace);             std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Promote to fine"<<std::endl;
+    _poly(_Linop,fin,fout);                    std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Poly "<<std::endl;
+    blockProject(out,fout,subspace);           std::cout<<GridLogIRL<<"ProjectedFunctionHermop : Project to coarse "<<std::endl;
+  }
+};
+
+template<class Fobj,class CComplex,int nbasis>
+class ImplicitlyRestartedLanczosSmoothedTester  : public ImplicitlyRestartedLanczosTester<Lattice<iVector<CComplex,nbasis > > >
+{
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<CComplex>   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj>          FineField;
+
+  LinearFunction<CoarseField> & _Poly;
+  OperatorFunction<FineField>   & _smoother;
+  LinearOperatorBase<FineField> &_Linop;
+  RealD                             _coarse_relax_tol;
+  std::vector<FineField>        &_subspace;
+  
+  ImplicitlyRestartedLanczosSmoothedTester(LinearFunction<CoarseField>   &Poly,
+					   OperatorFunction<FineField>   &smoother,
+					   LinearOperatorBase<FineField> &Linop,
+					   std::vector<FineField>        &subspace,
+					   RealD coarse_relax_tol=5.0e3) 
+    : _smoother(smoother), _Linop(Linop), _Poly(Poly), _subspace(subspace),
+      _coarse_relax_tol(coarse_relax_tol)  
+  {    };
+
+  int TestConvergence(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
+  {
+    CoarseField v(B);
+    RealD eval_poly = eval;
+
+    // Apply operator
+    _Poly(B,v);
+
+    RealD vnum = real(innerProduct(B,v)); // HermOp.
+    RealD vden = norm2(B);
+    RealD vv0  = norm2(v);
+    eval   = vnum/vden;
+    v -= eval*B;
+
+    RealD vv = norm2(v) / ::pow(evalMaxApprox,2.0);
+
+    std::cout.precision(13);
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<std::endl;
+
+    int conv=0;
+    if( (vv<eresid*eresid) ) conv = 1;
+    return conv;
+  }
+  int ReconstructEval(int j,RealD eresid,CoarseField &B, RealD &eval,RealD evalMaxApprox)
+  {
+    GridBase *FineGrid = _subspace[0].Grid();    
+    int checkerboard   = _subspace[0].Checkerboard();
+    FineField fB(FineGrid);fB.Checkerboard() =checkerboard;
+    FineField fv(FineGrid);fv.Checkerboard() =checkerboard;
+
+    blockPromote(B,fv,_subspace);  
+    
+    _smoother(_Linop,fv,fB); 
+
+    RealD eval_poly = eval;
+    _Linop.HermOp(fB,fv);
+
+    RealD vnum = real(innerProduct(fB,fv)); // HermOp.
+    RealD vden = norm2(fB);
+    RealD vv0  = norm2(fv);
+    eval   = vnum/vden;
+    fv -= eval*fB;
+    RealD vv = norm2(fv) / ::pow(evalMaxApprox,2.0);
+
+    std::cout.precision(13);
+    std::cout<<GridLogIRL  << "[" << std::setw(3)<<j<<"] "
+	     <<"eval = "<<std::setw(25)<< eval << " (" << eval_poly << ")"
+	     <<" |H B[i] - eval[i]B[i]|^2 / evalMaxApprox^2 " << std::setw(25) << vv
+	     <<std::endl;
+    if ( j > nbasis ) eresid = eresid*_coarse_relax_tol;
+    if( (vv<eresid*eresid) ) return 1;
+    return 0;
+  }
+};
+
+////////////////////////////////////////////
+// Make serializable Lanczos params
+////////////////////////////////////////////
+template<class Fobj,class CComplex,int nbasis>
+class LocalCoherenceLanczos 
+{
+public:
+  typedef iVector<CComplex,nbasis >           CoarseSiteVector;
+  typedef Lattice<CComplex>                   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<CoarseSiteVector>           CoarseField;
+  typedef Lattice<Fobj>                       FineField;
+
+protected:
+  GridBase *_CoarseGrid;
+  GridBase *_FineGrid;
+  int _checkerboard;
+  LinearOperatorBase<FineField>                 & _FineOp;
+  
+  std::vector<RealD>                              &evals_fine;
+  std::vector<RealD>                              &evals_coarse; 
+  std::vector<FineField>                          &subspace;
+  std::vector<CoarseField>                        &evec_coarse;
+
+private:
+  std::vector<RealD>                              _evals_fine;
+  std::vector<RealD>                              _evals_coarse; 
+  std::vector<FineField>                          _subspace;
+  std::vector<CoarseField>                        _evec_coarse;
+
+public:
+
+  LocalCoherenceLanczos(GridBase *FineGrid,
+			GridBase *CoarseGrid,
+			LinearOperatorBase<FineField> &FineOp,
+			int checkerboard) :
+    _CoarseGrid(CoarseGrid),
+    _FineGrid(FineGrid),
+    _FineOp(FineOp),
+    _checkerboard(checkerboard),
+    evals_fine  (_evals_fine),
+    evals_coarse(_evals_coarse),
+    subspace    (_subspace),
+    evec_coarse(_evec_coarse)
+  {
+    evals_fine.resize(0);
+    evals_coarse.resize(0);
+  };
+  //////////////////////////////////////////////////////////////////////////
+  // Alternate constructore, external storage for use by Hadrons module
+  //////////////////////////////////////////////////////////////////////////
+  LocalCoherenceLanczos(GridBase *FineGrid,
+			GridBase *CoarseGrid,
+			LinearOperatorBase<FineField> &FineOp,
+			int checkerboard,
+			std::vector<FineField>   &ext_subspace,
+			std::vector<CoarseField> &ext_coarse,
+			std::vector<RealD>       &ext_eval_fine,
+			std::vector<RealD>       &ext_eval_coarse
+			) :
+    _CoarseGrid(CoarseGrid),
+    _FineGrid(FineGrid),
+    _FineOp(FineOp),
+    _checkerboard(checkerboard),
+    evals_fine  (ext_eval_fine), 
+    evals_coarse(ext_eval_coarse),
+    subspace    (ext_subspace),
+    evec_coarse (ext_coarse)
+  {
+    evals_fine.resize(0);
+    evals_coarse.resize(0);
+  };
+
+  void Orthogonalise(void ) {
+    CoarseScalar InnerProd(_CoarseGrid);
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+    std::cout << GridLogMessage <<" Gramm-Schmidt pass 2"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+  };
+
+  template<typename T>  static RealD normalise(T& v) 
+  {
+    RealD nn = norm2(v);
+    nn = ::sqrt(nn);
+    v = v * (1.0/nn);
+    return nn;
+  }
+  /*
+  void fakeFine(void)
+  {
+    int Nk = nbasis;
+    subspace.resize(Nk,_FineGrid);
+    subspace[0]=1.0;
+    subspace[0].Checkerboard()=_checkerboard;
+    normalise(subspace[0]);
+    PlainHermOp<FineField>    Op(_FineOp);
+    for(int k=1;k<Nk;k++){
+      subspace[k].Checkerboard()=_checkerboard;
+      Op(subspace[k-1],subspace[k]);
+      normalise(subspace[k]);
+    }
+  }
+  */
+
+  void testFine(RealD resid) 
+  {
+    assert(evals_fine.size() == nbasis);
+    assert(subspace.size() == nbasis);
+    PlainHermOp<FineField>    Op(_FineOp);
+    ImplicitlyRestartedLanczosHermOpTester<FineField> SimpleTester(Op);
+    for(int k=0;k<nbasis;k++){
+      assert(SimpleTester.ReconstructEval(k,resid,subspace[k],evals_fine[k],1.0)==1);
+    }
+  }
+
+  void testCoarse(RealD resid,ChebyParams cheby_smooth,RealD relax) 
+  {
+    assert(evals_fine.size() == nbasis);
+    assert(subspace.size() == nbasis);
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+    // create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+    Chebyshev<FineField>                          ChebySmooth(cheby_smooth);
+    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (ChebySmooth,_FineOp,subspace);
+    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
+
+    for(int k=0;k<evec_coarse.size();k++){
+      if ( k < nbasis ) { 
+	assert(ChebySmoothTester.ReconstructEval(k,resid,evec_coarse[k],evals_coarse[k],1.0)==1);
+      } else { 
+	assert(ChebySmoothTester.ReconstructEval(k,resid*relax,evec_coarse[k],evals_coarse[k],1.0)==1);
+      }
+    }
+  }
+
+  void calcFine(ChebyParams cheby_parms,int Nstop,int Nk,int Nm,RealD resid, 
+		RealD MaxIt, RealD betastp, int MinRes)
+  {
+    assert(nbasis<=Nm);
+    Chebyshev<FineField>      Cheby(cheby_parms);
+    FunctionHermOp<FineField> ChebyOp(Cheby,_FineOp);
+    PlainHermOp<FineField>    Op(_FineOp);
+
+    evals_fine.resize(Nm);
+    subspace.resize(Nm,_FineGrid);
+
+    ImplicitlyRestartedLanczos<FineField> IRL(ChebyOp,Op,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
+
+    FineField src(_FineGrid); src=1.0; src.Checkerboard() = _checkerboard;
+
+    int Nconv;
+    IRL.calc(evals_fine,subspace,src,Nconv,false);
+    
+    // Shrink down to number saved
+    assert(Nstop>=nbasis);
+    assert(Nconv>=nbasis);
+    evals_fine.resize(nbasis);
+    subspace.resize(nbasis,_FineGrid);
+  }
+  void calcCoarse(ChebyParams cheby_op,ChebyParams cheby_smooth,RealD relax,
+		  int Nstop, int Nk, int Nm,RealD resid, 
+		  RealD MaxIt, RealD betastp, int MinRes)
+  {
+    Chebyshev<FineField>                          Cheby(cheby_op);
+    ProjectedHermOp<Fobj,CComplex,nbasis>         Op(_FineOp,subspace);
+    ProjectedFunctionHermOp<Fobj,CComplex,nbasis> ChebyOp (Cheby,_FineOp,subspace);
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+    // create a smoother and see if we can get a cheap convergence test and smooth inside the IRL
+    //////////////////////////////////////////////////////////////////////////////////////////////////
+
+    Chebyshev<FineField>                                           ChebySmooth(cheby_smooth);
+    ImplicitlyRestartedLanczosSmoothedTester<Fobj,CComplex,nbasis> ChebySmoothTester(ChebyOp,ChebySmooth,_FineOp,subspace,relax);
+
+    evals_coarse.resize(Nm);
+    evec_coarse.resize(Nm,_CoarseGrid);
+
+    CoarseField src(_CoarseGrid);     src=1.0; 
+
+    ImplicitlyRestartedLanczos<CoarseField> IRL(ChebyOp,ChebyOp,ChebySmoothTester,Nstop,Nk,Nm,resid,MaxIt,betastp,MinRes);
+    int Nconv=0;
+    IRL.calc(evals_coarse,evec_coarse,src,Nconv,false);
+    assert(Nconv>=Nstop);
+    evals_coarse.resize(Nstop);
+    evec_coarse.resize (Nstop,_CoarseGrid);
+    for (int i=0;i<Nstop;i++){
+      std::cout << i << " Coarse eval = " << evals_coarse[i]  << std::endl;
+    }
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/NormalEquations.h

@@ -0,0 +1,60 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/NormalEquations.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_NORMAL_EQUATIONS_H
+#define GRID_NORMAL_EQUATIONS_H
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+// Take a matrix and form an NE solver calling a Herm solver
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class Field> class NormalEquations : public OperatorFunction<Field>{
+private:
+  SparseMatrixBase<Field> & _Matrix;
+  OperatorFunction<Field> & _HermitianSolver;
+
+public:
+
+  /////////////////////////////////////////////////////
+  // Wrap the usual normal equations trick
+  /////////////////////////////////////////////////////
+  NormalEquations(SparseMatrixBase<Field> &Matrix, OperatorFunction<Field> &HermitianSolver) 
+    :  _Matrix(Matrix), _HermitianSolver(HermitianSolver) {}; 
+
+  void operator() (const Field &in, Field &out){
+ 
+    Field src(in.Grid());
+
+    _Matrix.Mdag(in,src);
+    _HermitianSolver(src,out);  // Mdag M out = Mdag in
+ 
+  }     
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/PrecConjugateResidual.h

@@ -0,0 +1,119 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/PrecConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PREC_CONJUGATE_RESIDUAL_H
+#define GRID_PREC_CONJUGATE_RESIDUAL_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////
+// Base classes for iterative processes based on operators
+// single input vec, single output vec.
+/////////////////////////////////////////////////////////////
+
+template<class Field> 
+class PrecConjugateResidual : public OperatorFunction<Field> {
+public:                                                
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+  LinearFunction<Field> &Preconditioner;
+
+  PrecConjugateResidual(RealD tol,Integer maxit,LinearFunction<Field> &Prec) : Tolerance(tol), MaxIterations(maxit),      Preconditioner(Prec)
+  { 
+    verbose=1;
+  };
+
+  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
+
+    RealD a, b, c, d;
+    RealD cp, ssq,rsq;
+      
+    RealD rAr, rAAr, rArp;
+    RealD pAp, pAAp;
+
+    GridBase *grid = src.Grid();
+    Field r(grid),  p(grid), Ap(grid), Ar(grid), z(grid);
+      
+    psi=zero;
+    r  = src;
+    Preconditioner(r,p);
+
+      
+
+    Linop.HermOpAndNorm(p,Ap,pAp,pAAp);
+    Ar=Ap;
+    rAr=pAp;
+    rAAr=pAAp;
+
+    cp =norm2(r);
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+
+    if (verbose) std::cout<<GridLogMessage<<"PrecConjugateResidual: iteration " <<0<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+    for(int k=0;k<MaxIterations;k++){
+
+
+      Preconditioner(Ap,z);
+      RealD rq= real(innerProduct(Ap,z)); 
+
+      a = rAr/rq;
+
+      axpy(psi,a,p,psi);
+      cp = axpy_norm(r,-a,z,r);
+
+      rArp=rAr;
+
+      Linop.HermOpAndNorm(r,Ar,rAr,rAAr);
+
+      b   =rAr/rArp;
+ 
+      axpy(p,b,p,r);
+      pAAp=axpy_norm(Ap,b,Ap,Ar);
+	
+      if(verbose) std::cout<<GridLogMessage<<"PrecConjugateResidual: iteration " <<k<<" residual "<<cp<< " target"<< rsq<<std::endl;
+
+      if(cp<rsq) {
+	Linop.HermOp(psi,Ap);
+	axpy(r,-1.0,src,Ap);
+	RealD true_resid = norm2(r)/ssq;
+	std::cout<<GridLogMessage<<"PrecConjugateResidual: Converged on iteration " <<k
+		 << " computed residual "<<sqrt(cp/ssq)
+		 << " true residual "<<sqrt(true_resid)
+		 << " target "       <<Tolerance <<std::endl;
+	return;
+      }
+
+    }
+
+    std::cout<<GridLogMessage<<"PrecConjugateResidual did NOT converge"<<std::endl;
+    assert(0);
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h

@@ -0,0 +1,230 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/PrecGeneralisedConjugateResidual.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PREC_GCR_H
+#define GRID_PREC_GCR_H
+
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+//VPGCR Abe and Zhang, 2005.
+//INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
+//Computing and Information Volume 2, Number 2, Pages 147-161
+//NB. Likely not original reference since they are focussing on a preconditioner variant.
+//    but VPGCR was nicely written up in their paper
+///////////////////////////////////////////////////////////////////////////////////////////////////////
+NAMESPACE_BEGIN(Grid);
+
+template<class Field>
+class PrecGeneralisedConjugateResidual : public OperatorFunction<Field> {
+public:                                                
+  RealD   Tolerance;
+  Integer MaxIterations;
+  int verbose;
+  int mmax;
+  int nstep;
+  int steps;
+  GridStopWatch PrecTimer;
+  GridStopWatch MatTimer;
+  GridStopWatch LinalgTimer;
+
+  LinearFunction<Field> &Preconditioner;
+
+  PrecGeneralisedConjugateResidual(RealD tol,Integer maxit,LinearFunction<Field> &Prec,int _mmax,int _nstep) : 
+    Tolerance(tol), 
+    MaxIterations(maxit),
+    Preconditioner(Prec),
+    mmax(_mmax),
+    nstep(_nstep)
+  { 
+    verbose=1;
+  };
+
+  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){
+
+    psi=Zero();
+    RealD cp, ssq,rsq;
+    ssq=norm2(src);
+    rsq=Tolerance*Tolerance*ssq;
+      
+    Field r(src.Grid());
+
+    PrecTimer.Reset();
+    MatTimer.Reset();
+    LinalgTimer.Reset();
+
+    GridStopWatch SolverTimer;
+    SolverTimer.Start();
+
+    steps=0;
+    for(int k=0;k<MaxIterations;k++){
+
+      cp=GCRnStep(Linop,src,psi,rsq);
+
+      std::cout<<GridLogMessage<<"VPGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<std::endl;
+
+      if(cp<rsq) {
+
+	SolverTimer.Stop();
+
+	Linop.HermOp(psi,r);
+	axpy(r,-1.0,src,r);
+	RealD tr = norm2(r);
+	std::cout<<GridLogMessage<<"PrecGeneralisedConjugateResidual: Converged on iteration " <<steps
+		 << " computed residual "<<sqrt(cp/ssq)
+		 << " true residual "    <<sqrt(tr/ssq)
+		 << " target "           <<Tolerance <<std::endl;
+
+	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Total  "<< SolverTimer.Elapsed() <<std::endl;
+	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Precon "<<   PrecTimer.Elapsed() <<std::endl;
+	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Matrix "<<    MatTimer.Elapsed() <<std::endl;
+	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Linalg "<< LinalgTimer.Elapsed() <<std::endl;
+	return;
+      }
+
+    }
+    std::cout<<GridLogMessage<<"Variable Preconditioned GCR did not converge"<<std::endl;
+    assert(0);
+  }
+
+  RealD GCRnStep(LinearOperatorBase<Field> &Linop,const Field &src, Field &psi,RealD rsq){
+
+    RealD cp;
+    RealD a, b;
+    RealD zAz, zAAz;
+    RealD rq;
+
+    GridBase *grid = src.Grid();
+
+    Field r(grid);
+    Field z(grid);
+    Field tmp(grid);
+    Field ttmp(grid);
+    Field Az(grid);
+
+    ////////////////////////////////
+    // history for flexible orthog
+    ////////////////////////////////
+    std::vector<Field> q(mmax,grid);
+    std::vector<Field> p(mmax,grid);
+    std::vector<RealD> qq(mmax);
+      
+    //////////////////////////////////
+    // initial guess x0 is taken as nonzero.
+    // r0=src-A x0 = src
+    //////////////////////////////////
+    MatTimer.Start();
+    Linop.HermOpAndNorm(psi,Az,zAz,zAAz); 
+    MatTimer.Stop();
+    r=src-Az;
+      
+    /////////////////////
+    // p = Prec(r)
+    /////////////////////
+    PrecTimer.Start();
+    Preconditioner(r,z);
+    PrecTimer.Stop();
+
+    MatTimer.Start();
+    Linop.HermOp(z,tmp); 
+    MatTimer.Stop();
+
+    ttmp=tmp;
+    tmp=tmp-r;
+
+    /*
+      std::cout<<GridLogMessage<<r<<std::endl;
+      std::cout<<GridLogMessage<<z<<std::endl;
+      std::cout<<GridLogMessage<<ttmp<<std::endl;
+      std::cout<<GridLogMessage<<tmp<<std::endl;
+    */
+
+    MatTimer.Start();
+    Linop.HermOpAndNorm(z,Az,zAz,zAAz); 
+    MatTimer.Stop();
+
+    //p[0],q[0],qq[0] 
+    p[0]= z;
+    q[0]= Az;
+    qq[0]= zAAz;
+
+    cp =norm2(r);
+
+    for(int k=0;k<nstep;k++){
+
+      steps++;
+
+      int kp     = k+1;
+      int peri_k = k %mmax;
+      int peri_kp= kp%mmax;
+
+      rq= real(innerProduct(r,q[peri_k])); // what if rAr not real?
+      a = rq/qq[peri_k];
+
+      axpy(psi,a,p[peri_k],psi);         
+
+      cp = axpy_norm(r,-a,q[peri_k],r);  
+
+      if((k==nstep-1)||(cp<rsq)){
+	return cp;
+      }
+
+      std::cout<<GridLogMessage<< " VPGCR_step["<<steps<<"]  resid " <<sqrt(cp/rsq)<<std::endl; 
+
+      PrecTimer.Start();
+      Preconditioner(r,z);// solve Az = r
+      PrecTimer.Stop();
+
+      MatTimer.Start();
+      Linop.HermOpAndNorm(z,Az,zAz,zAAz);
+      Linop.HermOp(z,tmp);
+      MatTimer.Stop();
+      tmp=tmp-r;
+      std::cout<<GridLogMessage<< " Preconditioner resid " <<sqrt(norm2(tmp)/norm2(r))<<std::endl; 
+
+      q[peri_kp]=Az;
+      p[peri_kp]=z;
+
+      int northog = ((kp)>(mmax-1))?(mmax-1):(kp);  // if more than mmax done, we orthog all mmax history.
+      for(int back=0;back<northog;back++){
+
+	int peri_back=(k-back)%mmax;   	  assert((k-back)>=0);
+
+	b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
+	p[peri_kp]=p[peri_kp]+b*p[peri_back];
+	q[peri_kp]=q[peri_kp]+b*q[peri_back];
+
+      }
+      qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm
+
+
+    }
+    assert(0); // never reached
+    return cp;
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/iterative/SchurRedBlack.h

@@ -0,0 +1,473 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/iterative/SchurRedBlack.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_SCHUR_RED_BLACK_H
+#define GRID_SCHUR_RED_BLACK_H
+
+
+  /*
+   * Red black Schur decomposition
+   *
+   *  M = (Mee Meo) =  (1             0 )   (Mee   0               )  (1 Mee^{-1} Meo)
+   *      (Moe Moo)    (Moe Mee^-1    1 )   (0   Moo-Moe Mee^-1 Meo)  (0   1         )
+   *                =         L                     D                     U
+   *
+   * L^-1 = (1              0 )
+   *        (-MoeMee^{-1}   1 )   
+   * L^{dag} = ( 1       Mee^{-dag} Moe^{dag} )
+   *           ( 0       1                    )
+   * L^{-d}  = ( 1      -Mee^{-dag} Moe^{dag} )
+   *           ( 0       1                    )
+   *
+   * U^-1 = (1   -Mee^{-1} Meo)
+   *        (0    1           )
+   * U^{dag} = ( 1                 0)
+   *           (Meo^dag Mee^{-dag} 1)
+   * U^{-dag} = (  1                 0)
+   *            (-Meo^dag Mee^{-dag} 1)
+   ***********************
+   *     M psi = eta
+   ***********************
+   *Odd
+   * i)                 D_oo psi_o =  L^{-1}  eta_o
+   *                        eta_o' = (D_oo)^dag (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * Wilson:
+   *      (D_oo)^{\dag} D_oo psi_o = (D_oo)^dag L^{-1}  eta_o
+   * Stag:
+   *      D_oo psi_o = L^{-1}  eta =    (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * L^-1 eta_o= (1              0 ) (e
+   *             (-MoeMee^{-1}   1 )   
+   *
+   *Even
+   * ii)  Mee psi_e + Meo psi_o = src_e
+   *
+   *   => sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+   *
+   * 
+   * TODO: Other options:
+   * 
+   * a) change checkerboards for Schur e<->o
+   *
+   * Left precon by Moo^-1
+   * b) Doo^{dag} M_oo^-dag Moo^-1 Doo psi_0 =  (D_oo)^dag M_oo^-dag Moo^-1 L^{-1}  eta_o
+   *                              eta_o'     = (D_oo)^dag  M_oo^-dag Moo^-1 (eta_o - Moe Mee^{-1} eta_e)
+   *
+   * Right precon by Moo^-1
+   * c) M_oo^-dag Doo^{dag} Doo Moo^-1 phi_0 = M_oo^-dag (D_oo)^dag L^{-1}  eta_o
+   *                              eta_o'     = M_oo^-dag (D_oo)^dag (eta_o - Moe Mee^{-1} eta_e)
+   *                              psi_o = M_oo^-1 phi_o
+   * TODO: Deflation 
+   */
+namespace Grid {
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Use base class to share code
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Take a matrix and form a Red Black solver calling a Herm solver
+  // Use of RB info prevents making SchurRedBlackSolve conform to standard interface
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackBase {
+  protected:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+    OperatorFunction<Field> & _HermitianRBSolver;
+    int CBfactorise;
+    bool subGuess;
+  public:
+
+    SchurRedBlackBase(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false)  :
+    _HermitianRBSolver(HermitianRBSolver) 
+    { 
+      CBfactorise = 0;
+      subtractGuess(initSubGuess);
+    };
+    void subtractGuess(const bool initSubGuess)
+    {
+      subGuess = initSubGuess;
+    }
+    bool isSubtractGuess(void)
+    {
+      return subGuess;
+    }
+
+    /////////////////////////////////////////////////////////////
+    // Shared code
+    /////////////////////////////////////////////////////////////
+    void operator() (Matrix & _Matrix,const Field &in, Field &out){
+      ZeroGuesser<Field> guess;
+      (*this)(_Matrix,in,out,guess);
+    }
+    void operator()(Matrix &_Matrix, const std::vector<Field> &in, std::vector<Field> &out) 
+    {
+      ZeroGuesser<Field> guess;
+      (*this)(_Matrix,in,out,guess);
+    }
+
+    template<class Guesser>
+    void operator()(Matrix &_Matrix, const std::vector<Field> &in, std::vector<Field> &out,Guesser &guess) 
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+      int nblock = in.size();
+
+      std::vector<Field> src_o(nblock,grid);
+      std::vector<Field> sol_o(nblock,grid);
+      
+      std::vector<Field> guess_save;
+
+      Field resid(fgrid);
+      Field tmp(grid);
+
+      ////////////////////////////////////////////////
+      // Prepare RedBlack source
+      ////////////////////////////////////////////////
+      for(int b=0;b<nblock;b++){
+	RedBlackSource(_Matrix,in[b],tmp,src_o[b]);
+      }
+      ////////////////////////////////////////////////
+      // Make the guesses
+      ////////////////////////////////////////////////
+      if ( subGuess ) guess_save.resize(nblock,grid);
+
+      for(int b=0;b<nblock;b++){
+	guess(src_o[b],sol_o[b]); 
+
+	if ( subGuess ) { 
+	  guess_save[b] = sol_o[b];
+	}
+      }
+      //////////////////////////////////////////////////////////////
+      // Call the block solver
+      //////////////////////////////////////////////////////////////
+      std::cout<<GridLogMessage << "SchurRedBlackBase calling the solver for "<<nblock<<" RHS" <<std::endl;
+      RedBlackSolve(_Matrix,src_o,sol_o);
+
+      ////////////////////////////////////////////////
+      // A2A boolean behavioural control & reconstruct other checkerboard
+      ////////////////////////////////////////////////
+      for(int b=0;b<nblock;b++) {
+
+	if (subGuess)   sol_o[b] = sol_o[b] - guess_save[b];
+
+	///////// Needs even source //////////////
+	pickCheckerboard(Even,tmp,in[b]);
+	RedBlackSolution(_Matrix,sol_o[b],tmp,out[b]);
+
+	/////////////////////////////////////////////////
+	// Check unprec residual if possible
+	/////////////////////////////////////////////////
+	if ( ! subGuess ) {
+	  _Matrix.M(out[b],resid); 
+	  resid = resid-in[b];
+	  RealD ns = norm2(in[b]);
+	  RealD nr = norm2(resid);
+	
+	  std::cout<<GridLogMessage<< "SchurRedBlackBase solver true unprec resid["<<b<<"] "<<std::sqrt(nr/ns) << std::endl;
+	} else {
+	  std::cout<<GridLogMessage<< "SchurRedBlackBase Guess subtracted after solve["<<b<<"] " << std::endl;
+	}
+
+      }
+    }
+    template<class Guesser>
+    void operator() (Matrix & _Matrix,const Field &in, Field &out,Guesser &guess){
+
+      // FIXME CGdiagonalMee not implemented virtual function
+      // FIXME use CBfactorise to control schur decomp
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field resid(fgrid);
+      Field src_o(grid);
+      Field src_e(grid);
+      Field sol_o(grid);
+
+      ////////////////////////////////////////////////
+      // RedBlack source
+      ////////////////////////////////////////////////
+      RedBlackSource(_Matrix,in,src_e,src_o);
+
+      ////////////////////////////////
+      // Construct the guess
+      ////////////////////////////////
+      Field   tmp(grid);
+      guess(src_o,sol_o);
+
+      Field  guess_save(grid);
+      guess_save = sol_o;
+
+      //////////////////////////////////////////////////////////////
+      // Call the red-black solver
+      //////////////////////////////////////////////////////////////
+      RedBlackSolve(_Matrix,src_o,sol_o);
+
+      ////////////////////////////////////////////////
+      // Fionn A2A boolean behavioural control
+      ////////////////////////////////////////////////
+      if (subGuess)      sol_o= sol_o-guess_save;
+
+      ///////////////////////////////////////////////////
+      // RedBlack solution needs the even source
+      ///////////////////////////////////////////////////
+      RedBlackSolution(_Matrix,sol_o,src_e,out);
+
+      // Verify the unprec residual
+      if ( ! subGuess ) {
+        _Matrix.M(out,resid); 
+        resid = resid-in;
+        RealD ns = norm2(in);
+        RealD nr = norm2(resid);
+
+        std::cout<<GridLogMessage << "SchurRedBlackBase solver true unprec resid "<< std::sqrt(nr/ns) << std::endl;
+      } else {
+        std::cout << GridLogMessage << "SchurRedBlackBase Guess subtracted after solve." << std::endl;
+      }
+    }     
+    
+    /////////////////////////////////////////////////////////////
+    // Override in derived. Not virtual as template methods
+    /////////////////////////////////////////////////////////////
+    virtual void RedBlackSource  (Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)                =0;
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)          =0;
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)                           =0;
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)=0;
+
+  };
+
+  template<class Field> class SchurRedBlackStaggeredSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    SchurRedBlackStaggeredSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false) 
+      :    SchurRedBlackBase<Field> (HermitianRBSolver,initSubGuess) 
+    {
+    }
+
+    //////////////////////////////////////////////////////
+    // Override RedBlack specialisation
+    //////////////////////////////////////////////////////
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+
+      /////////////////////////////////////////////////////
+      // src_o = (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      _Matrix.Mooee(tmp,src_o); // Extra factor of "m" in source from dumb choice of matrix norm.
+    }
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e_c,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field   sol_e(grid);
+      Field   src_e(grid);
+
+      src_e = src_e_c; // Const correctness
+
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o,tmp);        assert(  tmp.Checkerboard()   ==Even);
+      src_e = src_e-tmp;               assert(  src_e.Checkerboard() ==Even);
+      _Matrix.MooeeInv(src_e,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e); assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o); assert(  sol_o.Checkerboard() ==Odd );
+    }
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurStaggeredOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);  assert(sol_o.Checkerboard()==Odd);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurStaggeredOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+  template<class Field> using SchurRedBlackStagSolve = SchurRedBlackStaggeredSolve<Field>;
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Site diagonal has Mooee on it.
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackDiagMooeeSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    SchurRedBlackDiagMooeeSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false)  
+      : SchurRedBlackBase<Field> (HermitianRBSolver,initSubGuess) {};
+
+
+    //////////////////////////////////////////////////////
+    // Override RedBlack specialisation
+    //////////////////////////////////////////////////////
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+
+      /////////////////////////////////////////////////////
+      // src_o = Mdag * (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      // get the right MpcDag
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      _HermOpEO.MpcDag(tmp,src_o);     assert(src_o.Checkerboard() ==Odd);       
+
+    }
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   tmp(grid);
+      Field  sol_e(grid);
+      Field  src_e_i(grid);
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o,tmp);          assert(  tmp.Checkerboard()   ==Even);
+      src_e_i = src_e-tmp;               assert(  src_e_i.Checkerboard() ==Even);
+      _Matrix.MooeeInv(src_e_i,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e); assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o); assert(  sol_o.Checkerboard() ==Odd );
+    }
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);  assert(sol_o.Checkerboard()==Odd);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurDiagMooeeOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Site diagonal is identity, right preconditioned by Mee^inv
+  // ( 1 - Meo Moo^inv Moe Mee^inv  ) phi =( 1 - Meo Moo^inv Moe Mee^inv  ) Mee psi =  = eta  = eta
+  //=> psi = MeeInv phi
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class Field> class SchurRedBlackDiagTwoSolve : public SchurRedBlackBase<Field> {
+  public:
+    typedef CheckerBoardedSparseMatrixBase<Field> Matrix;
+
+    /////////////////////////////////////////////////////
+    // Wrap the usual normal equations Schur trick
+    /////////////////////////////////////////////////////
+  SchurRedBlackDiagTwoSolve(OperatorFunction<Field> &HermitianRBSolver, const bool initSubGuess = false)  
+    : SchurRedBlackBase<Field>(HermitianRBSolver,initSubGuess) {};
+
+    virtual void RedBlackSource(Matrix & _Matrix,const Field &src, Field &src_e,Field &src_o)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      
+      Field   tmp(grid);
+      Field  Mtmp(grid);
+
+      pickCheckerboard(Even,src_e,src);
+      pickCheckerboard(Odd ,src_o,src);
+    
+      /////////////////////////////////////////////////////
+      // src_o = Mdag * (source_o - Moe MeeInv source_e)
+      /////////////////////////////////////////////////////
+      _Matrix.MooeeInv(src_e,tmp);     assert(  tmp.Checkerboard() ==Even);
+      _Matrix.Meooe   (tmp,Mtmp);      assert( Mtmp.Checkerboard() ==Odd);     
+      tmp=src_o-Mtmp;                  assert(  tmp.Checkerboard() ==Odd);     
+
+      // get the right MpcDag
+      _HermOpEO.MpcDag(tmp,src_o);     assert(src_o.Checkerboard() ==Odd);       
+    }
+
+    virtual void RedBlackSolution(Matrix & _Matrix,const Field &sol_o, const Field &src_e,Field &sol)
+    {
+      GridBase *grid = _Matrix.RedBlackGrid();
+      GridBase *fgrid= _Matrix.Grid();
+
+      Field   sol_o_i(grid);
+      Field   tmp(grid);
+      Field   sol_e(grid);
+
+      ////////////////////////////////////////////////
+      // MooeeInv due to pecond
+      ////////////////////////////////////////////////
+      _Matrix.MooeeInv(sol_o,tmp);
+      sol_o_i = tmp;
+
+      ///////////////////////////////////////////////////
+      // sol_e = M_ee^-1 * ( src_e - Meo sol_o )...
+      ///////////////////////////////////////////////////
+      _Matrix.Meooe(sol_o_i,tmp);    assert(  tmp.Checkerboard()   ==Even);
+      tmp = src_e-tmp;               assert(  src_e.Checkerboard() ==Even);
+      _Matrix.MooeeInv(tmp,sol_e);   assert(  sol_e.Checkerboard() ==Even);
+     
+      setCheckerboard(sol,sol_e);    assert(  sol_e.Checkerboard() ==Even);
+      setCheckerboard(sol,sol_o_i);  assert(  sol_o_i.Checkerboard() ==Odd );
+    };
+
+    virtual void RedBlackSolve   (Matrix & _Matrix,const Field &src_o, Field &sol_o)
+    {
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o);
+    };
+    virtual void RedBlackSolve   (Matrix & _Matrix,const std::vector<Field> &src_o,  std::vector<Field> &sol_o)
+    {
+      SchurDiagTwoOperator<Matrix,Field> _HermOpEO(_Matrix);
+      this->_HermitianRBSolver(_HermOpEO,src_o,sol_o); 
+    }
+  };
+}
+#endif

Grid/allocator/AlignedAllocator.cc

@@ -0,0 +1,127 @@
+#include <Grid/GridCore.h>
+#include <fcntl.h>
+
+NAMESPACE_BEGIN(Grid);
+
+MemoryStats *MemoryProfiler::stats = nullptr;
+bool         MemoryProfiler::debug = false;
+
+#ifdef POINTER_CACHE
+int PointerCache::victim;
+
+PointerCache::PointerCacheEntry PointerCache::Entries[PointerCache::Ncache];
+
+void *PointerCache::Insert(void *ptr,size_t bytes) {
+
+  if (bytes < 4096 ) return ptr;
+
+#ifdef GRID_OMP
+  assert(omp_in_parallel()==0);
+#endif 
+
+  void * ret = NULL;
+  int v = -1;
+
+  for(int e=0;e<Ncache;e++) {
+    if ( Entries[e].valid==0 ) {
+      v=e; 
+      break;
+    }
+  }
+
+  if ( v==-1 ) {
+    v=victim;
+    victim = (victim+1)%Ncache;
+  }
+
+  if ( Entries[v].valid ) {
+    ret = Entries[v].address;
+    Entries[v].valid = 0;
+    Entries[v].address = NULL;
+    Entries[v].bytes = 0;
+  }
+
+  Entries[v].address=ptr;
+  Entries[v].bytes  =bytes;
+  Entries[v].valid  =1;
+
+  return ret;
+}
+
+void *PointerCache::Lookup(size_t bytes) {
+
+  if (bytes < 4096 ) return NULL;
+
+#ifdef GRID_OMP
+  assert(omp_in_parallel()==0);
+#endif 
+
+  for(int e=0;e<Ncache;e++){
+    if ( Entries[e].valid && ( Entries[e].bytes == bytes ) ) {
+      Entries[e].valid = 0;
+      return Entries[e].address;
+    }
+  }
+  return NULL;
+}
+#endif
+
+void check_huge_pages(void *Buf,uint64_t BYTES)
+{
+#ifdef __linux__
+  int fd = open("/proc/self/pagemap", O_RDONLY);
+  assert(fd >= 0);
+  const int page_size = 4096;
+  uint64_t virt_pfn = (uint64_t)Buf / page_size;
+  off_t offset = sizeof(uint64_t) * virt_pfn;
+  uint64_t npages = (BYTES + page_size-1) / page_size;
+  uint64_t pagedata[npages];
+  uint64_t ret = lseek(fd, offset, SEEK_SET);
+  assert(ret == offset);
+  ret = ::read(fd, pagedata, sizeof(uint64_t)*npages);
+  assert(ret == sizeof(uint64_t) * npages);
+  int nhugepages = npages / 512;
+  int n4ktotal, nnothuge;
+  n4ktotal = 0;
+  nnothuge = 0;
+  for (int i = 0; i < nhugepages; ++i) {
+    uint64_t baseaddr = (pagedata[i*512] & 0x7fffffffffffffULL) * page_size;
+    for (int j = 0; j < 512; ++j) {
+      uint64_t pageaddr = (pagedata[i*512+j] & 0x7fffffffffffffULL) * page_size;
+      ++n4ktotal;
+      if (pageaddr != baseaddr + j * page_size)
+	++nnothuge;
+    }
+  }
+  int rank = CartesianCommunicator::RankWorld();
+  printf("rank %d Allocated %d 4k pages, %d not in huge pages\n", rank, n4ktotal, nnothuge);
+#endif
+}
+
+std::string sizeString(const size_t bytes)
+{
+  constexpr unsigned int bufSize = 256;
+  const char             *suffixes[7] = {"", "K", "M", "G", "T", "P", "E"};
+  char                   buf[256];
+  size_t                 s     = 0;
+  double                 count = bytes;
+  
+  while (count >= 1024 && s < 7)
+    {
+      s++;
+      count /= 1024;
+    }
+  if (count - floor(count) == 0.0)
+    {
+      snprintf(buf, bufSize, "%d %sB", (int)count, suffixes[s]);
+    }
+  else
+    {
+      snprintf(buf, bufSize, "%.1f %sB", count, suffixes[s]);
+    }
+  
+  return std::string(buf);
+}
+
+NAMESPACE_END(Grid);
+

Grid/allocator/AlignedAllocator.h

@@ -0,0 +1,240 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/AlignedAllocator.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_ALIGNED_ALLOCATOR_H
+#define GRID_ALIGNED_ALLOCATOR_H
+
+#ifdef HAVE_MALLOC_MALLOC_H
+#include <malloc/malloc.h>
+#endif
+#ifdef HAVE_MALLOC_H
+#include <malloc.h>
+#endif
+
+#ifdef HAVE_MM_MALLOC_H
+#include <mm_malloc.h>
+#endif
+
+#define POINTER_CACHE
+#define GRID_ALLOC_ALIGN (2*1024*1024)
+
+NAMESPACE_BEGIN(Grid);
+
+// Move control to configure.ac and Config.h?
+#ifdef POINTER_CACHE
+class PointerCache {
+private:
+
+  static const int Ncache=8;
+  static int victim;
+
+  typedef struct { 
+    void *address;
+    size_t bytes;
+    int valid;
+  } PointerCacheEntry;
+    
+  static PointerCacheEntry Entries[Ncache];
+
+public:
+
+
+  static void *Insert(void *ptr,size_t bytes) ;
+  static void *Lookup(size_t bytes) ;
+
+};
+#endif  
+
+std::string sizeString(size_t bytes);
+
+struct MemoryStats
+{
+  size_t totalAllocated{0}, maxAllocated{0}, 
+    currentlyAllocated{0}, totalFreed{0};
+};
+    
+class MemoryProfiler
+{
+public:
+  static MemoryStats *stats;
+  static bool        debug;
+};
+
+#define memString(bytes) std::to_string(bytes) + " (" + sizeString(bytes) + ")"
+#define profilerDebugPrint						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      std::cout << GridLogDebug << "[Memory debug] Stats " << MemoryProfiler::stats << std::endl; \
+      std::cout << GridLogDebug << "[Memory debug] total  : " << memString(s->totalAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] max    : " << memString(s->maxAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] current: " << memString(s->currentlyAllocated) \
+		<< std::endl;						\
+      std::cout << GridLogDebug << "[Memory debug] freed  : " << memString(s->totalFreed) \
+		<< std::endl;						\
+    }
+
+#define profilerAllocate(bytes)						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      s->totalAllocated     += (bytes);					\
+      s->currentlyAllocated += (bytes);					\
+      s->maxAllocated        = std::max(s->maxAllocated, s->currentlyAllocated); \
+    }									\
+  if (MemoryProfiler::debug)						\
+    {									\
+      std::cout << GridLogDebug << "[Memory debug] allocating " << memString(bytes) << std::endl; \
+      profilerDebugPrint;						\
+    }
+
+#define profilerFree(bytes)						\
+  if (MemoryProfiler::stats)						\
+    {									\
+      auto s = MemoryProfiler::stats;					\
+      s->totalFreed         += (bytes);					\
+      s->currentlyAllocated -= (bytes);					\
+    }									\
+  if (MemoryProfiler::debug)						\
+    {									\
+      std::cout << GridLogDebug << "[Memory debug] freeing " << memString(bytes) << std::endl; \
+      profilerDebugPrint;						\
+    }
+
+void check_huge_pages(void *Buf,uint64_t BYTES);
+
+////////////////////////////////////////////////////////////////////
+// A lattice of something, but assume the something is SIMDized.
+////////////////////////////////////////////////////////////////////
+
+template<typename _Tp>
+class alignedAllocator {
+public: 
+  typedef std::size_t     size_type;
+  typedef std::ptrdiff_t  difference_type;
+  typedef _Tp*       pointer;
+  typedef const _Tp* const_pointer;
+  typedef _Tp&       reference;
+  typedef const _Tp& const_reference;
+  typedef _Tp        value_type;
+
+  template<typename _Tp1>  struct rebind { typedef alignedAllocator<_Tp1> other; };
+  alignedAllocator() throw() { }
+  alignedAllocator(const alignedAllocator&) throw() { }
+  template<typename _Tp1> alignedAllocator(const alignedAllocator<_Tp1>&) throw() { }
+  ~alignedAllocator() throw() { }
+  pointer       address(reference __x)       const { return &__x; }
+  size_type  max_size() const throw() { return size_t(-1) / sizeof(_Tp); }
+
+  pointer allocate(size_type __n, const void* _p= 0)
+  { 
+    size_type bytes = __n*sizeof(_Tp);
+    profilerAllocate(bytes);
+
+
+#ifdef POINTER_CACHE
+    _Tp *ptr = (_Tp *) PointerCache::Lookup(bytes);
+#else
+    pointer ptr = nullptr;
+#endif
+
+#ifdef GRID_NVCC
+    ////////////////////////////////////
+    // Unified (managed) memory
+    ////////////////////////////////////
+    if ( ptr == (_Tp *) NULL ) {
+      auto err = cudaMallocManaged((void **)&ptr,bytes);
+      if( err != cudaSuccess ) {
+	ptr = (_Tp *) NULL;
+	std::cerr << " cudaMallocManaged failed for " << bytes<<" bytes " <<cudaGetErrorString(err)<< std::endl;
+	assert(0);
+      }
+    }
+#else 
+    //////////////////////////////////////////////////////////////////////////////////////////
+    // 2MB align; could make option probably doesn't need configurability
+    //////////////////////////////////////////////////////////////////////////////////////////
+  #ifdef HAVE_MM_MALLOC_H
+    if ( ptr == (_Tp *) NULL ) ptr = (_Tp *) _mm_malloc(bytes,GRID_ALLOC_ALIGN);
+  #else
+    if ( ptr == (_Tp *) NULL ) ptr = (_Tp *) memalign(GRID_ALLOC_ALIGN,bytes);
+  #endif
+#endif
+    assert( ptr != (_Tp *)NULL);
+
+    /////////////////////////////////////////
+    // First touch optimise in threaded loop
+    /////////////////////////////////////////
+    uint8_t *cp = (uint8_t *)ptr;
+    thread_loop( (size_type n=0;n<bytes;n+=4096) , {
+      cp[n]=0;
+    });
+    return ptr;
+  }
+
+  void deallocate(pointer __p, size_type __n) { 
+    size_type bytes = __n * sizeof(_Tp);
+
+    profilerFree(bytes);
+
+#ifdef POINTER_CACHE
+    pointer __freeme = (pointer)PointerCache::Insert((void *)__p,bytes);
+#else 
+    pointer __freeme = __p;
+#endif
+
+#ifdef GRID_NVCC
+    if ( __freeme ) cudaFree((void *)__freeme);
+#else 
+  #ifdef HAVE_MM_MALLOC_H
+    if ( __freeme ) _mm_free((void *)__freeme); 
+  #else
+    if ( __freeme ) free((void *)__freeme);
+  #endif
+#endif
+  }
+  void construct(pointer __p, const _Tp& __val) { };
+  void construct(pointer __p) { };
+  void destroy(pointer __p) { };
+};
+template<typename _Tp>  inline bool operator==(const alignedAllocator<_Tp>&, const alignedAllocator<_Tp>&){ return true; }
+template<typename _Tp>  inline bool operator!=(const alignedAllocator<_Tp>&, const alignedAllocator<_Tp>&){ return false; }
+
+////////////////////////////////////////////////////////////////////////////////
+// Template typedefs
+////////////////////////////////////////////////////////////////////////////////
+template<class T> using commAllocator = alignedAllocator<T>;
+template<class T> using Vector     = std::vector<T,alignedAllocator<T> >;           
+template<class T> using commVector = std::vector<T,alignedAllocator<T> >;
+template<class T> using Matrix     = std::vector<std::vector<T,alignedAllocator<T> > >;
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/cartesian/Cartesian.h

@@ -0,0 +1,35 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Cartesian.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_H
+#define GRID_CARTESIAN_H
+
+#include <Grid/cartesian/Cartesian_base.h>
+#include <Grid/cartesian/Cartesian_full.h>
+#include <Grid/cartesian/Cartesian_red_black.h> 
+
+#endif

Grid/cartesian/Cartesian_base.h

@@ -0,0 +1,290 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_base.h
+
+    Copyright (C) 2015
+
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+    Author: paboyle <paboyle@ph.ed.ac.uk>
+    Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_BASE_H
+#define GRID_CARTESIAN_BASE_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////
+// Commicator provides information on the processor grid
+//////////////////////////////////////////////////////////////////////
+//    unsigned long _ndimension;
+//    Coordinate _processors; // processor grid
+//    int              _processor;  // linear processor rank
+//    Coordinate _processor_coor;  // linear processor rank
+//////////////////////////////////////////////////////////////////////
+class GridBase : public CartesianCommunicator , public GridThread {
+
+public:
+  int dummy;
+  // Give Lattice access
+  template<class object> friend class Lattice;
+
+  GridBase(const Coordinate & processor_grid) : CartesianCommunicator(processor_grid) {}; 
+
+  GridBase(const Coordinate & processor_grid,
+	   const CartesianCommunicator &parent,
+	   int &split_rank) 
+    : CartesianCommunicator(processor_grid,parent,split_rank) {};
+
+  GridBase(const Coordinate & processor_grid,
+	   const CartesianCommunicator &parent) 
+    : CartesianCommunicator(processor_grid,parent,dummy) {};
+
+  virtual ~GridBase() = default;
+
+
+  // Physics Grid information.
+  Coordinate _simd_layout;// Which dimensions get relayed out over simd lanes.
+  Coordinate _fdimensions;// (full) Global dimensions of array prior to cb removal
+  Coordinate _gdimensions;// Global dimensions of array after cb removal
+  Coordinate _ldimensions;// local dimensions of array with processor images removed
+  Coordinate _rdimensions;// Reduced local dimensions with simd lane images and processor images removed 
+  Coordinate _ostride;    // Outer stride for each dimension
+  Coordinate _istride;    // Inner stride i.e. within simd lane
+  int _osites;                  // _isites*_osites = product(dimensions).
+  int _isites;
+  int _fsites;                  // _isites*_osites = product(dimensions).
+  int _gsites;
+  Coordinate _slice_block;// subslice information
+  Coordinate _slice_stride;
+  Coordinate _slice_nblock;
+
+  Coordinate _lstart;     // local start of array in gcoors _processor_coor[d]*_ldimensions[d]
+  Coordinate _lend  ;     // local end of array in gcoors   _processor_coor[d]*_ldimensions[d]+_ldimensions_[d]-1
+
+    bool _isCheckerBoarded; 
+
+public:
+
+  ////////////////////////////////////////////////////////////////
+  // Checkerboarding interface is virtual and overridden by 
+  // GridCartesian / GridRedBlackCartesian
+  ////////////////////////////////////////////////////////////////
+  virtual int CheckerBoarded(int dim)=0;
+  virtual int CheckerBoard(const Coordinate &site)=0;
+  virtual int CheckerBoardDestination(int source_cb,int shift,int dim)=0;
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift,int osite)=0;
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift,int cb)=0;
+  virtual int CheckerBoardFromOindex (int Oindex)=0;
+  virtual int CheckerBoardFromOindexTable (int Oindex)=0;
+
+  //////////////////////////////////////////////////////////////////////////////////////////////
+  // Local layout calculations
+  //////////////////////////////////////////////////////////////////////////////////////////////
+  // These routines are key. Subdivide the linearised cartesian index into
+  //      "inner" index identifying which simd lane of object<vFcomplex> is associated with coord
+  //      "outer" index identifying which element of _odata in class "Lattice" is associated with coord.
+  //
+  // Compared to, say, Blitz++ we simply need to store BOTH an inner stride and an outer
+  // stride per dimension. The cost of evaluating the indexing information is doubled for an n-dimensional
+  // coordinate. Note, however, for data parallel operations the "inner" indexing cost is not paid and all
+  // lanes are operated upon simultaneously.
+  
+  virtual int oIndex(Coordinate &coor)
+  {
+    int idx=0;
+    // Works with either global or local coordinates
+    for(int d=0;d<_ndimension;d++) idx+=_ostride[d]*(coor[d]%_rdimensions[d]);
+    return idx;
+  }
+  virtual int iIndex(Coordinate &lcoor)
+  {
+    int idx=0;
+    for(int d=0;d<_ndimension;d++) idx+=_istride[d]*(lcoor[d]/_rdimensions[d]);
+    return idx;
+  }
+  inline int oIndexReduced(Coordinate &ocoor)
+  {
+    int idx=0; 
+    // ocoor is already reduced so can eliminate the modulo operation
+    // for fast indexing and inline the routine
+    for(int d=0;d<_ndimension;d++) idx+=_ostride[d]*ocoor[d];
+    return idx;
+  }
+  inline void oCoorFromOindex (Coordinate& coor,int Oindex){
+    Lexicographic::CoorFromIndex(coor,Oindex,_rdimensions);
+  }
+
+  inline void InOutCoorToLocalCoor (Coordinate &ocoor, Coordinate &icoor, Coordinate &lcoor) {
+    lcoor.resize(_ndimension);
+    for (int d = 0; d < _ndimension; d++)
+      lcoor[d] = ocoor[d] + _rdimensions[d] * icoor[d];
+  }
+
+  //////////////////////////////////////////////////////////
+  // SIMD lane addressing
+  //////////////////////////////////////////////////////////
+  inline void iCoorFromIindex(Coordinate &coor,int lane)
+  {
+    Lexicographic::CoorFromIndex(coor,lane,_simd_layout);
+  }
+
+  inline int PermuteDim(int dimension){
+    return _simd_layout[dimension]>1;
+  }
+  inline int PermuteType(int dimension){
+    int permute_type=0;
+    //
+    // Best way to encode this would be to present a mask 
+    // for which simd dimensions are rotated, and the rotation
+    // size. If there is only one simd dimension rotated, this is just 
+    // a permute. 
+    //
+    // Cases: PermuteType == 1,2,4,8
+    // Distance should be either 0,1,2..
+    //
+    if ( _simd_layout[dimension] > 2 ) { 
+      for(int d=0;d<_ndimension;d++){
+	if ( d != dimension ) assert ( (_simd_layout[d]==1)  );
+      }
+      permute_type = RotateBit; // How to specify distance; this is not just direction.
+      return permute_type;
+    }
+
+    for(int d=_ndimension-1;d>dimension;d--){
+      if (_simd_layout[d]>1 ) permute_type++;
+    }
+    return permute_type;
+  }
+  ////////////////////////////////////////////////////////////////
+  // Array sizing queries
+  ////////////////////////////////////////////////////////////////
+
+  inline int iSites(void) const { return _isites; };
+  inline int Nsimd(void)  const { return _isites; };// Synonymous with iSites
+  inline int oSites(void) const { return _osites; };
+  inline int lSites(void) const { return _isites*_osites; }; 
+  inline int gSites(void) const { return _isites*_osites*_Nprocessors; }; 
+  inline int Nd    (void) const { return _ndimension;};
+
+  inline const Coordinate LocalStarts(void)             { return _lstart;    };
+  inline const Coordinate &FullDimensions(void)         { return _fdimensions;};
+  inline const Coordinate &GlobalDimensions(void)       { return _gdimensions;};
+  inline const Coordinate &LocalDimensions(void)        { return _ldimensions;};
+  inline const Coordinate &VirtualLocalDimensions(void) { return _ldimensions;};
+
+  ////////////////////////////////////////////////////////////////
+  // Utility to print the full decomposition details 
+  ////////////////////////////////////////////////////////////////
+
+  void show_decomposition(){
+    std::cout << GridLogMessage << "\tFull Dimensions    : " << _fdimensions << std::endl;
+    std::cout << GridLogMessage << "\tSIMD layout        : " << _simd_layout << std::endl;
+    std::cout << GridLogMessage << "\tGlobal Dimensions  : " << _gdimensions << std::endl;
+    std::cout << GridLogMessage << "\tLocal Dimensions   : " << _ldimensions << std::endl;
+    std::cout << GridLogMessage << "\tReduced Dimensions : " << _rdimensions << std::endl;
+    std::cout << GridLogMessage << "\tOuter strides      : " << _ostride << std::endl;
+    std::cout << GridLogMessage << "\tInner strides      : " << _istride << std::endl;
+    std::cout << GridLogMessage << "\tiSites             : " << _isites << std::endl;
+    std::cout << GridLogMessage << "\toSites             : " << _osites << std::endl;
+    std::cout << GridLogMessage << "\tlSites             : " << lSites() << std::endl;        
+    std::cout << GridLogMessage << "\tgSites             : " << gSites() << std::endl;
+    std::cout << GridLogMessage << "\tNd                 : " << _ndimension << std::endl;             
+  } 
+
+  ////////////////////////////////////////////////////////////////
+  // Global addressing
+  ////////////////////////////////////////////////////////////////
+  void GlobalIndexToGlobalCoor(int gidx,Coordinate &gcoor){
+    assert(gidx< gSites());
+    Lexicographic::CoorFromIndex(gcoor,gidx,_gdimensions);
+  }
+  void LocalIndexToLocalCoor(int lidx,Coordinate &lcoor){
+    assert(lidx<lSites());
+    Lexicographic::CoorFromIndex(lcoor,lidx,_ldimensions);
+  }
+  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int & gidx){
+    gidx=0;
+    int mult=1;
+    for(int mu=0;mu<_ndimension;mu++) {
+      gidx+=mult*gcoor[mu];
+      mult*=_gdimensions[mu];
+    }
+  }
+  void GlobalCoorToProcessorCoorLocalCoor(Coordinate &pcoor,Coordinate &lcoor,const Coordinate &gcoor)
+  {
+    pcoor.resize(_ndimension);
+    lcoor.resize(_ndimension);
+    for(int mu=0;mu<_ndimension;mu++){
+      int _fld  = _fdimensions[mu]/_processors[mu];
+      pcoor[mu] = gcoor[mu]/_fld;
+      lcoor[mu] = gcoor[mu]%_fld;
+    }
+  }
+  void GlobalCoorToRankIndex(int &rank, int &o_idx, int &i_idx ,const Coordinate &gcoor)
+  {
+    Coordinate pcoor;
+    Coordinate lcoor;
+    GlobalCoorToProcessorCoorLocalCoor(pcoor,lcoor,gcoor);
+    rank = RankFromProcessorCoor(pcoor);
+    /*
+      Coordinate cblcoor(lcoor);
+      for(int d=0;d<cblcoor.size();d++){
+      if( this->CheckerBoarded(d) ) {
+      cblcoor[d] = lcoor[d]/2;
+      }
+      }
+    */
+    i_idx= iIndex(lcoor);
+    o_idx= oIndex(lcoor);
+  }
+
+  void RankIndexToGlobalCoor(int rank, int o_idx, int i_idx , Coordinate &gcoor)
+  {
+    gcoor.resize(_ndimension);
+    Coordinate coor(_ndimension);
+
+    ProcessorCoorFromRank(rank,coor);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] = _ldimensions[mu]*coor[mu];
+
+    iCoorFromIindex(coor,i_idx);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] += _rdimensions[mu]*coor[mu];
+
+    oCoorFromOindex (coor,o_idx);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] += coor[mu];
+      
+  }
+  void RankIndexCbToFullGlobalCoor(int rank, int o_idx, int i_idx, int cb,Coordinate &fcoor)
+  {
+    RankIndexToGlobalCoor(rank,o_idx,i_idx ,fcoor);
+    if(CheckerBoarded(0)){
+      fcoor[0] = fcoor[0]*2+cb;
+    }
+  }
+  void ProcessorCoorLocalCoorToGlobalCoor(Coordinate &Pcoor,Coordinate &Lcoor,Coordinate &gcoor)
+  {
+    gcoor.resize(_ndimension);
+    for(int mu=0;mu<_ndimension;mu++) gcoor[mu] = Pcoor[mu]*_ldimensions[mu]+Lcoor[mu];
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/cartesian/Cartesian_full.h

@@ -0,0 +1,174 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_full.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_FULL_H
+#define GRID_CARTESIAN_FULL_H
+
+NAMESPACE_BEGIN(Grid);
+    
+/////////////////////////////////////////////////////////////////////////////////////////
+// Grid Support.
+/////////////////////////////////////////////////////////////////////////////////////////
+
+class GridCartesian: public GridBase {
+
+public:
+  int dummy;
+  virtual int  CheckerBoardFromOindexTable (int Oindex) {
+    return 0;
+  }
+  virtual int  CheckerBoardFromOindex (int Oindex)
+  {
+    return 0;
+  }
+  virtual int CheckerBoarded(int dim){
+    return 0;
+  }
+  virtual int CheckerBoard(const Coordinate &site){
+    return 0;
+  }
+  virtual int CheckerBoardDestination(int cb,int shift,int dim){
+    return 0;
+  }
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift, int ocb){
+    return shift;
+  }
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift, int osite){
+    return shift;
+  }
+  /////////////////////////////////////////////////////////////////////////
+  // Constructor takes a parent grid and possibly subdivides communicator.
+  /////////////////////////////////////////////////////////////////////////
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid,
+		const GridCartesian &parent) : GridBase(processor_grid,parent,dummy)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid,
+		const GridCartesian &parent,int &split_rank) : GridBase(processor_grid,parent,split_rank)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+  /////////////////////////////////////////////////////////////////////////
+  // Construct from comm world
+  /////////////////////////////////////////////////////////////////////////
+  GridCartesian(const Coordinate &dimensions,
+		const Coordinate &simd_layout,
+		const Coordinate &processor_grid) : GridBase(processor_grid)
+  {
+    Init(dimensions,simd_layout,processor_grid);
+  }
+
+  virtual ~GridCartesian() = default;
+
+  void Init(const Coordinate &dimensions,
+	    const Coordinate &simd_layout,
+	    const Coordinate &processor_grid)
+  {
+    ///////////////////////
+    // Grid information
+    ///////////////////////
+      _isCheckerBoarded = false;
+    _ndimension = dimensions.size();
+
+    _fdimensions.resize(_ndimension);
+    _gdimensions.resize(_ndimension);
+    _ldimensions.resize(_ndimension);
+    _rdimensions.resize(_ndimension);
+    _simd_layout.resize(_ndimension);
+    _lstart.resize(_ndimension);
+    _lend.resize(_ndimension);
+
+    _ostride.resize(_ndimension);
+    _istride.resize(_ndimension);
+
+    _fsites = _gsites = _osites = _isites = 1;
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        _fdimensions[d] = dimensions[d];   // Global dimensions
+        _gdimensions[d] = _fdimensions[d]; // Global dimensions
+        _simd_layout[d] = simd_layout[d];
+        _fsites = _fsites * _fdimensions[d];
+        _gsites = _gsites * _gdimensions[d];
+
+        // Use a reduced simd grid
+        _ldimensions[d] = _gdimensions[d] / _processors[d]; //local dimensions
+        //std::cout << _ldimensions[d] << "  " << _gdimensions[d] << "  " << _processors[d] << std::endl;
+        assert(_ldimensions[d] * _processors[d] == _gdimensions[d]);
+
+        _rdimensions[d] = _ldimensions[d] / _simd_layout[d]; //overdecomposition
+        assert(_rdimensions[d] * _simd_layout[d] == _ldimensions[d]);
+
+        _lstart[d] = _processor_coor[d] * _ldimensions[d];
+        _lend[d] = _processor_coor[d] * _ldimensions[d] + _ldimensions[d] - 1;
+        _osites *= _rdimensions[d];
+        _isites *= _simd_layout[d];
+
+        // Addressing support
+        if (d == 0)
+	  {
+	    _ostride[d] = 1;
+	    _istride[d] = 1;
+	  }
+        else
+	  {
+	    _ostride[d] = _ostride[d - 1] * _rdimensions[d - 1];
+	    _istride[d] = _istride[d - 1] * _simd_layout[d - 1];
+	  }
+      }
+
+    ///////////////////////
+    // subplane information
+    ///////////////////////
+    _slice_block.resize(_ndimension);
+    _slice_stride.resize(_ndimension);
+    _slice_nblock.resize(_ndimension);
+
+    int block = 1;
+    int nblock = 1;
+    for (int d = 0; d < _ndimension; d++)
+      nblock *= _rdimensions[d];
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        nblock /= _rdimensions[d];
+        _slice_block[d] = block;
+        _slice_stride[d] = _ostride[d] * _rdimensions[d];
+        _slice_nblock[d] = nblock;
+        block = block * _rdimensions[d];
+      }
+  };
+
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/cartesian/Cartesian_red_black.h

@@ -0,0 +1,289 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cartesian/Cartesian_red_black.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_CARTESIAN_RED_BLACK_H
+#define GRID_CARTESIAN_RED_BLACK_H
+
+NAMESPACE_BEGIN(Grid);
+
+static const int CbRed  =0;
+static const int CbBlack=1;
+static const int Even   =CbRed;
+static const int Odd    =CbBlack;
+    
+// Specialise this for red black grids storing half the data like a chess board.
+class GridRedBlackCartesian : public GridBase
+{
+public:
+  Coordinate _checker_dim_mask;
+  int              _checker_dim;
+  std::vector<int> _checker_board;
+
+  virtual int CheckerBoarded(int dim){
+    if( dim==_checker_dim) return 1;
+    else return 0;
+  }
+  virtual int CheckerBoard(const Coordinate &site){
+    int linear=0;
+    assert(site.size()==_ndimension);
+    for(int d=0;d<_ndimension;d++){ 
+      if(_checker_dim_mask[d])
+	linear=linear+site[d];
+    }
+    return (linear&0x1);
+  }
+
+  // Depending on the cb of site, we toggle source cb.
+  // for block #b, element #e = (b, e)
+  // we need 
+  virtual int CheckerBoardShiftForCB(int source_cb,int dim,int shift,int ocb){
+    if(dim != _checker_dim) return shift;
+
+    int fulldim =_fdimensions[dim];
+    shift = (shift+fulldim)%fulldim;
+
+    // Probably faster with table lookup;
+    // or by looping over x,y,z and multiply rather than computing checkerboard.
+	  
+    if ( (source_cb+ocb)&1 ) {
+      return (shift)/2;
+    } else {
+      return (shift+1)/2;
+    }
+  }
+  virtual int  CheckerBoardFromOindexTable (int Oindex) {
+    return _checker_board[Oindex];
+  }
+  virtual int  CheckerBoardFromOindex (int Oindex)
+  {
+    Coordinate ocoor;
+    oCoorFromOindex(ocoor,Oindex);
+    return CheckerBoard(ocoor);
+  }
+  virtual int CheckerBoardShift(int source_cb,int dim,int shift,int osite){
+
+    if(dim != _checker_dim) return shift;
+
+    int ocb=CheckerBoardFromOindex(osite);
+      
+    return CheckerBoardShiftForCB(source_cb,dim,shift,ocb);
+  }
+    
+  virtual int CheckerBoardDestination(int source_cb,int shift,int dim){
+    if ( _checker_dim_mask[dim]  ) {
+      // If _fdimensions[checker_dim] is odd, then shifting by 1 in other dims
+      // does NOT cause a parity hop.
+      int add=(dim==_checker_dim) ? 0 : _fdimensions[_checker_dim];
+      if ( (shift+add) &0x1) {
+	return 1-source_cb;
+      } else {
+	return source_cb;
+      }
+    } else {
+      return source_cb;
+
+    }
+  };
+
+  ////////////////////////////////////////////////////////////
+  // Create Redblack from original grid; require full grid pointer ?
+  ////////////////////////////////////////////////////////////
+  GridRedBlackCartesian(const GridBase *base) : GridBase(base->_processors,*base)
+  {
+    int dims = base->_ndimension;
+    Coordinate checker_dim_mask(dims,1);
+    int checker_dim = 0;
+    Init(base->_fdimensions,base->_simd_layout,base->_processors,checker_dim_mask,checker_dim);
+  };
+
+  ////////////////////////////////////////////////////////////
+  // Create redblack from original grid, with non-trivial checker dim mask
+  ////////////////////////////////////////////////////////////
+  GridRedBlackCartesian(const GridBase *base,
+			const Coordinate &checker_dim_mask,
+			int checker_dim
+			) :  GridBase(base->_processors,*base) 
+  {
+    Init(base->_fdimensions,base->_simd_layout,base->_processors,checker_dim_mask,checker_dim)  ;
+  }
+
+  virtual ~GridRedBlackCartesian() = default;
+
+  void Init(const Coordinate &dimensions,
+	    const Coordinate &simd_layout,
+	    const Coordinate &processor_grid,
+	    const Coordinate &checker_dim_mask,
+	    int checker_dim)
+  {
+
+      _isCheckerBoarded = true;
+    _checker_dim = checker_dim;
+    assert(checker_dim_mask[checker_dim] == 1);
+    _ndimension = dimensions.size();
+    assert(checker_dim_mask.size() == _ndimension);
+    assert(processor_grid.size() == _ndimension);
+    assert(simd_layout.size() == _ndimension);
+
+    _fdimensions.resize(_ndimension);
+    _gdimensions.resize(_ndimension);
+    _ldimensions.resize(_ndimension);
+    _rdimensions.resize(_ndimension);
+    _simd_layout.resize(_ndimension);
+    _lstart.resize(_ndimension);
+    _lend.resize(_ndimension);
+
+    _ostride.resize(_ndimension);
+    _istride.resize(_ndimension);
+
+    _fsites = _gsites = _osites = _isites = 1;
+
+    _checker_dim_mask = checker_dim_mask;
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        _fdimensions[d] = dimensions[d];
+        _gdimensions[d] = _fdimensions[d];
+        _fsites = _fsites * _fdimensions[d];
+        _gsites = _gsites * _gdimensions[d];
+
+        if (d == _checker_dim)
+	  {
+	    assert((_gdimensions[d] & 0x1) == 0);
+	    _gdimensions[d] = _gdimensions[d] / 2; // Remove a checkerboard
+	    _gsites /= 2;
+	  }
+        _ldimensions[d] = _gdimensions[d] / _processors[d];
+        assert(_ldimensions[d] * _processors[d] == _gdimensions[d]);
+        _lstart[d] = _processor_coor[d] * _ldimensions[d];
+        _lend[d] = _processor_coor[d] * _ldimensions[d] + _ldimensions[d] - 1;
+
+        // Use a reduced simd grid
+        _simd_layout[d] = simd_layout[d];
+        _rdimensions[d] = _ldimensions[d] / _simd_layout[d]; // this is not checking if this is integer
+        assert(_rdimensions[d] * _simd_layout[d] == _ldimensions[d]);
+        assert(_rdimensions[d] > 0);
+
+        // all elements of a simd vector must have same checkerboard.
+        // If Ls vectorised, this must still be the case; e.g. dwf rb5d
+        if (_simd_layout[d] > 1)
+	  {
+	    if (checker_dim_mask[d])
+	      {
+		assert((_rdimensions[d] & 0x1) == 0);
+	      }
+	  }
+
+        _osites *= _rdimensions[d];
+        _isites *= _simd_layout[d];
+
+        // Addressing support
+        if (d == 0)
+	  {
+	    _ostride[d] = 1;
+	    _istride[d] = 1;
+	  }
+        else
+	  {
+	    _ostride[d] = _ostride[d - 1] * _rdimensions[d - 1];
+	    _istride[d] = _istride[d - 1] * _simd_layout[d - 1];
+	  }
+      }
+
+    ////////////////////////////////////////////////////////////////////////////////////////////
+    // subplane information
+    ////////////////////////////////////////////////////////////////////////////////////////////
+    _slice_block.resize(_ndimension);
+    _slice_stride.resize(_ndimension);
+    _slice_nblock.resize(_ndimension);
+
+    int block = 1;
+    int nblock = 1;
+    for (int d = 0; d < _ndimension; d++)
+      nblock *= _rdimensions[d];
+
+    for (int d = 0; d < _ndimension; d++)
+      {
+        nblock /= _rdimensions[d];
+        _slice_block[d] = block;
+        _slice_stride[d] = _ostride[d] * _rdimensions[d];
+        _slice_nblock[d] = nblock;
+        block = block * _rdimensions[d];
+      }
+
+    ////////////////////////////////////////////////
+    // Create a checkerboard lookup table
+    ////////////////////////////////////////////////
+    int rvol = 1;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        rvol = rvol * _rdimensions[d];
+      }
+    _checker_board.resize(rvol);
+    for (int osite = 0; osite < _osites; osite++)
+      {
+        _checker_board[osite] = CheckerBoardFromOindex(osite);
+      }
+  };
+
+protected:
+  virtual int oIndex(Coordinate &coor)
+  {
+    int idx = 0;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        if (d == _checker_dim)
+	  {
+	    idx += _ostride[d] * ((coor[d] / 2) % _rdimensions[d]);
+	  }
+        else
+	  {
+	    idx += _ostride[d] * (coor[d] % _rdimensions[d]);
+	  }
+      }
+    return idx;
+  };
+
+  virtual int iIndex(Coordinate &lcoor)
+  {
+    int idx = 0;
+    for (int d = 0; d < _ndimension; d++)
+      {
+        if (d == _checker_dim)
+	  {
+	    idx += _istride[d] * (lcoor[d] / (2 * _rdimensions[d]));
+	  }
+        else
+	  {
+	    idx += _istride[d] * (lcoor[d] / _rdimensions[d]);
+	  }
+      }
+    return idx;
+  }
+};
+NAMESPACE_END(Grid);
+#endif

Grid/communicator/Communicator.h

@@ -0,0 +1,35 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Communicator.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_COMMUNICATOR_H
+#define GRID_COMMUNICATOR_H
+
+#include <Grid/util/Coordinate.h>
+#include <Grid/communicator/SharedMemory.h>
+#include <Grid/communicator/Communicator_base.h>
+
+#endif

Grid/communicator/Communicator_base.cc

@@ -0,0 +1,77 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/Communicator_none.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <fcntl.h>
+#include <unistd.h>
+#include <limits.h>
+#include <sys/mman.h>
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////
+// Info that is setup once and indept of cartesian layout
+///////////////////////////////////////////////////////////////
+CartesianCommunicator::CommunicatorPolicy_t  
+CartesianCommunicator::CommunicatorPolicy= CartesianCommunicator::CommunicatorPolicyConcurrent;
+int CartesianCommunicator::nCommThreads = -1;
+
+/////////////////////////////////
+// Grid information queries
+/////////////////////////////////
+int                      CartesianCommunicator::Dimensions(void)        { return _ndimension; };
+int                      CartesianCommunicator::IsBoss(void)            { return _processor==0; };
+int                      CartesianCommunicator::BossRank(void)          { return 0; };
+int                      CartesianCommunicator::ThisRank(void)          { return _processor; };
+const Coordinate & CartesianCommunicator::ThisProcessorCoor(void) { return _processor_coor; };
+const Coordinate & CartesianCommunicator::ProcessorGrid(void)     { return _processors; };
+int                      CartesianCommunicator::ProcessorCount(void)    { return _Nprocessors; };
+
+////////////////////////////////////////////////////////////////////////////////
+// very VERY rarely (Log, serial RNG) we need world without a grid
+////////////////////////////////////////////////////////////////////////////////
+
+void CartesianCommunicator::GlobalSum(ComplexF &c)
+{
+  GlobalSumVector((float *)&c,2);
+}
+void CartesianCommunicator::GlobalSumVector(ComplexF *c,int N)
+{
+  GlobalSumVector((float *)c,2*N);
+}
+void CartesianCommunicator::GlobalSum(ComplexD &c)
+{
+  GlobalSumVector((double *)&c,2);
+}
+void CartesianCommunicator::GlobalSumVector(ComplexD *c,int N)
+{
+  GlobalSumVector((double *)c,2*N);
+}
+  
+NAMESPACE_END(Grid);
+
+

Grid/communicator/Communicator_base.h

@@ -0,0 +1,208 @@
+
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/Communicator_base.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_COMMUNICATOR_BASE_H
+#define GRID_COMMUNICATOR_BASE_H
+
+///////////////////////////////////
+// Processor layout information
+///////////////////////////////////
+#include <Grid/communicator/SharedMemory.h>
+
+NAMESPACE_BEGIN(Grid);
+
+class CartesianCommunicator : public SharedMemory {
+
+public:    
+
+  ////////////////////////////////////////////
+  // Policies
+  ////////////////////////////////////////////
+  enum CommunicatorPolicy_t { CommunicatorPolicyConcurrent, CommunicatorPolicySequential };
+  static CommunicatorPolicy_t CommunicatorPolicy;
+  static void SetCommunicatorPolicy(CommunicatorPolicy_t policy ) { CommunicatorPolicy = policy; }
+  static int       nCommThreads;
+
+  ////////////////////////////////////////////
+  // Communicator should know nothing of the physics grid, only processor grid.
+  ////////////////////////////////////////////
+  int              _Nprocessors;     // How many in all
+  Coordinate _processors;      // Which dimensions get relayed out over processors lanes.
+  int              _processor;       // linear processor rank
+  Coordinate _processor_coor;  // linear processor coordinate
+  unsigned long    _ndimension;
+  static Grid_MPI_Comm      communicator_world;
+  Grid_MPI_Comm             communicator;
+  std::vector<Grid_MPI_Comm> communicator_halo;
+  
+  ////////////////////////////////////////////////
+  // Must call in Grid startup
+  ////////////////////////////////////////////////
+  static void Init(int *argc, char ***argv);
+
+  ////////////////////////////////////////////////
+  // Constructors to sub-divide a parent communicator
+  // and default to comm world
+  ////////////////////////////////////////////////
+  CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank);
+  CartesianCommunicator(const Coordinate &pdimensions_in);
+  virtual ~CartesianCommunicator();
+
+private:
+
+  ////////////////////////////////////////////////
+  // Private initialise from an MPI communicator
+  // Can use after an MPI_Comm_split, but hidden from user so private
+  ////////////////////////////////////////////////
+  void InitFromMPICommunicator(const Coordinate &processors, Grid_MPI_Comm communicator_base);
+
+public:
+  
+  
+  ////////////////////////////////////////////////////////////////////////////////////////
+  // Wraps MPI_Cart routines, or implements equivalent on other impls
+  ////////////////////////////////////////////////////////////////////////////////////////
+  void ShiftedRanks(int dim,int shift,int & source, int & dest);
+  int  RankFromProcessorCoor(Coordinate &coor);
+  void ProcessorCoorFromRank(int rank,Coordinate &coor);
+  
+  int                      Dimensions(void)        ;
+  int                      IsBoss(void)            ;
+  int                      BossRank(void)          ;
+  int                      ThisRank(void)          ;
+  const Coordinate & ThisProcessorCoor(void) ;
+  const Coordinate & ProcessorGrid(void)     ;
+  int                      ProcessorCount(void)    ;
+
+  ////////////////////////////////////////////////////////////////////////////////
+  // very VERY rarely (Log, serial RNG) we need world without a grid
+  ////////////////////////////////////////////////////////////////////////////////
+  static int  RankWorld(void) ;
+  static void BroadcastWorld(int root,void* data, int bytes);
+  
+  ////////////////////////////////////////////////////////////
+  // Reduction
+  ////////////////////////////////////////////////////////////
+  void GlobalSum(RealF &);
+  void GlobalSumVector(RealF *,int N);
+  void GlobalSum(RealD &);
+  void GlobalSumVector(RealD *,int N);
+  void GlobalSum(uint32_t &);
+  void GlobalSum(uint64_t &);
+  void GlobalSum(ComplexF &c);
+  void GlobalSumVector(ComplexF *c,int N);
+  void GlobalSum(ComplexD &c);
+  void GlobalSumVector(ComplexD *c,int N);
+  void GlobalXOR(uint32_t &);
+  void GlobalXOR(uint64_t &);
+  
+  template<class obj> void GlobalSum(obj &o){
+    typedef typename obj::scalar_type scalar_type;
+    int words = sizeof(obj)/sizeof(scalar_type);
+    scalar_type * ptr = (scalar_type *)& o;
+    GlobalSumVector(ptr,words);
+  }
+  
+  ////////////////////////////////////////////////////////////
+  // Face exchange, buffer swap in translational invariant way
+  ////////////////////////////////////////////////////////////
+  void SendToRecvFrom(void *xmit,
+		      int xmit_to_rank,
+		      void *recv,
+		      int recv_from_rank,
+		      int bytes);
+  
+  void SendRecvPacket(void *xmit,
+		      void *recv,
+		      int xmit_to_rank,
+		      int recv_from_rank,
+		      int bytes);
+  
+  void SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+			   void *xmit,
+			   int xmit_to_rank,
+			   void *recv,
+			   int recv_from_rank,
+			   int bytes);
+  
+  void SendToRecvFromComplete(std::vector<CommsRequest_t> &waitall);
+
+  double StencilSendToRecvFrom(void *xmit,
+			       int xmit_to_rank,
+			       void *recv,
+			       int recv_from_rank,
+			       int bytes,int dir);
+
+  double StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+				    void *xmit,
+				    int xmit_to_rank,
+				    void *recv,
+				    int recv_from_rank,
+				    int bytes,int dir);
+  
+  
+  void StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int i);
+  void StencilBarrier(void);
+
+  ////////////////////////////////////////////////////////////
+  // Barrier
+  ////////////////////////////////////////////////////////////
+  void Barrier(void);
+  
+  ////////////////////////////////////////////////////////////
+  // Broadcast a buffer and composite larger
+  ////////////////////////////////////////////////////////////
+  void Broadcast(int root,void* data, int bytes);
+
+  ////////////////////////////////////////////////////////////
+  // All2All down one dimension
+  ////////////////////////////////////////////////////////////
+  template<class T> void AllToAll(int dim,std::vector<T> &in, std::vector<T> &out){
+    assert(dim>=0);
+    assert(dim<_ndimension);
+    assert(in.size()==out.size());
+    int numnode = _processors[dim];
+    uint64_t bytes=sizeof(T);
+    uint64_t words=in.size()/numnode;
+    assert(numnode * words == in.size());
+    assert(words < (1ULL<<31));
+    AllToAll(dim,(void *)&in[0],(void *)&out[0],words,bytes);
+  }
+  void AllToAll(int dim  ,void *in,void *out,uint64_t words,uint64_t bytes);
+  void AllToAll(void  *in,void *out,uint64_t words         ,uint64_t bytes);
+  
+  template<class obj> void Broadcast(int root,obj &data)
+  {
+    Broadcast(root,(void *)&data,sizeof(data));
+  }
+
+}; 
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/communicator/Communicator_mpi3.cc

@@ -0,0 +1,478 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/Communicator_mpi.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <Grid/communicator/SharedMemory.h>
+
+NAMESPACE_BEGIN(Grid);
+
+Grid_MPI_Comm       CartesianCommunicator::communicator_world;
+
+////////////////////////////////////////////
+// First initialise of comms system
+////////////////////////////////////////////
+void CartesianCommunicator::Init(int *argc, char ***argv) 
+{
+
+  int flag;
+  int provided;
+
+  MPI_Initialized(&flag); // needed to coexist with other libs apparently
+  if ( !flag ) {
+    MPI_Init_thread(argc,argv,MPI_THREAD_MULTIPLE,&provided);
+    //    assert (provided == MPI_THREAD_MULTIPLE);
+    //If only 1 comms thread we require any threading mode other than SINGLE, but for multiple comms threads we need MULTIPLE
+    if( (nCommThreads == 1 && provided == MPI_THREAD_SINGLE) ||
+        (nCommThreads > 1 && provided != MPI_THREAD_MULTIPLE) ) {
+      assert(0);
+    }
+  }
+
+  // Never clean up as done once.
+  MPI_Comm_dup (MPI_COMM_WORLD,&communicator_world);
+
+  GlobalSharedMemory::Init(communicator_world);
+  GlobalSharedMemory::SharedMemoryAllocate(GlobalSharedMemory::MAX_MPI_SHM_BYTES,
+					   GlobalSharedMemory::Hugepages);
+}
+
+///////////////////////////////////////////////////////////////////////////
+// Use cartesian communicators now even in MPI3
+///////////////////////////////////////////////////////////////////////////
+void CartesianCommunicator::ShiftedRanks(int dim,int shift,int &source,int &dest)
+{
+  int ierr=MPI_Cart_shift(communicator,dim,shift,&source,&dest);
+  assert(ierr==0);
+}
+int CartesianCommunicator::RankFromProcessorCoor(Coordinate &coor)
+{
+  int rank;
+  int ierr=MPI_Cart_rank  (communicator, &coor[0], &rank);
+  assert(ierr==0);
+  return rank;
+}
+void  CartesianCommunicator::ProcessorCoorFromRank(int rank, Coordinate &coor)
+{
+  coor.resize(_ndimension);
+  int ierr=MPI_Cart_coords  (communicator, rank, _ndimension,&coor[0]);
+  assert(ierr==0);
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Initialises from communicator_world
+////////////////////////////////////////////////////////////////////////////////////////////////////////
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors) 
+{
+  MPI_Comm optimal_comm;
+  ////////////////////////////////////////////////////
+  // Remap using the shared memory optimising routine
+  // The remap creates a comm which must be freed
+  ////////////////////////////////////////////////////
+  GlobalSharedMemory::OptimalCommunicator    (processors,optimal_comm);
+  InitFromMPICommunicator(processors,optimal_comm);
+  SetCommunicator(optimal_comm);
+  ///////////////////////////////////////////////////
+  // Free the temp communicator
+  ///////////////////////////////////////////////////
+  MPI_Comm_free(&optimal_comm);
+}
+
+//////////////////////////////////
+// Try to subdivide communicator
+//////////////////////////////////
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank)    
+{
+  _ndimension = processors.size();
+
+  int parent_ndimension = parent._ndimension; assert(_ndimension >= parent._ndimension);
+  Coordinate parent_processor_coor(_ndimension,0);
+  Coordinate parent_processors    (_ndimension,1);
+
+  // Can make 5d grid from 4d etc...
+  int pad = _ndimension-parent_ndimension;
+  for(int d=0;d<parent_ndimension;d++){
+    parent_processor_coor[pad+d]=parent._processor_coor[d];
+    parent_processors    [pad+d]=parent._processors[d];
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // split the communicator
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  //  int Nparent = parent._processors ; 
+  int Nparent;
+  MPI_Comm_size(parent.communicator,&Nparent);
+
+  int childsize=1;
+  for(int d=0;d<processors.size();d++) {
+    childsize *= processors[d];
+  }
+  int Nchild = Nparent/childsize;
+  assert (childsize * Nchild == Nparent);
+
+  Coordinate ccoor(_ndimension); // coor within subcommunicator
+  Coordinate scoor(_ndimension); // coor of split within parent
+  Coordinate ssize(_ndimension); // coor of split within parent
+
+  for(int d=0;d<_ndimension;d++){
+    ccoor[d] = parent_processor_coor[d] % processors[d];
+    scoor[d] = parent_processor_coor[d] / processors[d];
+    ssize[d] = parent_processors[d]     / processors[d];
+  }
+
+  // rank within subcomm ; srank is rank of subcomm within blocks of subcomms
+  int crank;  
+  // Mpi uses the reverse Lexico convention to us; so reversed routines called
+  Lexicographic::IndexFromCoorReversed(ccoor,crank,processors); // processors is the split grid dimensions
+  Lexicographic::IndexFromCoorReversed(scoor,srank,ssize);      // ssize is the number of split grids
+
+  MPI_Comm comm_split;
+  if ( Nchild > 1 ) { 
+
+    ////////////////////////////////////////////////////////////////
+    // Split the communicator
+    ////////////////////////////////////////////////////////////////
+    int ierr= MPI_Comm_split(parent.communicator,srank,crank,&comm_split);
+    assert(ierr==0);
+
+  } else {
+    srank = 0;
+    int ierr = MPI_Comm_dup (parent.communicator,&comm_split);
+    assert(ierr==0);
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Set up from the new split communicator
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  InitFromMPICommunicator(processors,comm_split);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Take the right SHM buffers
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  SetCommunicator(comm_split);
+
+  ///////////////////////////////////////////////
+  // Free the temp communicator 
+  ///////////////////////////////////////////////
+  MPI_Comm_free(&comm_split);
+
+  if(0){ 
+    std::cout << " ndim " <<_ndimension<<" " << parent._ndimension << std::endl;
+    for(int d=0;d<processors.size();d++){
+      std::cout << d<< " " << _processor_coor[d] <<" " <<  ccoor[d]<<std::endl;
+    }
+  }
+  for(int d=0;d<processors.size();d++){
+    assert(_processor_coor[d] == ccoor[d] );
+  }
+}
+
+void CartesianCommunicator::InitFromMPICommunicator(const Coordinate &processors, MPI_Comm communicator_base)
+{
+  ////////////////////////////////////////////////////
+  // Creates communicator, and the communicator_halo
+  ////////////////////////////////////////////////////
+  _ndimension = processors.size();
+  _processor_coor.resize(_ndimension);
+
+  /////////////////////////////////
+  // Count the requested nodes
+  /////////////////////////////////
+  _Nprocessors=1;
+  _processors = processors;
+  for(int i=0;i<_ndimension;i++){
+    _Nprocessors*=_processors[i];
+  }
+
+  Coordinate periodic(_ndimension,1);
+  MPI_Cart_create(communicator_base, _ndimension,&_processors[0],&periodic[0],0,&communicator);
+  MPI_Comm_rank(communicator,&_processor);
+  MPI_Cart_coords(communicator,_processor,_ndimension,&_processor_coor[0]);
+
+  if ( 0 && (communicator_base != communicator_world) ) {
+    std::cout << "InitFromMPICommunicator Cartesian communicator created with a non-world communicator"<<std::endl;
+    std::cout << " new communicator rank "<<_processor<< " coor ["<<_ndimension<<"] ";
+    for(int d=0;d<_processors.size();d++){
+      std::cout << _processor_coor[d]<<" ";
+    }
+    std::cout << std::endl;
+  }
+
+  int Size;
+  MPI_Comm_size(communicator,&Size);
+
+  communicator_halo.resize (2*_ndimension);
+  for(int i=0;i<_ndimension*2;i++){
+    MPI_Comm_dup(communicator,&communicator_halo[i]);
+  }
+  assert(Size==_Nprocessors);
+}
+
+CartesianCommunicator::~CartesianCommunicator()
+{
+  int MPI_is_finalised;
+  MPI_Finalized(&MPI_is_finalised);
+  if (communicator && !MPI_is_finalised) {
+    MPI_Comm_free(&communicator);
+    for(int i=0;i<communicator_halo.size();i++){
+      MPI_Comm_free(&communicator_halo[i]);
+    }
+  }  
+}
+void CartesianCommunicator::GlobalSum(uint32_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT32_T,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSum(uint64_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT64_T,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalXOR(uint32_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT32_T,MPI_BXOR,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalXOR(uint64_t &u){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&u,1,MPI_UINT64_T,MPI_BXOR,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSum(float &f){
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&f,1,MPI_FLOAT,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSumVector(float *f,int N)
+{
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,f,N,MPI_FLOAT,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSum(double &d)
+{
+  int ierr = MPI_Allreduce(MPI_IN_PLACE,&d,1,MPI_DOUBLE,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::GlobalSumVector(double *d,int N)
+{
+  int ierr = MPI_Allreduce(MPI_IN_PLACE,d,N,MPI_DOUBLE,MPI_SUM,communicator);
+  assert(ierr==0);
+}
+// Basic Halo comms primitive
+void CartesianCommunicator::SendToRecvFrom(void *xmit,
+					   int dest,
+					   void *recv,
+					   int from,
+					   int bytes)
+{
+  std::vector<CommsRequest_t> reqs(0);
+  //    unsigned long  xcrc = crc32(0L, Z_NULL, 0);
+  //    unsigned long  rcrc = crc32(0L, Z_NULL, 0);
+  //    xcrc = crc32(xcrc,(unsigned char *)xmit,bytes);
+  SendToRecvFromBegin(reqs,xmit,dest,recv,from,bytes);
+  SendToRecvFromComplete(reqs);
+  //    rcrc = crc32(rcrc,(unsigned char *)recv,bytes);
+  //    printf("proc %d SendToRecvFrom %d bytes %lx %lx\n",_processor,bytes,xcrc,rcrc);
+}
+void CartesianCommunicator::SendRecvPacket(void *xmit,
+					   void *recv,
+					   int sender,
+					   int receiver,
+					   int bytes)
+{
+  MPI_Status stat;
+  assert(sender != receiver);
+  int tag = sender;
+  if ( _processor == sender ) {
+    MPI_Send(xmit, bytes, MPI_CHAR,receiver,tag,communicator);
+  }
+  if ( _processor == receiver ) { 
+    MPI_Recv(recv, bytes, MPI_CHAR,sender,tag,communicator,&stat);
+  }
+}
+// Basic Halo comms primitive
+void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+						void *xmit,
+						int dest,
+						void *recv,
+						int from,
+						int bytes)
+{
+  int myrank = _processor;
+  int ierr;
+
+  if ( CommunicatorPolicy == CommunicatorPolicyConcurrent ) { 
+    MPI_Request xrq;
+    MPI_Request rrq;
+
+    ierr =MPI_Irecv(recv, bytes, MPI_CHAR,from,from,communicator,&rrq);
+    ierr|=MPI_Isend(xmit, bytes, MPI_CHAR,dest,_processor,communicator,&xrq);
+    
+    assert(ierr==0);
+    list.push_back(xrq);
+    list.push_back(rrq);
+  } else { 
+    // Give the CPU to MPI immediately; can use threads to overlap optionally
+    ierr=MPI_Sendrecv(xmit,bytes,MPI_CHAR,dest,myrank,
+		      recv,bytes,MPI_CHAR,from, from,
+		      communicator,MPI_STATUS_IGNORE);
+    assert(ierr==0);
+  }
+}
+
+double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
+						     int dest,
+						     void *recv,
+						     int from,
+						     int bytes,int dir)
+{
+  std::vector<CommsRequest_t> list;
+  double offbytes = StencilSendToRecvFromBegin(list,xmit,dest,recv,from,bytes,dir);
+  StencilSendToRecvFromComplete(list,dir);
+  return offbytes;
+}
+
+double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+							 void *xmit,
+							 int dest,
+							 void *recv,
+							 int from,
+							 int bytes,int dir)
+{
+  int ncomm  =communicator_halo.size(); 
+  int commdir=dir%ncomm;
+
+  MPI_Request xrq;
+  MPI_Request rrq;
+
+  int ierr;
+  int gdest = ShmRanks[dest];
+  int gfrom = ShmRanks[from];
+  int gme   = ShmRanks[_processor];
+
+  assert(dest != _processor);
+  assert(from != _processor);
+  assert(gme  == ShmRank);
+  double off_node_bytes=0.0;
+
+  if ( gfrom ==MPI_UNDEFINED) {
+    ierr=MPI_Irecv(recv, bytes, MPI_CHAR,from,from,communicator_halo[commdir],&rrq);
+    assert(ierr==0);
+    list.push_back(rrq);
+    off_node_bytes+=bytes;
+  }
+
+  if ( gdest == MPI_UNDEFINED ) {
+    ierr =MPI_Isend(xmit, bytes, MPI_CHAR,dest,_processor,communicator_halo[commdir],&xrq);
+    assert(ierr==0);
+    list.push_back(xrq);
+    off_node_bytes+=bytes;
+  }
+
+  if ( CommunicatorPolicy == CommunicatorPolicySequential ) { 
+    this->StencilSendToRecvFromComplete(list,dir);
+  }
+
+  return off_node_bytes;
+}
+void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int dir)
+{
+  SendToRecvFromComplete(waitall);
+}
+void CartesianCommunicator::StencilBarrier(void)
+{
+  MPI_Barrier  (ShmComm);
+}
+void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
+{
+  int nreq=list.size();
+
+  if (nreq==0) return;
+
+  std::vector<MPI_Status> status(nreq);
+  int ierr = MPI_Waitall(nreq,&list[0],&status[0]);
+  assert(ierr==0);
+  list.resize(0);
+}
+void CartesianCommunicator::Barrier(void)
+{
+  int ierr = MPI_Barrier(communicator);
+  assert(ierr==0);
+}
+void CartesianCommunicator::Broadcast(int root,void* data, int bytes)
+{
+  int ierr=MPI_Bcast(data,
+		     bytes,
+		     MPI_BYTE,
+		     root,
+		     communicator);
+  assert(ierr==0);
+}
+int CartesianCommunicator::RankWorld(void){ 
+  int r; 
+  MPI_Comm_rank(communicator_world,&r);
+  return r;
+}
+void CartesianCommunicator::BroadcastWorld(int root,void* data, int bytes)
+{
+  int ierr= MPI_Bcast(data,
+		      bytes,
+		      MPI_BYTE,
+		      root,
+		      communicator_world);
+  assert(ierr==0);
+}
+
+void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  Coordinate row(_ndimension,1);
+  assert(dim>=0 && dim<_ndimension);
+
+  //  Split the communicator
+  row[dim] = _processors[dim];
+
+  int me;
+  CartesianCommunicator Comm(row,*this,me);
+  Comm.AllToAll(in,out,words,bytes);
+}
+void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  // MPI is a pain and uses "int" arguments
+  // 64*64*64*128*16 == 500Million elements of data.
+  // When 24*4 bytes multiples get 50x 10^9 >>> 2x10^9 Y2K bug.
+  // (Turns up on 32^3 x 64 Gparity too)
+  MPI_Datatype object;
+  int iwords; 
+  int ibytes;
+  iwords = words;
+  ibytes = bytes;
+  assert(words == iwords); // safe to cast to int ?
+  assert(bytes == ibytes); // safe to cast to int ?
+  MPI_Type_contiguous(ibytes,MPI_BYTE,&object);
+  MPI_Type_commit(&object);
+  MPI_Alltoall(in,iwords,object,out,iwords,object,communicator);
+  MPI_Type_free(&object);
+}
+
+NAMESPACE_END(Grid);
+
+

Grid/communicator/Communicator_none.cc

@@ -0,0 +1,165 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/Communicator_none.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Info that is setup once and indept of cartesian layout
+///////////////////////////////////////////////////////////////////////////////////////////////////
+Grid_MPI_Comm       CartesianCommunicator::communicator_world;
+
+void CartesianCommunicator::Init(int *argc, char *** arv)
+{
+  GlobalSharedMemory::Init(communicator_world);
+  GlobalSharedMemory::SharedMemoryAllocate(
+					   GlobalSharedMemory::MAX_MPI_SHM_BYTES,
+					   GlobalSharedMemory::Hugepages);
+}
+
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors,const CartesianCommunicator &parent,int &srank) 
+  : CartesianCommunicator(processors) 
+{
+  srank=0;
+  SetCommunicator(communicator_world);
+}
+
+CartesianCommunicator::CartesianCommunicator(const Coordinate &processors)
+{
+  _processors = processors;
+  _ndimension = processors.size();
+  _processor_coor.resize(_ndimension);
+  
+  // Require 1^N processor grid for fake
+  _Nprocessors=1;
+  _processor = 0;
+  for(int d=0;d<_ndimension;d++) {
+    assert(_processors[d]==1);
+    _processor_coor[d] = 0;
+  }
+  SetCommunicator(communicator_world);
+}
+
+CartesianCommunicator::~CartesianCommunicator(){}
+
+void CartesianCommunicator::GlobalSum(float &){}
+void CartesianCommunicator::GlobalSumVector(float *,int N){}
+void CartesianCommunicator::GlobalSum(double &){}
+void CartesianCommunicator::GlobalSum(uint32_t &){}
+void CartesianCommunicator::GlobalSum(uint64_t &){}
+void CartesianCommunicator::GlobalSumVector(double *,int N){}
+void CartesianCommunicator::GlobalXOR(uint32_t &){}
+void CartesianCommunicator::GlobalXOR(uint64_t &){}
+
+void CartesianCommunicator::SendRecvPacket(void *xmit,
+					   void *recv,
+					   int xmit_to_rank,
+					   int recv_from_rank,
+					   int bytes)
+{
+  assert(0);
+}
+
+
+// Basic Halo comms primitive -- should never call in single node
+void CartesianCommunicator::SendToRecvFrom(void *xmit,
+					   int dest,
+					   void *recv,
+					   int from,
+					   int bytes)
+{
+  assert(0);
+}
+void CartesianCommunicator::SendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+						void *xmit,
+						int dest,
+						void *recv,
+						int from,
+						int bytes)
+{
+  assert(0);
+}
+
+void CartesianCommunicator::SendToRecvFromComplete(std::vector<CommsRequest_t> &list)
+{
+  assert(0);
+}
+void CartesianCommunicator::AllToAll(int dim,void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  bcopy(in,out,bytes*words);
+}
+void CartesianCommunicator::AllToAll(void  *in,void *out,uint64_t words,uint64_t bytes)
+{
+  bcopy(in,out,bytes*words);
+}
+
+int  CartesianCommunicator::RankWorld(void){return 0;}
+void CartesianCommunicator::Barrier(void){}
+void CartesianCommunicator::Broadcast(int root,void* data, int bytes) {}
+void CartesianCommunicator::BroadcastWorld(int root,void* data, int bytes) { }
+int  CartesianCommunicator::RankFromProcessorCoor(Coordinate &coor) {  return 0;}
+void CartesianCommunicator::ProcessorCoorFromRank(int rank, Coordinate &coor){  coor = _processor_coor; }
+void CartesianCommunicator::ShiftedRanks(int dim,int shift,int &source,int &dest)
+{
+  source =0;
+  dest=0;
+}
+
+double CartesianCommunicator::StencilSendToRecvFrom( void *xmit,
+						     int xmit_to_rank,
+						     void *recv,
+						     int recv_from_rank,
+						     int bytes, int dir)
+{
+  std::vector<CommsRequest_t> list;
+  // Discard the "dir"
+  SendToRecvFromBegin   (list,xmit,xmit_to_rank,recv,recv_from_rank,bytes);
+  SendToRecvFromComplete(list);
+  return 2.0*bytes;
+}
+double CartesianCommunicator::StencilSendToRecvFromBegin(std::vector<CommsRequest_t> &list,
+							 void *xmit,
+							 int xmit_to_rank,
+							 void *recv,
+							 int recv_from_rank,
+							 int bytes, int dir)
+{
+  // Discard the "dir"
+  SendToRecvFromBegin(list,xmit,xmit_to_rank,recv,recv_from_rank,bytes);
+  return 2.0*bytes;
+}
+void CartesianCommunicator::StencilSendToRecvFromComplete(std::vector<CommsRequest_t> &waitall,int dir)
+{
+  SendToRecvFromComplete(waitall);
+}
+
+void CartesianCommunicator::StencilBarrier(void){};
+
+NAMESPACE_END(Grid);
+
+

Grid/communicator/SharedMemory.cc

@@ -0,0 +1,93 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid); 
+
+// static data
+
+uint64_t            GlobalSharedMemory::MAX_MPI_SHM_BYTES   = 1024LL*1024LL*1024LL; 
+int                 GlobalSharedMemory::Hugepages = 0;
+int                 GlobalSharedMemory::_ShmSetup;
+int                 GlobalSharedMemory::_ShmAlloc;
+uint64_t            GlobalSharedMemory::_ShmAllocBytes;
+
+std::vector<void *> GlobalSharedMemory::WorldShmCommBufs;
+
+Grid_MPI_Comm       GlobalSharedMemory::WorldShmComm;
+int                 GlobalSharedMemory::WorldShmRank;
+int                 GlobalSharedMemory::WorldShmSize;
+std::vector<int>    GlobalSharedMemory::WorldShmRanks;
+
+Grid_MPI_Comm       GlobalSharedMemory::WorldComm;
+int                 GlobalSharedMemory::WorldSize;
+int                 GlobalSharedMemory::WorldRank;
+
+int                 GlobalSharedMemory::WorldNodes;
+int                 GlobalSharedMemory::WorldNode;
+
+void GlobalSharedMemory::SharedMemoryFree(void)
+{
+  assert(_ShmAlloc);
+  assert(_ShmAllocBytes>0);
+  for(int r=0;r<WorldShmSize;r++){
+    munmap(WorldShmCommBufs[r],_ShmAllocBytes);
+  }
+  _ShmAlloc = 0;
+  _ShmAllocBytes = 0;
+}
+/////////////////////////////////
+// Alloc, free shmem region
+/////////////////////////////////
+void *SharedMemory::ShmBufferMalloc(size_t bytes){
+  //  bytes = (bytes+sizeof(vRealD))&(~(sizeof(vRealD)-1));// align up bytes
+  void *ptr = (void *)heap_top;
+  heap_top  += bytes;
+  heap_bytes+= bytes;
+  if (heap_bytes >= heap_size) {
+    std::cout<< " ShmBufferMalloc exceeded shared heap size -- try increasing with --shm <MB> flag" <<std::endl;
+    std::cout<< " Parameter specified in units of MB (megabytes) " <<std::endl;
+    std::cout<< " Current value is " << (heap_size/(1024*1024)) <<std::endl;
+    assert(heap_bytes<heap_size);
+  }
+  //std::cerr << "ShmBufferMalloc "<<std::hex<< ptr<<" - "<<((uint64_t)ptr+bytes)<<std::dec<<std::endl;
+  return ptr;
+}
+void SharedMemory::ShmBufferFreeAll(void) { 
+  heap_top  =(size_t)ShmBufferSelf();
+  heap_bytes=0;
+}
+void *SharedMemory::ShmBufferSelf(void)
+{
+  //std::cerr << "ShmBufferSelf "<<ShmRank<<" "<<std::hex<< ShmCommBufs[ShmRank] <<std::dec<<std::endl;
+  return ShmCommBufs[ShmRank];
+}
+
+NAMESPACE_END(Grid); 
+

Grid/communicator/SharedMemory.h

@@ -0,0 +1,157 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+
+#include <Grid/GridCore.h>
+
+#if defined (GRID_COMMS_MPI3) 
+#include <mpi.h>
+#endif 
+#include <semaphore.h>
+#include <fcntl.h>
+#include <unistd.h>
+#include <limits.h>
+#include <sys/types.h>
+#include <sys/ipc.h>
+#include <sys/shm.h>
+#include <sys/mman.h>
+#include <zlib.h>
+#ifdef HAVE_NUMAIF_H
+#include <numaif.h>
+#endif
+
+NAMESPACE_BEGIN(Grid);
+
+#if defined (GRID_COMMS_MPI3) 
+typedef MPI_Comm    Grid_MPI_Comm;
+typedef MPI_Request CommsRequest_t;
+#else 
+typedef int CommsRequest_t;
+typedef int Grid_MPI_Comm;
+#endif
+
+class GlobalSharedMemory {
+private:
+  static const int     MAXLOG2RANKSPERNODE = 16;            
+
+  // Init once lock on the buffer allocation
+  static int      _ShmSetup;
+  static int      _ShmAlloc;
+  static uint64_t _ShmAllocBytes;
+
+public:
+  static int      ShmSetup(void)      { return _ShmSetup; }
+  static int      ShmAlloc(void)      { return _ShmAlloc; }
+  static uint64_t ShmAllocBytes(void) { return _ShmAllocBytes; }
+  static uint64_t      MAX_MPI_SHM_BYTES;
+  static int           Hugepages;
+
+  static std::vector<void *> WorldShmCommBufs;
+
+  static Grid_MPI_Comm WorldComm;
+  static int           WorldRank;
+  static int           WorldSize;
+
+  static Grid_MPI_Comm WorldShmComm;
+  static int           WorldShmRank;
+  static int           WorldShmSize;
+
+  static int           WorldNodes;
+  static int           WorldNode;
+
+  static std::vector<int>  WorldShmRanks;
+
+  //////////////////////////////////////////////////////////////////////////////////////
+  // Create an optimal reordered communicator that makes MPI_Cart_create get it right
+  //////////////////////////////////////////////////////////////////////////////////////
+  static void Init(Grid_MPI_Comm comm); // Typically MPI_COMM_WORLD
+  static void OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm);  // Turns MPI_COMM_WORLD into right layout for Cartesian
+  ///////////////////////////////////////////////////
+  // Provide shared memory facilities off comm world
+  ///////////////////////////////////////////////////
+  static void SharedMemoryAllocate(uint64_t bytes, int flags);
+  static void SharedMemoryFree(void);
+  static void SharedMemoryCopy(void *dest,const void *src,size_t bytes);
+  static void SharedMemoryZero(void *dest,size_t bytes);
+
+};
+
+//////////////////////////////
+// one per communicator
+//////////////////////////////
+class SharedMemory 
+{
+private:
+  static const int     MAXLOG2RANKSPERNODE = 16;            
+
+  size_t heap_top;
+  size_t heap_bytes;
+  size_t heap_size;
+
+protected:
+
+  Grid_MPI_Comm    ShmComm; // for barriers
+  int    ShmRank; 
+  int    ShmSize;
+  std::vector<void *> ShmCommBufs;
+  std::vector<int>    ShmRanks;// Mapping comm ranks to Shm ranks
+
+public:
+  SharedMemory() {};
+  ~SharedMemory();
+  ///////////////////////////////////////////////////////////////////////////////////////
+  // set the buffers & sizes
+  ///////////////////////////////////////////////////////////////////////////////////////
+  void SetCommunicator(Grid_MPI_Comm comm);
+
+  ////////////////////////////////////////////////////////////////////////
+  // For this instance ; disjoint buffer sets between splits if split grid
+  ////////////////////////////////////////////////////////////////////////
+  void ShmBarrier(void); 
+
+  ///////////////////////////////////////////////////
+  // Call on any instance
+  ///////////////////////////////////////////////////
+  void SharedMemoryTest(void);
+  
+  void *ShmBufferSelf(void);
+  void *ShmBuffer    (int rank);
+  void *ShmBufferTranslate(int rank,void * local_p);
+  void *ShmBufferMalloc(size_t bytes);
+  void  ShmBufferFreeAll(void) ;
+  
+  //////////////////////////////////////////////////////////////////////////
+  // Make info on Nodes & ranks and Shared memory available
+  //////////////////////////////////////////////////////////////////////////
+  int NodeCount(void) { return GlobalSharedMemory::WorldNodes;};
+  int RankCount(void) { return GlobalSharedMemory::WorldSize;};
+
+};
+
+NAMESPACE_END(Grid);
+

Grid/communicator/SharedMemoryMPI.cc

@@ -0,0 +1,761 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+#include <pwd.h>
+
+#ifdef GRID_NVCC
+#include <cuda_runtime_api.h>
+#endif
+
+NAMESPACE_BEGIN(Grid); 
+
+/*Construct from an MPI communicator*/
+void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
+{
+  assert(_ShmSetup==0);
+  WorldComm = comm;
+  MPI_Comm_rank(WorldComm,&WorldRank);
+  MPI_Comm_size(WorldComm,&WorldSize);
+  // WorldComm, WorldSize, WorldRank
+
+  /////////////////////////////////////////////////////////////////////
+  // Split into groups that can share memory
+  /////////////////////////////////////////////////////////////////////
+  MPI_Comm_split_type(comm, MPI_COMM_TYPE_SHARED, 0, MPI_INFO_NULL,&WorldShmComm);
+  MPI_Comm_rank(WorldShmComm     ,&WorldShmRank);
+  MPI_Comm_size(WorldShmComm     ,&WorldShmSize);
+
+  std::cout << " GRID initialisation: World communicator of size " <<WorldSize << std::endl;  
+  std::cout << " GRID initialisation: Node  communicator of size " <<WorldShmSize << std::endl;
+  // WorldShmComm, WorldShmSize, WorldShmRank
+
+  // WorldNodes
+  WorldNodes = WorldSize/WorldShmSize;
+  assert( (WorldNodes * WorldShmSize) == WorldSize );
+
+  // FIXME: Check all WorldShmSize are the same ?
+
+  /////////////////////////////////////////////////////////////////////
+  // find world ranks in our SHM group (i.e. which ranks are on our node)
+  /////////////////////////////////////////////////////////////////////
+  MPI_Group WorldGroup, ShmGroup;
+  MPI_Comm_group (WorldComm, &WorldGroup); 
+  MPI_Comm_group (WorldShmComm, &ShmGroup);
+
+  std::vector<int> world_ranks(WorldSize);   for(int r=0;r<WorldSize;r++) world_ranks[r]=r;
+
+  WorldShmRanks.resize(WorldSize); 
+  MPI_Group_translate_ranks (WorldGroup,WorldSize,&world_ranks[0],ShmGroup, &WorldShmRanks[0]); 
+
+  ///////////////////////////////////////////////////////////////////
+  // Identify who is in my group and nominate the leader
+  ///////////////////////////////////////////////////////////////////
+  int g=0;
+  std::vector<int> MyGroup;
+  MyGroup.resize(WorldShmSize);
+  for(int rank=0;rank<WorldSize;rank++){
+    if(WorldShmRanks[rank]!=MPI_UNDEFINED){
+      assert(g<WorldShmSize);
+      MyGroup[g++] = rank;
+    }
+  }
+  
+  std::sort(MyGroup.begin(),MyGroup.end(),std::less<int>());
+  int myleader = MyGroup[0];
+  
+  std::vector<int> leaders_1hot(WorldSize,0);
+  std::vector<int> leaders_group(WorldNodes,0);
+  leaders_1hot [ myleader ] = 1;
+    
+  ///////////////////////////////////////////////////////////////////
+  // global sum leaders over comm world
+  ///////////////////////////////////////////////////////////////////
+  int ierr=MPI_Allreduce(MPI_IN_PLACE,&leaders_1hot[0],WorldSize,MPI_INT,MPI_SUM,WorldComm);
+  assert(ierr==0);
+
+  ///////////////////////////////////////////////////////////////////
+  // find the group leaders world rank
+  ///////////////////////////////////////////////////////////////////
+  int group=0;
+  for(int l=0;l<WorldSize;l++){
+    if(leaders_1hot[l]){
+      leaders_group[group++] = l;
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////
+  // Identify the node of the group in which I (and my leader) live
+  ///////////////////////////////////////////////////////////////////
+  WorldNode=-1;
+  for(int g=0;g<WorldNodes;g++){
+    if (myleader == leaders_group[g]){
+      WorldNode=g;
+    }
+  }
+  assert(WorldNode!=-1);
+  _ShmSetup=1;
+}
+// Gray encode support 
+int BinaryToGray (int  binary) {
+  int gray = (binary>>1)^binary;
+  return gray;
+}
+int Log2Size(int TwoToPower,int MAXLOG2)
+{
+  int log2size = -1;
+  for(int i=0;i<=MAXLOG2;i++){
+    if ( (0x1<<i) == TwoToPower ) {
+      log2size = i;
+      break;
+    }
+  }
+  return log2size;
+}
+void GlobalSharedMemory::OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
+{
+#ifdef HYPERCUBE
+  ////////////////////////////////////////////////////////////////
+  // Assert power of two shm_size.
+  ////////////////////////////////////////////////////////////////
+  int log2size = Log2Size(WorldShmSize,MAXLOG2RANKSPERNODE);
+  assert(log2size != -1);
+
+  ////////////////////////////////////////////////////////////////
+  // Identify the hypercube coordinate of this node using hostname
+  ////////////////////////////////////////////////////////////////
+  // n runs 0...7 9...16 18...25 27...34     (8*4)  5 bits
+  // i runs 0..7                                    3 bits
+  // r runs 0..3                                    2 bits
+  // 2^10 = 1024 nodes
+  const int maxhdim = 10; 
+  std::vector<int> HyperCubeCoords(maxhdim,0);
+  std::vector<int> RootHyperCubeCoords(maxhdim,0);
+  int R;
+  int I;
+  int N;
+  const int namelen = _POSIX_HOST_NAME_MAX;
+  char name[namelen];
+
+  // Parse ICE-XA hostname to get hypercube location
+  gethostname(name,namelen);
+  int nscan = sscanf(name,"r%di%dn%d",&R,&I,&N) ;
+  assert(nscan==3);
+
+  int nlo = N%9;
+  int nhi = N/9;
+  uint32_t hypercoor = (R<<8)|(I<<5)|(nhi<<3)|nlo ;
+  uint32_t rootcoor  = hypercoor;
+
+  //////////////////////////////////////////////////////////////////
+  // Print debug info
+  //////////////////////////////////////////////////////////////////
+  for(int d=0;d<maxhdim;d++){
+    HyperCubeCoords[d] = (hypercoor>>d)&0x1;
+  }
+
+  std::string hname(name);
+  std::cout << "hostname "<<hname<<std::endl;
+  std::cout << "R " << R << " I " << I << " N "<< N
+            << " hypercoor 0x"<<std::hex<<hypercoor<<std::dec<<std::endl;
+
+  //////////////////////////////////////////////////////////////////
+  // broadcast node 0's base coordinate for this partition.
+  //////////////////////////////////////////////////////////////////
+  MPI_Bcast(&rootcoor, sizeof(rootcoor), MPI_BYTE, 0, WorldComm); 
+  hypercoor=hypercoor-rootcoor;
+  assert(hypercoor<WorldSize);
+  assert(hypercoor>=0);
+
+  //////////////////////////////////////
+  // Printing
+  //////////////////////////////////////
+  for(int d=0;d<maxhdim;d++){
+    HyperCubeCoords[d] = (hypercoor>>d)&0x1;
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // Identify subblock of ranks on node spreading across dims
+  // in a maximally symmetrical way
+  ////////////////////////////////////////////////////////////////
+  int ndimension              = processors.size();
+  std::vector<int> processor_coor(ndimension);
+  std::vector<int> WorldDims = processors;   std::vector<int> ShmDims  (ndimension,1);  std::vector<int> NodeDims (ndimension);
+  std::vector<int> ShmCoor  (ndimension);    std::vector<int> NodeCoor (ndimension);    std::vector<int> WorldCoor(ndimension);
+  std::vector<int> HyperCoor(ndimension);
+  int dim = 0;
+  for(int l2=0;l2<log2size;l2++){
+    while ( (WorldDims[dim] / ShmDims[dim]) <= 1 ) dim=(dim+1)%ndimension;
+    ShmDims[dim]*=2;
+    dim=(dim+1)%ndimension;
+    }
+
+  ////////////////////////////////////////////////////////////////
+  // Establish torus of processes and nodes with sub-blockings
+  ////////////////////////////////////////////////////////////////
+  for(int d=0;d<ndimension;d++){
+    NodeDims[d] = WorldDims[d]/ShmDims[d];
+  }
+  ////////////////////////////////////////////////////////////////
+  // Map Hcube according to physical lattice 
+  // must partition. Loop over dims and find out who would join.
+  ////////////////////////////////////////////////////////////////
+  int hcoor = hypercoor;
+  for(int d=0;d<ndimension;d++){
+     int bits = Log2Size(NodeDims[d],MAXLOG2RANKSPERNODE);
+     int msk  = (0x1<<bits)-1;
+     HyperCoor[d]=hcoor & msk;  
+     HyperCoor[d]=BinaryToGray(HyperCoor[d]); // Space filling curve magic
+     hcoor = hcoor >> bits;
+  }
+  ////////////////////////////////////////////////////////////////
+  // Check processor counts match
+  ////////////////////////////////////////////////////////////////
+  int Nprocessors=1;
+  for(int i=0;i<ndimension;i++){
+    Nprocessors*=processors[i];
+  }
+  assert(WorldSize==Nprocessors);
+
+  ////////////////////////////////////////////////////////////////
+  // Establish mapping between lexico physics coord and WorldRank
+  ////////////////////////////////////////////////////////////////
+  int rank;
+
+  Lexicographic::CoorFromIndexReversed(NodeCoor,WorldNode   ,NodeDims);
+
+  for(int d=0;d<ndimension;d++) NodeCoor[d]=HyperCoor[d];
+
+  Lexicographic::CoorFromIndexReversed(ShmCoor ,WorldShmRank,ShmDims);
+  for(int d=0;d<ndimension;d++) WorldCoor[d] = NodeCoor[d]*ShmDims[d]+ShmCoor[d];
+  Lexicographic::IndexFromCoorReversed(WorldCoor,rank,WorldDims);
+
+  /////////////////////////////////////////////////////////////////
+  // Build the new communicator
+  /////////////////////////////////////////////////////////////////
+  int ierr= MPI_Comm_split(WorldComm,0,rank,&optimal_comm);
+  assert(ierr==0);
+#else 
+  ////////////////////////////////////////////////////////////////
+  // Assert power of two shm_size.
+  ////////////////////////////////////////////////////////////////
+  int log2size = Log2Size(WorldShmSize,MAXLOG2RANKSPERNODE);
+  assert(log2size != -1);
+
+  ////////////////////////////////////////////////////////////////
+  // Identify subblock of ranks on node spreading across dims
+  // in a maximally symmetrical way
+  ////////////////////////////////////////////////////////////////
+  int ndimension              = processors.size();
+  Coordinate processor_coor(ndimension);
+  Coordinate WorldDims = processors; Coordinate ShmDims(ndimension,1);  Coordinate NodeDims (ndimension);
+  Coordinate ShmCoor(ndimension);    Coordinate NodeCoor(ndimension);   Coordinate WorldCoor(ndimension);
+  int dim = 0;
+  for(int l2=0;l2<log2size;l2++){
+    while ( (WorldDims[dim] / ShmDims[dim]) <= 1 ) dim=(dim+1)%ndimension;
+    ShmDims[dim]*=2;
+    dim=(dim+1)%ndimension;
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // Establish torus of processes and nodes with sub-blockings
+  ////////////////////////////////////////////////////////////////
+  for(int d=0;d<ndimension;d++){
+    NodeDims[d] = WorldDims[d]/ShmDims[d];
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // Check processor counts match
+  ////////////////////////////////////////////////////////////////
+  int Nprocessors=1;
+  for(int i=0;i<ndimension;i++){
+    Nprocessors*=processors[i];
+  }
+  assert(WorldSize==Nprocessors);
+
+  ////////////////////////////////////////////////////////////////
+  // Establish mapping between lexico physics coord and WorldRank
+  ////////////////////////////////////////////////////////////////
+  int rank;
+
+  Lexicographic::CoorFromIndexReversed(NodeCoor,WorldNode   ,NodeDims);
+  Lexicographic::CoorFromIndexReversed(ShmCoor ,WorldShmRank,ShmDims);
+  for(int d=0;d<ndimension;d++) WorldCoor[d] = NodeCoor[d]*ShmDims[d]+ShmCoor[d];
+  Lexicographic::IndexFromCoorReversed(WorldCoor,rank,WorldDims);
+
+  /////////////////////////////////////////////////////////////////
+  // Build the new communicator
+  /////////////////////////////////////////////////////////////////
+  int ierr= MPI_Comm_split(WorldComm,0,rank,&optimal_comm);
+  assert(ierr==0);
+#endif
+}
+////////////////////////////////////////////////////////////////////////////////////////////
+// SHMGET
+////////////////////////////////////////////////////////////////////////////////////////////
+#ifdef GRID_MPI3_SHMGET
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  std::cout << "SharedMemoryAllocate "<< bytes<< " shmget implementation "<<std::endl;
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // allocate the shared windows for our group
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  MPI_Barrier(WorldShmComm);
+  WorldShmCommBufs.resize(WorldShmSize);
+  std::vector<int> shmids(WorldShmSize);
+
+  if ( WorldShmRank == 0 ) {
+    for(int r=0;r<WorldShmSize;r++){
+      size_t size = bytes;
+      key_t key   = IPC_PRIVATE;
+      int flags = IPC_CREAT | SHM_R | SHM_W;
+#ifdef SHM_HUGETLB
+      if (Hugepages) flags|=SHM_HUGETLB;
+#endif
+      if ((shmids[r]= shmget(key,size, flags)) ==-1) {
+        int errsv = errno;
+        printf("Errno %d\n",errsv);
+        printf("key   %d\n",key);
+        printf("size  %lld\n",size);
+        printf("flags %d\n",flags);
+        perror("shmget");
+        exit(1);
+      }
+    }
+  }
+  MPI_Barrier(WorldShmComm);
+  MPI_Bcast(&shmids[0],WorldShmSize*sizeof(int),MPI_BYTE,0,WorldShmComm);
+  MPI_Barrier(WorldShmComm);
+
+  for(int r=0;r<WorldShmSize;r++){
+    WorldShmCommBufs[r] = (uint64_t *)shmat(shmids[r], NULL,0);
+    if (WorldShmCommBufs[r] == (uint64_t *)-1) {
+      perror("Shared memory attach failure");
+      shmctl(shmids[r], IPC_RMID, NULL);
+      exit(2);
+    }
+  }
+  MPI_Barrier(WorldShmComm);
+  ///////////////////////////////////
+  // Mark for clean up
+  ///////////////////////////////////
+  for(int r=0;r<WorldShmSize;r++){
+    shmctl(shmids[r], IPC_RMID,(struct shmid_ds *)NULL);
+  }
+  MPI_Barrier(WorldShmComm);
+
+  _ShmAlloc=1;
+  _ShmAllocBytes  = bytes;
+}
+#endif
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Hugetlbfs mapping intended
+////////////////////////////////////////////////////////////////////////////////////////////
+#ifdef GRID_NVCC
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  void * ShmCommBuf ; 
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // allocate the pointer array for shared windows for our group
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  MPI_Barrier(WorldShmComm);
+  WorldShmCommBufs.resize(WorldShmSize);
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // TODO/FIXME : NOT ALL NVLINK BOARDS have full Peer to peer connectivity.
+  // The annoyance is that they have partial peer 2 peer. This occurs on the 8 GPU blades.
+  // e.g. DGX1, supermicro board, 
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  //  cudaDeviceGetP2PAttribute(&perfRank, cudaDevP2PAttrPerformanceRank, device1, device2);
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Each MPI rank should allocate our own buffer
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  auto err =  cudaMalloc(&ShmCommBuf, bytes);
+  if ( err !=  cudaSuccess) {
+    std::cerr << " SharedMemoryMPI.cc cudaMallocManaged failed for " << bytes<<" bytes " <<cudaGetErrorString(err)<< std::endl;
+    exit(EXIT_FAILURE);  
+  }
+  if (ShmCommBuf == (void *)NULL ) {
+    std::cerr << " SharedMemoryMPI.cc cudaMallocManaged failed NULL pointer for " << bytes<<" bytes " << std::endl;
+    exit(EXIT_FAILURE);  
+  }
+  SharedMemoryZero(ShmCommBuf,bytes);
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Loop over ranks/gpu's on our node
+  ///////////////////////////////////////////////////////////////////////////////////////////////////////////
+  for(int r=0;r<WorldShmSize;r++){
+    
+    //////////////////////////////////////////////////
+    // If it is me, pass around the IPC access key
+    //////////////////////////////////////////////////
+    cudaIpcMemHandle_t handle;
+
+    if ( r==WorldShmRank ) { 
+      err = cudaIpcGetMemHandle(&handle,ShmCommBuf);
+      if ( err !=  cudaSuccess) {
+	std::cerr << " SharedMemoryMPI.cc cudaIpcGetMemHandle failed for rank" << r <<" "<<cudaGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+    //////////////////////////////////////////////////
+    // Share this IPC handle across the Shm Comm
+    //////////////////////////////////////////////////
+    { 
+      int ierr=MPI_Bcast(&handle,
+			 sizeof(handle),
+			 MPI_BYTE,
+			 r,
+			 WorldShmComm);
+      assert(ierr==0);
+    }
+    
+    ///////////////////////////////////////////////////////////////
+    // If I am not the source, overwrite thisBuf with remote buffer
+    ///////////////////////////////////////////////////////////////
+    void * thisBuf = ShmCommBuf;
+    if ( r!=WorldShmRank ) { 
+      err = cudaIpcOpenMemHandle(&thisBuf,handle,cudaIpcMemLazyEnablePeerAccess);
+      if ( err !=  cudaSuccess) {
+	std::cerr << " SharedMemoryMPI.cc cudaIpcOpenMemHandle failed for rank" << r <<" "<<cudaGetErrorString(err)<< std::endl;
+	exit(EXIT_FAILURE);
+      }
+    }
+    ///////////////////////////////////////////////////////////////
+    // Save a copy of the device buffers
+    ///////////////////////////////////////////////////////////////
+    WorldShmCommBufs[r] = thisBuf;
+  }
+
+  _ShmAllocBytes=bytes;
+  _ShmAlloc=1;
+}
+#else 
+#ifdef GRID_MPI3_SHMMMAP
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  std::cout << "SharedMemoryAllocate "<< bytes<< " MMAP implementation "<< GRID_SHM_PATH <<std::endl;
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // allocate the shared windows for our group
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  MPI_Barrier(WorldShmComm);
+  WorldShmCommBufs.resize(WorldShmSize);
+  
+  ////////////////////////////////////////////////////////////////////////////////////////////
+  // Hugetlbfs and others map filesystems as mappable huge pages
+  ////////////////////////////////////////////////////////////////////////////////////////////
+  char shm_name [NAME_MAX];
+  for(int r=0;r<WorldShmSize;r++){
+    
+    sprintf(shm_name,GRID_SHM_PATH "/Grid_mpi3_shm_%d_%d",WorldNode,r);
+    int fd=open(shm_name,O_RDWR|O_CREAT,0666);
+    if ( fd == -1) { 
+      printf("open %s failed\n",shm_name);
+      perror("open hugetlbfs");
+      exit(0);
+    }
+    int mmap_flag = MAP_SHARED ;
+#ifdef MAP_POPULATE    
+    mmap_flag|=MAP_POPULATE;
+#endif
+#ifdef MAP_HUGETLB
+    if ( flags ) mmap_flag |= MAP_HUGETLB;
+#endif
+    void *ptr = (void *) mmap(NULL, bytes, PROT_READ | PROT_WRITE, mmap_flag,fd, 0); 
+    if ( ptr == (void *)MAP_FAILED ) {    
+      printf("mmap %s failed\n",shm_name);
+      perror("failed mmap");      assert(0);    
+    }
+    assert(((uint64_t)ptr&0x3F)==0);
+    close(fd);
+    WorldShmCommBufs[r] =ptr;
+    //    std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
+  }
+  _ShmAlloc=1;
+  _ShmAllocBytes  = bytes;
+};
+#endif // MMAP
+
+#ifdef GRID_MPI3_SHM_NONE
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  std::cout << "SharedMemoryAllocate "<< bytes<< " MMAP anonymous implementation "<<std::endl;
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // allocate the shared windows for our group
+  //////////////////////////////////////////////////////////////////////////////////////////////////////////
+  MPI_Barrier(WorldShmComm);
+  WorldShmCommBufs.resize(WorldShmSize);
+  
+  ////////////////////////////////////////////////////////////////////////////////////////////
+  // Hugetlbf and others map filesystems as mappable huge pages
+  ////////////////////////////////////////////////////////////////////////////////////////////
+  char shm_name [NAME_MAX];
+  assert(WorldShmSize == 1);
+  for(int r=0;r<WorldShmSize;r++){
+    
+    int fd=-1;
+    int mmap_flag = MAP_SHARED |MAP_ANONYMOUS ;
+#ifdef MAP_POPULATE    
+    mmap_flag|=MAP_POPULATE;
+#endif
+#ifdef MAP_HUGETLB
+    if ( flags ) mmap_flag |= MAP_HUGETLB;
+#endif
+    void *ptr = (void *) mmap(NULL, bytes, PROT_READ | PROT_WRITE, mmap_flag,fd, 0); 
+    if ( ptr == (void *)MAP_FAILED ) {    
+      printf("mmap %s failed\n",shm_name);
+      perror("failed mmap");      assert(0);    
+    }
+    assert(((uint64_t)ptr&0x3F)==0);
+    close(fd);
+    WorldShmCommBufs[r] =ptr;
+    //    std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< bytes<< "bytes)"<<std::endl;
+  }
+  _ShmAlloc=1;
+  _ShmAllocBytes  = bytes;
+};
+#endif // MMAP
+
+#ifdef GRID_MPI3_SHMOPEN
+////////////////////////////////////////////////////////////////////////////////////////////
+// POSIX SHMOPEN ; as far as I know Linux does not allow EXPLICIT HugePages with this case
+// tmpfs (Larry Meadows says) does not support explicit huge page, and this is used for 
+// the posix shm virtual file system
+////////////////////////////////////////////////////////////////////////////////////////////
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{ 
+  std::cout << "SharedMemoryAllocate "<< bytes<< " SHMOPEN implementation "<<std::endl;
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0); 
+  MPI_Barrier(WorldShmComm);
+  WorldShmCommBufs.resize(WorldShmSize);
+
+  char shm_name [NAME_MAX];
+  if ( WorldShmRank == 0 ) {
+    for(int r=0;r<WorldShmSize;r++){
+	
+      size_t size = bytes;
+      
+      struct passwd *pw = getpwuid (getuid());
+      sprintf(shm_name,"/Grid_%s_mpi3_shm_%d_%d",pw->pw_name,WorldNode,r);
+      
+      shm_unlink(shm_name);
+      int fd=shm_open(shm_name,O_RDWR|O_CREAT,0666);
+      if ( fd < 0 ) {	perror("failed shm_open");	assert(0);      }
+      ftruncate(fd, size);
+	
+      int mmap_flag = MAP_SHARED;
+#ifdef MAP_POPULATE 
+      mmap_flag |= MAP_POPULATE;
+#endif
+#ifdef MAP_HUGETLB
+      if (flags) mmap_flag |= MAP_HUGETLB;
+#endif
+      void * ptr =  mmap(NULL,size, PROT_READ | PROT_WRITE, mmap_flag, fd, 0);
+      
+      //      std::cout << "Set WorldShmCommBufs["<<r<<"]="<<ptr<< "("<< size<< "bytes)"<<std::endl;
+      if ( ptr == (void * )MAP_FAILED ) {       
+	perror("failed mmap");     
+	assert(0);    
+      }
+      assert(((uint64_t)ptr&0x3F)==0);
+      
+      WorldShmCommBufs[r] =ptr;
+      close(fd);
+    }
+  }
+
+  MPI_Barrier(WorldShmComm);
+  
+  if ( WorldShmRank != 0 ) { 
+    for(int r=0;r<WorldShmSize;r++){
+
+      size_t size = bytes ;
+      
+      struct passwd *pw = getpwuid (getuid());
+      sprintf(shm_name,"/Grid_%s_mpi3_shm_%d_%d",pw->pw_name,WorldNode,r);
+      
+      int fd=shm_open(shm_name,O_RDWR,0666);
+      if ( fd<0 ) {	perror("failed shm_open");	assert(0);      }
+      
+      void * ptr =  mmap(NULL,size, PROT_READ | PROT_WRITE, MAP_SHARED, fd, 0);
+      if ( ptr == MAP_FAILED ) {       perror("failed mmap");      assert(0);    }
+      assert(((uint64_t)ptr&0x3F)==0);
+      WorldShmCommBufs[r] =ptr;
+
+      close(fd);
+    }
+  }
+  _ShmAlloc=1;
+  _ShmAllocBytes = bytes;
+}
+#endif
+#endif // End NVCC case for GPU device buffers
+
+/////////////////////////////////////////////////////////////////////////
+// Routines accessing shared memory should route through for GPU safety
+/////////////////////////////////////////////////////////////////////////
+void GlobalSharedMemory::SharedMemoryZero(void *dest,size_t bytes)
+{
+#ifdef GRID_NVCC
+  cudaMemset(dest,0,bytes);
+#else
+  bzero(dest,bytes);
+#endif
+}
+void GlobalSharedMemory::SharedMemoryCopy(void *dest,const void *src,size_t bytes)
+{
+#ifdef GRID_NVCC
+  cudaMemcpy(dest,src,bytes,cudaMemcpyDefault);
+#else   
+  bcopy(src,dest,bytes);
+#endif
+}
+////////////////////////////////////////////////////////
+// Global shared functionality finished
+// Now move to per communicator functionality
+////////////////////////////////////////////////////////
+void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
+{
+  int rank, size;
+  MPI_Comm_rank(comm,&rank);
+  MPI_Comm_size(comm,&size);
+  ShmRanks.resize(size);
+
+  /////////////////////////////////////////////////////////////////////
+  // Split into groups that can share memory
+  /////////////////////////////////////////////////////////////////////
+  MPI_Comm_split_type(comm, MPI_COMM_TYPE_SHARED, 0, MPI_INFO_NULL,&ShmComm);
+  MPI_Comm_rank(ShmComm     ,&ShmRank);
+  MPI_Comm_size(ShmComm     ,&ShmSize);
+  ShmCommBufs.resize(ShmSize);
+
+  //////////////////////////////////////////////////////////////////////
+  // Map ShmRank to WorldShmRank and use the right buffer
+  //////////////////////////////////////////////////////////////////////
+  assert (GlobalSharedMemory::ShmAlloc()==1);
+  heap_size = GlobalSharedMemory::ShmAllocBytes();
+  for(int r=0;r<ShmSize;r++){
+
+    uint32_t wsr = (r==ShmRank) ? GlobalSharedMemory::WorldShmRank : 0 ;
+
+    MPI_Allreduce(MPI_IN_PLACE,&wsr,1,MPI_UINT32_T,MPI_SUM,ShmComm);
+
+    ShmCommBufs[r] = GlobalSharedMemory::WorldShmCommBufs[wsr];
+  }
+  ShmBufferFreeAll();
+
+  /////////////////////////////////////////////////////////////////////
+  // find comm ranks in our SHM group (i.e. which ranks are on our node)
+  /////////////////////////////////////////////////////////////////////
+  MPI_Group FullGroup, ShmGroup;
+  MPI_Comm_group (comm   , &FullGroup); 
+  MPI_Comm_group (ShmComm, &ShmGroup);
+
+  std::vector<int> ranks(size);   for(int r=0;r<size;r++) ranks[r]=r;
+  MPI_Group_translate_ranks (FullGroup,size,&ranks[0],ShmGroup, &ShmRanks[0]); 
+
+  SharedMemoryTest();
+}
+//////////////////////////////////////////////////////////////////
+// On node barrier
+//////////////////////////////////////////////////////////////////
+void SharedMemory::ShmBarrier(void)
+{
+  MPI_Barrier  (ShmComm);
+}
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Test the shared memory is working
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+void SharedMemory::SharedMemoryTest(void)
+{
+  ShmBarrier();
+  uint64_t check[3];
+  uint64_t magic = 0x5A5A5A;
+  if ( ShmRank == 0 ) {
+    for(uint64_t r=0;r<ShmSize;r++){
+       check[0]=GlobalSharedMemory::WorldNode;
+       check[1]=r;
+       check[2]=magic;
+       GlobalSharedMemory::SharedMemoryCopy( ShmCommBufs[r], check, 3*sizeof(uint64_t));
+    }
+  }
+  ShmBarrier();
+  for(uint64_t r=0;r<ShmSize;r++){
+    ShmBarrier();
+    GlobalSharedMemory::SharedMemoryCopy(check,ShmCommBufs[r], 3*sizeof(uint64_t));
+    ShmBarrier();
+    assert(check[0]==GlobalSharedMemory::WorldNode);
+    assert(check[1]==r);
+    assert(check[2]==magic);
+    ShmBarrier();
+  }
+}
+
+void *SharedMemory::ShmBuffer(int rank)
+{
+  int gpeer = ShmRanks[rank];
+  if (gpeer == MPI_UNDEFINED){
+    return NULL;
+  } else { 
+    return ShmCommBufs[gpeer];
+  }
+}
+void *SharedMemory::ShmBufferTranslate(int rank,void * local_p)
+{
+  int gpeer = ShmRanks[rank];
+  assert(gpeer!=ShmRank); // never send to self
+  if (gpeer == MPI_UNDEFINED){
+    return NULL;
+  } else { 
+    uint64_t offset = (uint64_t)local_p - (uint64_t)ShmCommBufs[ShmRank];
+    uint64_t remote = (uint64_t)ShmCommBufs[gpeer]+offset;
+    return (void *) remote;
+  }
+}
+SharedMemory::~SharedMemory()
+{
+  int MPI_is_finalised;  MPI_Finalized(&MPI_is_finalised);
+  if ( !MPI_is_finalised ) { 
+    MPI_Comm_free(&ShmComm);
+  }
+};
+
+NAMESPACE_END(Grid); 
+

Grid/communicator/SharedMemoryNone.cc

@@ -0,0 +1,129 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/communicator/SharedMemory.cc
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+
+NAMESPACE_BEGIN(Grid); 
+
+/*Construct from an MPI communicator*/
+void GlobalSharedMemory::Init(Grid_MPI_Comm comm)
+{
+  assert(_ShmSetup==0);
+  WorldComm = 0;
+  WorldRank = 0;
+  WorldSize = 1;
+  WorldShmComm = 0 ;
+  WorldShmRank = 0 ;
+  WorldShmSize = 1 ;
+  WorldNodes   = 1 ;
+  WorldNode    = 0 ;
+  WorldShmRanks.resize(WorldSize); WorldShmRanks[0] = 0;
+  WorldShmCommBufs.resize(1);
+  _ShmSetup=1;
+}
+
+void GlobalSharedMemory::OptimalCommunicator(const Coordinate &processors,Grid_MPI_Comm & optimal_comm)
+{
+  optimal_comm = WorldComm;
+}
+
+////////////////////////////////////////////////////////////////////////////////////////////
+// Hugetlbfs mapping intended, use anonymous mmap
+////////////////////////////////////////////////////////////////////////////////////////////
+void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
+{
+  void * ShmCommBuf ; 
+  assert(_ShmSetup==1);
+  assert(_ShmAlloc==0);
+  int mmap_flag =0;
+#ifdef MAP_ANONYMOUS
+  mmap_flag = mmap_flag| MAP_SHARED | MAP_ANONYMOUS;
+#endif
+#ifdef MAP_ANON
+  mmap_flag = mmap_flag| MAP_SHARED | MAP_ANON;
+#endif
+#ifdef MAP_HUGETLB
+  if ( flags ) mmap_flag |= MAP_HUGETLB;
+#endif
+  ShmCommBuf =(void *) mmap(NULL, bytes, PROT_READ | PROT_WRITE, mmap_flag, -1, 0); 
+  if (ShmCommBuf == (void *)MAP_FAILED) {
+    perror("mmap failed ");
+    exit(EXIT_FAILURE);  
+  }
+#ifdef MADV_HUGEPAGE
+  if (!Hugepages ) madvise(ShmCommBuf,bytes,MADV_HUGEPAGE);
+#endif
+  bzero(ShmCommBuf,bytes);
+  WorldShmCommBufs[0] = ShmCommBuf;
+  _ShmAllocBytes=bytes;
+  _ShmAlloc=1;
+};
+
+////////////////////////////////////////////////////////
+// Global shared functionality finished
+// Now move to per communicator functionality
+////////////////////////////////////////////////////////
+void SharedMemory::SetCommunicator(Grid_MPI_Comm comm)
+{
+  assert(GlobalSharedMemory::ShmAlloc()==1);
+  ShmRanks.resize(1);
+  ShmCommBufs.resize(1);
+  ShmRanks[0] = 0;
+  ShmRank     = 0;
+  ShmSize     = 1;
+  //////////////////////////////////////////////////////////////////////
+  // Map ShmRank to WorldShmRank and use the right buffer
+  //////////////////////////////////////////////////////////////////////
+  ShmCommBufs[0] = GlobalSharedMemory::WorldShmCommBufs[0];
+  heap_size      = GlobalSharedMemory::ShmAllocBytes();
+  ShmBufferFreeAll();
+  return;
+}
+//////////////////////////////////////////////////////////////////
+// On node barrier
+//////////////////////////////////////////////////////////////////
+void SharedMemory::ShmBarrier(void){ return ; }
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Test the shared memory is working
+//////////////////////////////////////////////////////////////////////////////////////////////////////////
+void SharedMemory::SharedMemoryTest(void) { return; }
+
+void *SharedMemory::ShmBuffer(int rank)
+{
+  return NULL;
+}
+void *SharedMemory::ShmBufferTranslate(int rank,void * local_p)
+{
+  return NULL;
+}
+SharedMemory::~SharedMemory()
+{};
+
+NAMESPACE_END(Grid); 
+

Grid/cshift/Cshift.h

@@ -0,0 +1,52 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Cshift.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_CSHIFT_H_
+#define _GRID_CSHIFT_H_
+
+#include <Grid/cshift/Cshift_common.h>
+
+#ifdef GRID_COMMS_NONE
+#include <Grid/cshift/Cshift_none.h>
+#endif
+
+#ifdef GRID_COMMS_MPI
+#include <Grid/cshift/Cshift_mpi.h>
+#endif 
+
+#ifdef GRID_COMMS_MPI3
+#include <Grid/cshift/Cshift_mpi.h>
+#endif 
+
+#ifdef GRID_COMMS_MPIT
+#include <Grid/cshift/Cshift_mpi.h>
+#endif 
+
+#ifdef GRID_COMMS_SHMEM
+#include <Grid/cshift/Cshift_mpi.h> // uses same implementation of communicator
+#endif 
+#endif

Grid/cshift/Cshift_common.h

@@ -0,0 +1,400 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cshift/Cshift_common.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////////////////
+// Gather for when there is no need to SIMD split 
+///////////////////////////////////////////////////////////////////
+template<class vobj> void 
+Gather_plane_simple (const Lattice<vobj> &rhs,commVector<vobj> &buffer,int dimension,int plane,int cbmask, int off=0)
+{
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask = 0x3;
+  }
+  
+  int so=plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int ent = 0;
+
+  static Vector<std::pair<int,int> > table; table.resize(e1*e2);
+  int stride=rhs.Grid()->_slice_stride[dimension];
+
+  auto rhs_v = rhs.View();
+  if ( cbmask == 0x3 ) { 
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int o  = n*stride;
+	int bo = n*e2;
+	table[ent++] = std::pair<int,int>(off+bo+b,so+o+b);
+      }
+    }
+  } else { 
+     int bo=0;
+     for(int n=0;n<e1;n++){
+       for(int b=0;b<e2;b++){
+	 int o  = n*stride;
+	 int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);
+	 if ( ocb &cbmask ) {
+	   table[ent++]=std::pair<int,int> (off+bo++,so+o+b);
+	 }
+       }
+     }
+  }
+  thread_loop( (int i=0;i<ent;i++),{
+    buffer[table[i].first]=rhs_v[table[i].second];
+  });
+}
+
+///////////////////////////////////////////////////////////////////
+// Gather for when there *is* need to SIMD split 
+///////////////////////////////////////////////////////////////////
+template<class vobj> void 
+Gather_plane_extract(const Lattice<vobj> &rhs,
+		     ExtractPointerArray<typename vobj::scalar_object> pointers,
+		     int dimension,int plane,int cbmask)
+{
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask = 0x3;
+  }
+
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int n1=rhs.Grid()->_slice_stride[dimension];
+
+  auto rhs_v = rhs.View();
+  if ( cbmask ==0x3){
+    thread_loop_collapse2( (int n=0;n<e1;n++), {
+      for(int b=0;b<e2;b++){
+
+	int o      =   n*n1;
+	int offset = b+n*e2;
+	
+	vobj temp =rhs_v[so+o+b];
+	extract<vobj>(temp,pointers,offset);
+      }
+    });
+  } else { 
+
+    // Case of SIMD split AND checker dim cannot currently be hit, except in 
+    // Test_cshift_red_black code.
+    std::cout << " Dense packed buffer WARNING " <<std::endl;
+    thread_loop_collapse2( (int n=0;n<e1;n++),{
+      for(int b=0;b<e2;b++){
+
+	int o=n*n1;
+	int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);
+	int offset = b+n*e2;
+
+	if ( ocb & cbmask ) {
+	  vobj temp =rhs_v[so+o+b];
+	  extract<vobj>(temp,pointers,offset);
+	}
+      }
+    });
+  }
+}
+
+//////////////////////////////////////////////////////
+// Scatter for when there is no need to SIMD split
+//////////////////////////////////////////////////////
+template<class vobj> void Scatter_plane_simple (Lattice<vobj> &rhs,commVector<vobj> &buffer, int dimension,int plane,int cbmask)
+{
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask=0x3;
+  }
+
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+    
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int stride=rhs.Grid()->_slice_stride[dimension];
+
+  static std::vector<std::pair<int,int> > table; table.resize(e1*e2);
+  int ent    =0;
+
+  if ( cbmask ==0x3 ) {
+
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int o   =n*rhs.Grid()->_slice_stride[dimension];
+	int bo  =n*rhs.Grid()->_slice_block[dimension];
+	table[ent++] = std::pair<int,int>(so+o+b,bo+b);
+      }
+    }
+
+  } else { 
+    int bo=0;
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int o   =n*rhs.Grid()->_slice_stride[dimension];
+	int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);// Could easily be a table lookup
+	if ( ocb & cbmask ) {
+	  table[ent++]=std::pair<int,int> (so+o+b,bo++);
+	}
+      }
+    }
+  }
+  
+  auto rhs_v = rhs.View();
+  thread_loop( (int i=0;i<ent;i++), {
+    rhs_v[table[i].first]=buffer[table[i].second];
+  });
+}
+
+//////////////////////////////////////////////////////
+// Scatter for when there *is* need to SIMD split
+//////////////////////////////////////////////////////
+template<class vobj> void Scatter_plane_merge(Lattice<vobj> &rhs,ExtractPointerArray<typename vobj::scalar_object> pointers,int dimension,int plane,int cbmask)
+{
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask=0x3;
+  }
+
+  int so  = plane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+    
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block[dimension];
+
+  if(cbmask ==0x3 ) {
+    auto rhs_v = rhs.View();
+    thread_loop_collapse2( (int n=0;n<e1;n++),{
+      for(int b=0;b<e2;b++){
+	int o      = n*rhs.Grid()->_slice_stride[dimension];
+	int offset = b+n*rhs.Grid()->_slice_block[dimension];
+	merge(rhs_v[so+o+b],pointers,offset);
+      }
+    });
+  } else { 
+
+    // Case of SIMD split AND checker dim cannot currently be hit, except in 
+    // Test_cshift_red_black code.
+    //    std::cout << "Scatter_plane merge assert(0); think this is buggy FIXME "<< std::endl;// think this is buggy FIXME
+    std::cout<<" Unthreaded warning -- buffer is not densely packed ??"<<std::endl;
+    auto rhs_v = rhs.View();
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int o      = n*rhs.Grid()->_slice_stride[dimension];
+	int offset = b+n*rhs.Grid()->_slice_block[dimension];
+	int ocb=1<<rhs.Grid()->CheckerBoardFromOindex(o+b);
+	if ( ocb&cbmask ) {
+	  merge(rhs_v[so+o+b],pointers,offset);
+	}
+      }
+    }
+  }
+}
+
+//////////////////////////////////////////////////////
+// local to node block strided copies
+//////////////////////////////////////////////////////
+template<class vobj> void Copy_plane(Lattice<vobj>& lhs,const Lattice<vobj> &rhs, int dimension,int lplane,int rplane,int cbmask)
+{
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask=0x3;
+  }
+
+  int ro  = rplane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int lo  = lplane*lhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+
+  int e1=rhs.Grid()->_slice_nblock[dimension]; // clearly loop invariant for icpc
+  int e2=rhs.Grid()->_slice_block[dimension];
+  int stride = rhs.Grid()->_slice_stride[dimension];
+  static std::vector<std::pair<int,int> > table; table.resize(e1*e2);
+  int ent=0;
+
+  if(cbmask == 0x3 ){
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+        int o =n*stride+b;
+	table[ent++] = std::pair<int,int>(lo+o,ro+o);
+      }
+    }
+  } else { 
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+        int o =n*stride+b;
+        int ocb=1<<lhs.Grid()->CheckerBoardFromOindex(o);
+        if ( ocb&cbmask ) {
+	  table[ent++] = std::pair<int,int>(lo+o,ro+o);
+	}
+      }
+    }
+  }
+
+  auto rhs_v = rhs.View();
+  auto lhs_v = lhs.View();
+  thread_loop( (int i=0;i<ent;i++),{
+    lhs_v[table[i].first]=rhs_v[table[i].second];
+  });
+
+}
+
+template<class vobj> void Copy_plane_permute(Lattice<vobj>& lhs,const Lattice<vobj> &rhs, int dimension,int lplane,int rplane,int cbmask,int permute_type)
+{
+ 
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  if ( !rhs.Grid()->CheckerBoarded(dimension) ) {
+    cbmask=0x3;
+  }
+
+  int ro  = rplane*rhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+  int lo  = lplane*lhs.Grid()->_ostride[dimension]; // base offset for start of plane 
+
+  int e1=rhs.Grid()->_slice_nblock[dimension];
+  int e2=rhs.Grid()->_slice_block [dimension];
+  int stride = rhs.Grid()->_slice_stride[dimension];
+
+  static std::vector<std::pair<int,int> > table;  table.resize(e1*e2);
+  int ent=0;
+
+  double t_tab,t_perm;
+  if ( cbmask == 0x3 ) {
+    for(int n=0;n<e1;n++){
+    for(int b=0;b<e2;b++){
+      int o  =n*stride;
+      table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+    }}
+  } else {
+    for(int n=0;n<e1;n++){
+    for(int b=0;b<e2;b++){
+      int o  =n*stride;
+      int ocb=1<<lhs.Grid()->CheckerBoardFromOindex(o+b);
+      if ( ocb&cbmask ) table[ent++] = std::pair<int,int>(lo+o+b,ro+o+b);
+    }}
+  }
+
+  auto rhs_v = rhs.View();
+  auto lhs_v = lhs.View();
+  thread_loop( (int i=0;i<ent;i++),{
+    permute(lhs_v[table[i].first],rhs_v[table[i].second],permute_type);
+  });
+}
+
+//////////////////////////////////////////////////////
+// Local to node Cshift
+//////////////////////////////////////////////////////
+template<class vobj> void Cshift_local(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
+
+  double t_local;
+  
+  if ( sshift[0] == sshift[1] ) {
+    Cshift_local(ret,rhs,dimension,shift,0x3);
+  } else {
+    Cshift_local(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_local(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+
+template<class vobj> void Cshift_local(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  GridBase *grid = rhs.Grid();
+  int fd = grid->_fdimensions[dimension];
+  int rd = grid->_rdimensions[dimension];
+  int ld = grid->_ldimensions[dimension];
+  int gd = grid->_gdimensions[dimension];
+  int ly = grid->_simd_layout[dimension];
+
+  // Map to always positive shift modulo global full dimension.
+  shift = (shift+fd)%fd;
+
+  // the permute type
+  ret.Checkerboard() = grid->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
+  int permute_dim =grid->PermuteDim(dimension);
+  int permute_type=grid->PermuteType(dimension);
+  int permute_type_dist;
+
+  for(int x=0;x<rd;x++){       
+
+    int o   = 0;
+    int bo  = x * grid->_ostride[dimension];
+    int cb= (cbmask==0x2)? Odd : Even;
+
+    int sshift = grid->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+    int sx     = (x+sshift)%rd;
+    
+    // wrap is whether sshift > rd.
+    //  num is sshift mod rd.
+    // 
+    //  shift 7
+    //
+    //  XoXo YcYc 
+    //  oXoX cYcY
+    //  XoXo YcYc
+    //  oXoX cYcY
+    //
+    //  sshift -- 
+    //
+    //  XX YY ; 3
+    //  XX YY ; 0
+    //  XX YY ; 3
+    //  XX YY ; 0
+    //
+    int permute_slice=0;
+    if(permute_dim){
+      int wrap = sshift/rd; wrap=wrap % ly;
+      int  num = sshift%rd;
+
+      if ( x< rd-num ) permute_slice=wrap;
+      else permute_slice = (wrap+1)%ly;
+
+      if ( (ly>2) && (permute_slice) ) {
+	assert(permute_type & RotateBit);
+	permute_type_dist = permute_type|permute_slice;
+      } else {
+	permute_type_dist = permute_type;
+      }
+    }
+
+    if ( permute_slice ) Copy_plane_permute(ret,rhs,dimension,x,sx,cbmask,permute_type_dist);
+    else                 Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+  
+  }
+}
+NAMESPACE_END(Grid);
+

Grid/cshift/Cshift_mpi.h

@@ -0,0 +1,264 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cshift/Cshift_mpi.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_CSHIFT_MPI_H_
+#define _GRID_CSHIFT_MPI_H_
+
+
+NAMESPACE_BEGIN(Grid); 
+
+template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  Lattice<vobj> ret(rhs.Grid()); 
+  
+  int fd = rhs.Grid()->_fdimensions[dimension];
+  int rd = rhs.Grid()->_rdimensions[dimension];
+
+  // Map to always positive shift modulo global full dimension.
+  shift = (shift+fd)%fd;
+
+  ret.Checkerboard() = rhs.Grid()->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
+        
+  // the permute type
+  int simd_layout     = rhs.Grid()->_simd_layout[dimension];
+  int comm_dim        = rhs.Grid()->_processors[dimension] >1 ;
+  int splice_dim      = rhs.Grid()->_simd_layout[dimension]>1 && (comm_dim);
+
+
+  if ( !comm_dim ) {
+    //std::cout << "CSHIFT: Cshift_local" <<std::endl;
+    Cshift_local(ret,rhs,dimension,shift); // Handles checkerboarding
+  } else if ( splice_dim ) {
+    //std::cout << "CSHIFT: Cshift_comms_simd call - splice_dim = " << splice_dim << " shift " << shift << " dimension = " << dimension << std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift);
+  } else {
+    //std::cout << "CSHIFT: Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift);
+  }
+  return ret;
+}
+
+template<class vobj> void Cshift_comms(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
+
+  //  std::cout << "Cshift_comms dim "<<dimension<<"cb "<<rhs.Checkerboard()<<"shift "<<shift<<" sshift " << sshift[0]<<" "<<sshift[1]<<std::endl;
+  if ( sshift[0] == sshift[1] ) {
+    //    std::cout << "Single pass Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift,0x3);
+  } else {
+    //    std::cout << "Two pass Cshift_comms" <<std::endl;
+    Cshift_comms(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_comms(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+
+template<class vobj> void Cshift_comms_simd(Lattice<vobj>& ret,const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  int sshift[2];
+
+  sshift[0] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Even);
+  sshift[1] = rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,Odd);
+
+  //std::cout << "Cshift_comms_simd dim "<<dimension<<"cb "<<rhs.checkerboard<<"shift "<<shift<<" sshift " << sshift[0]<<" "<<sshift[1]<<std::endl;
+  if ( sshift[0] == sshift[1] ) {
+    //std::cout << "Single pass Cshift_comms" <<std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x3);
+  } else {
+    //std::cout << "Two pass Cshift_comms" <<std::endl;
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x1);// if checkerboard is unfavourable take two passes
+    Cshift_comms_simd(ret,rhs,dimension,shift,0x2);// both with block stride loop iteration
+  }
+}
+
+template<class vobj> void Cshift_comms(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_type scalar_type;
+
+  GridBase *grid=rhs.Grid();
+  Lattice<vobj> temp(rhs.Grid());
+
+  int fd              = rhs.Grid()->_fdimensions[dimension];
+  int rd              = rhs.Grid()->_rdimensions[dimension];
+  int pd              = rhs.Grid()->_processors[dimension];
+  int simd_layout     = rhs.Grid()->_simd_layout[dimension];
+  int comm_dim        = rhs.Grid()->_processors[dimension] >1 ;
+  assert(simd_layout==1);
+  assert(comm_dim==1);
+  assert(shift>=0);
+  assert(shift<fd);
+  
+  int buffer_size = rhs.Grid()->_slice_nblock[dimension]*rhs.Grid()->_slice_block[dimension];
+  commVector<vobj> send_buf(buffer_size);
+  commVector<vobj> recv_buf(buffer_size);
+
+  int cb= (cbmask==0x2)? Odd : Even;
+  int sshift= rhs.Grid()->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+
+  for(int x=0;x<rd;x++){       
+
+    int sx        =  (x+sshift)%rd;
+    int comm_proc = ((x+sshift)/rd)%pd;
+    
+    if (comm_proc==0) {
+
+      Copy_plane(ret,rhs,dimension,x,sx,cbmask); 
+
+    } else {
+
+      int words = send_buf.size();
+      if (cbmask != 0x3) words=words>>1;
+
+      int bytes = words * sizeof(vobj);
+
+      Gather_plane_simple (rhs,send_buf,dimension,sx,cbmask);
+
+      //      int rank           = grid->_processor;
+      int recv_from_rank;
+      int xmit_to_rank;
+      grid->ShiftedRanks(dimension,comm_proc,xmit_to_rank,recv_from_rank);
+
+
+      grid->SendToRecvFrom((void *)&send_buf[0],
+			   xmit_to_rank,
+			   (void *)&recv_buf[0],
+			   recv_from_rank,
+			   bytes);
+      grid->Barrier();
+
+      Scatter_plane_simple (ret,recv_buf,dimension,x,cbmask);
+    }
+  }
+}
+
+template<class vobj> void  Cshift_comms_simd(Lattice<vobj> &ret,const Lattice<vobj> &rhs,int dimension,int shift,int cbmask)
+{
+  GridBase *grid=rhs.Grid();
+  const int Nsimd = grid->Nsimd();
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+   
+  int fd = grid->_fdimensions[dimension];
+  int rd = grid->_rdimensions[dimension];
+  int ld = grid->_ldimensions[dimension];
+  int pd = grid->_processors[dimension];
+  int simd_layout     = grid->_simd_layout[dimension];
+  int comm_dim        = grid->_processors[dimension] >1 ;
+
+  //std::cout << "Cshift_comms_simd dim "<< dimension << " fd "<<fd<<" rd "<<rd
+  //    << " ld "<<ld<<" pd " << pd<<" simd_layout "<<simd_layout 
+  //    << " comm_dim " << comm_dim << " cbmask " << cbmask <<std::endl;
+
+  assert(comm_dim==1);
+  assert(simd_layout==2);
+  assert(shift>=0);
+  assert(shift<fd);
+
+  int permute_type=grid->PermuteType(dimension);
+
+  ///////////////////////////////////////////////
+  // Simd direction uses an extract/merge pair
+  ///////////////////////////////////////////////
+  int buffer_size = grid->_slice_nblock[dimension]*grid->_slice_block[dimension];
+  //  int words = sizeof(vobj)/sizeof(vector_type);
+
+  std::vector<commVector<scalar_object> >   send_buf_extract(Nsimd,commVector<scalar_object>(buffer_size) );
+  std::vector<commVector<scalar_object> >   recv_buf_extract(Nsimd,commVector<scalar_object>(buffer_size) );
+
+  int bytes = buffer_size*sizeof(scalar_object);
+
+  ExtractPointerArray<scalar_object>  pointers(Nsimd); // 
+  ExtractPointerArray<scalar_object> rpointers(Nsimd); // received pointers
+
+  ///////////////////////////////////////////
+  // Work out what to send where
+  ///////////////////////////////////////////
+  int cb    = (cbmask==0x2)? Odd : Even;
+  int sshift= grid->CheckerBoardShiftForCB(rhs.Checkerboard(),dimension,shift,cb);
+
+  // loop over outer coord planes orthog to dim
+  for(int x=0;x<rd;x++){       
+
+    // FIXME call local permute copy if none are offnode.
+    for(int i=0;i<Nsimd;i++){       
+      pointers[i] = &send_buf_extract[i][0];
+    }
+    int sx   = (x+sshift)%rd;
+    Gather_plane_extract(rhs,pointers,dimension,sx,cbmask);
+
+    for(int i=0;i<Nsimd;i++){
+      
+      int inner_bit = (Nsimd>>(permute_type+1));
+      int ic= (i&inner_bit)? 1:0;
+
+      int my_coor          = rd*ic + x;
+      int nbr_coor         = my_coor+sshift;
+      int nbr_proc = ((nbr_coor)/ld) % pd;// relative shift in processors
+
+      int nbr_ic   = (nbr_coor%ld)/rd;    // inner coord of peer
+      int nbr_ox   = (nbr_coor%rd);       // outer coord of peer
+      int nbr_lane = (i&(~inner_bit));
+
+      int recv_from_rank;
+      int xmit_to_rank;
+
+      if (nbr_ic) nbr_lane|=inner_bit;
+
+      assert (sx == nbr_ox);
+
+      if(nbr_proc){
+	grid->ShiftedRanks(dimension,nbr_proc,xmit_to_rank,recv_from_rank); 
+
+	grid->SendToRecvFrom((void *)&send_buf_extract[nbr_lane][0],
+			     xmit_to_rank,
+			     (void *)&recv_buf_extract[i][0],
+			     recv_from_rank,
+			     bytes);
+	grid->Barrier();
+	rpointers[i] = &recv_buf_extract[i][0];
+      } else { 
+	rpointers[i] = &send_buf_extract[nbr_lane][0];
+      }
+
+    }
+    Scatter_plane_merge(ret,rpointers,dimension,x,cbmask);
+  }
+
+}
+
+NAMESPACE_END(Grid); 
+
+#endif

Grid/cshift/Cshift_none.h

@@ -0,0 +1,40 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/cshift/Cshift_none.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef _GRID_CSHIFT_NONE_H_
+#define _GRID_CSHIFT_NONE_H_
+NAMESPACE_BEGIN(Grid);
+template<class vobj> Lattice<vobj> Cshift(const Lattice<vobj> &rhs,int dimension,int shift)
+{
+  Lattice<vobj> ret(rhs.Grid());
+  ret.Checkerboard() = rhs.Grid()->CheckerBoardDestination(rhs.Checkerboard(),shift,dimension);
+  Cshift_local(ret,rhs,dimension,shift);
+  return ret;
+}
+NAMESPACE_END(Grid);
+
+#endif

Grid/lattice/Lattice.h

@@ -0,0 +1,46 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Lattice.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#pragma once
+#include <Grid/lattice/Lattice_base.h>
+#include <Grid/lattice/Lattice_conformable.h>
+#include <Grid/lattice/Lattice_ET.h>
+#include <Grid/lattice/Lattice_arith.h>
+#include <Grid/lattice/Lattice_trace.h>
+#include <Grid/lattice/Lattice_transpose.h>
+#include <Grid/lattice/Lattice_local.h>
+#include <Grid/lattice/Lattice_reduction.h>
+#include <Grid/lattice/Lattice_peekpoke.h>
+#include <Grid/lattice/Lattice_reality.h>
+#include <Grid/lattice/Lattice_comparison_utils.h>
+#include <Grid/lattice/Lattice_comparison.h>
+#include <Grid/lattice/Lattice_coordinate.h>
+//#include <Grid/lattice/Lattice_where.h>
+#include <Grid/lattice/Lattice_rng.h>
+#include <Grid/lattice/Lattice_unary.h>
+#include <Grid/lattice/Lattice_transfer.h>
+

Grid/lattice/Lattice_ET.h

@@ -0,0 +1,407 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/lattice/Lattice_ET.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#ifndef GRID_LATTICE_ET_H
+#define GRID_LATTICE_ET_H
+
+#include <iostream>
+#include <tuple>
+#include <typeinfo>
+#include <vector>
+
+NAMESPACE_BEGIN(Grid);
+
+////////////////////////////////////////////////////
+// Predicated where support
+////////////////////////////////////////////////////
+template <class iobj, class vobj, class robj>
+accelerator_inline vobj predicatedWhere(const iobj &predicate, const vobj &iftrue,
+                            const robj &iffalse) {
+  typename std::remove_const<vobj>::type ret;
+
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  const int Nsimd = vobj::vector_type::Nsimd();
+
+  ExtractBuffer<Integer> mask(Nsimd);
+  ExtractBuffer<scalar_object> truevals(Nsimd);
+  ExtractBuffer<scalar_object> falsevals(Nsimd);
+
+  extract(iftrue, truevals);
+  extract(iffalse, falsevals);
+  extract<vInteger, Integer>(TensorRemove(predicate), mask);
+
+  for (int s = 0; s < Nsimd; s++) {
+    if (mask[s]) falsevals[s] = truevals[s];
+  }
+
+  merge(ret, falsevals);
+  return ret;
+}
+
+/////////////////////////////////////////////////////
+//Specialization of getVectorType for lattices
+/////////////////////////////////////////////////////
+template<typename T>
+struct getVectorType<Lattice<T> >{
+  typedef typename Lattice<T>::vector_object type;
+};
+
+////////////////////////////////////////////
+//--  recursive evaluation of expressions; --
+// handle leaves of syntax tree
+///////////////////////////////////////////////////
+template<class sobj> accelerator_inline 
+sobj eval(const uint64_t ss, const sobj &arg)
+{
+  return arg;
+}
+
+template <class lobj> accelerator_inline 
+const lobj & eval(const uint64_t ss, const LatticeView<lobj> &arg) 
+{
+  return arg[ss];
+}
+template <class lobj> accelerator_inline 
+const lobj & eval(const uint64_t ss, const Lattice<lobj> &arg) 
+{
+  auto view = arg.View();
+  return view[ss];
+}
+
+///////////////////////////////////////////////////
+// handle nodes in syntax tree- eval one operand
+///////////////////////////////////////////////////
+template <typename Op, typename T1> accelerator_inline 
+auto eval(const uint64_t ss, const LatticeUnaryExpression<Op, T1> &expr)  
+  -> decltype(expr.op.func( eval(ss, expr.arg1)))
+{
+  return expr.op.func( eval(ss, expr.arg1) );
+}
+///////////////////////
+// eval two operands
+///////////////////////
+template <typename Op, typename T1, typename T2> accelerator_inline
+auto eval(const uint64_t ss, const LatticeBinaryExpression<Op, T1, T2> &expr)  
+  -> decltype(expr.op.func( eval(ss,expr.arg1),eval(ss,expr.arg2)))
+{
+  return expr.op.func( eval(ss,expr.arg1), eval(ss,expr.arg2) );
+}
+///////////////////////
+// eval three operands
+///////////////////////
+template <typename Op, typename T1, typename T2, typename T3> accelerator_inline
+auto eval(const uint64_t ss, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr)  
+  -> decltype(expr.op.func(eval(ss, expr.arg1), eval(ss, expr.arg2), eval(ss, expr.arg3)))
+{
+  return expr.op.func(eval(ss, expr.arg1), eval(ss, expr.arg2), eval(ss, expr.arg3));
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Obtain the grid from an expression, ensuring conformable. This must follow a
+// tree recursion; must retain grid pointer in the LatticeView class which sucks
+// Use a different method, and make it void *.
+// Perhaps a conformable method.
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+accelerator_inline void GridFromExpression(GridBase *&grid, const T1 &lat)  // Lattice leaf
+{
+  lat.Conformable(grid);
+}
+
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid,const T1 &notlat)  // non-lattice leaf
+{}
+
+template <typename Op, typename T1>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid,const LatticeUnaryExpression<Op, T1> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+}
+
+template <typename Op, typename T1, typename T2>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid, const LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+  GridFromExpression(grid, expr.arg2);
+}
+template <typename Op, typename T1, typename T2, typename T3>
+accelerator_inline 
+void GridFromExpression(GridBase *&grid, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  GridFromExpression(grid, expr.arg1);  // recurse
+  GridFromExpression(grid, expr.arg2);  // recurse
+  GridFromExpression(grid, expr.arg3);  // recurse
+}
+
+//////////////////////////////////////////////////////////////////////////
+// Obtain the CB from an expression, ensuring conformable. This must follow a
+// tree recursion
+//////////////////////////////////////////////////////////////////////////
+template <class T1,typename std::enable_if<is_lattice<T1>::value, T1>::type * = nullptr>
+inline void CBFromExpression(int &cb, const T1 &lat)  // Lattice leaf
+{
+  if ((cb == Odd) || (cb == Even)) {
+    assert(cb == lat.Checkerboard());
+  }
+  cb = lat.Checkerboard();
+}
+template <class T1,typename std::enable_if<!is_lattice<T1>::value, T1>::type * = nullptr>
+inline void CBFromExpression(int &cb, const T1 &notlat)  // non-lattice leaf
+{
+}
+
+template <typename Op, typename T1> inline 
+void CBFromExpression(int &cb,const LatticeUnaryExpression<Op, T1> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+}
+
+template <typename Op, typename T1, typename T2> inline 
+void CBFromExpression(int &cb,const LatticeBinaryExpression<Op, T1, T2> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+  CBFromExpression(cb, expr.arg2);  // recurse AST
+}
+template <typename Op, typename T1, typename T2, typename T3>
+inline void CBFromExpression(int &cb, const LatticeTrinaryExpression<Op, T1, T2, T3> &expr) 
+{
+  CBFromExpression(cb, expr.arg1);  // recurse AST
+  CBFromExpression(cb, expr.arg2);  // recurse AST
+  CBFromExpression(cb, expr.arg3);  // recurse AST
+}
+
+////////////////////////////////////////////
+// Unary operators and funcs
+////////////////////////////////////////////
+#define GridUnopClass(name, ret)					\
+  template <class arg>							\
+  struct name {								\
+    static auto accelerator_inline func(const arg a) -> decltype(ret) { return ret; } \
+  };
+
+GridUnopClass(UnarySub, -a);
+GridUnopClass(UnaryNot, Not(a));
+GridUnopClass(UnaryAdj, adj(a));
+GridUnopClass(UnaryConj, conjugate(a));
+GridUnopClass(UnaryTrace, trace(a));
+GridUnopClass(UnaryTranspose, transpose(a));
+GridUnopClass(UnaryTa, Ta(a));
+GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
+GridUnopClass(UnaryReal, real(a));
+GridUnopClass(UnaryImag, imag(a));
+GridUnopClass(UnaryToReal, toReal(a));
+GridUnopClass(UnaryToComplex, toComplex(a));
+GridUnopClass(UnaryTimesI, timesI(a));
+GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
+GridUnopClass(UnaryAbs, abs(a));
+GridUnopClass(UnarySqrt, sqrt(a));
+GridUnopClass(UnaryRsqrt, rsqrt(a));
+GridUnopClass(UnarySin, sin(a));
+GridUnopClass(UnaryCos, cos(a));
+GridUnopClass(UnaryAsin, asin(a));
+GridUnopClass(UnaryAcos, acos(a));
+GridUnopClass(UnaryLog, log(a));
+GridUnopClass(UnaryExp, exp(a));
+
+////////////////////////////////////////////
+// Binary operators
+////////////////////////////////////////////
+#define GridBinOpClass(name, combination)			\
+  template <class left, class right>				\
+  struct name {							\
+    static auto accelerator_inline				\
+    func(const left &lhs, const right &rhs)			\
+      -> decltype(combination) const				\
+    {								\
+      return combination;					\
+    }								\
+  };
+
+GridBinOpClass(BinaryAdd, lhs + rhs);
+GridBinOpClass(BinarySub, lhs - rhs);
+GridBinOpClass(BinaryMul, lhs *rhs);
+GridBinOpClass(BinaryDiv, lhs /rhs);
+GridBinOpClass(BinaryAnd, lhs &rhs);
+GridBinOpClass(BinaryOr, lhs | rhs);
+GridBinOpClass(BinaryAndAnd, lhs &&rhs);
+GridBinOpClass(BinaryOrOr, lhs || rhs);
+
+////////////////////////////////////////////////////
+// Trinary conditional op
+////////////////////////////////////////////////////
+#define GridTrinOpClass(name, combination)				\
+  template <class predicate, class left, class right>			\
+  struct name {								\
+    static auto accelerator_inline					\
+    func(const predicate &pred, const left &lhs, const right &rhs)	\
+      -> decltype(combination) const					\
+    {									\
+      return combination;						\
+    }									\
+  };
+
+GridTrinOpClass(TrinaryWhere,
+		(predicatedWhere<predicate, 
+		 typename std::remove_reference<left>::type,
+		 typename std::remove_reference<right>::type>(pred, lhs,rhs)));
+
+////////////////////////////////////////////
+// Operator syntactical glue
+////////////////////////////////////////////
+
+#define GRID_UNOP(name)   name<decltype(eval(0, arg))>
+#define GRID_BINOP(name)  name<decltype(eval(0, lhs)), decltype(eval(0, rhs))>
+#define GRID_TRINOP(name) name<decltype(eval(0, pred)), decltype(eval(0, lhs)), decltype(eval(0, rhs))>
+
+#define GRID_DEF_UNOP(op, name)						\
+  template <typename T1, typename std::enable_if<is_lattice<T1>::value||is_lattice_expr<T1>::value,T1>::type * = nullptr> \
+  inline auto op(const T1 &arg) ->decltype(LatticeUnaryExpression<GRID_UNOP(name),T1>(GRID_UNOP(name)(), arg)) \
+  {									\
+    return     LatticeUnaryExpression<GRID_UNOP(name),T1>(GRID_UNOP(name)(), arg); \
+  }
+
+#define GRID_BINOP_LEFT(op, name)					\
+  template <typename T1, typename T2,					\
+            typename std::enable_if<is_lattice<T1>::value||is_lattice_expr<T1>::value,T1>::type * = nullptr> \
+  inline auto op(const T1 &lhs, const T2 &rhs)				\
+    ->decltype(LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs,rhs)) \
+  {									\
+    return     LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs,rhs);\
+  }
+
+#define GRID_BINOP_RIGHT(op, name)					\
+  template <typename T1, typename T2,					\
+            typename std::enable_if<!is_lattice<T1>::value&&!is_lattice_expr<T1>::value,T1>::type * = nullptr, \
+            typename std::enable_if< is_lattice<T2>::value|| is_lattice_expr<T2>::value,T2>::type * = nullptr> \
+  inline auto op(const T1 &lhs, const T2 &rhs)				\
+    ->decltype(LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs, rhs)) \
+  {									\
+    return     LatticeBinaryExpression<GRID_BINOP(name),T1,T2>(GRID_BINOP(name)(),lhs, rhs); \
+  }
+
+#define GRID_DEF_BINOP(op, name)		\
+  GRID_BINOP_LEFT(op, name);			\
+  GRID_BINOP_RIGHT(op, name);
+
+#define GRID_DEF_TRINOP(op, name)					\
+  template <typename T1, typename T2, typename T3>			\
+  inline auto op(const T1 &pred, const T2 &lhs, const T3 &rhs)		\
+    ->decltype(LatticeTrinaryExpression<GRID_TRINOP(name),T1,T2,T3>(GRID_TRINOP(name)(),pred, lhs, rhs)) \
+  {									\
+    return LatticeTrinaryExpression<GRID_TRINOP(name),T1,T2,T3>(GRID_TRINOP(name)(),pred, lhs, rhs); \
+  }
+
+////////////////////////
+// Operator definitions
+////////////////////////
+GRID_DEF_UNOP(operator-, UnarySub);
+GRID_DEF_UNOP(Not, UnaryNot);
+GRID_DEF_UNOP(operator!, UnaryNot);
+GRID_DEF_UNOP(adj, UnaryAdj);
+GRID_DEF_UNOP(conjugate, UnaryConj);
+GRID_DEF_UNOP(trace, UnaryTrace);
+GRID_DEF_UNOP(transpose, UnaryTranspose);
+GRID_DEF_UNOP(Ta, UnaryTa);
+GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
+GRID_DEF_UNOP(real, UnaryReal);
+GRID_DEF_UNOP(imag, UnaryImag);
+GRID_DEF_UNOP(toReal, UnaryToReal);
+GRID_DEF_UNOP(toComplex, UnaryToComplex);
+GRID_DEF_UNOP(timesI, UnaryTimesI);
+GRID_DEF_UNOP(timesMinusI, UnaryTimesMinusI);
+GRID_DEF_UNOP(abs, UnaryAbs);  // abs overloaded in cmath C++98; DON'T do the
+                               // abs-fabs-dabs-labs thing
+GRID_DEF_UNOP(sqrt, UnarySqrt);
+GRID_DEF_UNOP(rsqrt, UnaryRsqrt);
+GRID_DEF_UNOP(sin, UnarySin);
+GRID_DEF_UNOP(cos, UnaryCos);
+GRID_DEF_UNOP(asin, UnaryAsin);
+GRID_DEF_UNOP(acos, UnaryAcos);
+GRID_DEF_UNOP(log, UnaryLog);
+GRID_DEF_UNOP(exp, UnaryExp);
+
+GRID_DEF_BINOP(operator+, BinaryAdd);
+GRID_DEF_BINOP(operator-, BinarySub);
+GRID_DEF_BINOP(operator*, BinaryMul);
+GRID_DEF_BINOP(operator/, BinaryDiv);
+
+GRID_DEF_BINOP(operator&, BinaryAnd);
+GRID_DEF_BINOP(operator|, BinaryOr);
+GRID_DEF_BINOP(operator&&, BinaryAndAnd);
+GRID_DEF_BINOP(operator||, BinaryOrOr);
+
+GRID_DEF_TRINOP(where, TrinaryWhere);
+
+/////////////////////////////////////////////////////////////
+// Closure convenience to force expression to evaluate
+/////////////////////////////////////////////////////////////
+template <class Op, class T1>
+auto closure(const LatticeUnaryExpression<Op, T1> &expr)
+  -> Lattice<decltype(expr.op.func(eval(0, expr.arg1)))> 
+{
+  Lattice<decltype(expr.op.func(eval(0, expr.arg1)))> ret(expr);
+  return ret;
+}
+template <class Op, class T1, class T2>
+auto closure(const LatticeBinaryExpression<Op, T1, T2> &expr)
+  -> Lattice<decltype(expr.op.func(eval(0, expr.arg1),eval(0, expr.arg2)))> 
+{
+  Lattice<decltype(expr.op.func(eval(0, expr.arg1),eval(0, expr.arg2)))> ret(expr);
+  return ret;
+}
+template <class Op, class T1, class T2, class T3>
+auto closure(const LatticeTrinaryExpression<Op, T1, T2, T3> &expr)
+  -> Lattice<decltype(expr.op.func(eval(0, expr.arg1),
+				   eval(0, expr.arg2),
+				   eval(0, expr.arg3)))> 
+{
+  Lattice<decltype(expr.op.func(eval(0, expr.arg1),
+				eval(0, expr.arg2),
+				eval(0, expr.arg3)))>  ret(expr);
+  return ret;
+}
+
+#undef GRID_UNOP
+#undef GRID_BINOP
+#undef GRID_TRINOP
+
+#undef GRID_DEF_UNOP
+#undef GRID_DEF_BINOP
+#undef GRID_DEF_TRINOP
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/lattice/Lattice_arith.h

@@ -0,0 +1,314 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_arith.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_ARITH_H
+#define GRID_LATTICE_ARITH_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    mult(&tmp,&lhs_v[ss],&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,lhs_v,{
+    mult(&ret_v[ss],&lhs_v[ss],&rhs_v[ss]);
+  });
+#endif
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    mac(&tmp,&lhs_v[ss],&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,lhs_v,{
+    mac(&ret_v[ss],&lhs_v[ss],&rhs_v[ss]);
+  });
+#endif
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    sub(&tmp,&lhs_v[ss],&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,lhs_v,{
+    sub(&ret[ss],&lhs_v[ss],&rhs_v[ss]);
+  });
+#endif
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,rhs);
+  conformable(lhs,rhs);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    add(&tmp,&lhs_v[ss],&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,lhs_v,{
+    add(&ret_v[ss],&lhs_v[ss],&rhs_v[ss]);
+  });
+#endif
+}
+  
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(lhs,ret);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    mult(&tmp,&lhs_v[ss],&rhs);
+    vstream(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,lhs);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    mac(&tmp,&lhs_v[ss],&rhs);
+    vstream(ret_v[ss],tmp);
+  });
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(ret,lhs);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    sub(&tmp,&lhs_v[ss],&rhs);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,lhs_v,{
+    sub(&ret_v[ss],&lhs_v[ss],&rhs);
+  });
+#endif
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const Lattice<obj2> &lhs,const obj3 &rhs){
+  ret.Checkerboard() = lhs.Checkerboard();
+  conformable(lhs,ret);
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,lhs_v,{
+    obj1 tmp;
+    add(&tmp,&lhs_v[ss],&rhs);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,lhs_v,{
+    add(&ret_v[ss],&lhs_v[ss],&rhs);
+  });
+#endif
+}
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+//  avoid copy back routines for mult, mac, sub, add
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class obj1,class obj2,class obj3> inline
+void mult(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  auto ret_v = ret.View();
+  auto rhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,rhs_v,{
+    obj1 tmp;
+    mult(&tmp,&lhs,&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,rhs_v,{
+    mult(&ret_v[ss],&lhs,&rhs_v[ss]);
+  });
+#endif
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void mac(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  auto ret_v = ret.View();
+  auto rhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,rhs_v,{
+    obj1 tmp;
+    mac(&tmp,&lhs,&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,rhs_v,{
+    mac(&ret_v[ss],&lhs,&rhs_v[ss]);
+  });
+#endif
+}
+  
+template<class obj1,class obj2,class obj3> inline
+void sub(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  auto ret_v = ret.View();
+  auto rhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,rhs_v,{
+    obj1 tmp;
+    sub(&tmp,&lhs,&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,rhs_v,{
+    sub(&ret_v[ss],&lhs,&rhs_v[ss]);
+  });
+#endif
+}
+template<class obj1,class obj2,class obj3> inline
+void add(Lattice<obj1> &ret,const obj2 &lhs,const Lattice<obj3> &rhs){
+  ret.Checkerboard() = rhs.Checkerboard();
+  conformable(ret,rhs);
+  auto ret_v = ret.View();
+  auto rhs_v = lhs.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,rhs_v,{
+    obj1 tmp;
+    add(&tmp,&lhs,&rhs_v[ss]);
+    vstream(ret_v[ss],tmp);
+  });
+#else 
+  accelerator_loop(ss,rhs_v,{
+    add(&ret_v[ss],&lhs,&rhs_v[ss]);
+  });
+#endif
+}
+  
+template<class sobj,class vobj> inline
+void axpy(Lattice<vobj> &ret,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y){
+  ret.Checkerboard() = x.Checkerboard();
+  conformable(ret,x);
+  conformable(x,y);
+  auto ret_v = ret.View();
+  auto x_v = x.View();
+  auto y_v = y.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,x_v,{
+    vobj tmp = a*x_v[ss]+y_v[ss];
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,x_v,{
+    ret_v[ss]=a*x_v[ss]+y_v[ss];
+  });
+#endif
+}
+template<class sobj,class vobj> inline
+void axpby(Lattice<vobj> &ret,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y){
+  ret.Checkerboard() = x.Checkerboard();
+  conformable(ret,x);
+  conformable(x,y);
+  auto ret_v = ret.View();
+  auto x_v = x.View();
+  auto y_v = y.View();
+#ifdef STREAMING_STORES
+  accelerator_loop(ss,x_v,{
+    vobj tmp = a*x_v[ss]+b*y_v[ss];
+    vstream(ret_v[ss],tmp);
+  });
+#else
+  accelerator_loop(ss,x_v,{
+    ret_v[ss]=a*x_v[ss]+b*y_v[ss];
+  });
+#endif
+}
+
+template<class sobj,class vobj> inline
+RealD axpy_norm(Lattice<vobj> &ret,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y)
+{
+    return axpy_norm_fast(ret,a,x,y);
+}
+template<class sobj,class vobj> inline
+RealD axpby_norm(Lattice<vobj> &ret,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y)
+{
+    return axpby_norm_fast(ret,a,b,x,y);
+}
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_base.h

@@ -0,0 +1,488 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/lattice/Lattice_base.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#pragma once 
+
+#define STREAMING_STORES
+
+NAMESPACE_BEGIN(Grid);
+
+extern int GridCshiftPermuteMap[4][16];
+
+///////////////////////////////////////////////////////////////////
+// Base class which can be used by traits to pick up behaviour
+///////////////////////////////////////////////////////////////////
+class LatticeBase {};
+
+/////////////////////////////////////////////////////////////////////////////////////////
+// Conformable checks; same instance of Grid required
+/////////////////////////////////////////////////////////////////////////////////////////
+void accelerator_inline conformable(GridBase *lhs,GridBase *rhs)
+{
+  assert(lhs == rhs);
+}
+
+////////////////////////////////////////////////////////////////////////////
+// Minimal base class containing only data valid to access from accelerator
+// _odata will be a managed pointer in CUDA
+////////////////////////////////////////////////////////////////////////////
+// Force access to lattice through a view object.
+// prevents writing of code that will not offload to GPU, but perhaps annoyingly
+// strict since host could could in principle direct access through the lattice object
+// Need to decide programming model.
+#define LATTICE_VIEW_STRICT
+template<class vobj> class LatticeAccelerator : public LatticeBase
+{
+protected:
+  GridBase *_grid;
+  int checkerboard;
+  vobj     *_odata;    // A managed pointer
+  uint64_t _odata_size;    
+public:
+  accelerator_inline LatticeAccelerator() : checkerboard(0), _odata(nullptr), _odata_size(0), _grid(nullptr) { }; 
+  accelerator_inline uint64_t oSites(void) const { return _odata_size; };
+  accelerator_inline int  Checkerboard(void) const { return checkerboard; };
+  accelerator_inline int &Checkerboard(void) { return this->checkerboard; }; // can assign checkerboard on a container, not a view
+  accelerator_inline void Conformable(GridBase * &grid) const
+  { 
+    if (grid) conformable(grid, _grid);
+    else      grid = _grid;
+  };
+#ifndef LATTICE_VIEW_STRICT
+  accelerator_inline vobj       & operator[](size_t i)       { return this->_odata[i]; };
+  accelerator_inline const vobj & operator[](size_t i) const { return this->_odata[i]; };
+#endif
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////
+// A View class which provides accessor to the data.
+// This will be safe to call from accelerator_loops and is trivially copy constructible
+// The copy constructor for this will need to be used by device lambda functions
+/////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj> 
+class LatticeView : public LatticeAccelerator<vobj>
+{
+public:
+#ifdef LATTICE_VIEW_STRICT
+  accelerator_inline vobj       & operator[](size_t i)       { return this->_odata[i]; };
+  accelerator_inline const vobj & operator[](size_t i) const { return this->_odata[i]; };
+#endif
+  accelerator_inline uint64_t begin(void) const { return 0;};
+  accelerator_inline uint64_t end(void)   const { return this->_odata_size; };
+  accelerator_inline uint64_t size(void)  const { return this->_odata_size; };
+
+  LatticeView(const LatticeAccelerator<vobj> &refer_to_me) : LatticeAccelerator<vobj> (refer_to_me)
+  {
+  }
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////
+// Lattice expression types used by ET to assemble the AST
+// 
+// Need to be able to detect code paths according to the whether a lattice object or not
+// so introduce some trait type things
+/////////////////////////////////////////////////////////////////////////////////////////
+
+class LatticeExpressionBase {};
+
+template <typename T> using is_lattice = std::is_base_of<LatticeBase, T>;
+template <typename T> using is_lattice_expr = std::is_base_of<LatticeExpressionBase,T >;
+
+template<class T, bool isLattice> struct ViewMapBase { typedef T Type; };
+template<class T>                 struct ViewMapBase<T,true> { typedef LatticeView<typename T::vector_object> Type; };
+template<class T> using ViewMap = ViewMapBase<T,std::is_base_of<LatticeBase, T>::value >;
+
+template <typename Op, typename _T1>                           
+class LatticeUnaryExpression : public  LatticeExpressionBase 
+{
+public:
+  typedef typename ViewMap<_T1>::Type T1;
+  Op op;
+  T1 arg1;
+  LatticeUnaryExpression(Op _op,const _T1 &_arg1) : op(_op), arg1(_arg1) {};
+};
+
+template <typename Op, typename _T1, typename _T2>              
+class LatticeBinaryExpression : public LatticeExpressionBase 
+{
+public:
+  typedef typename ViewMap<_T1>::Type T1;
+  typedef typename ViewMap<_T2>::Type T2;
+  Op op;
+  T1 arg1;
+  T2 arg2;
+  LatticeBinaryExpression(Op _op,const _T1 &_arg1,const _T2 &_arg2) : op(_op), arg1(_arg1), arg2(_arg2) {};
+};
+
+template <typename Op, typename _T1, typename _T2, typename _T3> 
+class LatticeTrinaryExpression : public LatticeExpressionBase 
+{
+public:
+  typedef typename ViewMap<_T1>::Type T1;
+  typedef typename ViewMap<_T2>::Type T2;
+  typedef typename ViewMap<_T3>::Type T3;
+  Op op;
+  T1 arg1;
+  T2 arg2;
+  T3 arg3;
+  LatticeTrinaryExpression(Op _op,const _T1 &_arg1,const _T2 &_arg2,const _T3 &_arg3) : op(_op), arg1(_arg1), arg2(_arg2), arg3(_arg3) {};
+};
+
+/////////////////////////////////////////////////////////////////////////////////////////
+// The real lattice class, with normal copy and assignment semantics.
+// This contains extra (host resident) grid pointer data that may be accessed by host code
+/////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj>
+class Lattice : public LatticeAccelerator<vobj>
+{
+public:
+  GridBase *Grid(void) const { return this->_grid; }
+  ///////////////////////////////////////////////////
+  // Member types
+  ///////////////////////////////////////////////////
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  typedef vobj vector_object;
+
+private:
+  void dealloc(void)
+  {
+    alignedAllocator<vobj> alloc;
+    if( this->_odata_size ) {
+      alloc.deallocate(this->_odata,this->_odata_size);
+      this->_odata=nullptr;
+      this->_odata_size=0;
+    }
+  }
+  void resize(uint64_t size)
+  {
+    alignedAllocator<vobj> alloc;
+    if ( this->_odata_size != size ) {
+      dealloc();
+    }
+    this->_odata_size = size;
+    if ( size ) 
+      this->_odata      = alloc.allocate(this->_odata_size);
+    else 
+      this->_odata      = nullptr;
+  }
+#if 0
+  void copy_vec(vobj *ptr,uint64_t count)
+  {
+    dealloc();
+    this->_odata = ptr;
+    assert(this->_odata_size == count);
+  }
+#endif
+public:
+  /////////////////////////////////////////////////////////////////////////////////
+  // Return a view object that may be dereferenced in site loops.
+  // The view is trivially copy constructible and may be copied to an accelerator device
+  // in device lambdas
+  /////////////////////////////////////////////////////////////////////////////////
+  LatticeView<vobj> View (void) const 
+  {
+    LatticeView<vobj> accessor(*( (LatticeAccelerator<vobj> *) this));
+    return accessor;
+  }
+  
+  ~Lattice() { 
+    if ( this->_odata_size ) {
+      dealloc();
+    }
+   }
+  ////////////////////////////////////////////////////////////////////////////////
+  // Expression Template closure support
+  ////////////////////////////////////////////////////////////////////////////////
+  template <typename Op, typename T1> inline Lattice<vobj> & operator=(const LatticeUnaryExpression<Op,T1> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    auto me  = View();
+#ifdef STREAMING_STORES
+    accelerator_loop(ss,me,{
+      vobj tmp = eval(ss,expr);
+      vstream(me[ss] ,tmp);
+    });
+#else
+    accelerator_loop(ss,me,{
+      me[ss]=eval(ss,expr);
+    });
+#endif
+    return *this;
+  }
+  template <typename Op, typename T1,typename T2> inline Lattice<vobj> & operator=(const LatticeBinaryExpression<Op,T1,T2> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    auto me  = View();
+#ifdef STREAMING_STORES
+    accelerator_loop(ss,me,{
+      vobj tmp = eval(ss,expr);
+      vstream(me[ss] ,tmp);
+    });
+#else
+    accelerator_loop(ss,me,{
+      me[ss]=eval(ss,expr);
+    });
+#endif
+    return *this;
+  }
+  template <typename Op, typename T1,typename T2,typename T3> inline Lattice<vobj> & operator=(const LatticeTrinaryExpression<Op,T1,T2,T3> &expr)
+  {
+    GridBase *egrid(nullptr);
+    GridFromExpression(egrid,expr);
+    assert(egrid!=nullptr);
+    conformable(this->_grid,egrid);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+    auto me  = View();
+#ifdef STREAMING_STORES
+    accelerator_loop(ss,me,{
+      vobj tmp = eval(ss,expr);
+      vstream(me[ss] ,tmp);
+    });
+#else
+    accelerator_loop(ss,me,{
+      me[ss] = eval(ss,expr);
+    });
+#endif
+    return *this;
+  }
+  //GridFromExpression is tricky to do
+  template<class Op,class T1>
+  Lattice(const LatticeUnaryExpression<Op,T1> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+  template<class Op,class T1, class T2>
+  Lattice(const LatticeBinaryExpression<Op,T1,T2> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+  template<class Op,class T1, class T2, class T3>
+  Lattice(const LatticeTrinaryExpression<Op,T1,T2,T3> & expr) {
+    this->_grid = nullptr;
+    GridFromExpression(this->_grid,expr);
+    assert(this->_grid!=nullptr);
+
+    int cb=-1;
+    CBFromExpression(cb,expr);
+    assert( (cb==Odd) || (cb==Even));
+    this->checkerboard=cb;
+
+    resize(this->_grid->oSites());
+
+    *this = expr;
+  }
+
+  template<class sobj> inline Lattice<vobj> & operator = (const sobj & r){
+    auto me  = View();
+    accelerator_loop(ss,me,{
+      me[ss]=r;
+    });
+    return *this;
+  }
+
+  //////////////////////////////////////////////////////////////////
+  // Follow rule of five, with Constructor requires "grid" passed
+  // to user defined constructor
+  ///////////////////////////////////////////
+  // user defined constructor
+  ///////////////////////////////////////////
+  Lattice(GridBase *grid) { 
+    this->_grid = grid;
+    resize(this->_grid->oSites());
+    assert((((uint64_t)&this->_odata[0])&0xF) ==0);
+    this->checkerboard=0;
+  }
+  
+  //  virtual ~Lattice(void) = default;
+    
+  void reset(GridBase* grid) {
+    if (this->_grid != grid) {
+      this->_grid = grid;
+      this->_odata.resize(grid->oSites());
+      this->checkerboard = 0;
+    }
+  }
+  ///////////////////////////////////////////
+  // copy constructor
+  ///////////////////////////////////////////
+  Lattice(const Lattice& r){ 
+    //    std::cout << "Lattice constructor(const Lattice &) "<<this<<std::endl; 
+    this->_grid = r.Grid();
+    resize(this->_grid->oSites());
+    *this = r;
+  }
+  ///////////////////////////////////////////
+  // move constructor
+  ///////////////////////////////////////////
+  Lattice(Lattice && r){ 
+    this->_grid = r.Grid();
+    this->_odata      = r._odata;
+    this->_odata_size = r._odata_size;
+    this->checkerboard= r.Checkerboard();
+    r._odata      = nullptr;
+    r._odata_size = 0;
+  }
+  ///////////////////////////////////////////
+  // assignment template
+  ///////////////////////////////////////////
+  template<class robj> inline Lattice<vobj> & operator = (const Lattice<robj> & r){
+    typename std::enable_if<!std::is_same<robj,vobj>::value,int>::type i=0;
+    conformable(*this,r);
+    this->checkerboard = r.Checkerboard();
+    auto me =   View();
+    auto him= r.View();
+    accelerator_loop(ss,me,{
+      me[ss]=him[ss];
+    });
+    return *this;
+  }
+
+  ///////////////////////////////////////////
+  // Copy assignment 
+  ///////////////////////////////////////////
+  inline Lattice<vobj> & operator = (const Lattice<vobj> & r){
+    this->checkerboard = r.Checkerboard();
+    conformable(*this,r);
+    auto me =   View();
+    auto him= r.View();
+    accelerator_loop(ss,me,{
+      me[ss]=him[ss];
+    });
+    return *this;
+  }
+  ///////////////////////////////////////////
+  // Move assignment possible if same type
+  ///////////////////////////////////////////
+  inline Lattice<vobj> & operator = (Lattice<vobj> && r){
+
+    resize(0); // deletes if appropriate
+    this->_grid       = r.Grid();
+    this->_odata      = r._odata;
+    this->_odata_size = r._odata_size;
+    this->checkerboard= r.Checkerboard();
+
+    r._odata      = nullptr;
+    r._odata_size = 0;
+    
+    return *this;
+  }
+
+  /////////////////////////////////////////////////////////////////////////////
+  // *=,+=,-= operators inherit behvour from correspond */+/- operation
+  /////////////////////////////////////////////////////////////////////////////
+  template<class T> inline Lattice<vobj> &operator *=(const T &r) {
+    *this = (*this)*r;
+    return *this;
+  }
+  
+  template<class T> inline Lattice<vobj> &operator -=(const T &r) {
+    *this = (*this)-r;
+    return *this;
+  }
+  template<class T> inline Lattice<vobj> &operator +=(const T &r) {
+    *this = (*this)+r;
+    return *this;
+  }
+
+  friend inline void swap(Lattice &l, Lattice &r) { 
+    conformable(l,r);
+    LatticeAccelerator<vobj> tmp;
+    LatticeAccelerator<vobj> *lp = (LatticeAccelerator<vobj> *)&l;
+    LatticeAccelerator<vobj> *rp = (LatticeAccelerator<vobj> *)&r;
+    tmp = *lp;    *lp=*rp;    *rp=tmp;
+  }
+
+}; // class Lattice
+
+template<class vobj> std::ostream& operator<< (std::ostream& stream, const Lattice<vobj> &o){
+  typedef typename vobj::scalar_object sobj;
+  for(int g=0;g<o.Grid()->_gsites;g++){
+
+    Coordinate gcoor;
+    o.Grid()->GlobalIndexToGlobalCoor(g,gcoor);
+
+    sobj ss;
+    peekSite(ss,o,gcoor);
+    stream<<"[";
+    for(int d=0;d<gcoor.size();d++){
+      stream<<gcoor[d];
+      if(d!=gcoor.size()-1) stream<<",";
+    }
+    stream<<"]\t";
+    stream<<ss<<std::endl;
+  }
+  return stream;
+}
+  
+NAMESPACE_END(Grid);
+

Grid/lattice/Lattice_comparison.h

@@ -0,0 +1,176 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_comparison.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_COMPARISON_H
+#define GRID_LATTICE_COMPARISON_H
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////
+// relational operators
+// 
+// Support <,>,<=,>=,==,!=
+//
+//Query supporting bitwise &, |, ^, !
+//Query supporting logical &&, ||, 
+//////////////////////////////////////////////////////////////////////////
+
+//////////////////////////////////////////////////////////////////////////
+// compare lattice to lattice
+//////////////////////////////////////////////////////////////////////////
+template<class vfunctor,class lobj,class robj>  
+inline Lattice<vInteger> LLComparison(vfunctor op,const Lattice<lobj> &lhs,const Lattice<robj> &rhs)
+{
+  Lattice<vInteger> ret(rhs.Grid());
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop( ss, rhs_v, {
+    ret_v[ss]=op(lhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+//////////////////////////////////////////////////////////////////////////
+// compare lattice to scalar
+//////////////////////////////////////////////////////////////////////////
+template<class vfunctor,class lobj,class robj> 
+inline Lattice<vInteger> LSComparison(vfunctor op,const Lattice<lobj> &lhs,const robj &rhs)
+{
+  Lattice<vInteger> ret(lhs.Grid());
+  auto lhs_v = lhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop( ss, lhs_v, {
+    ret_v[ss]=op(lhs_v[ss],rhs);
+  });
+  return ret;
+}
+//////////////////////////////////////////////////////////////////////////
+// compare scalar to lattice
+//////////////////////////////////////////////////////////////////////////
+template<class vfunctor,class lobj,class robj> 
+inline Lattice<vInteger> SLComparison(vfunctor op,const lobj &lhs,const Lattice<robj> &rhs)
+{
+  Lattice<vInteger> ret(rhs.Grid());
+  auto rhs_v = rhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop( ss, rhs_v, {
+    ret_v[ss]=op(lhs,rhs_v[ss]);
+  });
+  return ret;
+}
+  
+//////////////////////////////////////////////////////////////////////////
+// Map to functors
+//////////////////////////////////////////////////////////////////////////
+// Less than
+template<class lobj,class robj>
+inline Lattice<vInteger> operator < (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator < (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator < (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vlt<lobj,robj>(),lhs,rhs);
+}
+  
+// Less than equal
+template<class lobj,class robj>
+inline Lattice<vInteger> operator <= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vle<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator <= (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vle<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator <= (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vle<lobj,robj>(),lhs,rhs);
+}
+  
+// Greater than 
+template<class lobj,class robj>
+inline Lattice<vInteger> operator > (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator > (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator > (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vgt<lobj,robj>(),lhs,rhs);
+}
+  
+  
+// Greater than equal
+template<class lobj,class robj>
+inline Lattice<vInteger> operator >= (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vge<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator >= (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vge<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator >= (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vge<lobj,robj>(),lhs,rhs);
+}
+   
+// equal
+template<class lobj,class robj>
+inline Lattice<vInteger> operator == (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(veq<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator == (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(veq<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator == (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(veq<lobj,robj>(),lhs,rhs);
+}
+   
+   
+// not equal
+template<class lobj,class robj>
+inline Lattice<vInteger> operator != (const Lattice<lobj> & lhs, const Lattice<robj> & rhs) {
+  return LLComparison(vne<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator != (const Lattice<lobj> & lhs, const robj & rhs) {
+  return LSComparison(vne<lobj,robj>(),lhs,rhs);
+}
+template<class lobj,class robj>
+inline Lattice<vInteger> operator != (const lobj & lhs, const Lattice<robj> & rhs) {
+  return SLComparison(vne<lobj,robj>(),lhs,rhs);
+}
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_comparison_utils.h

@@ -0,0 +1,231 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_comparison_utils.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_COMPARISON_H
+#define GRID_COMPARISON_H
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////
+// This implementation is a bit poor.
+//
+// Only support relational logical operations (<, >  etc)
+// on scalar objects. Therefore can strip any tensor structures.
+//
+// Should guard this with isGridTensor<> enable if?
+/////////////////////////////////////////
+//
+// Generic list of functors
+//
+template<class lobj,class robj> class veq {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) == (rhs);
+  }
+};
+template<class lobj,class robj> class vne {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) != (rhs);
+  }
+};
+template<class lobj,class robj> class vlt {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) < (rhs);
+  }
+};
+template<class lobj,class robj> class vle {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) <= (rhs);
+  }
+};
+template<class lobj,class robj> class vgt {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) > (rhs);
+  }
+};
+template<class lobj,class robj> class vge {
+public:
+  accelerator vInteger operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) >= (rhs);
+  }
+};
+  
+// Generic list of functors
+template<class lobj,class robj> class seq {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) == (rhs);
+  }
+};
+template<class lobj,class robj> class sne {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) != (rhs);
+  }
+};
+template<class lobj,class robj> class slt {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) < (rhs);
+  }
+};
+template<class lobj,class robj> class sle {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) <= (rhs);
+  }
+};
+template<class lobj,class robj> class sgt {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) > (rhs);
+  }
+};
+template<class lobj,class robj> class sge {
+public:
+  accelerator Integer operator()(const lobj &lhs, const robj &rhs)
+  { 
+    return (lhs) >= (rhs);
+  }
+};
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+// Integer and real get extra relational functions.
+//////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
+accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const vsimd & rhs)
+{
+  typedef typename vsimd::scalar_type scalar;
+  ExtractBuffer<scalar> vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+  ExtractBuffer<scalar> vrhs(vsimd::Nsimd());
+  ExtractBuffer<Integer> vpred(vsimd::Nsimd());
+  vInteger ret;
+  extract<vsimd,scalar>(lhs,vlhs);
+  extract<vsimd,scalar>(rhs,vrhs);
+  for(int s=0;s<vsimd::Nsimd();s++){
+    vpred[s] = sop(vlhs[s],vrhs[s]);
+  }
+  merge<vInteger,Integer>(ret,vpred);
+  return ret;
+}
+
+template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
+accelerator_inline vInteger Comparison(sfunctor sop,const vsimd & lhs, const typename vsimd::scalar_type & rhs)
+{
+  typedef typename vsimd::scalar_type scalar;
+  ExtractBuffer<scalar>  vlhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+  ExtractBuffer<Integer> vpred(vsimd::Nsimd());
+  vInteger ret;
+  extract<vsimd,scalar>(lhs,vlhs);
+  for(int s=0;s<vsimd::Nsimd();s++){
+    vpred[s] = sop(vlhs[s],rhs);
+  }
+  merge<vInteger,Integer>(ret,vpred);
+  return ret;
+}
+
+template<class sfunctor, class vsimd,IfNotComplex<vsimd> = 0> 
+accelerator_inline vInteger Comparison(sfunctor sop,const typename vsimd::scalar_type & lhs, const vsimd & rhs)
+{
+  typedef typename vsimd::scalar_type scalar;
+  ExtractBuffer<scalar> vrhs(vsimd::Nsimd());   // Use functors to reduce this to single implementation
+  ExtractBuffer<Integer> vpred(vsimd::Nsimd());
+  vInteger ret;
+  extract<vsimd,scalar>(rhs,vrhs);
+  for(int s=0;s<vsimd::Nsimd();s++){
+    vpred[s] = sop(lhs,vrhs[s]);
+  }
+  merge<vInteger,Integer>(ret,vpred);
+  return ret;
+}
+
+#define DECLARE_RELATIONAL_EQ(op,functor) \
+  template<class vsimd,IfSimd<vsimd> = 0>				\
+  accelerator_inline vInteger operator op (const vsimd & lhs, const vsimd & rhs)	\
+  {									\
+    typedef typename vsimd::scalar_type scalar;				\
+    return Comparison(functor<scalar,scalar>(),lhs,rhs);		\
+  }									\
+  template<class vsimd,IfSimd<vsimd> = 0>				\
+  accelerator_inline vInteger operator op (const vsimd & lhs, const typename vsimd::scalar_type & rhs) \
+  {									\
+    typedef typename vsimd::scalar_type scalar;				\
+    return Comparison(functor<scalar,scalar>(),lhs,rhs);		\
+  }									\
+  template<class vsimd,IfSimd<vsimd> = 0>				\
+  accelerator_inline vInteger operator op (const typename vsimd::scalar_type & lhs, const vsimd & rhs) \
+  {									\
+    typedef typename vsimd::scalar_type scalar;				\
+    return Comparison(functor<scalar,scalar>(),lhs,rhs);		\
+  }									\
+  template<class vsimd>							\
+  accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const iScalar<vsimd> &rhs) \
+  {									\
+    return lhs._internal op rhs._internal;				\
+  }									\
+  template<class vsimd>							\
+  accelerator_inline vInteger operator op(const iScalar<vsimd> &lhs,const typename vsimd::scalar_type &rhs) \
+  {									\
+    return lhs._internal op rhs;					\
+  }									\
+  template<class vsimd>							\
+  accelerator_inline vInteger operator op(const typename vsimd::scalar_type &lhs,const iScalar<vsimd> &rhs) \
+  {									\
+    return lhs op rhs._internal;					\
+    }									\
+
+#define DECLARE_RELATIONAL(op,functor) DECLARE_RELATIONAL_EQ(op,functor)    
+
+DECLARE_RELATIONAL(<,slt);
+DECLARE_RELATIONAL(<=,sle);
+DECLARE_RELATIONAL(>,sgt);
+DECLARE_RELATIONAL(>=,sge);
+DECLARE_RELATIONAL_EQ(==,seq);
+DECLARE_RELATIONAL(!=,sne);
+
+#undef DECLARE_RELATIONAL
+
+NAMESPACE_END(Grid);
+
+
+#endif

Grid/lattice/Lattice_conformable.h

@@ -0,0 +1,40 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_conformable.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_CONFORMABLE_H
+#define GRID_LATTICE_CONFORMABLE_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class obj1,class obj2> void conformable(const Lattice<obj1> &lhs,const Lattice<obj2> &rhs)
+{
+  assert(lhs.Grid() == rhs.Grid());
+  assert(lhs.Checkerboard() == rhs.Checkerboard());
+}
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_coordinate.h

@@ -0,0 +1,74 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_coordinate.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+
+NAMESPACE_BEGIN(Grid);
+
+template<class iobj> inline void LatticeCoordinate(Lattice<iobj> &l,int mu)
+{
+  typedef typename iobj::scalar_type scalar_type;
+  typedef typename iobj::vector_type vector_type;
+
+  GridBase *grid = l.Grid();
+  int Nsimd = grid->iSites();
+
+  Coordinate gcoor;
+  ExtractBuffer<scalar_type> mergebuf(Nsimd);
+
+  vector_type vI;
+  auto l_v = l.View();
+  for(int o=0;o<grid->oSites();o++){
+    for(int i=0;i<grid->iSites();i++){
+      grid->RankIndexToGlobalCoor(grid->ThisRank(),o,i,gcoor);
+      mergebuf[i]=(Integer)gcoor[mu];
+    }
+    merge<vector_type,scalar_type>(vI,mergebuf);
+    l_v[o]=vI;
+  }
+};
+
+// LatticeCoordinate();
+// FIXME for debug; deprecate this; made obscelete by 
+template<class vobj> void lex_sites(Lattice<vobj> &l){
+  auto l_v = l.View();
+  Real *v_ptr = (Real *)&l_v[0];
+  size_t o_len = l.Grid()->oSites();
+  size_t v_len = sizeof(vobj)/sizeof(vRealF);
+  size_t vec_len = vRealF::Nsimd();
+
+  for(int i=0;i<o_len;i++){
+    for(int j=0;j<v_len;j++){
+      for(int vv=0;vv<vec_len;vv+=2){
+	v_ptr[i*v_len*vec_len+j*vec_len+vv  ]= i+vv*500;
+	v_ptr[i*v_len*vec_len+j*vec_len+vv+1]= i+vv*500;
+      }
+    }}
+}
+
+NAMESPACE_END(Grid);
+

Grid/lattice/Lattice_local.h

@@ -0,0 +1,83 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_local.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_LOCALREDUCTION_H
+#define GRID_LATTICE_LOCALREDUCTION_H
+
+///////////////////////////////////////////////
+// localInner, localNorm, outerProduct
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////
+// Non site, reduced locally reduced routines
+/////////////////////////////////////////////////////
+  
+// localNorm2,
+template<class vobj>
+inline auto localNorm2 (const Lattice<vobj> &rhs)-> Lattice<typename vobj::tensor_reduced>
+{
+  Lattice<typename vobj::tensor_reduced> ret(rhs.Grid());
+  auto rhs_v = rhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop(ss,rhs_v,{
+    ret_v[ss]=innerProduct(rhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+  
+// localInnerProduct
+template<class vobj>
+inline auto localInnerProduct (const Lattice<vobj> &lhs,const Lattice<vobj> &rhs) -> Lattice<typename vobj::tensor_reduced>
+{
+  Lattice<typename vobj::tensor_reduced> ret(rhs.Grid());
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop(ss,rhs_v,{
+    ret_v[ss]=innerProduct(lhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+  
+// outerProduct Scalar x Scalar -> Scalar
+//              Vector x Vector -> Matrix
+template<class ll,class rr>
+inline auto outerProduct (const Lattice<ll> &lhs,const Lattice<rr> &rhs) -> Lattice<decltype(outerProduct(ll(),rr()))>
+{
+  Lattice<decltype(outerProduct(ll(),rr()))> ret(rhs.Grid());
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop(ss,rhs_v,{
+    ret_v[ss]=outerProduct(lhs_v[ss],rhs_v[ss]);
+  });
+  return ret;
+}
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_matrix_reduction.h

@@ -0,0 +1,202 @@
+/*************************************************************************************
+    Grid physics library, www.github.com/paboyle/Grid 
+    Source file: ./lib/lattice/Lattice_reduction.h
+    Copyright (C) 2015
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once 
+#include <Grid/Grid_Eigen_Dense.h>
+
+#ifdef GRID_WARN_SUBOPTIMAL
+#warning "Optimisation alert all these reduction loops are NOT threaded "
+#endif     
+
+NAMESPACE_BEGIN(Grid);
+
+template<class vobj>
+static void sliceMaddMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,const Lattice<vobj> &Y,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+
+  //  Lattice<vobj> Xslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+  auto X_v = X.View();
+  auto Y_v = Y.View();
+  auto R_v = R.View();
+  thread_region
+  {
+    std::vector<vobj> s_x(Nblock);
+
+    thread_loop_collapse2( (int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  s_x[i] = X_v[o+i*ostride];
+	}
+
+	vobj dot;
+	for(int i=0;i<Nblock;i++){
+	  dot = Y_v[o+i*ostride];
+	  for(int j=0;j<Nblock;j++){
+	    dot = dot + s_x[j]*(scale*aa(j,i));
+	  }
+	  R_v[o+i*ostride]=dot;
+	}
+      }});
+  }
+};
+
+template<class vobj>
+static void sliceMulMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  assert( FullGrid->_simd_layout[Orthog]==1);
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+
+  auto X_v = X.View();
+  auto R_v = R.View();
+
+  thread_region
+  {
+    std::vector<vobj> s_x(Nblock);
+    
+    thread_loop_collapse2( (int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  s_x[i] = X_v[o+i*ostride];
+	}
+
+	vobj dot;
+	for(int i=0;i<Nblock;i++){
+	  dot = s_x[0]*(scale*aa(0,i));
+	  for(int j=1;j<Nblock;j++){
+	    dot = dot + s_x[j]*(scale*aa(j,i));
+	  }
+	  R_v[o+i*ostride]=dot;
+	}
+    }});
+  }
+
+};
+
+
+template<class vobj>
+static void sliceInnerProductMatrix(  Eigen::MatrixXcd &mat, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int Orthog) 
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  
+  GridBase *FullGrid  = lhs.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+  
+  int Nblock = FullGrid->GlobalDimensions()[Orthog];
+  
+  //  Lattice<vobj> Lslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+  
+  mat = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+  //  int nh =  FullGrid->_ndimension;
+  //  int nl = SliceGrid->_ndimension;
+  //  int nl = nh-1;
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+
+  typedef typename vobj::vector_typeD vector_typeD;
+  auto lhs_v = lhs.View();
+  auto rhs_v = rhs.View();
+  thread_region {
+    std::vector<vobj> Left(Nblock);
+    std::vector<vobj> Right(Nblock);
+    Eigen::MatrixXcd  mat_thread = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+    thread_loop_collapse2((int n=0;n<nblock;n++),{
+      for(int b=0;b<block;b++){
+
+	int o  = n*stride + b;
+
+	for(int i=0;i<Nblock;i++){
+	  Left [i] = lhs_v[o+i*ostride];
+	  Right[i] = rhs_v[o+i*ostride];
+	}
+
+	for(int i=0;i<Nblock;i++){
+	  for(int j=0;j<Nblock;j++){
+	    auto tmp = innerProduct(Left[i],Right[j]);
+	    auto rtmp = TensorRemove(tmp);
+	    ComplexD z = Reduce(rtmp);
+	    mat_thread(i,j) += std::complex<double>(real(z),imag(z));
+	  }}
+    }});
+    thread_critical {
+      mat += mat_thread;
+    }  
+  }
+
+  for(int i=0;i<Nblock;i++){
+    for(int j=0;j<Nblock;j++){
+      ComplexD sum = mat(i,j);
+      FullGrid->GlobalSum(sum);
+      mat(i,j)=sum;
+    }}
+
+  return;
+}
+
+NAMESPACE_END(Grid);
+
+
+

Grid/lattice/Lattice_overload.h

@@ -0,0 +1,138 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_overload.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_LATTICE_OVERLOAD_H
+#define GRID_LATTICE_OVERLOAD_H
+
+namespace Grid {
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  // unary negation
+  //////////////////////////////////////////////////////////////////////////////////////////////////////
+  template<class vobj>
+  inline Lattice<vobj> operator -(const Lattice<vobj> &r)
+  {
+    Lattice<vobj> ret(r._grid);
+    parallel_for(int ss=0;ss<r._grid->oSites();ss++){
+      vstream(ret._odata[ss], -r._odata[ss]);
+    }
+    return ret;
+  } 
+  /////////////////////////////////////////////////////////////////////////////////////
+  // Lattice BinOp Lattice,
+  //NB mult performs conformable check. Do not reapply here for performance.
+  /////////////////////////////////////////////////////////////////////////////////////
+  template<class left,class right>
+    inline auto operator * (const Lattice<left> &lhs,const Lattice<right> &rhs)-> Lattice<decltype(lhs._odata[0]*rhs._odata[0])>
+  {
+    Lattice<decltype(lhs._odata[0]*rhs._odata[0])> ret(rhs._grid);
+    mult(ret,lhs,rhs);
+    return ret;
+  }
+  template<class left,class right>
+    inline auto operator + (const Lattice<left> &lhs,const Lattice<right> &rhs)-> Lattice<decltype(lhs._odata[0]+rhs._odata[0])>
+  {
+    Lattice<decltype(lhs._odata[0]+rhs._odata[0])> ret(rhs._grid);
+    add(ret,lhs,rhs);
+    return ret;
+  }
+  template<class left,class right>
+    inline auto operator - (const Lattice<left> &lhs,const Lattice<right> &rhs)-> Lattice<decltype(lhs._odata[0]-rhs._odata[0])>
+  {
+    Lattice<decltype(lhs._odata[0]-rhs._odata[0])> ret(rhs._grid);
+    sub(ret,lhs,rhs);
+    return ret;
+  }
+  
+  // Scalar BinOp Lattice ;generate return type
+  template<class left,class right>
+  inline auto operator * (const left &lhs,const Lattice<right> &rhs) -> Lattice<decltype(lhs*rhs._odata[0])>
+  {
+    Lattice<decltype(lhs*rhs._odata[0])> ret(rhs._grid);
+    parallel_for(int ss=0;ss<rhs._grid->oSites(); ss++){
+      decltype(lhs*rhs._odata[0]) tmp=lhs*rhs._odata[ss]; 
+      vstream(ret._odata[ss],tmp);
+	   //      ret._odata[ss]=lhs*rhs._odata[ss];
+    }
+    return ret;
+  }
+  template<class left,class right>
+    inline auto operator + (const left &lhs,const Lattice<right> &rhs) -> Lattice<decltype(lhs+rhs._odata[0])>
+    {
+      Lattice<decltype(lhs+rhs._odata[0])> ret(rhs._grid);
+      parallel_for(int ss=0;ss<rhs._grid->oSites(); ss++){
+	decltype(lhs+rhs._odata[0]) tmp =lhs-rhs._odata[ss];  
+	vstream(ret._odata[ss],tmp);
+	//	ret._odata[ss]=lhs+rhs._odata[ss];
+      }
+        return ret;
+    }
+  template<class left,class right>
+    inline auto operator - (const left &lhs,const Lattice<right> &rhs) -> Lattice<decltype(lhs-rhs._odata[0])>
+  {
+    Lattice<decltype(lhs-rhs._odata[0])> ret(rhs._grid);
+    parallel_for(int ss=0;ss<rhs._grid->oSites(); ss++){
+      decltype(lhs-rhs._odata[0]) tmp=lhs-rhs._odata[ss];  
+      vstream(ret._odata[ss],tmp);
+    }
+    return ret;
+  }
+    template<class left,class right>
+      inline auto operator * (const Lattice<left> &lhs,const right &rhs) -> Lattice<decltype(lhs._odata[0]*rhs)>
+    {
+      Lattice<decltype(lhs._odata[0]*rhs)> ret(lhs._grid);
+      parallel_for(int ss=0;ss<lhs._grid->oSites(); ss++){
+	decltype(lhs._odata[0]*rhs) tmp =lhs._odata[ss]*rhs;
+	vstream(ret._odata[ss],tmp);
+	//            ret._odata[ss]=lhs._odata[ss]*rhs;
+      }
+      return ret;
+    }
+    template<class left,class right>
+      inline auto operator + (const Lattice<left> &lhs,const right &rhs) -> Lattice<decltype(lhs._odata[0]+rhs)>
+    {
+        Lattice<decltype(lhs._odata[0]+rhs)> ret(lhs._grid);
+	parallel_for(int ss=0;ss<rhs._grid->oSites(); ss++){
+	  decltype(lhs._odata[0]+rhs) tmp=lhs._odata[ss]+rhs; 
+	  vstream(ret._odata[ss],tmp);
+	  //	  ret._odata[ss]=lhs._odata[ss]+rhs;
+        }
+        return ret;
+    }
+    template<class left,class right>
+      inline auto operator - (const Lattice<left> &lhs,const right &rhs) -> Lattice<decltype(lhs._odata[0]-rhs)>
+    {
+      Lattice<decltype(lhs._odata[0]-rhs)> ret(lhs._grid);
+      parallel_for(int ss=0;ss<rhs._grid->oSites(); ss++){
+	  decltype(lhs._odata[0]-rhs) tmp=lhs._odata[ss]-rhs;
+	  vstream(ret._odata[ss],tmp);
+	  //	ret._odata[ss]=lhs._odata[ss]-rhs;
+      }
+      return ret;
+    }
+}
+#endif

Grid/lattice/Lattice_peekpoke.h

@@ -0,0 +1,217 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_peekpoke.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_PEEK_H
+#define GRID_LATTICE_PEEK_H
+
+///////////////////////////////////////////////
+// Peeking and poking around
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+
+// FIXME accelerator_loop and accelerator_inline these
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Peek internal indices of a Lattice object
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj> 
+auto PeekIndex(const Lattice<vobj> &lhs,int i) -> Lattice<decltype(peekIndex<Index>(vobj(),i))>
+{
+  Lattice<decltype(peekIndex<Index>(vobj(),i))> ret(lhs.Grid());
+  ret.Checkerboard()=lhs.Checkerboard();
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  cpu_loop( ss, lhs_v, {
+      ret_v[ss] = peekIndex<Index>(lhs_v[ss],i);
+  });
+  return ret;
+};
+template<int Index,class vobj> 
+auto PeekIndex(const Lattice<vobj> &lhs,int i,int j) -> Lattice<decltype(peekIndex<Index>(vobj(),i,j))>
+{
+  Lattice<decltype(peekIndex<Index>(vobj(),i,j))> ret(lhs.Grid());
+  ret.Checkerboard()=lhs.Checkerboard();
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  cpu_loop( ss, lhs_v, {
+    ret_v[ss] = peekIndex<Index>(lhs_v[ss],i,j);
+  });
+  return ret;
+};
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Poke internal indices of a Lattice object
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj>  
+void PokeIndex(Lattice<vobj> &lhs,const Lattice<decltype(peekIndex<Index>(vobj(),0))> & rhs,int i)
+{
+  auto rhs_v = rhs.View();
+  auto lhs_v = lhs.View();
+  cpu_loop( ss, lhs_v, {
+    pokeIndex<Index>(lhs_v[ss],rhs_v[ss],i);
+  });
+}
+template<int Index,class vobj> 
+void PokeIndex(Lattice<vobj> &lhs,const Lattice<decltype(peekIndex<Index>(vobj(),0,0))> & rhs,int i,int j)
+{
+  auto rhs_v = rhs.View();
+  auto lhs_v = lhs.View();
+  cpu_loop( ss, lhs_v, {
+    pokeIndex<Index>(lhs_v[ss],rhs_v[ss],i,j);
+  });
+}
+
+//////////////////////////////////////////////////////
+// Poke a scalar object into the SIMD array
+//////////////////////////////////////////////////////
+template<class vobj,class sobj> 
+void pokeSite(const sobj &s,Lattice<vobj> &l,const Coordinate &site){
+
+  GridBase *grid=l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== l.Grid()->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  int rank,odx,idx;
+  // Optional to broadcast from node 0.
+  grid->GlobalCoorToRankIndex(rank,odx,idx,site);
+  grid->Broadcast(grid->BossRank(),s);
+
+  // extract-modify-merge cycle is easiest way and this is not perf critical
+  ExtractBuffer<sobj> buf(Nsimd);
+  auto l_v = l.View();
+  if ( rank == grid->ThisRank() ) {
+    extract(l_v[odx],buf);
+    buf[idx] = s;
+    merge(l_v[odx],buf);
+  }
+
+  return;
+};
+
+
+//////////////////////////////////////////////////////////
+// Peek a scalar object from the SIMD array
+//////////////////////////////////////////////////////////
+template<class vobj,class sobj>
+void peekSite(sobj &s,const Lattice<vobj> &l,const Coordinate &site){
+        
+  GridBase *grid=l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard() == l.Grid()->CheckerBoard(site));
+
+  int rank,odx,idx;
+  grid->GlobalCoorToRankIndex(rank,odx,idx,site);
+
+  ExtractBuffer<sobj> buf(Nsimd);
+  auto l_v = l.View();
+  extract(l_v[odx],buf);
+
+  s = buf[idx];
+
+  grid->Broadcast(rank,s);
+
+  return;
+};
+
+
+//////////////////////////////////////////////////////////
+// Peek a scalar object from the SIMD array
+//////////////////////////////////////////////////////////
+template<class vobj,class sobj>
+void peekLocalSite(sobj &s,const Lattice<vobj> &l,Coordinate &site){
+        
+  GridBase *grid = l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== l.Grid()->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  static const int words=sizeof(vobj)/sizeof(vector_type);
+  int odx,idx;
+  idx= grid->iIndex(site);
+  odx= grid->oIndex(site);
+  
+  auto l_v = l.View();
+  scalar_type * vp = (scalar_type *)&l_v[odx];
+  scalar_type * pt = (scalar_type *)&s;
+      
+  for(int w=0;w<words;w++){
+    pt[w] = vp[idx+w*Nsimd];
+  }
+      
+  return;
+};
+
+template<class vobj,class sobj>
+void pokeLocalSite(const sobj &s,Lattice<vobj> &l,Coordinate &site){
+
+  GridBase *grid=l.Grid();
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nsimd = grid->Nsimd();
+
+  assert( l.Checkerboard()== l.Grid()->CheckerBoard(site));
+  assert( sizeof(sobj)*Nsimd == sizeof(vobj));
+
+  static const int words=sizeof(vobj)/sizeof(vector_type);
+  int odx,idx;
+  idx= grid->iIndex(site);
+  odx= grid->oIndex(site);
+
+  auto l_v = l.View();
+  scalar_type * vp = (scalar_type *)&l_v[odx];
+  scalar_type * pt = (scalar_type *)&s;
+  for(int w=0;w<words;w++){
+    vp[idx+w*Nsimd] = pt[w];
+  }
+
+  return;
+};
+
+NAMESPACE_END(Grid);
+#endif
+

Grid/lattice/Lattice_reality.h

@@ -0,0 +1,63 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_reality.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_REALITY_H
+#define GRID_LATTICE_REALITY_H
+
+
+// FIXME .. this is the sector of the code 
+// I am most worried about the directions
+// The choice of burying complex in the SIMD
+// is making the use of "real" and "imag" very cumbersome
+
+NAMESPACE_BEGIN(Grid);
+
+template<class vobj> inline Lattice<vobj> adj(const Lattice<vobj> &lhs){
+  Lattice<vobj> ret(lhs.Grid());
+  auto lhs_v = lhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop( ss, lhs_v, {
+    ret_v[ss] = adj(lhs_v[ss]);
+  });
+  return ret;
+};
+
+template<class vobj> inline Lattice<vobj> conjugate(const Lattice<vobj> &lhs){
+  Lattice<vobj> ret(lhs.Grid());
+  auto lhs_v = lhs.View();
+  auto ret_v = ret.View();
+  accelerator_loop( ss, lhs_v, {
+    ret_v[ss] = conjugate(lhs_v[ss]);
+  });
+  return ret;
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/lattice/Lattice_reduction.h

@@ -0,0 +1,738 @@
+/*************************************************************************************
+    Grid physics library, www.github.com/paboyle/Grid 
+    Source file: ./lib/lattice/Lattice_reduction.h
+    Copyright (C) 2015
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#pragma once
+
+#include <Grid/Grid_Eigen_Dense.h>
+
+NAMESPACE_BEGIN(Grid);
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Deterministic Reduction operations
+  ////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj> inline RealD norm2(const Lattice<vobj> &arg){
+  ComplexD nrm = innerProduct(arg,arg);
+  return real(nrm); 
+}
+
+// Double inner product
+template<class vobj>
+inline ComplexD innerProduct(const Lattice<vobj> &left,const Lattice<vobj> &right)
+{
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_typeD vector_type;
+  scalar_type  nrm;
+  
+  GridBase *grid = left.Grid();
+  
+  Vector<vector_type> sumarray(grid->SumArraySize());
+
+  auto left_v = left.View();
+  auto right_v=right.View();
+
+  thread_loop( (int thr=0;thr<grid->SumArraySize();thr++),{
+    int mywork, myoff;
+    GridThread::GetWork(left.Grid()->oSites(),thr,mywork,myoff);
+    
+    decltype(innerProductD(left_v[0],right_v[0])) vnrm=Zero(); // private to thread; sub summation
+    for(int ss=myoff;ss<mywork+myoff; ss++){
+      vnrm = vnrm + innerProductD(left_v[ss],right_v[ss]);
+    }
+    sumarray[thr]=TensorRemove(vnrm) ;
+  });
+  
+  vector_type vvnrm; vvnrm=Zero();  // sum across threads
+  for(int i=0;i<grid->SumArraySize();i++){
+    vvnrm = vvnrm+sumarray[i];
+  } 
+  nrm = Reduce(vvnrm);// sum across simd
+  right.Grid()->GlobalSum(nrm);
+  return nrm;
+}
+
+/////////////////////////
+// Fast axpby_norm
+// z = a x + b y
+// return norm z
+/////////////////////////
+template<class sobj,class vobj> strong_inline RealD 
+axpy_norm_fast(Lattice<vobj> &z,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y) 
+{
+  sobj one(1.0);
+  return axpby_norm_fast(z,a,one,x,y);
+}
+
+template<class sobj,class vobj> strong_inline RealD 
+axpby_norm_fast(Lattice<vobj> &z,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y) 
+{
+  const int pad = 8;
+  z.Checkerboard() = x.Checkerboard();
+  conformable(z,x);
+  conformable(x,y);
+
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_typeD vector_type;
+  RealD  nrm;
+  
+  GridBase *grid = x.Grid();
+  
+  Vector<RealD> sumarray(grid->SumArraySize()*pad);
+  
+  auto x_v=x.View();
+  auto y_v=y.View();
+  auto z_v=z.View();
+  thread_loop( (int thr=0;thr<grid->SumArraySize();thr++),
+  {
+    int nwork, mywork, myoff;
+    GridThread::GetWork(x.Grid()->oSites(),thr,mywork,myoff);
+    
+    // private to thread; sub summation
+    decltype(innerProductD(z_v[0],z_v[0])) vnrm=Zero(); 
+    for(int ss=myoff;ss<mywork+myoff; ss++){
+      vobj tmp = a*x_v[ss]+b*y_v[ss];
+      vnrm = vnrm + innerProductD(tmp,tmp);
+      vstream(z_v[ss],tmp);
+    }
+    vstream(sumarray[thr*pad],real(Reduce(TensorRemove(vnrm)))) ;
+  });
+  
+  nrm = 0.0; // sum across threads; linear in thread count but fast
+  for(int i=0;i<grid->SumArraySize();i++){
+    nrm = nrm+sumarray[i*pad];
+  } 
+  z.Grid()->GlobalSum(nrm);
+  return nrm; 
+}
+
+ 
+template<class Op,class T1>
+inline auto sum(const LatticeUnaryExpression<Op,T1> & expr)
+  ->typename decltype(expr.op.func(eval(0,expr.arg1)))::scalar_object
+{
+  return sum(closure(expr));
+}
+
+template<class Op,class T1,class T2>
+inline auto sum(const LatticeBinaryExpression<Op,T1,T2> & expr)
+      ->typename decltype(expr.op.func(eval(0,expr.arg1),eval(0,expr.arg2)))::scalar_object
+{
+  return sum(closure(expr));
+}
+
+
+template<class Op,class T1,class T2,class T3>
+inline auto sum(const LatticeTrinaryExpression<Op,T1,T2,T3> & expr)
+  ->typename decltype(expr.op.func(eval(0,expr.arg1),
+				      eval(0,expr.arg2),
+				      eval(0,expr.arg3)
+				      ))::scalar_object
+{
+  return sum(closure(expr));
+}
+
+template<class vobj>
+inline typename vobj::scalar_object sum(const Lattice<vobj> &arg)
+{
+  GridBase *grid=arg.Grid();
+  int Nsimd = grid->Nsimd();
+  
+  Vector<vobj> sumarray(grid->SumArraySize());
+  for(int i=0;i<grid->SumArraySize();i++){
+    sumarray[i]=Zero();
+  }
+  
+  auto arg_v=arg.View();
+  thread_loop( (int thr=0;thr<grid->SumArraySize();thr++),{
+    int nwork, mywork, myoff;
+    GridThread::GetWork(grid->oSites(),thr,mywork,myoff);
+    
+    vobj vvsum=Zero();
+    for(int ss=myoff;ss<mywork+myoff; ss++){
+      vvsum = vvsum + arg_v[ss];
+    }
+    sumarray[thr]=vvsum;
+  });
+  
+  vobj vsum=Zero();  // sum across threads
+  for(int i=0;i<grid->SumArraySize();i++){
+    vsum = vsum+sumarray[i];
+  } 
+  
+  typedef typename vobj::scalar_object sobj;
+  sobj ssum=Zero();
+  
+  ExtractBuffer<sobj>               buf(Nsimd);
+  extract(vsum,buf);
+  
+  for(int i=0;i<Nsimd;i++) ssum = ssum + buf[i];
+  arg.Grid()->GlobalSum(ssum);
+  
+  return ssum;
+}
+
+
+//////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// sliceSum, sliceInnerProduct, sliceAxpy, sliceNorm etc...
+//////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+template<class vobj> inline void sliceSum(const Lattice<vobj> &Data,std::vector<typename vobj::scalar_object> &result,int orthogdim)
+{
+  ///////////////////////////////////////////////////////
+  // FIXME precision promoted summation
+  // may be important for correlation functions
+  // But easily avoided by using double precision fields
+  ///////////////////////////////////////////////////////
+  typedef typename vobj::scalar_object sobj;
+  GridBase  *grid = Data.Grid();
+  assert(grid!=NULL);
+
+  const int    Nd = grid->_ndimension;
+  const int Nsimd = grid->Nsimd();
+
+  assert(orthogdim >= 0);
+  assert(orthogdim < Nd);
+
+  int fd=grid->_fdimensions[orthogdim];
+  int ld=grid->_ldimensions[orthogdim];
+  int rd=grid->_rdimensions[orthogdim];
+
+  Vector<vobj> lvSum(rd); // will locally sum vectors first
+  Vector<sobj> lsSum(ld,Zero());                    // sum across these down to scalars
+  ExtractBuffer<sobj> extracted(Nsimd);                  // splitting the SIMD
+
+  result.resize(fd); // And then global sum to return the same vector to every node 
+  for(int r=0;r<rd;r++){
+    lvSum[r]=Zero();
+  }
+
+  int e1=    grid->_slice_nblock[orthogdim];
+  int e2=    grid->_slice_block [orthogdim];
+  int stride=grid->_slice_stride[orthogdim];
+
+  // sum over reduced dimension planes, breaking out orthog dir
+  // Parallel over orthog direction
+  auto Data_v=Data.View();
+  thread_loop( (int r=0;r<rd;r++), {
+
+    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 
+
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int ss= so+n*stride+b;
+	lvSum[r]=lvSum[r]+Data_v[ss];
+      }
+    }
+  });
+
+  // Sum across simd lanes in the plane, breaking out orthog dir.
+  Coordinate icoor(Nd);
+
+  for(int rt=0;rt<rd;rt++){
+
+    extract(lvSum[rt],extracted);
+
+    for(int idx=0;idx<Nsimd;idx++){
+
+      grid->iCoorFromIindex(icoor,idx);
+
+      int ldx =rt+icoor[orthogdim]*rd;
+
+      lsSum[ldx]=lsSum[ldx]+extracted[idx];
+
+    }
+  }
+  
+  // sum over nodes.
+  sobj gsum;
+  for(int t=0;t<fd;t++){
+    int pt = t/ld; // processor plane
+    int lt = t%ld;
+    if ( pt == grid->_processor_coor[orthogdim] ) {
+      gsum=lsSum[lt];
+    } else {
+      gsum=Zero();
+    }
+
+    grid->GlobalSum(gsum);
+
+    result[t]=gsum;
+  }
+}
+
+template<class vobj>
+static void mySliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim)
+{
+  // std::cout << GridLogMessage << "Start mySliceInnerProductVector" << std::endl;
+
+  typedef typename vobj::scalar_type scalar_type;
+  std::vector<scalar_type> lsSum;
+  localSliceInnerProductVector(result, lhs, rhs, lsSum, orthogdim);
+  globalSliceInnerProductVector(result, lhs, lsSum, orthogdim);
+  // std::cout << GridLogMessage << "End mySliceInnerProductVector" << std::endl;
+}
+
+template <class vobj>
+static void localSliceInnerProductVector(std::vector<ComplexD> &result, const Lattice<vobj> &lhs, const Lattice<vobj> &rhs, std::vector<typename vobj::scalar_type> &lsSum, int orthogdim)
+{
+  // std::cout << GridLogMessage << "Start prep" << std::endl;
+  typedef typename vobj::vector_type   vector_type;
+  typedef typename vobj::scalar_type   scalar_type;
+  GridBase  *grid = lhs.Grid();
+  assert(grid!=NULL);
+  conformable(grid,rhs.Grid());
+
+  const int    Nd = grid->_ndimension;
+  const int Nsimd = grid->Nsimd();
+
+  assert(orthogdim >= 0);
+  assert(orthogdim < Nd);
+
+  int fd=grid->_fdimensions[orthogdim];
+  int ld=grid->_ldimensions[orthogdim];
+  int rd=grid->_rdimensions[orthogdim];
+  // std::cout << GridLogMessage << "Start alloc" << std::endl;
+
+  Vector<vector_type> lvSum(rd); // will locally sum vectors first
+  lsSum.resize(ld,scalar_type(0.0));                    // sum across these down to scalars
+  ExtractBuffer<iScalar<scalar_type> > extracted(Nsimd);   // splitting the SIMD  
+  // std::cout << GridLogMessage << "End alloc" << std::endl;
+
+  result.resize(fd); // And then global sum to return the same vector to every node for IO to file
+  for(int r=0;r<rd;r++){
+    lvSum[r]=Zero();
+  }
+
+  int e1=    grid->_slice_nblock[orthogdim];
+  int e2=    grid->_slice_block [orthogdim];
+  int stride=grid->_slice_stride[orthogdim];
+  // std::cout << GridLogMessage << "End prep" << std::endl;
+  // std::cout << GridLogMessage << "Start parallel inner product, _rd = " << rd << std::endl;
+  vector_type vv;
+  auto l_v=lhs.View();
+  auto r_v=rhs.View();
+  thread_loop( (int r=0;r<rd;r++),{
+
+    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 
+
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+        int ss = so + n * stride + b;
+        vv = TensorRemove(innerProduct(l_v[ss], r_v[ss]));
+        lvSum[r] = lvSum[r] + vv;
+      }
+    }
+  });
+  // std::cout << GridLogMessage << "End parallel inner product" << std::endl;
+
+  // Sum across simd lanes in the plane, breaking out orthog dir.
+  Coordinate icoor(Nd);
+  for(int rt=0;rt<rd;rt++){
+
+    iScalar<vector_type> temp; 
+    temp._internal = lvSum[rt];
+    extract(temp,extracted);
+
+    for(int idx=0;idx<Nsimd;idx++){
+
+      grid->iCoorFromIindex(icoor,idx);
+
+      int ldx =rt+icoor[orthogdim]*rd;
+
+      lsSum[ldx]=lsSum[ldx]+extracted[idx]._internal;
+
+    }
+  }
+  // std::cout << GridLogMessage << "End sum over simd lanes" << std::endl;
+}
+template <class vobj>
+static void globalSliceInnerProductVector(std::vector<ComplexD> &result, const Lattice<vobj> &lhs, std::vector<typename vobj::scalar_type> &lsSum, int orthogdim)
+{
+  typedef typename vobj::scalar_type scalar_type;
+  GridBase *grid = lhs.Grid();
+  int fd = result.size();
+  int ld = lsSum.size();
+  // sum over nodes.
+  std::vector<scalar_type> gsum;
+  gsum.resize(fd, scalar_type(0.0));
+  // std::cout << GridLogMessage << "Start of gsum[t] creation:" << std::endl;
+  for(int t=0;t<fd;t++){
+    int pt = t/ld; // processor plane
+    int lt = t%ld;
+    if ( pt == grid->_processor_coor[orthogdim] ) {
+      gsum[t]=lsSum[lt];
+    }
+  }
+  // std::cout << GridLogMessage << "End of gsum[t] creation:" << std::endl;
+  // std::cout << GridLogMessage << "Start of GlobalSumVector:" << std::endl;
+  grid->GlobalSumVector(&gsum[0], fd);
+  // std::cout << GridLogMessage << "End of GlobalSumVector:" << std::endl;
+
+  result = gsum;
+}
+template<class vobj>
+static void sliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim) 
+{
+  typedef typename vobj::vector_type   vector_type;
+  typedef typename vobj::scalar_type   scalar_type;
+  GridBase  *grid = lhs.Grid();
+  assert(grid!=NULL);
+  conformable(grid,rhs.Grid());
+
+  const int    Nd = grid->_ndimension;
+  const int Nsimd = grid->Nsimd();
+
+  assert(orthogdim >= 0);
+  assert(orthogdim < Nd);
+
+  int fd=grid->_fdimensions[orthogdim];
+  int ld=grid->_ldimensions[orthogdim];
+  int rd=grid->_rdimensions[orthogdim];
+
+  Vector<vector_type> lvSum(rd); // will locally sum vectors first
+  Vector<scalar_type > lsSum(ld,scalar_type(0.0));                    // sum across these down to scalars
+  ExtractBuffer<iScalar<scalar_type> > extracted(Nsimd);   // splitting the SIMD  
+
+  result.resize(fd); // And then global sum to return the same vector to every node for IO to file
+  for(int r=0;r<rd;r++){
+    lvSum[r]=Zero();
+  }
+
+  int e1=    grid->_slice_nblock[orthogdim];
+  int e2=    grid->_slice_block [orthogdim];
+  int stride=grid->_slice_stride[orthogdim];
+
+  auto lhv=lhs.View();
+  auto rhv=rhs.View();
+  thread_loop( (int r=0;r<rd;r++),{
+
+    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 
+
+    for(int n=0;n<e1;n++){
+      for(int b=0;b<e2;b++){
+	int ss= so+n*stride+b;
+	vector_type vv = TensorRemove(innerProduct(lhv[ss],rhv[ss]));
+	lvSum[r]=lvSum[r]+vv;
+      }
+    }
+  });
+
+  // Sum across simd lanes in the plane, breaking out orthog dir.
+  Coordinate icoor(Nd);
+  for(int rt=0;rt<rd;rt++){
+
+    iScalar<vector_type> temp; 
+    temp._internal = lvSum[rt];
+    extract(temp,extracted);
+
+    for(int idx=0;idx<Nsimd;idx++){
+
+      grid->iCoorFromIindex(icoor,idx);
+
+      int ldx =rt+icoor[orthogdim]*rd;
+
+      lsSum[ldx]=lsSum[ldx]+extracted[idx]._internal;
+
+    }
+  }
+  
+  // sum over nodes.
+  scalar_type gsum;
+  for(int t=0;t<fd;t++){
+    int pt = t/ld; // processor plane
+    int lt = t%ld;
+    if ( pt == grid->_processor_coor[orthogdim] ) {
+      gsum=lsSum[lt];
+    } else {
+      gsum=scalar_type(0.0);
+    }
+
+    grid->GlobalSum(gsum);
+
+    result[t]=gsum;
+  }
+}
+template<class vobj>
+static void sliceNorm (std::vector<RealD> &sn,const Lattice<vobj> &rhs,int Orthog) 
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  
+  int Nblock = rhs.Grid()->GlobalDimensions()[Orthog];
+  Vector<ComplexD> ip(Nblock);
+  sn.resize(Nblock);
+  
+  sliceInnerProductVector(ip,rhs,rhs,Orthog);
+  for(int ss=0;ss<Nblock;ss++){
+    sn[ss] = real(ip[ss]);
+  }
+};
+
+
+template<class vobj>
+static void sliceMaddVector(Lattice<vobj> &R,std::vector<RealD> &a,const Lattice<vobj> &X,const Lattice<vobj> &Y,
+			    int orthogdim,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  typedef typename vobj::tensor_reduced tensor_reduced;
+  
+  scalar_type zscale(scale);
+
+  GridBase *grid  = X.Grid();
+
+  int Nsimd  =grid->Nsimd();
+  int Nblock =grid->GlobalDimensions()[orthogdim];
+
+  int fd     =grid->_fdimensions[orthogdim];
+  int ld     =grid->_ldimensions[orthogdim];
+  int rd     =grid->_rdimensions[orthogdim];
+
+  int e1     =grid->_slice_nblock[orthogdim];
+  int e2     =grid->_slice_block [orthogdim];
+  int stride =grid->_slice_stride[orthogdim];
+
+  Coordinate icoor;
+  for(int r=0;r<rd;r++){
+
+    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 
+
+    vector_type    av;
+
+    for(int l=0;l<Nsimd;l++){
+      grid->iCoorFromIindex(icoor,l);
+      int ldx =r+icoor[orthogdim]*rd;
+      scalar_type *as =(scalar_type *)&av;
+      as[l] = scalar_type(a[ldx])*zscale;
+    }
+
+    tensor_reduced at; at=av;
+
+    auto Rv=R.View();
+    auto Xv=X.View();
+    auto Yv=Y.View();
+    thread_loop_collapse2( (int n=0;n<e1;n++) , {
+      for(int b=0;b<e2;b++){
+	int ss= so+n*stride+b;
+	Rv[ss] = at*Xv[ss]+Yv[ss];
+      }
+    });
+  }
+};
+
+/*
+inline GridBase         *makeSubSliceGrid(const GridBase *BlockSolverGrid,int Orthog)
+{
+  int NN    = BlockSolverGrid->_ndimension;
+  int nsimd = BlockSolverGrid->Nsimd();
+  
+  std::vector<int> latt_phys(0);
+  std::vector<int> simd_phys(0);
+  std::vector<int>  mpi_phys(0);
+  
+  for(int d=0;d<NN;d++){
+    if( d!=Orthog ) { 
+      latt_phys.push_back(BlockSolverGrid->_fdimensions[d]);
+      simd_phys.push_back(BlockSolverGrid->_simd_layout[d]);
+      mpi_phys.push_back(BlockSolverGrid->_processors[d]);
+    }
+  }
+  return (GridBase *)new GridCartesian(latt_phys,simd_phys,mpi_phys); 
+}
+*/
+
+template<class vobj>
+static void sliceMaddMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,const Lattice<vobj> &Y,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+
+  //  Lattice<vobj> Xslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+  int nh =  FullGrid->_ndimension;
+  //  int nl = SliceGrid->_ndimension;
+  int nl = nh-1;
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+  thread_region
+  {
+    Vector<vobj> s_x(Nblock);
+
+    thread_loop_collapse_in_region(2 ,(int n=0;n<nblock;n++), {
+     for(int b=0;b<block;b++){
+      int o  = n*stride + b;
+
+      for(int i=0;i<Nblock;i++){
+	s_x[i] = X[o+i*ostride];
+      }
+
+      vobj dot;
+      for(int i=0;i<Nblock;i++){
+	dot = Y[o+i*ostride];
+	for(int j=0;j<Nblock;j++){
+	  dot = dot + s_x[j]*(scale*aa(j,i));
+	}
+	R[o+i*ostride]=dot;
+      }
+    }});
+  }
+};
+
+template<class vobj>
+static void sliceMulMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,int Orthog,RealD scale=1.0) 
+{    
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+
+  int Nblock = X.Grid()->GlobalDimensions()[Orthog];
+
+  GridBase *FullGrid  = X.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+  //  Lattice<vobj> Xslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+  int nh =  FullGrid->_ndimension;
+  //  int nl = SliceGrid->_ndimension;
+  int nl=1;
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+  thread_region
+  {
+    std::vector<vobj> s_x(Nblock);
+
+
+    thread_loop_collapse_in_region( 2 , (int n=0;n<nblock;n++),{
+    for(int b=0;b<block;b++){
+      int o  = n*stride + b;
+
+      for(int i=0;i<Nblock;i++){
+	s_x[i] = X[o+i*ostride];
+      }
+
+      vobj dot;
+      for(int i=0;i<Nblock;i++){
+	dot = s_x[0]*(scale*aa(0,i));
+	for(int j=1;j<Nblock;j++){
+	  dot = dot + s_x[j]*(scale*aa(j,i));
+	}
+	R[o+i*ostride]=dot;
+      }
+    }});
+  }
+};
+
+
+template<class vobj>
+static void sliceInnerProductMatrix(  Eigen::MatrixXcd &mat, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int Orthog) 
+{
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  
+  GridBase *FullGrid  = lhs.Grid();
+  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
+  
+  int Nblock = FullGrid->GlobalDimensions()[Orthog];
+  
+  //  Lattice<vobj> Lslice(SliceGrid);
+  //  Lattice<vobj> Rslice(SliceGrid);
+  
+  mat = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+  assert( FullGrid->_simd_layout[Orthog]==1);
+  int nh =  FullGrid->_ndimension;
+  //  int nl = SliceGrid->_ndimension;
+  int nl = nh-1;
+
+  //FIXME package in a convenient iterator
+  //Should loop over a plane orthogonal to direction "Orthog"
+  int stride=FullGrid->_slice_stride[Orthog];
+  int block =FullGrid->_slice_block [Orthog];
+  int nblock=FullGrid->_slice_nblock[Orthog];
+  int ostride=FullGrid->_ostride[Orthog];
+
+  typedef typename vobj::vector_typeD vector_typeD;
+
+  thread_region
+  {
+    std::vector<vobj> Left(Nblock);
+    std::vector<vobj> Right(Nblock);
+    Eigen::MatrixXcd  mat_thread = Eigen::MatrixXcd::Zero(Nblock,Nblock);
+
+    thread_loop_collapse_in_region( 2, (int n=0;n<nblock;n++),{
+    for(int b=0;b<block;b++){
+
+      int o  = n*stride + b;
+
+      for(int i=0;i<Nblock;i++){
+	Left [i] = lhs[o+i*ostride];
+	Right[i] = rhs[o+i*ostride];
+      }
+
+      for(int i=0;i<Nblock;i++){
+      for(int j=0;j<Nblock;j++){
+	auto tmp = innerProduct(Left[i],Right[j]);
+	auto rtmp = TensorRemove(tmp);
+	mat_thread(i,j) += Reduce(rtmp);
+      }}
+    }});
+    thread_critical
+    {
+      mat += mat_thread;
+    }  
+  }
+
+  for(int i=0;i<Nblock;i++){
+  for(int j=0;j<Nblock;j++){
+    ComplexD sum = mat(i,j);
+    FullGrid->GlobalSum(sum);
+    mat(i,j)=sum;
+  }}
+
+  return;
+}
+
+NAMESPACE_END(Grid);
+
+
+
+

Grid/lattice/Lattice_rng.h

@@ -0,0 +1,518 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_rng.h
+
+    Copyright (C) 2015
+
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+    Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_RNG_H
+#define GRID_LATTICE_RNG_H
+
+#include <random>
+
+#ifdef RNG_SITMO
+#include <Grid/sitmo_rng/sitmo_prng_engine.hpp>
+#endif 
+
+#if defined(RNG_SITMO)
+#define RNG_FAST_DISCARD
+#else 
+#undef  RNG_FAST_DISCARD
+#endif
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////
+// Allow the RNG state to be less dense than the fine grid
+//////////////////////////////////////////////////////////////
+inline int RNGfillable(GridBase *coarse,GridBase *fine)
+{
+
+  int rngdims = coarse->_ndimension;
+
+  // trivially extended in higher dims, with locality guaranteeing RNG state is local to node
+  int lowerdims   = fine->_ndimension - coarse->_ndimension;
+  assert(lowerdims >= 0);
+  for(int d=0;d<lowerdims;d++){
+    assert(fine->_simd_layout[d]==1);
+    assert(fine->_processors[d]==1);
+  }
+
+  int multiplicity=1;
+  for(int d=0;d<lowerdims;d++){
+    multiplicity=multiplicity*fine->_rdimensions[d];
+  }
+  // local and global volumes subdivide cleanly after SIMDization
+  for(int d=0;d<rngdims;d++){
+    int fd= d+lowerdims;
+    assert(coarse->_processors[d]  == fine->_processors[fd]);
+    assert(coarse->_simd_layout[d] == fine->_simd_layout[fd]);
+    assert(((fine->_rdimensions[fd] / coarse->_rdimensions[d])* coarse->_rdimensions[d])==fine->_rdimensions[fd]); 
+
+    multiplicity = multiplicity *fine->_rdimensions[fd] / coarse->_rdimensions[d]; 
+  }
+  return multiplicity;
+}
+
+  
+// merge of April 11 2017
+// this function is necessary for the LS vectorised field
+inline int RNGfillable_general(GridBase *coarse,GridBase *fine)
+{
+  int rngdims = coarse->_ndimension;
+    
+  // trivially extended in higher dims, with locality guaranteeing RNG state is local to node
+  int lowerdims   = fine->_ndimension - coarse->_ndimension;  assert(lowerdims >= 0);
+  // assumes that the higher dimensions are not using more processors
+  // all further divisions are local
+  for(int d=0;d<lowerdims;d++) assert(fine->_processors[d]==1);
+  for(int d=0;d<rngdims;d++) assert(coarse->_processors[d] == fine->_processors[d+lowerdims]);
+
+  // then divide the number of local sites
+  // check that the total number of sims agree, meanse the iSites are the same
+  assert(fine->Nsimd() == coarse->Nsimd());
+
+  // check that the two grids divide cleanly
+  assert( (fine->lSites() / coarse->lSites() ) * coarse->lSites() == fine->lSites() );
+
+  return fine->lSites() / coarse->lSites();
+}
+  
+// real scalars are one component
+template<class scalar,class distribution,class generator> 
+void fillScalar(scalar &s,distribution &dist,generator & gen)
+{
+  s=dist(gen);
+}
+template<class distribution,class generator> 
+void fillScalar(ComplexF &s,distribution &dist, generator &gen)
+{
+  s=ComplexF(dist(gen),dist(gen));
+}
+template<class distribution,class generator> 
+void fillScalar(ComplexD &s,distribution &dist,generator &gen)
+{
+  s=ComplexD(dist(gen),dist(gen));
+}
+  
+class GridRNGbase {
+public:
+  // One generator per site.
+  // Uniform and Gaussian distributions from these generators.
+#ifdef RNG_RANLUX
+  typedef std::ranlux48 RngEngine;
+  typedef uint64_t      RngStateType;
+  static const int RngStateCount = 15;
+#endif 
+#ifdef RNG_MT19937 
+  typedef std::mt19937 RngEngine;
+  typedef uint32_t     RngStateType;
+  static const int     RngStateCount = std::mt19937::state_size;
+#endif
+#ifdef RNG_SITMO
+  typedef sitmo::prng_engine 	RngEngine;
+  typedef uint64_t    	RngStateType;
+  static const int    	RngStateCount = 13;
+#endif
+
+  std::vector<RngEngine>                             _generators;
+  std::vector<std::uniform_real_distribution<RealD> > _uniform;
+  std::vector<std::normal_distribution<RealD> >       _gaussian;
+  std::vector<std::discrete_distribution<int32_t> >   _bernoulli;
+  std::vector<std::uniform_int_distribution<uint32_t> > _uid;
+
+  ///////////////////////
+  // support for parallel init
+  ///////////////////////
+#ifdef RNG_FAST_DISCARD
+  static void Skip(RngEngine &eng,uint64_t site)
+  {
+    /////////////////////////////////////////////////////////////////////////////////////
+    // Skip by 2^40 elements between successive lattice sites
+    // This goes by 10^12.
+    // Consider quenched updating; likely never exceeding rate of 1000 sweeps
+    // per second on any machine. This gives us of order 10^9 seconds, or 100 years
+    // skip ahead.
+    // For HMC unlikely to go at faster than a solve per second, and 
+    // tens of seconds per trajectory so this is clean in all reasonable cases,
+    // and margin of safety is orders of magnitude.
+    // We could hack Sitmo to skip in the higher order words of state if necessary
+      //
+      // Replace with 2^30 ; avoid problem on large volumes
+      //
+    /////////////////////////////////////////////////////////////////////////////////////
+    //      uint64_t skip = site+1;  //   Old init Skipped then drew.  Checked compat with faster init
+      const int shift = 30;
+
+    uint64_t skip = site;
+
+      skip = skip<<shift;
+
+      assert((skip >> shift)==site); // check for overflow
+
+    eng.discard(skip);
+    //      std::cout << " Engine  " <<site << " state " <<eng<<std::endl;
+  } 
+#endif
+  static RngEngine Reseed(RngEngine &eng)
+  {
+    std::vector<uint32_t> newseed;
+    std::uniform_int_distribution<uint32_t> uid;
+    return Reseed(eng,newseed,uid);
+  }
+  static RngEngine Reseed(RngEngine &eng,std::vector<uint32_t> & newseed,
+			  std::uniform_int_distribution<uint32_t> &uid)
+  {
+    const int reseeds=4;
+      
+    newseed.resize(reseeds);
+    for(int i=0;i<reseeds;i++){
+      newseed[i] = uid(eng);
+    }
+    std::seed_seq sseq(newseed.begin(),newseed.end());
+    return RngEngine(sseq);
+  }    
+
+  void GetState(std::vector<RngStateType> & saved,RngEngine &eng) {
+    saved.resize(RngStateCount);
+    std::stringstream ss;
+    ss<<eng;
+    ss.seekg(0,ss.beg);
+    for(int i=0;i<RngStateCount;i++){
+      ss>>saved[i];
+    }
+  }
+  void GetState(std::vector<RngStateType> & saved,int gen) {
+    GetState(saved,_generators[gen]);
+  }
+  void SetState(std::vector<RngStateType> & saved,RngEngine &eng){
+    assert(saved.size()==RngStateCount);
+    std::stringstream ss;
+    for(int i=0;i<RngStateCount;i++){
+      ss<< saved[i]<<" ";
+    }
+    ss.seekg(0,ss.beg);
+    ss>>eng;
+  }
+  void SetState(std::vector<RngStateType> & saved,int gen){
+    SetState(saved,_generators[gen]);
+  }
+  void SetEngine(RngEngine &Eng, int gen){
+    _generators[gen]=Eng;
+  }
+  void GetEngine(RngEngine &Eng, int gen){
+    Eng=_generators[gen];
+  }
+  template<class source> void Seed(source &src, int gen)
+  {
+    _generators[gen] = RngEngine(src);
+  }    
+};
+
+class GridSerialRNG : public GridRNGbase {
+public:
+
+  GridSerialRNG() : GridRNGbase() {
+    _generators.resize(1);
+    _uniform.resize(1,std::uniform_real_distribution<RealD>{0,1});
+    _gaussian.resize(1,std::normal_distribution<RealD>(0.0,1.0) );
+    _bernoulli.resize(1,std::discrete_distribution<int32_t>{1,1});
+    _uid.resize(1,std::uniform_int_distribution<uint32_t>() );
+  }
+
+  template <class sobj,class distribution> inline void fill(sobj &l,std::vector<distribution> &dist){
+
+    typedef typename sobj::scalar_type scalar_type;
+ 
+    int words = sizeof(sobj)/sizeof(scalar_type);
+
+    scalar_type *buf = (scalar_type *) & l;
+
+    dist[0].reset();
+    for(int idx=0;idx<words;idx++){
+      fillScalar(buf[idx],dist[0],_generators[0]);
+    }
+
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+
+  }
+
+  template <class distribution>  inline void fill(ComplexF &l,std::vector<distribution> &dist){
+    dist[0].reset();
+    fillScalar(l,dist[0],_generators[0]);
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(ComplexD &l,std::vector<distribution> &dist){
+    dist[0].reset();
+    fillScalar(l,dist[0],_generators[0]);
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(RealF &l,std::vector<distribution> &dist){
+    dist[0].reset();
+    fillScalar(l,dist[0],_generators[0]);
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(RealD &l,std::vector<distribution> &dist){
+    dist[0].reset();
+    fillScalar(l,dist[0],_generators[0]);
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  // vector fill
+  template <class distribution>  inline void fill(vComplexF &l,std::vector<distribution> &dist){
+    RealF *pointer=(RealF *)&l;
+    dist[0].reset();
+    for(int i=0;i<2*vComplexF::Nsimd();i++){
+      fillScalar(pointer[i],dist[0],_generators[0]);
+    }
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(vComplexD &l,std::vector<distribution> &dist){
+    RealD *pointer=(RealD *)&l;
+    dist[0].reset();
+    for(int i=0;i<2*vComplexD::Nsimd();i++){
+      fillScalar(pointer[i],dist[0],_generators[0]);
+    }
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(vRealF &l,std::vector<distribution> &dist){
+    RealF *pointer=(RealF *)&l;
+    dist[0].reset();
+    for(int i=0;i<vRealF::Nsimd();i++){
+      fillScalar(pointer[i],dist[0],_generators[0]);
+    }
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+  template <class distribution>  inline void fill(vRealD &l,std::vector<distribution> &dist){
+    RealD *pointer=(RealD *)&l;
+    dist[0].reset();
+    for(int i=0;i<vRealD::Nsimd();i++){
+      fillScalar(pointer[i],dist[0],_generators[0]);
+    }
+    CartesianCommunicator::BroadcastWorld(0,(void *)&l,sizeof(l));
+  }
+    
+  void SeedFixedIntegers(const std::vector<int> &seeds){
+    CartesianCommunicator::BroadcastWorld(0,(void *)&seeds[0],sizeof(int)*seeds.size());
+    std::seed_seq src(seeds.begin(),seeds.end());
+    Seed(src,0);
+  }
+
+    void SeedUniqueString(const std::string &s){
+      std::vector<int> seeds;
+      std::stringstream sha;
+      seeds = GridChecksum::sha256_seeds(s);
+      for(int i=0;i<seeds.size();i++) { 
+        sha << std::hex << seeds[i];
+      }
+      std::cout << GridLogMessage << "Intialising serial RNG with unique string '" 
+                << s << "'" << std::endl;
+      std::cout << GridLogMessage << "Seed SHA256: " << sha.str() << std::endl;
+      SeedFixedIntegers(seeds);
+    }
+};
+
+class GridParallelRNG : public GridRNGbase {
+private:
+  double _time_counter;
+  GridBase *_grid;
+  unsigned int _vol;
+
+public:
+  GridBase *Grid(void) const { return _grid; }
+  int generator_idx(int os,int is) {
+    return is*_grid->oSites()+os;
+  }
+
+  GridParallelRNG(GridBase *grid) : GridRNGbase() {
+    _grid = grid;
+    _vol  =_grid->iSites()*_grid->oSites();
+
+    _generators.resize(_vol);
+    _uniform.resize(_vol,std::uniform_real_distribution<RealD>{0,1});
+    _gaussian.resize(_vol,std::normal_distribution<RealD>(0.0,1.0) );
+    _bernoulli.resize(_vol,std::discrete_distribution<int32_t>{1,1});
+    _uid.resize(_vol,std::uniform_int_distribution<uint32_t>() );
+  }
+
+  template <class vobj,class distribution> inline void fill(Lattice<vobj> &l,std::vector<distribution> &dist){
+
+    typedef typename vobj::scalar_object scalar_object;
+    typedef typename vobj::scalar_type scalar_type;
+    typedef typename vobj::vector_type vector_type;
+
+    double inner_time_counter = usecond();
+
+    int multiplicity = RNGfillable_general(_grid, l.Grid()); // l has finer or same grid
+    int Nsimd  = _grid->Nsimd();  // guaranteed to be the same for l.Grid() too
+    int osites = _grid->oSites();  // guaranteed to be <= l.Grid()->oSites() by a factor multiplicity
+    int words  = sizeof(scalar_object) / sizeof(scalar_type);
+
+    auto l_v = l.View();
+    thread_loop( (int ss=0;ss<osites;ss++), {
+      ExtractBuffer<scalar_object> buf(Nsimd);
+      for (int m = 0; m < multiplicity; m++) {  // Draw from same generator multiplicity times
+
+	int sm = multiplicity * ss + m;  // Maps the generator site to the fine site
+
+	for (int si = 0; si < Nsimd; si++) {
+            
+	  int gdx = generator_idx(ss, si);  // index of generator state
+	  scalar_type *pointer = (scalar_type *)&buf[si];
+	  dist[gdx].reset();
+	  for (int idx = 0; idx < words; idx++) 
+	    fillScalar(pointer[idx], dist[gdx], _generators[gdx]);
+	}
+	// merge into SIMD lanes, FIXME suboptimal implementation
+	merge(l_v[sm], buf);
+      }
+      });
+    //    });
+
+    _time_counter += usecond()- inner_time_counter;
+  }
+
+    void SeedUniqueString(const std::string &s){
+      std::vector<int> seeds;
+      seeds = GridChecksum::sha256_seeds(s);
+      std::cout << GridLogMessage << "Intialising parallel RNG with unique string '" 
+                << s << "'" << std::endl;
+      std::cout << GridLogMessage << "Seed SHA256: " << GridChecksum::sha256_string(seeds) << std::endl;
+      SeedFixedIntegers(seeds);
+    }
+  void SeedFixedIntegers(const std::vector<int> &seeds){
+
+    // Everyone generates the same seed_seq based on input seeds
+    CartesianCommunicator::BroadcastWorld(0,(void *)&seeds[0],sizeof(int)*seeds.size());
+
+    std::seed_seq source(seeds.begin(),seeds.end());
+
+    RngEngine master_engine(source);
+
+#ifdef RNG_FAST_DISCARD
+    ////////////////////////////////////////////////
+    // Skip ahead through a single stream.
+    // Applicable to SITMO and other has based/crypto RNGs
+    // Should be applicable to Mersenne Twister, but the C++11
+    // MT implementation does not implement fast discard even though
+    // in principle this is possible
+    ////////////////////////////////////////////////
+
+    // Everybody loops over global volume.
+    thread_loop( (int gidx=0;gidx<_grid->_gsites;gidx++) , {
+	// Where is it?
+	int rank;
+	int o_idx;
+	int i_idx;
+
+	Coordinate gcoor;
+	_grid->GlobalIndexToGlobalCoor(gidx,gcoor);
+	_grid->GlobalCoorToRankIndex(rank,o_idx,i_idx,gcoor);
+	
+	// If this is one of mine we take it
+	if( rank == _grid->ThisRank() ){
+	  int l_idx=generator_idx(o_idx,i_idx);
+	  _generators[l_idx] = master_engine;
+	  Skip(_generators[l_idx],gidx); // Skip to next RNG sequence
+	}
+    });
+#else 
+    ////////////////////////////////////////////////////////////////
+    // Machine and thread decomposition dependent seeding is efficient
+    // and maximally parallel; but NOT reproducible from machine to machine. 
+    // Not ideal, but fastest way to reseed all nodes.
+    ////////////////////////////////////////////////////////////////
+    {
+      // Obtain one Reseed per processor
+      int Nproc = _grid->ProcessorCount();
+      std::vector<RngEngine> seeders(Nproc);
+      int me= _grid->ThisRank();
+      for(int p=0;p<Nproc;p++){
+	seeders[p] = Reseed(master_engine);
+      }
+      master_engine = seeders[me];
+    }
+
+    {
+      // Obtain one reseeded generator per thread
+      int Nthread = GridThread::GetThreads();
+      std::vector<RngEngine> seeders(Nthread);
+      for(int t=0;t<Nthread;t++){
+	seeders[t] = Reseed(master_engine);
+      }
+
+      thread_loop( (int t=0;t<Nthread;t++), {
+	// set up one per local site in threaded fashion
+	std::vector<uint32_t> newseeds;
+	std::uniform_int_distribution<uint32_t> uid;	
+	for(int l=0;l<_grid->lSites();l++) {
+	  if ( (l%Nthread)==t ) {
+	    _generators[l] = Reseed(seeders[t],newseeds,uid);
+	  }
+	}
+      });
+    }
+#endif
+  }
+
+  void Report(){
+    std::cout << GridLogMessage << "Time spent in the fill() routine by GridParallelRNG: "<< _time_counter/1e3 << " ms" << std::endl;
+  }
+
+
+  ////////////////////////////////////////////////////////////////////////
+  // Support for rigorous test of RNG's
+  // Return uniform random uint32_t from requested site generator
+  ////////////////////////////////////////////////////////////////////////
+  uint32_t GlobalU01(int gsite){
+
+    uint32_t the_number;
+    // who
+    int rank,o_idx,i_idx;
+    Coordinate gcoor;
+    _grid->GlobalIndexToGlobalCoor(gsite,gcoor);
+    _grid->GlobalCoorToRankIndex(rank,o_idx,i_idx,gcoor);
+
+    // draw
+    int l_idx=generator_idx(o_idx,i_idx);
+    if( rank == _grid->ThisRank() ){
+      the_number = _uid[l_idx](_generators[l_idx]);
+    }
+      
+    // share & return
+    _grid->Broadcast(rank,(void *)&the_number,sizeof(the_number));
+    return the_number;
+  }
+
+};
+
+template <class vobj> inline void random(GridParallelRNG &rng,Lattice<vobj> &l)   { rng.fill(l,rng._uniform);  }
+template <class vobj> inline void gaussian(GridParallelRNG &rng,Lattice<vobj> &l) { rng.fill(l,rng._gaussian); }
+template <class vobj> inline void bernoulli(GridParallelRNG &rng,Lattice<vobj> &l){ rng.fill(l,rng._bernoulli);}
+
+template <class sobj> inline void random(GridSerialRNG &rng,sobj &l)   { rng.fill(l,rng._uniform  ); }
+template <class sobj> inline void gaussian(GridSerialRNG &rng,sobj &l) { rng.fill(l,rng._gaussian ); }
+template <class sobj> inline void bernoulli(GridSerialRNG &rng,sobj &l){ rng.fill(l,rng._bernoulli); }
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_trace.h

@@ -0,0 +1,69 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_trace.h
+
+    Copyright (C) 2015
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_TRACE_H
+#define GRID_LATTICE_TRACE_H
+
+///////////////////////////////////////////////
+// Tracing, transposing, peeking, poking
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Trace
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj>
+inline auto trace(const Lattice<vobj> &lhs)  -> Lattice<decltype(trace(vobj()))>
+{
+  Lattice<decltype(trace(vobj()))> ret(lhs.Grid());
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop( ss, lhs_v, {
+    ret_v[ss] = trace(lhs_v[ss]);
+  });
+  return ret;
+};
+    
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Trace Index level dependent operation
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj>
+inline auto TraceIndex(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<Index>(vobj()))>
+{
+  Lattice<decltype(traceIndex<Index>(vobj()))> ret(lhs.Grid());
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop( ss, lhs_v, {
+    ret_v[ss] = traceIndex<Index>(lhs_v[ss]);
+  });
+  return ret;
+};
+
+NAMESPACE_END(Grid);
+#endif
+

Grid/lattice/Lattice_transpose.h

@@ -0,0 +1,68 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_transpose.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_TRANSPOSE_H
+#define GRID_LATTICE_TRANSPOSE_H
+
+///////////////////////////////////////////////
+// Transpose
+///////////////////////////////////////////////
+
+NAMESPACE_BEGIN(Grid);
+
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Transpose
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<class vobj>
+inline Lattice<vobj> transpose(const Lattice<vobj> &lhs){
+  Lattice<vobj> ret(lhs.Grid());
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop(ss,lhs_v,{
+    ret_v[ss] = transpose(lhs_v[ss]);
+  });
+  return ret;
+};
+    
+////////////////////////////////////////////////////////////////////////////////////////////////////
+// Index level dependent transpose
+////////////////////////////////////////////////////////////////////////////////////////////////////
+template<int Index,class vobj>
+inline auto TransposeIndex(const Lattice<vobj> &lhs) -> Lattice<decltype(transposeIndex<Index>(vobj()))>
+{
+  Lattice<decltype(transposeIndex<Index>(vobj()))> ret(lhs.Grid());
+  auto ret_v = ret.View();
+  auto lhs_v = lhs.View();
+  accelerator_loop(ss,lhs_v,{
+      ret_v[ss] = transposeIndex<Index>(lhs_v[ss]);
+  });
+  return ret;
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_unary.h

@@ -0,0 +1,80 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_unary.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LATTICE_UNARY_H
+#define GRID_LATTICE_UNARY_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<class obj> Lattice<obj> pow(const Lattice<obj> &rhs_i,RealD y){
+  Lattice<obj> ret_i(rhs_i.Grid());
+  auto rhs = rhs_i.View();
+  auto ret = ret_i.View();
+  ret.Checkerboard() = rhs.Checkerboard();
+  accelerator_loop(ss,rhs,{
+    ret[ss]=pow(rhs[ss],y);
+  });
+  return ret_i;
+}
+template<class obj> Lattice<obj> mod(const Lattice<obj> &rhs_i,Integer y){
+  Lattice<obj> ret_i(rhs_i.Grid());
+  auto rhs = rhs_i.View();
+  auto ret = ret_i.View();
+  ret.Checkerboard() = rhs.Checkerboard();
+  accelerator_loop(ss,rhs,{
+    ret[ss]=mod(rhs[ss],y);
+  });
+  return ret_i;
+}
+
+template<class obj> Lattice<obj> div(const Lattice<obj> &rhs_i,Integer y){
+  Lattice<obj> ret_i(rhs_i.Grid());
+  auto ret = ret_i.View();
+  auto rhs = rhs_i.View();
+  ret.Checkerboard() = rhs_i.Checkerboard();
+  accelerator_loop(ss,rhs,{
+    ret[ss]=div(rhs[ss],y);
+  });
+  return ret_i;
+}
+
+template<class obj> Lattice<obj> expMat(const Lattice<obj> &rhs_i, RealD alpha, Integer Nexp = DEFAULT_MAT_EXP){
+  Lattice<obj> ret_i(rhs_i.Grid());
+  auto rhs = rhs_i.View();
+  auto ret = ret_i.View();
+  ret.Checkerboard() = rhs.Checkerboard();
+  accelerator_loop(ss,rhs,{
+    ret[ss]=Exponentiate(rhs[ss],alpha, Nexp);
+  });
+  return ret_i;
+}
+
+NAMESPACE_END(Grid);
+#endif

Grid/lattice/Lattice_where.h

@@ -0,0 +1,86 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/lattice/Lattice_where.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_LATTICE_WHERE_H
+#define GRID_LATTICE_WHERE_H
+namespace Grid {
+// Must implement the predicate gating the 
+// Must be able to reduce the predicate down to a single vInteger per site.
+// Must be able to require the type be iScalar x iScalar x ....
+//                              give a GetVtype method in iScalar
+//                              and blow away the tensor structures.
+//
+template<class vobj,class iobj>
+inline void whereWolf(Lattice<vobj> &ret,const Lattice<iobj> &predicate,Lattice<vobj> &iftrue,Lattice<vobj> &iffalse)
+{
+  conformable(iftrue,iffalse);
+  conformable(iftrue,predicate);
+  conformable(iftrue,ret);
+
+  GridBase *grid=iftrue._grid;
+
+  typedef typename vobj::scalar_object scalar_object;
+  typedef typename vobj::scalar_type scalar_type;
+  typedef typename vobj::vector_type vector_type;
+  typedef typename iobj::vector_type mask_type;
+
+  const int Nsimd = grid->Nsimd();
+
+  std::vector<Integer> mask(Nsimd);
+  std::vector<scalar_object> truevals (Nsimd);
+  std::vector<scalar_object> falsevals(Nsimd);
+
+  parallel_for(int ss=0;ss<iftrue._grid->oSites(); ss++){
+
+    extract(iftrue._odata[ss]   ,truevals);
+    extract(iffalse._odata[ss]  ,falsevals);
+    extract<vInteger,Integer>(TensorRemove(predicate._odata[ss]),mask);
+
+    for(int s=0;s<Nsimd;s++){
+      if (mask[s]) falsevals[s]=truevals[s];
+    }
+
+    merge(ret._odata[ss],falsevals);
+  }
+}
+
+template<class vobj,class iobj>
+inline Lattice<vobj> whereWolf(const Lattice<iobj> &predicate,Lattice<vobj> &iftrue,Lattice<vobj> &iffalse)
+{
+  conformable(iftrue,iffalse);
+  conformable(iftrue,predicate);
+
+  Lattice<vobj> ret(iftrue._grid);
+
+  where(ret,predicate,iftrue,iffalse);
+
+  return ret;
+}
+}
+#endif

Grid/log/Log.cc

@@ -0,0 +1,117 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/Log.cc
+
+Copyright (C) 2015
+
+Author: Antonin Portelli <antonin.portelli@me.com>
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#include <Grid/GridCore.h>
+#include <Grid/util/CompilerCompatible.h>
+
+#include <cxxabi.h>
+#include <memory>
+
+NAMESPACE_BEGIN(Grid);
+
+std::string demangle(const char* name) {
+    
+  int status = -4; // some arbitrary value to eliminate the compiler warning
+    
+  // enable c++11 by passing the flag -std=c++11 to g++
+  std::unique_ptr<char, void(*)(void*)> res {
+    abi::__cxa_demangle(name, NULL, NULL, &status),
+      std::free
+      };
+    
+  return (status==0) ? res.get() : name ;
+}
+  
+GridStopWatch Logger::GlobalStopWatch;
+int Logger::timestamp;
+std::ostream Logger::devnull(0);
+
+void GridLogTimestamp(int on){
+  Logger::Timestamp(on);
+}
+
+Colours GridLogColours(0);
+GridLogger GridLogIRL    (1, "IRL"   , GridLogColours, "NORMAL");
+GridLogger GridLogSolver (1, "Solver", GridLogColours, "NORMAL");
+GridLogger GridLogError  (1, "Error" , GridLogColours, "RED");
+GridLogger GridLogWarning(1, "Warning", GridLogColours, "YELLOW");
+GridLogger GridLogMessage(1, "Message", GridLogColours, "NORMAL");
+GridLogger GridLogDebug  (1, "Debug", GridLogColours, "PURPLE");
+GridLogger GridLogPerformance(1, "Performance", GridLogColours, "GREEN");
+GridLogger GridLogIterative  (1, "Iterative", GridLogColours, "BLUE");
+GridLogger GridLogIntegrator (1, "Integrator", GridLogColours, "BLUE");
+
+void GridLogConfigure(std::vector<std::string> &logstreams) {
+  GridLogError.Active(0);
+  GridLogWarning.Active(0);
+  GridLogMessage.Active(1); // at least the messages should be always on
+  GridLogIterative.Active(0);
+  GridLogDebug.Active(0);
+  GridLogPerformance.Active(0);
+  GridLogIntegrator.Active(0);
+  GridLogColours.Active(0);
+
+  for (int i = 0; i < logstreams.size(); i++) {
+    if (logstreams[i] == std::string("Error")) GridLogError.Active(1);
+    if (logstreams[i] == std::string("Warning")) GridLogWarning.Active(1);
+    if (logstreams[i] == std::string("NoMessage")) GridLogMessage.Active(0);
+    if (logstreams[i] == std::string("Iterative")) GridLogIterative.Active(1);
+    if (logstreams[i] == std::string("Debug")) GridLogDebug.Active(1);
+    if (logstreams[i] == std::string("Performance"))
+      GridLogPerformance.Active(1);
+    if (logstreams[i] == std::string("Integrator")) GridLogIntegrator.Active(1);
+    if (logstreams[i] == std::string("Colours")) GridLogColours.Active(1);
+  }
+}
+
+////////////////////////////////////////////////////////////
+// Verbose limiter on MPI tasks
+////////////////////////////////////////////////////////////
+void Grid_quiesce_nodes(void) {
+  int me = 0;
+#if defined(GRID_COMMS_MPI) || defined(GRID_COMMS_MPI3) || defined(GRID_COMMS_MPIT)
+  MPI_Comm_rank(MPI_COMM_WORLD, &me);
+#endif
+#ifdef GRID_COMMS_SHMEM
+  me = shmem_my_pe();
+#endif
+  if (me) {
+    std::cout.setstate(std::ios::badbit);
+  }
+}
+
+void Grid_unquiesce_nodes(void) {
+#if defined(GRID_COMMS_MPI) || defined(GRID_COMMS_MPI3) || defined(GRID_COMMS_MPIT)
+  std::cout.clear();
+#endif
+}
+NAMESPACE_END(Grid);
+

Grid/log/Log.h

@@ -0,0 +1,217 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Log.h
+
+    Copyright (C) 2015
+
+    Author: Antonin Portelli <antonin.portelli@me.com>
+    Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <map>
+
+#ifndef GRID_LOG_H
+#define GRID_LOG_H
+
+#ifdef HAVE_EXECINFO_H
+#include <execinfo.h>
+#endif
+
+NAMESPACE_BEGIN(Grid);
+
+//////////////////////////////////////////////////////////////////////////////////////////////////
+// Dress the output; use std::chrono for time stamping via the StopWatch class
+//////////////////////////////////////////////////////////////////////////////////////////////////
+
+class Colours{
+protected:
+  bool is_active;
+public:
+  std::map<std::string, std::string> colour;
+
+  Colours(bool activate=false){
+    Active(activate);
+  };
+
+  void Active(bool activate){
+    is_active=activate;
+    if (is_active){
+      colour["BLACK"]  ="\033[30m";
+      colour["RED"]    ="\033[31m";
+      colour["GREEN"]  ="\033[32m";
+      colour["YELLOW"] ="\033[33m";
+      colour["BLUE"]   ="\033[34m";
+      colour["PURPLE"] ="\033[35m";
+      colour["CYAN"]   ="\033[36m";
+      colour["WHITE"]  ="\033[37m";
+      colour["NORMAL"] ="\033[0;39m";
+    } else {
+      colour["BLACK"] ="";
+      colour["RED"]   ="";
+      colour["GREEN"] ="";
+      colour["YELLOW"]="";
+      colour["BLUE"]  ="";
+      colour["PURPLE"]="";
+      colour["CYAN"]  ="";
+      colour["WHITE"] ="";
+      colour["NORMAL"]="";
+    }
+  };
+};
+
+
+class Logger {
+protected:
+  Colours &Painter;
+  int active;
+  int timing_mode;
+  int topWidth{-1}, chanWidth{-1};
+  static int timestamp;
+  std::string name, topName;
+  std::string COLOUR;
+
+public:
+  static GridStopWatch GlobalStopWatch;
+  GridStopWatch         LocalStopWatch;
+  GridStopWatch *StopWatch;
+  static std::ostream devnull;
+
+  std::string background() {return Painter.colour["NORMAL"];}
+  std::string evidence() {return Painter.colour["YELLOW"];}
+  std::string colour() {return Painter.colour[COLOUR];}
+
+  Logger(std::string topNm, int on, std::string nm, Colours& col_class, std::string col)  : active(on),
+											    name(nm),
+											    topName(topNm),
+											    Painter(col_class),
+											    timing_mode(0),
+											    COLOUR(col) 
+  {
+    StopWatch = & GlobalStopWatch;
+  };
+  
+  void Active(int on) {active = on;};
+  int  isActive(void) {return active;};
+  static void Timestamp(int on) {timestamp = on;};
+  void Reset(void) { 
+    StopWatch->Reset(); 
+    StopWatch->Start(); 
+  }
+  void TimingMode(int on) { 
+    timing_mode = on; 
+    if(on) { 
+      StopWatch = &LocalStopWatch;
+      Reset(); 
+    }
+  }
+  void setTopWidth(const int w) {topWidth = w;}
+  void setChanWidth(const int w) {chanWidth = w;}
+
+  friend std::ostream& operator<< (std::ostream& stream, Logger& log){
+
+    if ( log.active ) {
+      stream << log.background()<<  std::left;
+      if (log.topWidth > 0)
+      {
+        stream << std::setw(log.topWidth);
+      }
+      stream << log.topName << log.background()<< " : ";
+      stream << log.colour() <<  std::left;
+      if (log.chanWidth > 0)
+      {
+        stream << std::setw(log.chanWidth);
+      }
+      stream << log.name << log.background() << " : ";
+      if ( log.timestamp ) {
+	log.StopWatch->Stop();
+	GridTime now = log.StopWatch->Elapsed();
+	
+	if ( log.timing_mode==1 ) log.StopWatch->Reset();
+	log.StopWatch->Start();
+	stream << log.evidence()
+	       << now	       << log.background() << " : " ;
+      }
+      stream << log.colour();
+      return stream;
+    } else { 
+      return devnull;
+    }
+  }
+
+};
+
+class GridLogger: public Logger {
+public:
+  GridLogger(int on, std::string nm, Colours&col_class, std::string col_key = "NORMAL"):
+    Logger("Grid", on, nm, col_class, col_key){};
+};
+
+void GridLogConfigure(std::vector<std::string> &logstreams);
+
+extern GridLogger GridLogIRL;
+extern GridLogger GridLogSolver;
+extern GridLogger GridLogError;
+extern GridLogger GridLogWarning;
+extern GridLogger GridLogMessage;
+extern GridLogger GridLogDebug  ;
+extern GridLogger GridLogPerformance;
+extern GridLogger GridLogIterative  ;
+extern GridLogger GridLogIntegrator  ;
+extern Colours    GridLogColours;
+
+std::string demangle(const char* name) ;
+
+#define _NBACKTRACE (256)
+extern void * Grid_backtrace_buffer[_NBACKTRACE];
+
+#define BACKTRACEFILE() {						\
+    char string[20];							\
+    std::sprintf(string,"backtrace.%d",CartesianCommunicator::RankWorld()); \
+    std::FILE * fp = std::fopen(string,"w");				\
+    BACKTRACEFP(fp)							\
+      std::fclose(fp);							\
+  }
+
+
+#ifdef HAVE_EXECINFO_H
+#define BACKTRACEFP(fp) {						\
+    int symbols    = backtrace        (Grid_backtrace_buffer,_NBACKTRACE); \
+    char **strings = backtrace_symbols(Grid_backtrace_buffer,symbols);	\
+    for (int i = 0; i < symbols; i++){					\
+      std::fprintf (fp,"BackTrace Strings: %d %s\n",i, demangle(strings[i]).c_str()); std::fflush(fp); \
+    }									\
+  }
+#else 
+#define BACKTRACEFP(fp) {						\
+    std::fprintf (fp,"BT %d %lx\n",0, __builtin_return_address(0)); std::fflush(fp); \
+    std::fprintf (fp,"BT %d %lx\n",1, __builtin_return_address(1)); std::fflush(fp); \
+    std::fprintf (fp,"BT %d %lx\n",2, __builtin_return_address(2)); std::fflush(fp); \
+    std::fprintf (fp,"BT %d %lx\n",3, __builtin_return_address(3)); std::fflush(fp); \
+  }
+#endif
+
+#define BACKTRACE() BACKTRACEFP(stdout) 
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/parallelIO/BinaryIO.cc

@@ -0,0 +1,3 @@
+#include <Grid/GridCore.h>
+
+int Grid::BinaryIO::latticeWriteMaxRetry = -1;

Grid/parallelIO/BinaryIO.h

@@ -0,0 +1,751 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/parallelIO/BinaryIO.h
+
+    Copyright (C) 2015
+
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+    Author: Guido Cossu<guido.cossu@ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#pragma once
+
+#if defined(GRID_COMMS_MPI) || defined(GRID_COMMS_MPI3) || defined(GRID_COMMS_MPIT) 
+#define USE_MPI_IO
+#else
+#undef  USE_MPI_IO
+#endif
+
+#ifdef HAVE_ENDIAN_H
+#include <endian.h>
+#endif
+
+#include <arpa/inet.h>
+#include <algorithm>
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////
+// Byte reversal garbage
+/////////////////////////////////////////////////////////////////////////////////
+inline uint32_t byte_reverse32(uint32_t f) { 
+      f = ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+      return f;
+}
+inline uint64_t byte_reverse64(uint64_t f) { 
+  uint64_t g;
+  g = ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+  g = g << 32;
+  f = f >> 32;
+  g|= ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+  return g;
+}
+
+#if BYTE_ORDER == BIG_ENDIAN 
+inline uint64_t Grid_ntohll(uint64_t A) { return A; }
+#else
+inline uint64_t Grid_ntohll(uint64_t A) { 
+  return byte_reverse64(A);
+}
+#endif
+
+// A little helper
+inline void removeWhitespace(std::string &key)
+{
+  key.erase(std::remove_if(key.begin(), key.end(), ::isspace),key.end());
+}
+
+///////////////////////////////////////////////////////////////////////////////////////////////////
+// Static class holding the parallel IO code
+// Could just use a namespace
+///////////////////////////////////////////////////////////////////////////////////////////////////
+class BinaryIO {
+ public:
+  static int latticeWriteMaxRetry;
+
+  /////////////////////////////////////////////////////////////////////////////
+  // more byte manipulation helpers
+  /////////////////////////////////////////////////////////////////////////////
+
+  template<class vobj> static inline void Uint32Checksum(Lattice<vobj> &lat,uint32_t &nersc_csum)
+  {
+    typedef typename vobj::scalar_object sobj;
+
+    GridBase *grid = lat.Grid();
+    uint64_t lsites = grid->lSites();
+
+    std::vector<sobj> scalardata(lsites); 
+    unvectorizeToLexOrdArray(scalardata,lat);    
+
+    NerscChecksum(grid,scalardata,nersc_csum);
+  }
+
+  template <class fobj>
+  static inline void NerscChecksum(GridBase *grid, std::vector<fobj> &fbuf, uint32_t &nersc_csum)
+  {
+    const uint64_t size32 = sizeof(fobj) / sizeof(uint32_t);
+
+    uint64_t lsites = grid->lSites();
+    if (fbuf.size() == 1)
+    {
+      lsites = 1;
+    }
+
+    thread_region
+    {
+      uint32_t nersc_csum_thr = 0;
+
+      thread_loop_in_region( (uint64_t local_site = 0; local_site < lsites; local_site++),
+      {
+        uint32_t *site_buf = (uint32_t *)&fbuf[local_site];
+        for (uint64_t j = 0; j < size32; j++)
+        {
+          nersc_csum_thr = nersc_csum_thr + site_buf[j];
+        }
+      });
+
+      thread_critical
+      {
+        nersc_csum += nersc_csum_thr;
+      }
+    }
+  }
+
+  template<class fobj> static inline void ScidacChecksum(GridBase *grid,std::vector<fobj> &fbuf,uint32_t &scidac_csuma,uint32_t &scidac_csumb)
+  {
+    int nd = grid->_ndimension;
+
+    uint64_t lsites              =grid->lSites();
+    if (fbuf.size()==1) {
+      lsites=1;
+    }
+    Coordinate local_vol   =grid->LocalDimensions();
+    Coordinate local_start =grid->LocalStarts();
+    Coordinate global_vol  =grid->FullDimensions();
+
+    thread_region
+    { 
+      Coordinate coor(nd);
+      uint32_t scidac_csuma_thr=0;
+      uint32_t scidac_csumb_thr=0;
+      uint32_t site_crc=0;
+
+      thread_loop_in_region( (uint64_t local_site=0;local_site<lsites;local_site++),{
+
+	uint32_t * site_buf = (uint32_t *)&fbuf[local_site];
+
+	/* 
+	 * Scidac csum  is rather more heavyweight
+	 * FIXME -- 128^3 x 256 x 16 will overflow.
+	 */
+	
+	int global_site;
+
+	Lexicographic::CoorFromIndex(coor,local_site,local_vol);
+
+	for(int d=0;d<nd;d++) {
+	  coor[d] = coor[d]+local_start[d];
+	}
+
+	Lexicographic::IndexFromCoor(coor,global_site,global_vol);
+
+	uint32_t gsite29   = global_site%29;
+	uint32_t gsite31   = global_site%31;
+	
+	site_crc = crc32(0,(unsigned char *)site_buf,sizeof(fobj));
+	//	std::cout << "Site "<<local_site << " crc "<<std::hex<<site_crc<<std::dec<<std::endl;
+	//	std::cout << "Site "<<local_site << std::hex<<site_buf[0] <<site_buf[1]<<std::dec <<std::endl;
+	scidac_csuma_thr ^= site_crc<<gsite29 | site_crc>>(32-gsite29);
+	scidac_csumb_thr ^= site_crc<<gsite31 | site_crc>>(32-gsite31);
+      });
+
+      thread_critical
+      {
+	scidac_csuma^= scidac_csuma_thr;
+	scidac_csumb^= scidac_csumb_thr;
+      }
+    }
+  }
+
+  // Network is big endian
+  static inline void htobe32_v(void *file_object,uint32_t bytes){ be32toh_v(file_object,bytes);} 
+  static inline void htobe64_v(void *file_object,uint32_t bytes){ be64toh_v(file_object,bytes);} 
+  static inline void htole32_v(void *file_object,uint32_t bytes){ le32toh_v(file_object,bytes);} 
+  static inline void htole64_v(void *file_object,uint32_t bytes){ le64toh_v(file_object,bytes);} 
+
+  static inline void be32toh_v(void *file_object,uint64_t bytes)
+  {
+    uint32_t * f = (uint32_t *)file_object;
+    uint64_t count = bytes/sizeof(uint32_t);
+    thread_loop( (uint64_t i=0;i<count;i++),{  
+      f[i] = ntohl(f[i]);
+    });
+  }
+  // LE must Swap and switch to host
+  static inline void le32toh_v(void *file_object,uint64_t bytes)
+  {
+    uint32_t *fp = (uint32_t *)file_object;
+    uint32_t f;
+
+    uint64_t count = bytes/sizeof(uint32_t);
+    thread_loop( (uint64_t i=0;i<count;i++),{  
+      f = fp[i];
+      // got network order and the network to host
+      f = ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+      fp[i] = ntohl(f);
+    });
+  }
+
+  // BE is same as network
+  static inline void be64toh_v(void *file_object,uint64_t bytes)
+  {
+    uint64_t * f = (uint64_t *)file_object;
+    uint64_t count = bytes/sizeof(uint64_t);
+    thread_loop( (uint64_t i=0;i<count;i++),{  
+      f[i] = Grid_ntohll(f[i]);
+    });
+  }
+  
+  // LE must swap and switch;
+  static inline void le64toh_v(void *file_object,uint64_t bytes)
+  {
+    uint64_t *fp = (uint64_t *)file_object;
+    uint64_t f,g;
+    
+    uint64_t count = bytes/sizeof(uint64_t);
+    thread_loop( (uint64_t i=0;i<count;i++),{  
+      f = fp[i];
+      // got network order and the network to host
+      g = ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+      g = g << 32;
+      f = f >> 32;
+      g|= ((f&0xFF)<<24) | ((f&0xFF00)<<8) | ((f&0xFF0000)>>8) | ((f&0xFF000000UL)>>24) ; 
+      fp[i] = Grid_ntohll(g);
+    });
+  }
+  /////////////////////////////////////////////////////////////////////////////
+  // Real action:
+  // Read or Write distributed lexico array of ANY object to a specific location in file 
+  //////////////////////////////////////////////////////////////////////////////////////
+
+  static const int BINARYIO_MASTER_APPEND = 0x10;
+  static const int BINARYIO_UNORDERED     = 0x08;
+  static const int BINARYIO_LEXICOGRAPHIC = 0x04;
+  static const int BINARYIO_READ          = 0x02;
+  static const int BINARYIO_WRITE         = 0x01;
+
+  template<class word,class fobj>
+  static inline void IOobject(word w,
+			      GridBase *grid,
+			      std::vector<fobj> &iodata,
+			      std::string file,
+			      uint64_t& offset,
+			      const std::string &format, int control,
+			      uint32_t &nersc_csum,
+			      uint32_t &scidac_csuma,
+			      uint32_t &scidac_csumb)
+  {
+    grid->Barrier();
+    GridStopWatch timer; 
+    GridStopWatch bstimer;
+    
+    nersc_csum=0;
+    scidac_csuma=0;
+    scidac_csumb=0;
+
+    int ndim                 = grid->Dimensions();
+    int nrank                = grid->ProcessorCount();
+    int myrank               = grid->ThisRank();
+
+    Coordinate  psizes = grid->ProcessorGrid(); 
+    Coordinate  pcoor  = grid->ThisProcessorCoor();
+    Coordinate gLattice= grid->GlobalDimensions();
+    Coordinate lLattice= grid->LocalDimensions();
+
+    Coordinate lStart(ndim);
+    Coordinate gStart(ndim);
+
+    // Flatten the file
+    uint64_t lsites = grid->lSites();
+    if ( control & BINARYIO_MASTER_APPEND )  {
+      assert(iodata.size()==1);
+    } else {
+      assert(lsites==iodata.size());
+    }
+    for(int d=0;d<ndim;d++){
+      gStart[d] = lLattice[d]*pcoor[d];
+      lStart[d] = 0;
+    }
+
+#ifdef USE_MPI_IO
+    std::vector<int> distribs(ndim,MPI_DISTRIBUTE_BLOCK);
+    std::vector<int> dargs   (ndim,MPI_DISTRIBUTE_DFLT_DARG);
+    MPI_Datatype mpiObject;
+    MPI_Datatype fileArray;
+    MPI_Datatype localArray;
+    MPI_Datatype mpiword;
+    MPI_Offset disp = offset;
+    MPI_File fh ;
+    MPI_Status status;
+    int numword;
+
+    if ( sizeof( word ) == sizeof(float ) ) {
+      numword = sizeof(fobj)/sizeof(float);
+      mpiword = MPI_FLOAT;
+    } else {
+      numword = sizeof(fobj)/sizeof(double);
+      mpiword = MPI_DOUBLE;
+    }
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Sobj in MPI phrasing
+    //////////////////////////////////////////////////////////////////////////////
+    int ierr;
+    ierr = MPI_Type_contiguous(numword,mpiword,&mpiObject);    assert(ierr==0);
+    ierr = MPI_Type_commit(&mpiObject);
+
+    //////////////////////////////////////////////////////////////////////////////
+    // File global array data type
+    //////////////////////////////////////////////////////////////////////////////
+    ierr=MPI_Type_create_subarray(ndim,&gLattice[0],&lLattice[0],&gStart[0],MPI_ORDER_FORTRAN, mpiObject,&fileArray);    assert(ierr==0);
+    ierr=MPI_Type_commit(&fileArray);    assert(ierr==0);
+
+    //////////////////////////////////////////////////////////////////////////////
+    // local lattice array
+    //////////////////////////////////////////////////////////////////////////////
+    ierr=MPI_Type_create_subarray(ndim,&lLattice[0],&lLattice[0],&lStart[0],MPI_ORDER_FORTRAN, mpiObject,&localArray);    assert(ierr==0);
+    ierr=MPI_Type_commit(&localArray);    assert(ierr==0);
+#endif
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Byte order
+    //////////////////////////////////////////////////////////////////////////////
+    int ieee32big = (format == std::string("IEEE32BIG"));
+    int ieee32    = (format == std::string("IEEE32"));
+    int ieee64big = (format == std::string("IEEE64BIG"));
+    int ieee64    = (format == std::string("IEEE64"));
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Do the I/O
+    //////////////////////////////////////////////////////////////////////////////
+    if ( control & BINARYIO_READ ) { 
+
+      timer.Start();
+
+      if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
+#ifdef USE_MPI_IO
+	std::cout<< GridLogMessage<<"IOobject: MPI read I/O "<< file<< std::endl;
+	ierr=MPI_File_open(grid->communicator,(char *) file.c_str(), MPI_MODE_RDONLY, MPI_INFO_NULL, &fh);    assert(ierr==0);
+	ierr=MPI_File_set_view(fh, disp, mpiObject, fileArray, "native", MPI_INFO_NULL);    assert(ierr==0);
+	ierr=MPI_File_read_all(fh, &iodata[0], 1, localArray, &status);    assert(ierr==0);
+	MPI_File_close(&fh);
+	MPI_Type_free(&fileArray);
+	MPI_Type_free(&localArray);
+#else 
+	assert(0);
+#endif
+      } else {
+	std::cout << GridLogMessage <<"IOobject: C++ read I/O " << file << " : "
+                  << iodata.size() * sizeof(fobj) << " bytes and offset " << offset << std::endl;
+        std::ifstream fin;
+	fin.open(file, std::ios::binary | std::ios::in);
+        if (control & BINARYIO_MASTER_APPEND)
+        {
+          fin.seekg(-sizeof(fobj), fin.end);
+        }
+        else
+        {
+          fin.seekg(offset + myrank * lsites * sizeof(fobj));
+        }
+        fin.read((char *)&iodata[0], iodata.size() * sizeof(fobj));
+        assert(fin.fail() == 0);
+        fin.close();
+      }
+      timer.Stop();
+
+      grid->Barrier();
+
+      bstimer.Start();
+      ScidacChecksum(grid,iodata,scidac_csuma,scidac_csumb);
+      if (ieee32big) be32toh_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee32)    le32toh_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee64big) be64toh_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee64)    le64toh_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      NerscChecksum(grid,iodata,nersc_csum);
+      bstimer.Stop();
+    }
+    
+    if ( control & BINARYIO_WRITE ) { 
+
+      bstimer.Start();
+      NerscChecksum(grid,iodata,nersc_csum);
+      if (ieee32big) htobe32_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee32)    htole32_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee64big) htobe64_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      if (ieee64)    htole64_v((void *)&iodata[0], sizeof(fobj)*iodata.size());
+      ScidacChecksum(grid,iodata,scidac_csuma,scidac_csumb);
+      bstimer.Stop();
+
+      grid->Barrier();
+
+      timer.Start();
+      if ( (control & BINARYIO_LEXICOGRAPHIC) && (nrank > 1) ) {
+#ifdef USE_MPI_IO
+        std::cout << GridLogMessage <<"IOobject: MPI write I/O " << file << std::endl;
+        ierr = MPI_File_open(grid->communicator, (char *)file.c_str(), MPI_MODE_RDWR | MPI_MODE_CREATE, MPI_INFO_NULL, &fh);
+	//        std::cout << GridLogMessage << "Checking for errors" << std::endl;
+        if (ierr != MPI_SUCCESS)
+        {
+          char error_string[BUFSIZ];
+          int length_of_error_string, error_class;
+
+          MPI_Error_class(ierr, &error_class);
+          MPI_Error_string(error_class, error_string, &length_of_error_string);
+          fprintf(stderr, "%3d: %s\n", myrank, error_string);
+          MPI_Error_string(ierr, error_string, &length_of_error_string);
+          fprintf(stderr, "%3d: %s\n", myrank, error_string);
+          MPI_Abort(MPI_COMM_WORLD, 1); //assert(ierr == 0);
+        }
+
+        std::cout << GridLogDebug << "MPI write I/O set view " << file << std::endl;
+        ierr = MPI_File_set_view(fh, disp, mpiObject, fileArray, "native", MPI_INFO_NULL);
+        assert(ierr == 0);
+
+        std::cout << GridLogDebug << "MPI write I/O write all " << file << std::endl;
+        ierr = MPI_File_write_all(fh, &iodata[0], 1, localArray, &status);
+        assert(ierr == 0);
+
+        MPI_Offset os;
+        MPI_File_get_position(fh, &os);
+        MPI_File_get_byte_offset(fh, os, &disp);
+        offset = disp;
+
+
+        MPI_File_close(&fh);
+        MPI_Type_free(&fileArray);
+        MPI_Type_free(&localArray);
+#else 
+	assert(0);
+#endif
+      } else { 
+
+        std::cout << GridLogMessage << "IOobject: C++ write I/O " << file << " : "
+                  << iodata.size() * sizeof(fobj) << " bytes and offset " << offset << std::endl;
+        
+	std::ofstream fout; 
+	fout.exceptions ( std::fstream::failbit | std::fstream::badbit );
+	try {
+	  if (offset) { // Must already exist and contain data
+	    fout.open(file,std::ios::binary|std::ios::out|std::ios::in);
+	  } else {     // Allow create
+	    fout.open(file,std::ios::binary|std::ios::out);
+	  }
+	} catch (const std::fstream::failure& exc) {
+	  std::cout << GridLogError << "Error in opening the file " << file << " for output" <<std::endl;
+	  std::cout << GridLogError << "Exception description: " << exc.what() << std::endl;
+	  //	  std::cout << GridLogError << "Probable cause: wrong path, inaccessible location "<< std::endl;
+#ifdef USE_MPI_IO
+	  MPI_Abort(MPI_COMM_WORLD,1);
+#else
+	  exit(1);
+#endif
+	}
+	
+	if ( control & BINARYIO_MASTER_APPEND )  {
+	  try {
+	    fout.seekp(0,fout.end);
+	  } catch (const std::fstream::failure& exc) {
+	    std::cout << "Exception in seeking file end " << file << std::endl;
+	  }
+	} else {
+	  try { 
+	    fout.seekp(offset+myrank*lsites*sizeof(fobj));
+	  } catch (const std::fstream::failure& exc) {
+	    std::cout << "Exception in seeking file " << file <<" offset "<< offset << std::endl;
+	  }
+	}
+
+	try {
+	  fout.write((char *)&iodata[0],iodata.size()*sizeof(fobj));//assert( fout.fail()==0);
+	}
+	catch (const std::fstream::failure& exc) {
+	  std::cout << "Exception in writing file " << file << std::endl;
+	  std::cout << GridLogError << "Exception description: "<< exc.what() << std::endl;
+#ifdef USE_MPI_IO
+	  MPI_Abort(MPI_COMM_WORLD,1);
+#else
+	  exit(1);
+#endif
+	}
+  offset  = fout.tellp();
+	fout.close();
+      }
+      timer.Stop();
+    }
+    
+    std::cout<<GridLogMessage<<"IOobject: ";
+    if ( control & BINARYIO_READ) std::cout << " read  ";
+    else                          std::cout << " write ";
+    uint64_t bytes = sizeof(fobj)*iodata.size()*nrank;
+    std::cout<< bytes <<" bytes in "<<timer.Elapsed() <<" "
+	     << (double)bytes/ (double)timer.useconds() <<" MB/s "<<std::endl;
+
+    std::cout<<GridLogMessage<<"IOobject: endian and checksum overhead "<<bstimer.Elapsed()  <<std::endl;
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Safety check
+    //////////////////////////////////////////////////////////////////////////////
+    // if the data size is 1 we do not want to sum over the MPI ranks
+    if (iodata.size() != 1){
+      grid->Barrier();
+      grid->GlobalSum(nersc_csum);
+      grid->GlobalXOR(scidac_csuma);
+      grid->GlobalXOR(scidac_csumb);
+      grid->Barrier();
+    }
+  }
+
+  /////////////////////////////////////////////////////////////////////////////
+  // Read a Lattice of object
+  //////////////////////////////////////////////////////////////////////////////////////
+  template<class vobj,class fobj,class munger>
+  static inline void readLatticeObject(Lattice<vobj> &Umu,
+				       std::string file,
+				       munger munge,
+				       uint64_t offset,
+				       const std::string &format,
+				       uint32_t &nersc_csum,
+				       uint32_t &scidac_csuma,
+				       uint32_t &scidac_csumb)
+  {
+    typedef typename vobj::scalar_object sobj;
+    typedef typename vobj::Realified::scalar_type word;    word w=0;
+
+    GridBase *grid = Umu.Grid();
+    uint64_t lsites = grid->lSites();
+
+    std::vector<sobj> scalardata(lsites); 
+    std::vector<fobj>     iodata(lsites); // Munge, checksum, byte order in here
+    
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+	     nersc_csum,scidac_csuma,scidac_csumb);
+
+    GridStopWatch timer; 
+    timer.Start();
+
+    thread_loop( (uint64_t x=0;x<lsites;x++), { munge(iodata[x], scalardata[x]); });
+
+    vectorizeFromLexOrdArray(scalardata,Umu);    
+    grid->Barrier();
+
+    timer.Stop();
+    std::cout<<GridLogMessage<<"readLatticeObject: vectorize overhead "<<timer.Elapsed()  <<std::endl;
+  }
+
+  /////////////////////////////////////////////////////////////////////////////
+  // Write a Lattice of object
+  //////////////////////////////////////////////////////////////////////////////////////
+  template<class vobj,class fobj,class munger>
+    static inline void writeLatticeObject(Lattice<vobj> &Umu,
+					  std::string file,
+					  munger munge,
+					  uint64_t offset,
+					  const std::string &format,
+					  uint32_t &nersc_csum,
+					  uint32_t &scidac_csuma,
+					  uint32_t &scidac_csumb)
+  {
+    typedef typename vobj::scalar_object sobj;
+    typedef typename vobj::Realified::scalar_type word;    word w=0;
+    GridBase *grid = Umu.Grid();
+    uint64_t lsites = grid->lSites(), offsetCopy = offset;
+    int attemptsLeft = std::max(0, BinaryIO::latticeWriteMaxRetry);
+    bool checkWrite = (BinaryIO::latticeWriteMaxRetry >= 0);
+
+    std::vector<sobj> scalardata(lsites); 
+    std::vector<fobj>     iodata(lsites); // Munge, checksum, byte order in here
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Munge [ .e.g 3rd row recon ]
+    //////////////////////////////////////////////////////////////////////////////
+    GridStopWatch timer; timer.Start();
+    unvectorizeToLexOrdArray(scalardata,Umu);    
+
+    thread_loop( (uint64_t x=0;x<lsites;x++), { munge(scalardata[x],iodata[x]); });
+
+    grid->Barrier();
+    timer.Stop();
+    while (attemptsLeft >= 0)
+    {
+      grid->Barrier();
+      IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC,
+	             nersc_csum,scidac_csuma,scidac_csumb);
+      if (checkWrite)
+      {
+        std::vector<fobj> ckiodata(lsites);
+        uint32_t          cknersc_csum, ckscidac_csuma, ckscidac_csumb;
+        uint64_t          ckoffset = offsetCopy;
+
+        std::cout << GridLogMessage << "writeLatticeObject: read back object" << std::endl;
+        grid->Barrier();
+        IOobject(w,grid,ckiodata,file,ckoffset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+	               cknersc_csum,ckscidac_csuma,ckscidac_csumb);
+        if ((cknersc_csum != nersc_csum) or (ckscidac_csuma != scidac_csuma) or (ckscidac_csumb != scidac_csumb))
+        {
+          std::cout << GridLogMessage << "writeLatticeObject: read test checksum failure, re-writing (" << attemptsLeft << " attempt(s) remaining)" << std::endl;
+          offset = offsetCopy;
+        }
+        else
+        {
+          std::cout << GridLogMessage << "writeLatticeObject: read test checksum correct" << std::endl;
+          break;
+        }
+      }
+      attemptsLeft--;
+    }
+    
+
+    std::cout<<GridLogMessage<<"writeLatticeObject: unvectorize overhead "<<timer.Elapsed()  <<std::endl;
+  }
+  
+  /////////////////////////////////////////////////////////////////////////////
+  // Read a RNG;  use IOobject and lexico map to an array of state 
+  //////////////////////////////////////////////////////////////////////////////////////
+  static inline void readRNG(GridSerialRNG &serial,
+			     GridParallelRNG &parallel,
+			     std::string file,
+			     uint64_t offset,
+			     uint32_t &nersc_csum,
+			     uint32_t &scidac_csuma,
+			     uint32_t &scidac_csumb)
+  {
+    typedef typename GridSerialRNG::RngStateType RngStateType;
+    const int RngStateCount = GridSerialRNG::RngStateCount;
+    typedef std::array<RngStateType,RngStateCount> RNGstate;
+    typedef RngStateType word;    word w=0;
+
+    std::string format = "IEEE32BIG";
+
+    GridBase *grid = parallel.Grid();
+    uint64_t gsites = grid->gSites();
+    uint64_t lsites = grid->lSites();
+
+    uint32_t nersc_csum_tmp   = 0;
+    uint32_t scidac_csuma_tmp = 0;
+    uint32_t scidac_csumb_tmp = 0;
+
+    GridStopWatch timer;
+
+    std::cout << GridLogMessage << "RNG read I/O on file " << file << std::endl;
+
+    std::vector<RNGstate> iodata(lsites);
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_LEXICOGRAPHIC,
+	     nersc_csum,scidac_csuma,scidac_csumb);
+
+    timer.Start();
+    thread_loop( (uint64_t lidx=0;lidx<lsites;lidx++),{
+      std::vector<RngStateType> tmp(RngStateCount);
+      std::copy(iodata[lidx].begin(),iodata[lidx].end(),tmp.begin());
+      parallel.SetState(tmp,lidx);
+    });
+    timer.Stop();
+
+    iodata.resize(1);
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_READ|BINARYIO_MASTER_APPEND,
+	     nersc_csum_tmp,scidac_csuma_tmp,scidac_csumb_tmp);
+
+    {
+      std::vector<RngStateType> tmp(RngStateCount);
+      std::copy(iodata[0].begin(),iodata[0].end(),tmp.begin());
+      serial.SetState(tmp,0);
+    }
+
+    nersc_csum   = nersc_csum   + nersc_csum_tmp;
+    scidac_csuma = scidac_csuma ^ scidac_csuma_tmp;
+    scidac_csumb = scidac_csumb ^ scidac_csumb_tmp;
+
+    std::cout << GridLogMessage << "RNG file nersc_checksum   " << std::hex << nersc_csum << std::dec << std::endl;
+    std::cout << GridLogMessage << "RNG file scidac_checksuma " << std::hex << scidac_csuma << std::dec << std::endl;
+    std::cout << GridLogMessage << "RNG file scidac_checksumb " << std::hex << scidac_csumb << std::dec << std::endl;
+
+    std::cout << GridLogMessage << "RNG state overhead " << timer.Elapsed() << std::endl;
+  }
+  /////////////////////////////////////////////////////////////////////////////
+  // Write a RNG; lexico map to an array of state and use IOobject
+  //////////////////////////////////////////////////////////////////////////////////////
+  static inline void writeRNG(GridSerialRNG &serial,
+			      GridParallelRNG &parallel,
+			      std::string file,
+			      uint64_t offset,
+			      uint32_t &nersc_csum,
+			      uint32_t &scidac_csuma,
+			      uint32_t &scidac_csumb)
+  {
+    typedef typename GridSerialRNG::RngStateType RngStateType;
+    typedef RngStateType word; word w=0;
+    const int RngStateCount = GridSerialRNG::RngStateCount;
+    typedef std::array<RngStateType,RngStateCount> RNGstate;
+
+    GridBase *grid = parallel.Grid();
+    uint64_t gsites = grid->gSites();
+    uint64_t lsites = grid->lSites();
+
+    uint32_t nersc_csum_tmp;
+    uint32_t scidac_csuma_tmp;
+    uint32_t scidac_csumb_tmp;
+
+    GridStopWatch timer;
+    std::string format = "IEEE32BIG";
+
+    std::cout << GridLogMessage << "RNG write I/O on file " << file << std::endl;
+
+    timer.Start();
+    std::vector<RNGstate> iodata(lsites);
+    thread_loop( (uint64_t lidx=0;lidx<lsites;lidx++),{
+      std::vector<RngStateType> tmp(RngStateCount);
+      parallel.GetState(tmp,lidx);
+      std::copy(tmp.begin(),tmp.end(),iodata[lidx].begin());
+    });
+    timer.Stop();
+
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_LEXICOGRAPHIC,
+	     nersc_csum,scidac_csuma,scidac_csumb);
+    iodata.resize(1);
+    {
+      std::vector<RngStateType> tmp(RngStateCount);
+      serial.GetState(tmp,0);
+      std::copy(tmp.begin(),tmp.end(),iodata[0].begin());
+    }
+    IOobject(w,grid,iodata,file,offset,format,BINARYIO_WRITE|BINARYIO_MASTER_APPEND,
+	     nersc_csum_tmp,scidac_csuma_tmp,scidac_csumb_tmp);
+
+    nersc_csum   = nersc_csum   + nersc_csum_tmp;
+    scidac_csuma = scidac_csuma ^ scidac_csuma_tmp;
+    scidac_csumb = scidac_csumb ^ scidac_csumb_tmp;
+    
+    std::cout << GridLogMessage << "RNG file checksum " << std::hex << nersc_csum    << std::dec << std::endl;
+    std::cout << GridLogMessage << "RNG file checksuma " << std::hex << scidac_csuma << std::dec << std::endl;
+    std::cout << GridLogMessage << "RNG file checksumb " << std::hex << scidac_csumb << std::dec << std::endl;
+    std::cout << GridLogMessage << "RNG state overhead " << timer.Elapsed() << std::endl;
+  }
+};
+
+NAMESPACE_END(Grid);

Grid/parallelIO/IldgIO.h

@@ -0,0 +1,874 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/parallelIO/IldgIO.h
+
+Copyright (C) 2015
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+#ifdef HAVE_LIME
+#include <algorithm>
+#include <fstream>
+#include <iomanip>
+#include <iostream>
+#include <map>
+
+#include <pwd.h>
+#include <sys/utsname.h>
+#include <unistd.h>
+
+//C-Lime is a must have for this functionality
+extern "C" {  
+#include "lime.h"
+}
+
+NAMESPACE_BEGIN(Grid);
+
+  /////////////////////////////////
+  // Encode word types as strings
+  /////////////////////////////////
+ template<class word> inline std::string ScidacWordMnemonic(void){ return std::string("unknown"); }
+ template<> inline std::string ScidacWordMnemonic<double>  (void){ return std::string("D"); }
+ template<> inline std::string ScidacWordMnemonic<float>   (void){ return std::string("F"); }
+ template<> inline std::string ScidacWordMnemonic< int32_t>(void){ return std::string("I32_t"); }
+ template<> inline std::string ScidacWordMnemonic<uint32_t>(void){ return std::string("U32_t"); }
+ template<> inline std::string ScidacWordMnemonic< int64_t>(void){ return std::string("I64_t"); }
+ template<> inline std::string ScidacWordMnemonic<uint64_t>(void){ return std::string("U64_t"); }
+
+  /////////////////////////////////////////
+  // Encode a generic tensor as a string
+  /////////////////////////////////////////
+ template<class vobj> std::string ScidacRecordTypeString(int &colors, int &spins, int & typesize,int &datacount) { 
+
+   typedef typename getPrecision<vobj>::real_scalar_type stype;
+
+   int _ColourN       = indexRank<ColourIndex,vobj>();
+   int _ColourScalar  =  isScalar<ColourIndex,vobj>();
+   int _ColourVector  =  isVector<ColourIndex,vobj>();
+   int _ColourMatrix  =  isMatrix<ColourIndex,vobj>();
+
+   int _SpinN       = indexRank<SpinIndex,vobj>();
+   int _SpinScalar  =  isScalar<SpinIndex,vobj>();
+   int _SpinVector  =  isVector<SpinIndex,vobj>();
+   int _SpinMatrix  =  isMatrix<SpinIndex,vobj>();
+
+   int _LorentzN       = indexRank<LorentzIndex,vobj>();
+   int _LorentzScalar  =  isScalar<LorentzIndex,vobj>();
+   int _LorentzVector  =  isVector<LorentzIndex,vobj>();
+   int _LorentzMatrix  =  isMatrix<LorentzIndex,vobj>();
+
+   std::stringstream stream;
+
+   stream << "GRID_";
+   stream << ScidacWordMnemonic<stype>();
+
+   if ( _LorentzVector )   stream << "_LorentzVector"<<_LorentzN;
+   if ( _LorentzMatrix )   stream << "_LorentzMatrix"<<_LorentzN;
+
+   if ( _SpinVector )   stream << "_SpinVector"<<_SpinN;
+   if ( _SpinMatrix )   stream << "_SpinMatrix"<<_SpinN;
+
+   if ( _ColourVector )   stream << "_ColourVector"<<_ColourN;
+   if ( _ColourMatrix )   stream << "_ColourMatrix"<<_ColourN;
+
+   if ( _ColourScalar && _LorentzScalar && _SpinScalar )   stream << "_Complex";
+
+
+   typesize = sizeof(typename vobj::scalar_type);
+
+   if ( _ColourMatrix ) typesize*= _ColourN*_ColourN;
+   else                 typesize*= _ColourN;
+
+   if ( _SpinMatrix )   typesize*= _SpinN*_SpinN;
+   else                 typesize*= _SpinN;
+
+   colors    = _ColourN;
+   spins     = _SpinN;
+   datacount = _LorentzN;
+
+   return stream.str();
+ }
+ 
+ template<class vobj> std::string ScidacRecordTypeString(Lattice<vobj> & lat,int &colors, int &spins, int & typesize,int &datacount) { 
+   return ScidacRecordTypeString<vobj>(colors,spins,typesize,datacount);
+ };
+
+
+ ////////////////////////////////////////////////////////////
+ // Helper to fill out metadata
+ ////////////////////////////////////////////////////////////
+ template<class vobj> void ScidacMetaData(Lattice<vobj> & field,
+					  FieldMetaData &header,
+					  scidacRecord & _scidacRecord,
+					  scidacFile   & _scidacFile) 
+ {
+   typedef typename getPrecision<vobj>::real_scalar_type stype;
+
+   /////////////////////////////////////
+   // Pull Grid's metadata
+   /////////////////////////////////////
+   PrepareMetaData(field,header);
+
+   /////////////////////////////////////
+   // Scidac Private File structure
+   /////////////////////////////////////
+   _scidacFile              = scidacFile(field.Grid());
+
+   /////////////////////////////////////
+   // Scidac Private Record structure
+   /////////////////////////////////////
+   scidacRecord sr;
+   sr.datatype   = ScidacRecordTypeString(field,sr.colors,sr.spins,sr.typesize,sr.datacount);
+   sr.date       = header.creation_date;
+   sr.precision  = ScidacWordMnemonic<stype>();
+   sr.recordtype = GRID_IO_FIELD;
+
+   _scidacRecord = sr;
+
+   //   std::cout << GridLogMessage << "Build SciDAC datatype " <<sr.datatype<<std::endl;
+ }
+ 
+ ///////////////////////////////////////////////////////
+ // Scidac checksum
+ ///////////////////////////////////////////////////////
+ static int scidacChecksumVerify(scidacChecksum &scidacChecksum_,uint32_t scidac_csuma,uint32_t scidac_csumb)
+ {
+   uint32_t scidac_checksuma = stoull(scidacChecksum_.suma,0,16);
+   uint32_t scidac_checksumb = stoull(scidacChecksum_.sumb,0,16);
+   if ( scidac_csuma !=scidac_checksuma) return 0;
+   if ( scidac_csumb !=scidac_checksumb) return 0;
+   return 1;
+ }
+
+////////////////////////////////////////////////////////////////////////////////////
+// Lime, ILDG and Scidac I/O classes
+////////////////////////////////////////////////////////////////////////////////////
+class GridLimeReader : public BinaryIO {
+ public:
+   ///////////////////////////////////////////////////
+   // FIXME: format for RNG? Now just binary out instead
+   ///////////////////////////////////////////////////
+
+   FILE       *File;
+   LimeReader *LimeR;
+   std::string filename;
+
+   /////////////////////////////////////////////
+   // Open the file
+   /////////////////////////////////////////////
+   void open(const std::string &_filename) 
+   {
+     filename= _filename;
+     File = fopen(filename.c_str(), "r");
+     if (File == nullptr)
+     {
+       std::cerr << "cannot open file '" << filename << "'" << std::endl;
+       abort();
+     }
+     LimeR = limeCreateReader(File);
+   }
+   /////////////////////////////////////////////
+   // Close the file
+   /////////////////////////////////////////////
+   void close(void){
+     fclose(File);
+     //     limeDestroyReader(LimeR);
+   }
+
+  ////////////////////////////////////////////
+  // Read a generic lattice field and verify checksum
+  ////////////////////////////////////////////
+  template<class vobj>
+  void readLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name)
+  {
+    typedef typename vobj::scalar_object sobj;
+    scidacChecksum scidacChecksum_;
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+
+    std::string format = getFormatString<vobj>();
+
+    while ( limeReaderNextRecord(LimeR) == LIME_SUCCESS ) { 
+
+      uint64_t file_bytes =limeReaderBytes(LimeR);
+
+      //      std::cout << GridLogMessage << limeReaderType(LimeR) << " "<< file_bytes <<" bytes "<<std::endl;
+      //      std::cout << GridLogMessage<< " readLimeObject seeking "<<  record_name <<" found record :" <<limeReaderType(LimeR) <<std::endl;
+
+      if ( !strncmp(limeReaderType(LimeR), record_name.c_str(),strlen(record_name.c_str()) )  ) {
+
+	//	std::cout << GridLogMessage<< " readLimeLatticeBinaryObject matches ! " <<std::endl;
+
+	uint64_t PayloadSize = sizeof(sobj) * field.Grid()->_gsites;
+
+	//	std::cout << "R sizeof(sobj)= " <<sizeof(sobj)<<std::endl;
+	//	std::cout << "R Gsites " <<field.Grid()->_gsites<<std::endl;
+	//	std::cout << "R Payload expected " <<PayloadSize<<std::endl;
+	//	std::cout << "R file size " <<file_bytes <<std::endl;
+
+	assert(PayloadSize == file_bytes);// Must match or user error
+
+	uint64_t offset= ftello(File);
+	//	std::cout << " ReadLatticeObject from offset "<<offset << std::endl;
+	BinarySimpleMunger<sobj,sobj> munge;
+	BinaryIO::readLatticeObject< vobj, sobj >(field, filename, munge, offset, format,nersc_csum,scidac_csuma,scidac_csumb);
+  std::cout << GridLogMessage << "SciDAC checksum A " << std::hex << scidac_csuma << std::dec << std::endl;
+  std::cout << GridLogMessage << "SciDAC checksum B " << std::hex << scidac_csumb << std::dec << std::endl;
+	/////////////////////////////////////////////
+	// Insist checksum is next record
+	/////////////////////////////////////////////
+	readLimeObject(scidacChecksum_,std::string("scidacChecksum"),std::string(SCIDAC_CHECKSUM));
+
+	/////////////////////////////////////////////
+	// Verify checksums
+	/////////////////////////////////////////////
+	assert(scidacChecksumVerify(scidacChecksum_,scidac_csuma,scidac_csumb)==1);
+	return;
+      }
+    }
+  }
+  ////////////////////////////////////////////
+  // Read a generic serialisable object
+  ////////////////////////////////////////////
+  void readLimeObject(std::string &xmlstring,std::string record_name)
+  {
+    // should this be a do while; can we miss a first record??
+    while ( limeReaderNextRecord(LimeR) == LIME_SUCCESS ) { 
+
+      //      std::cout << GridLogMessage<< " readLimeObject seeking "<< record_name <<" found record :" <<limeReaderType(LimeR) <<std::endl;
+      uint64_t nbytes = limeReaderBytes(LimeR);//size of this record (configuration)
+
+      if ( !strncmp(limeReaderType(LimeR), record_name.c_str(),strlen(record_name.c_str()) )  ) {
+
+	//	std::cout << GridLogMessage<< " readLimeObject matches ! " << record_name <<std::endl;
+	std::vector<char> xmlc(nbytes+1,'\0');
+	limeReaderReadData((void *)&xmlc[0], &nbytes, LimeR);    
+	//	std::cout << GridLogMessage<< " readLimeObject matches XML " << &xmlc[0] <<std::endl;
+
+   xmlstring = std::string(&xmlc[0]);
+	return;
+      }
+
+    }  
+    assert(0);
+  }
+
+  template<class serialisable_object>
+  void readLimeObject(serialisable_object &object,std::string object_name,std::string record_name)
+  {
+    std::string xmlstring;
+
+    readLimeObject(xmlstring, record_name);
+	  XmlReader RD(xmlstring, true, "");
+	  read(RD,object_name,object);
+  }
+};
+
+class GridLimeWriter : public BinaryIO 
+{
+ public:
+
+   ///////////////////////////////////////////////////
+   // FIXME: format for RNG? Now just binary out instead
+   // FIXME: collective calls or not ?
+   //      : must know if I am the I/O boss
+   ///////////////////////////////////////////////////
+   FILE       *File;
+   LimeWriter *LimeW;
+   std::string filename;
+   bool        boss_node;
+   GridLimeWriter( bool isboss = true) {
+     boss_node = isboss;
+   }
+   void open(const std::string &_filename) { 
+     filename= _filename;
+     if ( boss_node ) {
+       File = fopen(filename.c_str(), "w");
+       LimeW = limeCreateWriter(File); assert(LimeW != NULL );
+     }
+   }
+   /////////////////////////////////////////////
+   // Close the file
+   /////////////////////////////////////////////
+   void close(void) {
+     if ( boss_node ) {
+       fclose(File);
+     }
+     //  limeDestroyWriter(LimeW);
+   }
+  ///////////////////////////////////////////////////////
+  // Lime utility functions
+  ///////////////////////////////////////////////////////
+  int createLimeRecordHeader(std::string message, int MB, int ME, size_t PayloadSize)
+  {
+    if ( boss_node ) {
+      LimeRecordHeader *h;
+      h = limeCreateHeader(MB, ME, const_cast<char *>(message.c_str()), PayloadSize);
+      assert(limeWriteRecordHeader(h, LimeW) >= 0);
+      limeDestroyHeader(h);
+    }
+    return LIME_SUCCESS;
+  }
+  ////////////////////////////////////////////
+  // Write a generic serialisable object
+  ////////////////////////////////////////////
+  void writeLimeObject(int MB,int ME,XmlWriter &writer,std::string object_name,std::string record_name)
+  {
+    if ( boss_node ) {
+      std::string xmlstring = writer.docString();
+
+      //    std::cout << "WriteLimeObject" << record_name <<std::endl;
+      uint64_t nbytes = xmlstring.size();
+      //    std::cout << " xmlstring "<< nbytes<< " " << xmlstring <<std::endl;
+      int err;
+      LimeRecordHeader *h = limeCreateHeader(MB, ME,const_cast<char *>(record_name.c_str()), nbytes); 
+      assert(h!= NULL);
+      
+      err=limeWriteRecordHeader(h, LimeW);                    assert(err>=0);
+      err=limeWriteRecordData(&xmlstring[0], &nbytes, LimeW); assert(err>=0);
+      err=limeWriterCloseRecord(LimeW);                       assert(err>=0);
+      limeDestroyHeader(h);
+    }
+  }
+
+  template<class serialisable_object>
+  void writeLimeObject(int MB,int ME,serialisable_object &object,std::string object_name,std::string record_name, const unsigned int scientificPrec = 0)
+  {
+    XmlWriter WR("","");
+
+    if (scientificPrec)
+    {
+      WR.scientificFormat(true);
+      WR.setPrecision(scientificPrec);
+    }
+    write(WR,object_name,object);
+    writeLimeObject(MB, ME, WR, object_name, record_name);
+  }
+  ////////////////////////////////////////////////////
+  // Write a generic lattice field and csum
+  // This routine is Collectively called by all nodes
+  // in communicator used by the field.Grid()
+  ////////////////////////////////////////////////////
+  template<class vobj>
+  void writeLimeLatticeBinaryObject(Lattice<vobj> &field,std::string record_name)
+  {
+    ////////////////////////////////////////////////////////////////////
+    // NB: FILE and iostream are jointly writing disjoint sequences in the
+    // the same file through different file handles (integer units).
+    // 
+    // These are both buffered, so why I think this code is right is as follows.
+    //
+    // i)  write record header to FILE *File, telegraphing the size; flush
+    // ii) ftello reads the offset from FILE *File . 
+    // iii) iostream / MPI Open independently seek this offset. Write sequence direct to disk.
+    //      Closes iostream and flushes.
+    // iv) fseek on FILE * to end of this disjoint section.
+    //  v) Continue writing scidac record.
+    ////////////////////////////////////////////////////////////////////
+    
+    GridBase *grid = field.Grid();
+    assert(boss_node == field.Grid()->IsBoss() );
+
+    ////////////////////////////////////////////
+    // Create record header
+    ////////////////////////////////////////////
+    typedef typename vobj::scalar_object sobj;
+    int err;
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+    uint64_t PayloadSize = sizeof(sobj) * grid->_gsites;
+    if ( boss_node ) {
+      createLimeRecordHeader(record_name, 0, 0, PayloadSize);
+      fflush(File);
+    }
+    
+    //    std::cout << "W sizeof(sobj)"      <<sizeof(sobj)<<std::endl;
+    //    std::cout << "W Gsites "           <<field.Grid()->_gsites<<std::endl;
+    //    std::cout << "W Payload expected " <<PayloadSize<<std::endl;
+
+    ////////////////////////////////////////////////
+    // Check all nodes agree on file position
+    ////////////////////////////////////////////////
+    uint64_t offset1;
+    if ( boss_node ) {
+      offset1 = ftello(File);    
+    }
+    grid->Broadcast(0,(void *)&offset1,sizeof(offset1));
+
+    ///////////////////////////////////////////
+    // The above is collective. Write by other means into the binary record
+    ///////////////////////////////////////////
+    std::string format = getFormatString<vobj>();
+    BinarySimpleMunger<sobj,sobj> munge;
+    BinaryIO::writeLatticeObject<vobj,sobj>(field, filename, munge, offset1, format,nersc_csum,scidac_csuma,scidac_csumb);
+
+    ///////////////////////////////////////////
+    // Wind forward and close the record
+    ///////////////////////////////////////////
+    if ( boss_node ) {
+      fseek(File,0,SEEK_END);             
+      uint64_t offset2 = ftello(File);     //    std::cout << " now at offset "<<offset2 << std::endl;
+      assert( (offset2-offset1) == PayloadSize);
+    }
+
+    /////////////////////////////////////////////////////////////
+    // Check MPI-2 I/O did what we expect to file
+    /////////////////////////////////////////////////////////////
+
+    if ( boss_node ) { 
+      err=limeWriterCloseRecord(LimeW);  assert(err>=0);
+    }
+    ////////////////////////////////////////
+    // Write checksum element, propagaing forward from the BinaryIO
+    // Always pair a checksum with a binary object, and close message
+    ////////////////////////////////////////
+    scidacChecksum checksum;
+    std::stringstream streama; streama << std::hex << scidac_csuma;
+    std::stringstream streamb; streamb << std::hex << scidac_csumb;
+    checksum.suma= streama.str();
+    checksum.sumb= streamb.str();
+    if ( boss_node ) { 
+      writeLimeObject(0,1,checksum,std::string("scidacChecksum"),std::string(SCIDAC_CHECKSUM));
+    }
+  }
+};
+
+class ScidacWriter : public GridLimeWriter {
+ public:
+
+  ScidacWriter(bool isboss =true ) : GridLimeWriter(isboss)  { };
+
+  template<class SerialisableUserFile>
+  void writeScidacFileRecord(GridBase *grid,SerialisableUserFile &_userFile)
+  {
+    scidacFile    _scidacFile(grid);
+    if ( this->boss_node ) {
+      writeLimeObject(1,0,_scidacFile,_scidacFile.SerialisableClassName(),std::string(SCIDAC_PRIVATE_FILE_XML));
+      writeLimeObject(0,1,_userFile,_userFile.SerialisableClassName(),std::string(SCIDAC_FILE_XML));
+    }
+  }
+  ////////////////////////////////////////////////
+  // Write generic lattice field in scidac format
+  ////////////////////////////////////////////////
+  template <class vobj, class userRecord>
+  void writeScidacFieldRecord(Lattice<vobj> &field,userRecord _userRecord,
+                              const unsigned int recordScientificPrec = 0) 
+  {
+    GridBase * grid = field.Grid();
+
+    ////////////////////////////////////////
+    // fill the Grid header
+    ////////////////////////////////////////
+    FieldMetaData header;
+    scidacRecord  _scidacRecord;
+    scidacFile    _scidacFile;
+
+    ScidacMetaData(field,header,_scidacRecord,_scidacFile);
+
+    //////////////////////////////////////////////
+    // Fill the Lime file record by record
+    //////////////////////////////////////////////
+    if ( this->boss_node ) {
+      writeLimeObject(1,0,header ,std::string("FieldMetaData"),std::string(GRID_FORMAT)); // Open message 
+      writeLimeObject(0,0,_userRecord,_userRecord.SerialisableClassName(),std::string(SCIDAC_RECORD_XML), recordScientificPrec);
+      writeLimeObject(0,0,_scidacRecord,_scidacRecord.SerialisableClassName(),std::string(SCIDAC_PRIVATE_RECORD_XML));
+    }
+    // Collective call
+    writeLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA));      // Closes message with checksum
+  }
+};
+
+
+class ScidacReader : public GridLimeReader {
+ public:
+
+   template<class SerialisableUserFile>
+   void readScidacFileRecord(GridBase *grid,SerialisableUserFile &_userFile)
+   {
+     scidacFile    _scidacFile(grid);
+     readLimeObject(_scidacFile,_scidacFile.SerialisableClassName(),std::string(SCIDAC_PRIVATE_FILE_XML));
+     readLimeObject(_userFile,_userFile.SerialisableClassName(),std::string(SCIDAC_FILE_XML));
+   }
+  ////////////////////////////////////////////////
+  // Write generic lattice field in scidac format
+  ////////////////////////////////////////////////
+  template <class vobj, class userRecord>
+  void readScidacFieldRecord(Lattice<vobj> &field,userRecord &_userRecord) 
+  {
+    typedef typename vobj::scalar_object sobj;
+    GridBase * grid = field.Grid();
+
+    ////////////////////////////////////////
+    // fill the Grid header
+    ////////////////////////////////////////
+    FieldMetaData header;
+    scidacRecord  _scidacRecord;
+    scidacFile    _scidacFile;
+
+    //////////////////////////////////////////////
+    // Fill the Lime file record by record
+    //////////////////////////////////////////////
+    readLimeObject(header ,std::string("FieldMetaData"),std::string(GRID_FORMAT)); // Open message 
+    readLimeObject(_userRecord,_userRecord.SerialisableClassName(),std::string(SCIDAC_RECORD_XML));
+    readLimeObject(_scidacRecord,_scidacRecord.SerialisableClassName(),std::string(SCIDAC_PRIVATE_RECORD_XML));
+    readLimeLatticeBinaryObject(field,std::string(ILDG_BINARY_DATA));
+  }
+  void skipPastBinaryRecord(void) {
+    std::string rec_name(ILDG_BINARY_DATA);
+    while ( limeReaderNextRecord(LimeR) == LIME_SUCCESS ) { 
+      if ( !strncmp(limeReaderType(LimeR), rec_name.c_str(),strlen(rec_name.c_str()) )  ) {
+	skipPastObjectRecord(std::string(SCIDAC_CHECKSUM));
+	return;
+      }
+    }    
+  }
+  void skipPastObjectRecord(std::string rec_name) {
+    while ( limeReaderNextRecord(LimeR) == LIME_SUCCESS ) { 
+      if ( !strncmp(limeReaderType(LimeR), rec_name.c_str(),strlen(rec_name.c_str()) )  ) {
+	return;
+      }
+    }
+  }
+  void skipScidacFieldRecord() {
+    skipPastObjectRecord(std::string(GRID_FORMAT));
+    skipPastObjectRecord(std::string(SCIDAC_RECORD_XML));
+    skipPastObjectRecord(std::string(SCIDAC_PRIVATE_RECORD_XML));
+    skipPastBinaryRecord();
+  }
+};
+
+
+class IldgWriter : public ScidacWriter {
+ public:
+  
+  IldgWriter(bool isboss) : ScidacWriter(isboss) {};
+
+  ///////////////////////////////////
+  // A little helper
+  ///////////////////////////////////
+  void writeLimeIldgLFN(std::string &LFN)
+  {
+    uint64_t PayloadSize = LFN.size();
+    int err;
+    createLimeRecordHeader(ILDG_DATA_LFN, 0 , 0, PayloadSize);
+    err=limeWriteRecordData(const_cast<char*>(LFN.c_str()), &PayloadSize,LimeW); assert(err>=0);
+    err=limeWriterCloseRecord(LimeW); assert(err>=0);
+  }
+
+  ////////////////////////////////////////////////////////////////
+  // Special ILDG operations ; gauge configs only.
+  // Don't require scidac records EXCEPT checksum
+  // Use Grid MetaData object if present.
+  ////////////////////////////////////////////////////////////////
+  template <class vsimd>
+  void writeConfiguration(Lattice<iLorentzColourMatrix<vsimd> > &Umu,int sequence,std::string LFN,std::string description) 
+  {
+    GridBase * grid = Umu.Grid();
+    typedef Lattice<iLorentzColourMatrix<vsimd> > GaugeField;
+    typedef iLorentzColourMatrix<vsimd> vobj;
+    typedef typename vobj::scalar_object sobj;
+
+    ////////////////////////////////////////
+    // fill the Grid header
+    ////////////////////////////////////////
+    FieldMetaData header;
+    scidacRecord  _scidacRecord;
+    scidacFile    _scidacFile;
+
+    ScidacMetaData(Umu,header,_scidacRecord,_scidacFile);
+
+    std::string format = header.floating_point;
+    header.ensemble_id    = description;
+    header.ensemble_label = description;
+    header.sequence_number = sequence;
+    header.ildg_lfn = LFN;
+
+    assert ( (format == std::string("IEEE32BIG"))  
+           ||(format == std::string("IEEE64BIG")) );
+
+    //////////////////////////////////////////////////////
+    // Fill ILDG header data struct
+    //////////////////////////////////////////////////////
+    ildgFormat ildgfmt ;
+    ildgfmt.field     = std::string("su3gauge");
+
+    if ( format == std::string("IEEE32BIG") ) { 
+      ildgfmt.precision = 32;
+    } else { 
+      ildgfmt.precision = 64;
+    }
+    ildgfmt.version = 1.0;
+    ildgfmt.lx = header.dimension[0];
+    ildgfmt.ly = header.dimension[1];
+    ildgfmt.lz = header.dimension[2];
+    ildgfmt.lt = header.dimension[3];
+    assert(header.nd==4);
+    assert(header.nd==header.dimension.size());
+
+    //////////////////////////////////////////////////////////////////////////////
+    // Fill the USQCD info field
+    //////////////////////////////////////////////////////////////////////////////
+    usqcdInfo info;
+    info.version=1.0;
+    info.plaq   = header.plaquette;
+    info.linktr = header.link_trace;
+
+    std::cout << GridLogMessage << " Writing config; IldgIO "<<std::endl;
+    //////////////////////////////////////////////
+    // Fill the Lime file record by record
+    //////////////////////////////////////////////
+    writeLimeObject(1,0,header ,std::string("FieldMetaData"),std::string(GRID_FORMAT)); // Open message 
+    writeLimeObject(0,0,_scidacFile,_scidacFile.SerialisableClassName(),std::string(SCIDAC_PRIVATE_FILE_XML));
+    writeLimeObject(0,1,info,info.SerialisableClassName(),std::string(SCIDAC_FILE_XML));
+    writeLimeObject(1,0,_scidacRecord,_scidacRecord.SerialisableClassName(),std::string(SCIDAC_PRIVATE_RECORD_XML));
+    writeLimeObject(0,0,info,info.SerialisableClassName(),std::string(SCIDAC_RECORD_XML));
+    writeLimeObject(0,0,ildgfmt,std::string("ildgFormat")   ,std::string(ILDG_FORMAT)); // rec
+    writeLimeIldgLFN(header.ildg_lfn);                                                 // rec
+    writeLimeLatticeBinaryObject(Umu,std::string(ILDG_BINARY_DATA));      // Closes message with checksum
+    //    limeDestroyWriter(LimeW);
+  }
+};
+
+class IldgReader : public GridLimeReader {
+ public:
+
+  ////////////////////////////////////////////////////////////////
+  // Read either Grid/SciDAC/ILDG configuration
+  // Don't require scidac records EXCEPT checksum
+  // Use Grid MetaData object if present.
+  // Else use ILDG MetaData object if present.
+  // Else use SciDAC MetaData object if present.
+  ////////////////////////////////////////////////////////////////
+  template <class vsimd>
+  void readConfiguration(Lattice<iLorentzColourMatrix<vsimd> > &Umu, FieldMetaData &FieldMetaData_) {
+
+    typedef Lattice<iLorentzColourMatrix<vsimd> > GaugeField;
+    typedef typename GaugeField::vector_object  vobj;
+    typedef typename vobj::scalar_object sobj;
+
+    typedef LorentzColourMatrixF fobj;
+    typedef LorentzColourMatrixD dobj;
+
+    GridBase *grid = Umu.Grid();
+
+    Coordinate dims = Umu.Grid()->FullDimensions();
+
+    assert(dims.size()==4);
+
+    // Metadata holders
+    ildgFormat     ildgFormat_    ;
+    std::string    ildgLFN_       ;
+    scidacChecksum scidacChecksum_; 
+    usqcdInfo      usqcdInfo_     ;
+
+    // track what we read from file
+    int found_ildgFormat    =0;
+    int found_ildgLFN       =0;
+    int found_scidacChecksum=0;
+    int found_usqcdInfo     =0;
+    int found_ildgBinary =0;
+    int found_FieldMetaData =0;
+
+    uint32_t nersc_csum;
+    uint32_t scidac_csuma;
+    uint32_t scidac_csumb;
+
+    // Binary format
+    std::string format;
+
+    //////////////////////////////////////////////////////////////////////////
+    // Loop over all records
+    // -- Order is poorly guaranteed except ILDG header preceeds binary section.
+    // -- Run like an event loop.
+    // -- Impose trust hierarchy. Grid takes precedence & look for ILDG, and failing
+    //    that Scidac. 
+    // -- Insist on Scidac checksum record.
+    //////////////////////////////////////////////////////////////////////////
+
+    while ( limeReaderNextRecord(LimeR) == LIME_SUCCESS ) { 
+
+      uint64_t nbytes = limeReaderBytes(LimeR);//size of this record (configuration)
+      
+      //////////////////////////////////////////////////////////////////
+      // If not BINARY_DATA read a string and parse
+      //////////////////////////////////////////////////////////////////
+      if ( strncmp(limeReaderType(LimeR), ILDG_BINARY_DATA,strlen(ILDG_BINARY_DATA) )  ) {
+	
+	// Copy out the string
+	std::vector<char> xmlc(nbytes+1,'\0');
+	limeReaderReadData((void *)&xmlc[0], &nbytes, LimeR);    
+	//	std::cout << GridLogMessage<< "Non binary record :" <<limeReaderType(LimeR) <<std::endl; //<<"\n"<<(&xmlc[0])<<std::endl;
+
+	//////////////////////////////////
+	// ILDG format record
+
+  std::string xmlstring(&xmlc[0]);
+	if ( !strncmp(limeReaderType(LimeR), ILDG_FORMAT,strlen(ILDG_FORMAT)) ) { 
+
+	  XmlReader RD(xmlstring, true, "");
+	  read(RD,"ildgFormat",ildgFormat_);
+
+	  if ( ildgFormat_.precision == 64 ) format = std::string("IEEE64BIG");
+	  if ( ildgFormat_.precision == 32 ) format = std::string("IEEE32BIG");
+
+	  assert( ildgFormat_.lx == dims[0]);
+	  assert( ildgFormat_.ly == dims[1]);
+	  assert( ildgFormat_.lz == dims[2]);
+	  assert( ildgFormat_.lt == dims[3]);
+
+	  found_ildgFormat = 1;
+	}
+
+	if ( !strncmp(limeReaderType(LimeR), ILDG_DATA_LFN,strlen(ILDG_DATA_LFN)) ) {
+	  FieldMetaData_.ildg_lfn = xmlstring;
+	  found_ildgLFN = 1;
+	}
+
+	if ( !strncmp(limeReaderType(LimeR), GRID_FORMAT,strlen(ILDG_FORMAT)) ) { 
+
+	  XmlReader RD(xmlstring, true, "");
+	  read(RD,"FieldMetaData",FieldMetaData_);
+
+	  format = FieldMetaData_.floating_point;
+
+	  assert(FieldMetaData_.dimension[0] == dims[0]);
+	  assert(FieldMetaData_.dimension[1] == dims[1]);
+	  assert(FieldMetaData_.dimension[2] == dims[2]);
+	  assert(FieldMetaData_.dimension[3] == dims[3]);
+
+	  found_FieldMetaData = 1;
+	}
+
+	if ( !strncmp(limeReaderType(LimeR), SCIDAC_RECORD_XML,strlen(SCIDAC_RECORD_XML)) ) { 
+	  // is it a USQCD info field
+	  if ( xmlstring.find(std::string("usqcdInfo")) != std::string::npos ) { 
+	    //	    std::cout << GridLogMessage<<"...found a usqcdInfo field"<<std::endl;
+	    XmlReader RD(xmlstring, true, "");
+	    read(RD,"usqcdInfo",usqcdInfo_);
+	    found_usqcdInfo = 1;
+	  }
+	}
+
+	if ( !strncmp(limeReaderType(LimeR), SCIDAC_CHECKSUM,strlen(SCIDAC_CHECKSUM)) ) { 
+	  XmlReader RD(xmlstring, true, "");
+	  read(RD,"scidacChecksum",scidacChecksum_);
+	  found_scidacChecksum = 1;
+	}
+
+      } else {  
+	/////////////////////////////////
+	// Binary data
+	/////////////////////////////////
+	std::cout << GridLogMessage << "ILDG Binary record found : "  ILDG_BINARY_DATA << std::endl;
+	uint64_t offset= ftello(File);
+	if ( format == std::string("IEEE64BIG") ) {
+	  GaugeSimpleMunger<dobj, sobj> munge;
+	  BinaryIO::readLatticeObject< vobj, dobj >(Umu, filename, munge, offset, format,nersc_csum,scidac_csuma,scidac_csumb);
+	} else { 
+	  GaugeSimpleMunger<fobj, sobj> munge;
+	  BinaryIO::readLatticeObject< vobj, fobj >(Umu, filename, munge, offset, format,nersc_csum,scidac_csuma,scidac_csumb);
+	}
+
+	found_ildgBinary = 1;
+      }
+
+    }
+
+    //////////////////////////////////////////////////////
+    // Minimally must find binary segment and checksum
+    // Since this is an ILDG reader require ILDG format
+    //////////////////////////////////////////////////////
+    assert(found_ildgBinary);
+    assert(found_ildgFormat);
+    assert(found_scidacChecksum);
+
+    // Must find something with the lattice dimensions
+    assert(found_FieldMetaData||found_ildgFormat);
+
+    if ( found_FieldMetaData ) {
+
+      std::cout << GridLogMessage<<"Grid MetaData was record found: configuration was probably written by Grid ! Yay ! "<<std::endl;
+
+    } else { 
+
+      assert(found_ildgFormat);
+      assert ( ildgFormat_.field == std::string("su3gauge") );
+
+      ///////////////////////////////////////////////////////////////////////////////////////
+      // Populate our Grid metadata as best we can
+      ///////////////////////////////////////////////////////////////////////////////////////
+
+      std::ostringstream vers; vers << ildgFormat_.version;
+      FieldMetaData_.hdr_version = vers.str();
+      FieldMetaData_.data_type = std::string("4D_SU3_GAUGE_3X3");
+
+      FieldMetaData_.nd=4;
+      FieldMetaData_.dimension.resize(4);
+
+      FieldMetaData_.dimension[0] = ildgFormat_.lx ;
+      FieldMetaData_.dimension[1] = ildgFormat_.ly ;
+      FieldMetaData_.dimension[2] = ildgFormat_.lz ;
+      FieldMetaData_.dimension[3] = ildgFormat_.lt ;
+
+      if ( found_usqcdInfo ) { 
+	FieldMetaData_.plaquette = usqcdInfo_.plaq;
+	FieldMetaData_.link_trace= usqcdInfo_.linktr;
+	std::cout << GridLogMessage <<"This configuration was probably written by USQCD "<<std::endl;
+	std::cout << GridLogMessage <<"USQCD xml record Plaquette : "<<FieldMetaData_.plaquette<<std::endl;
+	std::cout << GridLogMessage <<"USQCD xml record LinkTrace : "<<FieldMetaData_.link_trace<<std::endl;
+      } else { 
+	FieldMetaData_.plaquette = 0.0;
+	FieldMetaData_.link_trace= 0.0;
+	std::cout << GridLogWarning << "This configuration is unsafe with no plaquette records that can verify it !!! "<<std::endl;
+      }
+    }
+
+    ////////////////////////////////////////////////////////////
+    // Really really want to mandate a scidac checksum
+    ////////////////////////////////////////////////////////////
+    if ( found_scidacChecksum ) {
+      FieldMetaData_.scidac_checksuma = stoull(scidacChecksum_.suma,0,16);
+      FieldMetaData_.scidac_checksumb = stoull(scidacChecksum_.sumb,0,16);
+      scidacChecksumVerify(scidacChecksum_,scidac_csuma,scidac_csumb);
+      assert( scidac_csuma ==FieldMetaData_.scidac_checksuma);
+      assert( scidac_csumb ==FieldMetaData_.scidac_checksumb);
+      std::cout << GridLogMessage<<"SciDAC checksums match " << std::endl;
+    } else { 
+      std::cout << GridLogWarning<<"SciDAC checksums not found. This is unsafe. " << std::endl;
+      assert(0); // Can I insist always checksum ?
+    }
+
+    if ( found_FieldMetaData || found_usqcdInfo ) {
+      FieldMetaData checker;
+      GaugeStatistics(Umu,checker);
+      assert(fabs(checker.plaquette  - FieldMetaData_.plaquette )<1.0e-5);
+      assert(fabs(checker.link_trace - FieldMetaData_.link_trace)<1.0e-5);
+      std::cout << GridLogMessage<<"Plaquette and link trace match " << std::endl;
+    }
+  }
+ };
+
+NAMESPACE_END(Grid);
+
+
+//HAVE_LIME
+#endif
+

Grid/parallelIO/IldgIOtypes.h

@@ -0,0 +1,237 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/parallelIO/IldgIO.h
+
+Copyright (C) 2015
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+			   /*  END LEGAL */
+#ifndef GRID_ILDGTYPES_IO_H
+#define GRID_ILDGTYPES_IO_H
+
+#ifdef HAVE_LIME
+extern "C" { // for linkage
+#include "lime.h"
+}
+
+NAMESPACE_BEGIN(Grid);
+
+/////////////////////////////////////////////////////////////////////////////////
+// Data representation of records that enter ILDG and SciDac formats
+/////////////////////////////////////////////////////////////////////////////////
+
+#define GRID_FORMAT      "grid-format"
+#define ILDG_FORMAT      "ildg-format"
+#define ILDG_BINARY_DATA "ildg-binary-data"
+#define ILDG_DATA_LFN    "ildg-data-lfn"
+#define SCIDAC_CHECKSUM           "scidac-checksum"
+#define SCIDAC_PRIVATE_FILE_XML   "scidac-private-file-xml"
+#define SCIDAC_FILE_XML           "scidac-file-xml"
+#define SCIDAC_PRIVATE_RECORD_XML "scidac-private-record-xml"
+#define SCIDAC_RECORD_XML         "scidac-record-xml"
+#define SCIDAC_BINARY_DATA        "scidac-binary-data"
+// Unused SCIDAC records names; could move to support this functionality
+#define SCIDAC_SITELIST           "scidac-sitelist"
+
+////////////////////////////////////////////////////////////
+const int GRID_IO_SINGLEFILE = 0; // hardcode lift from QIO compat
+const int GRID_IO_MULTIFILE  = 1; // hardcode lift from QIO compat
+const int GRID_IO_FIELD      = 0; // hardcode lift from QIO compat
+const int GRID_IO_GLOBAL     = 1; // hardcode lift from QIO compat
+////////////////////////////////////////////////////////////
+
+/////////////////////////////////////////////////////////////////////////////////
+// QIO uses mandatory "private" records fixed format
+// Private is in principle "opaque" however it can't be changed now because that would break existing 
+// file compatability, so should be correct to assume the undocumented but defacto file structure.
+/////////////////////////////////////////////////////////////////////////////////
+
+struct emptyUserRecord : Serializable { 
+  GRID_SERIALIZABLE_CLASS_MEMBERS(emptyUserRecord,int,dummy);
+  emptyUserRecord() { dummy=0; };
+};
+
+////////////////////////
+// Scidac private file xml
+// <?xml version="1.0" encoding="UTF-8"?><scidacFile><version>1.1</version><spacetime>4</spacetime><dims>16 16 16 32 </dims><volfmt>0</volfmt></scidacFile>
+////////////////////////
+struct scidacFile : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(scidacFile,
+                                  double, version,
+                                  int, spacetime,
+				  std::string, dims, // must convert to int
+                                  int, volfmt);
+
+  std::vector<int> getDimensions(void) { 
+    std::stringstream stream(dims);
+    std::vector<int> dimensions;
+    int n;
+    while(stream >> n){
+      dimensions.push_back(n);
+    }
+    return dimensions;
+  }
+
+  void setDimensions(Coordinate dimensions) { 
+    char delimiter = ' ';
+    std::stringstream stream;
+    for(int i=0;i<dimensions.size();i++){ 
+      stream << dimensions[i];
+      if ( i != dimensions.size()-1) { 
+	stream << delimiter <<std::endl;
+      }
+    }
+    dims = stream.str();
+  }
+
+  // Constructor provides Grid
+  scidacFile() =default; // default constructor
+  scidacFile(GridBase * grid){
+    version      = 1.0;
+    spacetime    = grid->_ndimension;
+    setDimensions(grid->FullDimensions()); 
+    volfmt       = GRID_IO_SINGLEFILE;
+  }
+
+};
+
+///////////////////////////////////////////////////////////////////////
+// scidac-private-record-xml : example
+// <scidacRecord>
+// <version>1.1</version><date>Tue Jul 26 21:14:44 2011 UTC</date><recordtype>0</recordtype>
+// <datatype>QDP_D3_ColorMatrix</datatype><precision>D</precision><colors>3</colors><spins>4</spins>
+// <typesize>144</typesize><datacount>4</datacount>
+// </scidacRecord>
+///////////////////////////////////////////////////////////////////////
+
+struct scidacRecord : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(scidacRecord,
+                                  double, version,
+                                  std::string, date,
+				  int, recordtype,
+				  std::string, datatype,
+				  std::string, precision,
+				  int, colors,
+				  int, spins,
+				  int, typesize,
+				  int, datacount);
+
+  scidacRecord()
+  : version(1.0), recordtype(0), colors(0), spins(0), typesize(0), datacount(0)
+  {}
+};
+
+////////////////////////
+// ILDG format
+////////////////////////
+struct ildgFormat : Serializable {
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(ildgFormat,
+				  double, version,
+				  std::string, field,
+				  int, precision,
+				  int, lx,
+				  int, ly,
+				  int, lz,
+				  int, lt);
+  ildgFormat() { version=1.0; };
+};
+////////////////////////
+// USQCD info
+////////////////////////
+struct usqcdInfo : Serializable { 
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(usqcdInfo,
+				  double, version,
+				  double, plaq,
+				  double, linktr,
+				  std::string, info);
+  usqcdInfo() { 
+    version=1.0; 
+  };
+};
+////////////////////////
+// Scidac Checksum
+////////////////////////
+struct scidacChecksum : Serializable { 
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(scidacChecksum,
+				  double, version,
+				  std::string, suma,
+				  std::string, sumb);
+  scidacChecksum() { 
+    version=1.0; 
+  };
+};
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Type:           scidac-file-xml         <title>MILC ILDG archival gauge configuration</title>
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+// Type:           
+////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+////////////////////////
+// Scidac private file xml 
+// <?xml version="1.0" encoding="UTF-8"?><scidacFile><version>1.1</version><spacetime>4</spacetime><dims>16 16 16 32 </dims><volfmt>0</volfmt></scidacFile> 
+////////////////////////                                                                                                                                                                              
+
+#if 0
+////////////////////////////////////////////////////////////////////////////////////////
+// From http://www.physics.utah.edu/~detar/scidac/qio_2p3.pdf
+////////////////////////////////////////////////////////////////////////////////////////
+struct usqcdPropFile : Serializable { 
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(usqcdPropFile,
+				  double, version,
+				  std::string, type,
+				  std::string, info);
+  usqcdPropFile() { 
+    version=1.0; 
+  };
+};
+struct usqcdSourceInfo : Serializable { 
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(usqcdSourceInfo,
+				  double, version,
+				  std::string, info);
+  usqcdSourceInfo() { 
+    version=1.0; 
+  };
+};
+struct usqcdPropInfo : Serializable { 
+public:
+  GRID_SERIALIZABLE_CLASS_MEMBERS(usqcdPropInfo,
+				  double, version,
+				  int, spin,
+				  int, color,
+				  std::string, info);
+  usqcdPropInfo() { 
+    version=1.0; 
+  };
+};
+#endif
+
+NAMESPACE_END(Grid);
+#endif
+#endif

Grid/parallelIO/MetaData.h

@@ -0,0 +1,325 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/parallelIO/NerscIO.h
+
+    Copyright (C) 2015
+
+
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <algorithm>
+#include <iostream>
+#include <iomanip>
+#include <fstream>
+#include <map>
+#include <unistd.h>
+#include <sys/utsname.h>
+#include <pwd.h>
+
+NAMESPACE_BEGIN(Grid);
+
+///////////////////////////////////////////////////////
+// Precision mapping
+///////////////////////////////////////////////////////
+template<class vobj> static std::string getFormatString (void)
+{
+  std::string format;
+  typedef typename getPrecision<vobj>::real_scalar_type stype;
+  if ( sizeof(stype) == sizeof(float) ) {
+    format = std::string("IEEE32BIG");
+  }
+  if ( sizeof(stype) == sizeof(double) ) {
+    format = std::string("IEEE64BIG");
+  }
+  return format;
+}
+////////////////////////////////////////////////////////////////////////////////
+// header specification/interpretation
+////////////////////////////////////////////////////////////////////////////////
+class FieldMetaData : Serializable {
+public:
+
+  GRID_SERIALIZABLE_CLASS_MEMBERS(FieldMetaData,
+				  int, nd,
+				  std::vector<int>, dimension,
+				  std::vector<std::string>, boundary,
+				  int, data_start,
+				  std::string, hdr_version,
+				  std::string, storage_format,
+				  double, link_trace,
+				  double, plaquette,
+				  uint32_t, checksum,
+				  uint32_t, scidac_checksuma,
+				  uint32_t, scidac_checksumb,
+				  unsigned int, sequence_number,
+				  std::string, data_type,
+				  std::string, ensemble_id,
+				  std::string, ensemble_label,
+				  std::string, ildg_lfn,
+				  std::string, creator,
+				  std::string, creator_hardware,
+				  std::string, creation_date,
+				  std::string, archive_date,
+				  std::string, floating_point);
+      // WARNING: non-initialised values might lead to twisted parallel IO
+      // issues, std::string are fine because they initliase to size 0
+      // as per C++ standard.
+      FieldMetaData(void) 
+      : nd(4), dimension(4,0), boundary(4, ""), data_start(0),
+      link_trace(0.), plaquette(0.), checksum(0),
+      scidac_checksuma(0), scidac_checksumb(0), sequence_number(0)
+      {}
+};
+
+// PB disable using namespace - this is a header and forces namesapce visibility for all 
+// including files
+//using namespace Grid;
+
+//////////////////////////////////////////////////////////////////////
+// Bit and Physical Checksumming and QA of data
+//////////////////////////////////////////////////////////////////////
+inline void GridMetaData(GridBase *grid,FieldMetaData &header)
+{
+  int nd = grid->_ndimension;
+  header.nd = nd;
+  header.dimension.resize(nd);
+  header.boundary.resize(nd);
+  header.data_start = 0;
+  for(int d=0;d<nd;d++) {
+    header.dimension[d] = grid->_fdimensions[d];
+  }
+  for(int d=0;d<nd;d++) {
+    header.boundary[d] = std::string("PERIODIC");
+  }
+}
+
+inline void MachineCharacteristics(FieldMetaData &header)
+{
+  // Who
+  struct passwd *pw = getpwuid (getuid());
+  if (pw) header.creator = std::string(pw->pw_name); 
+
+  // When
+  std::time_t t = std::time(nullptr);
+  std::tm tm_ = *std::localtime(&t);
+  std::ostringstream oss; 
+  //      oss << std::put_time(&tm_, "%c %Z");
+  header.creation_date = oss.str();
+  header.archive_date  = header.creation_date;
+
+  // What
+  struct utsname name;  uname(&name);
+  header.creator_hardware = std::string(name.nodename)+"-";
+  header.creator_hardware+= std::string(name.machine)+"-";
+  header.creator_hardware+= std::string(name.sysname)+"-";
+  header.creator_hardware+= std::string(name.release);
+}
+
+#define dump_meta_data(field, s)					\
+  s << "BEGIN_HEADER"      << std::endl;				\
+  s << "HDR_VERSION = "    << field.hdr_version    << std::endl;	\
+  s << "DATATYPE = "       << field.data_type      << std::endl;	\
+  s << "STORAGE_FORMAT = " << field.storage_format << std::endl;	\
+  for(int i=0;i<4;i++){							\
+    s << "DIMENSION_" << i+1 << " = " << field.dimension[i] << std::endl ; \
+  }									\
+  s << "LINK_TRACE = " << std::setprecision(10) << field.link_trace << std::endl; \
+  s << "PLAQUETTE  = " << std::setprecision(10) << field.plaquette  << std::endl; \
+  for(int i=0;i<4;i++){							\
+    s << "BOUNDARY_"<<i+1<<" = " << field.boundary[i] << std::endl;	\
+  }									\
+									\
+  s << "CHECKSUM = "<< std::hex << std::setw(10) << field.checksum << std::dec<<std::endl; \
+  s << "SCIDAC_CHECKSUMA = "<< std::hex << std::setw(10) << field.scidac_checksuma << std::dec<<std::endl; \
+  s << "SCIDAC_CHECKSUMB = "<< std::hex << std::setw(10) << field.scidac_checksumb << std::dec<<std::endl; \
+  s << "ENSEMBLE_ID = "     << field.ensemble_id      << std::endl;	\
+  s << "ENSEMBLE_LABEL = "  << field.ensemble_label   << std::endl;	\
+  s << "SEQUENCE_NUMBER = " << field.sequence_number  << std::endl;	\
+  s << "CREATOR = "         << field.creator          << std::endl;	\
+  s << "CREATOR_HARDWARE = "<< field.creator_hardware << std::endl;	\
+  s << "CREATION_DATE = "   << field.creation_date    << std::endl;	\
+  s << "ARCHIVE_DATE = "    << field.archive_date     << std::endl;	\
+  s << "FLOATING_POINT = "  << field.floating_point   << std::endl;	\
+  s << "END_HEADER"         << std::endl;
+
+template<class vobj> inline void PrepareMetaData(Lattice<vobj> & field, FieldMetaData &header)
+{
+  GridBase *grid = field.Grid();
+  std::string format = getFormatString<vobj>();
+  header.floating_point = format;
+  header.checksum = 0x0; // Nersc checksum unused in ILDG, Scidac
+  GridMetaData(grid,header); 
+  MachineCharacteristics(header);
+}
+inline void GaugeStatistics(Lattice<vLorentzColourMatrixF> & data,FieldMetaData &header)
+{
+  // How to convert data precision etc...
+  header.link_trace=WilsonLoops<PeriodicGimplF>::linkTrace(data);
+  header.plaquette =WilsonLoops<PeriodicGimplF>::avgPlaquette(data);
+}
+inline void GaugeStatistics(Lattice<vLorentzColourMatrixD> & data,FieldMetaData &header)
+{
+  // How to convert data precision etc...
+  header.link_trace=WilsonLoops<PeriodicGimplD>::linkTrace(data);
+  header.plaquette =WilsonLoops<PeriodicGimplD>::avgPlaquette(data);
+}
+template<> inline void PrepareMetaData<vLorentzColourMatrixF>(Lattice<vLorentzColourMatrixF> & field, FieldMetaData &header)
+{
+   
+  GridBase *grid = field.Grid();
+  std::string format = getFormatString<vLorentzColourMatrixF>();
+  header.floating_point = format;
+  header.checksum = 0x0; // Nersc checksum unused in ILDG, Scidac
+  GridMetaData(grid,header); 
+  GaugeStatistics(field,header);
+  MachineCharacteristics(header);
+}
+template<> inline void PrepareMetaData<vLorentzColourMatrixD>(Lattice<vLorentzColourMatrixD> & field, FieldMetaData &header)
+{
+  GridBase *grid = field.Grid();
+  std::string format = getFormatString<vLorentzColourMatrixD>();
+  header.floating_point = format;
+  header.checksum = 0x0; // Nersc checksum unused in ILDG, Scidac
+  GridMetaData(grid,header); 
+  GaugeStatistics(field,header);
+  MachineCharacteristics(header);
+}
+
+//////////////////////////////////////////////////////////////////////
+// Utilities ; these are QCD aware
+//////////////////////////////////////////////////////////////////////
+inline void reconstruct3(LorentzColourMatrix & cm)
+{
+  const int x=0;
+  const int y=1;
+  const int z=2;
+  for(int mu=0;mu<Nd;mu++){
+    cm(mu)()(2,x) = adj(cm(mu)()(0,y)*cm(mu)()(1,z)-cm(mu)()(0,z)*cm(mu)()(1,y)); //x= yz-zy
+    cm(mu)()(2,y) = adj(cm(mu)()(0,z)*cm(mu)()(1,x)-cm(mu)()(0,x)*cm(mu)()(1,z)); //y= zx-xz
+    cm(mu)()(2,z) = adj(cm(mu)()(0,x)*cm(mu)()(1,y)-cm(mu)()(0,y)*cm(mu)()(1,x)); //z= xy-yx
+  }
+}
+
+////////////////////////////////////////////////////////////////////////////////
+// Some data types for intermediate storage
+////////////////////////////////////////////////////////////////////////////////
+template<typename vtype> using iLorentzColour2x3 = iVector<iVector<iVector<vtype, Nc>, 2>, Nd >;
+
+typedef iLorentzColour2x3<Complex>  LorentzColour2x3;
+typedef iLorentzColour2x3<ComplexF> LorentzColour2x3F;
+typedef iLorentzColour2x3<ComplexD> LorentzColour2x3D;
+
+/////////////////////////////////////////////////////////////////////////////////
+// Simple classes for precision conversion
+/////////////////////////////////////////////////////////////////////////////////
+template <class fobj, class sobj>
+struct BinarySimpleUnmunger {
+  typedef typename getPrecision<fobj>::real_scalar_type fobj_stype;
+  typedef typename getPrecision<sobj>::real_scalar_type sobj_stype;
+  
+  void operator()(sobj &in, fobj &out) {
+    // take word by word and transform accoding to the status
+    fobj_stype *out_buffer = (fobj_stype *)&out;
+    sobj_stype *in_buffer = (sobj_stype *)&in;
+    size_t fobj_words = sizeof(out) / sizeof(fobj_stype);
+    size_t sobj_words = sizeof(in) / sizeof(sobj_stype);
+    assert(fobj_words == sobj_words);
+    
+    for (unsigned int word = 0; word < sobj_words; word++)
+      out_buffer[word] = in_buffer[word];  // type conversion on the fly
+    
+  }
+};
+
+template <class fobj, class sobj>
+struct BinarySimpleMunger {
+  typedef typename getPrecision<fobj>::real_scalar_type fobj_stype;
+  typedef typename getPrecision<sobj>::real_scalar_type sobj_stype;
+
+  void operator()(fobj &in, sobj &out) {
+    // take word by word and transform accoding to the status
+    fobj_stype *in_buffer = (fobj_stype *)&in;
+    sobj_stype *out_buffer = (sobj_stype *)&out;
+    size_t fobj_words = sizeof(in) / sizeof(fobj_stype);
+    size_t sobj_words = sizeof(out) / sizeof(sobj_stype);
+    assert(fobj_words == sobj_words);
+    
+    for (unsigned int word = 0; word < sobj_words; word++)
+      out_buffer[word] = in_buffer[word];  // type conversion on the fly
+    
+  }
+};
+
+
+template<class fobj,class sobj>
+struct GaugeSimpleMunger{
+  void operator()(fobj &in, sobj &out) {
+    for (int mu = 0; mu < Nd; mu++) {
+      for (int i = 0; i < Nc; i++) {
+	for (int j = 0; j < Nc; j++) {
+	  out(mu)()(i, j) = in(mu)()(i, j);
+	}}
+    }
+  };
+};
+
+template <class fobj, class sobj>
+struct GaugeSimpleUnmunger {
+
+  void operator()(sobj &in, fobj &out) {
+    for (int mu = 0; mu < Nd; mu++) {
+      for (int i = 0; i < Nc; i++) {
+	for (int j = 0; j < Nc; j++) {
+	  out(mu)()(i, j) = in(mu)()(i, j);
+	}}
+    }
+  };
+};
+
+template<class fobj,class sobj>
+struct Gauge3x2munger{
+  void operator() (fobj &in,sobj &out){
+    for(int mu=0;mu<Nd;mu++){
+      for(int i=0;i<2;i++){
+	for(int j=0;j<3;j++){
+	  out(mu)()(i,j) = in(mu)(i)(j);
+	}}
+    }
+    reconstruct3(out);
+  }
+};
+
+template<class fobj,class sobj>
+struct Gauge3x2unmunger{
+  void operator() (sobj &in,fobj &out){
+    for(int mu=0;mu<Nd;mu++){
+      for(int i=0;i<2;i++){
+	for(int j=0;j<3;j++){
+	  out(mu)(i)(j) = in(mu)()(i,j);
+	}}
+    }
+  }
+};
+
+NAMESPACE_END(Grid);
+

Grid/parallelIO/NerscIO.h

@@ -0,0 +1,360 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/parallelIO/NerscIO.h
+
+    Copyright (C) 2015
+
+    Author: Matt Spraggs <matthew.spraggs@gmail.com>
+    Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+    Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_NERSC_IO_H
+#define GRID_NERSC_IO_H
+
+NAMESPACE_BEGIN(Grid);
+
+using namespace Grid;
+
+////////////////////////////////////////////////////////////////////////////////
+// Write and read from fstream; comput header offset for payload
+////////////////////////////////////////////////////////////////////////////////
+class NerscIO : public BinaryIO { 
+public:
+
+  static inline void truncate(std::string file){
+    std::ofstream fout(file,std::ios::out);
+  }
+  
+  static inline unsigned int writeHeader(FieldMetaData &field,std::string file)
+  {
+    std::ofstream fout(file,std::ios::out|std::ios::in);
+    fout.seekp(0,std::ios::beg);
+    dump_meta_data(field, fout);
+    field.data_start = fout.tellp();
+    return field.data_start;
+  }
+
+  // for the header-reader
+  static inline int readHeader(std::string file,GridBase *grid,  FieldMetaData &field)
+  {
+    uint64_t offset=0;
+    std::map<std::string,std::string> header;
+    std::string line;
+
+    //////////////////////////////////////////////////
+    // read the header
+    //////////////////////////////////////////////////
+    std::ifstream fin(file);
+
+    getline(fin,line); // read one line and insist is 
+
+    removeWhitespace(line);
+    std::cout << GridLogMessage << "* " << line << std::endl;
+
+    assert(line==std::string("BEGIN_HEADER"));
+
+    do {
+      getline(fin,line); // read one line
+      std::cout << GridLogMessage << "* "<<line<< std::endl;
+      int eq = line.find("=");
+      if(eq >0) {
+	std::string key=line.substr(0,eq);
+	std::string val=line.substr(eq+1);
+	removeWhitespace(key);
+	removeWhitespace(val);
+      
+	header[key] = val;
+      }
+    } while( line.find("END_HEADER") == std::string::npos );
+
+    field.data_start = fin.tellg();
+
+    //////////////////////////////////////////////////
+    // chomp the values
+    //////////////////////////////////////////////////
+    field.hdr_version    = header["HDR_VERSION"];
+    field.data_type      = header["DATATYPE"];
+    field.storage_format = header["STORAGE_FORMAT"];
+  
+    field.dimension[0] = std::stol(header["DIMENSION_1"]);
+    field.dimension[1] = std::stol(header["DIMENSION_2"]);
+    field.dimension[2] = std::stol(header["DIMENSION_3"]);
+    field.dimension[3] = std::stol(header["DIMENSION_4"]);
+
+    assert(grid->_ndimension == 4);
+    for(int d=0;d<4;d++){
+      assert(grid->_fdimensions[d]==field.dimension[d]);
+    }
+
+    field.link_trace = std::stod(header["LINK_TRACE"]);
+    field.plaquette  = std::stod(header["PLAQUETTE"]);
+
+    field.boundary[0] = header["BOUNDARY_1"];
+    field.boundary[1] = header["BOUNDARY_2"];
+    field.boundary[2] = header["BOUNDARY_3"];
+    field.boundary[3] = header["BOUNDARY_4"];
+
+    field.checksum = std::stoul(header["CHECKSUM"],0,16);
+    field.ensemble_id      = header["ENSEMBLE_ID"];
+    field.ensemble_label   = header["ENSEMBLE_LABEL"];
+    field.sequence_number  = std::stol(header["SEQUENCE_NUMBER"]);
+    field.creator          = header["CREATOR"];
+    field.creator_hardware = header["CREATOR_HARDWARE"];
+    field.creation_date    = header["CREATION_DATE"];
+    field.archive_date     = header["ARCHIVE_DATE"];
+    field.floating_point   = header["FLOATING_POINT"];
+
+    return field.data_start;
+  }
+
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+  // Now the meat: the object readers
+  /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+
+  template<class vsimd>
+  static inline void readConfiguration(Lattice<iLorentzColourMatrix<vsimd> > &Umu,
+				       FieldMetaData& header,
+				       std::string file)
+  {
+    typedef Lattice<iLorentzColourMatrix<vsimd> > GaugeField;
+
+    GridBase *grid = Umu.Grid();
+    uint64_t offset = readHeader(file,Umu.Grid(),header);
+
+    FieldMetaData clone(header);
+
+    std::string format(header.floating_point);
+
+    int ieee32big = (format == std::string("IEEE32BIG"));
+    int ieee32    = (format == std::string("IEEE32"));
+    int ieee64big = (format == std::string("IEEE64BIG"));
+    int ieee64    = (format == std::string("IEEE64"));
+
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+    // depending on datatype, set up munger;
+    // munger is a function of <floating point, Real, data_type>
+    if ( header.data_type == std::string("4D_SU3_GAUGE") ) {
+      if ( ieee32 || ieee32big ) {
+	BinaryIO::readLatticeObject<iLorentzColourMatrix<vsimd>, LorentzColour2x3F> 
+	  (Umu,file,Gauge3x2munger<LorentzColour2x3F,LorentzColourMatrix>(), offset,format,
+	   nersc_csum,scidac_csuma,scidac_csumb);
+      }
+      if ( ieee64 || ieee64big ) {
+	BinaryIO::readLatticeObject<iLorentzColourMatrix<vsimd>, LorentzColour2x3D> 
+	  (Umu,file,Gauge3x2munger<LorentzColour2x3D,LorentzColourMatrix>(),offset,format,
+	   nersc_csum,scidac_csuma,scidac_csumb);
+      }
+    } else if ( header.data_type == std::string("4D_SU3_GAUGE_3x3") ) {
+      if ( ieee32 || ieee32big ) {
+	BinaryIO::readLatticeObject<iLorentzColourMatrix<vsimd>,LorentzColourMatrixF>
+	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixF,LorentzColourMatrix>(),offset,format,
+	   nersc_csum,scidac_csuma,scidac_csumb);
+      }
+      if ( ieee64 || ieee64big ) {
+	BinaryIO::readLatticeObject<iLorentzColourMatrix<vsimd>,LorentzColourMatrixD>
+	  (Umu,file,GaugeSimpleMunger<LorentzColourMatrixD,LorentzColourMatrix>(),offset,format,
+	   nersc_csum,scidac_csuma,scidac_csumb);
+      }
+    } else {
+      assert(0);
+    }
+
+    GaugeStatistics(Umu,clone);
+
+    std::cout<<GridLogMessage <<"NERSC Configuration "<<file<<" checksum "<<std::hex<<nersc_csum<< std::dec
+	     <<" header   "<<std::hex<<header.checksum<<std::dec <<std::endl;
+    std::cout<<GridLogMessage <<"NERSC Configuration "<<file<<" plaquette "<<clone.plaquette
+	     <<" header    "<<header.plaquette<<std::endl;
+    std::cout<<GridLogMessage <<"NERSC Configuration "<<file<<" link_trace "<<clone.link_trace
+	     <<" header    "<<header.link_trace<<std::endl;
+
+    if ( fabs(clone.plaquette -header.plaquette ) >=  1.0e-5 ) { 
+      std::cout << " Plaquette mismatch "<<std::endl;
+    }
+    if ( nersc_csum != header.checksum ) { 
+      std::cerr << " checksum mismatch " << std::endl;
+      std::cerr << " plaqs " << clone.plaquette << " " << header.plaquette << std::endl;
+      std::cerr << " trace " << clone.link_trace<< " " << header.link_trace<< std::endl;
+      std::cerr << " nersc_csum  " <<std::hex<< nersc_csum << " " << header.checksum<< std::dec<< std::endl;
+      exit(0);
+    }
+    assert(fabs(clone.plaquette -header.plaquette ) < 1.0e-5 );
+    assert(fabs(clone.link_trace-header.link_trace) < 1.0e-6 );
+    assert(nersc_csum == header.checksum );
+      
+    std::cout<<GridLogMessage <<"NERSC Configuration "<<file<< " and plaquette, link trace, and checksum agree"<<std::endl;
+  }
+
+  template<class vsimd>
+  static inline void writeConfiguration(Lattice<iLorentzColourMatrix<vsimd> > &Umu,
+					std::string file, 
+					int two_row,
+					int bits32)
+  {
+    typedef Lattice<iLorentzColourMatrix<vsimd> > GaugeField;
+
+    typedef iLorentzColourMatrix<vsimd> vobj;
+    typedef typename vobj::scalar_object sobj;
+
+    FieldMetaData header;
+    ///////////////////////////////////////////
+    // Following should become arguments
+    ///////////////////////////////////////////
+    header.sequence_number = 1;
+    header.ensemble_id     = "UKQCD";
+    header.ensemble_label  = "DWF";
+
+    typedef LorentzColourMatrixD fobj3D;
+    typedef LorentzColour2x3D    fobj2D;
+  
+    GridBase *grid = Umu.Grid();
+
+    GridMetaData(grid,header);
+    assert(header.nd==4);
+    GaugeStatistics(Umu,header);
+    MachineCharacteristics(header);
+
+	uint64_t offset;
+
+    // Sod it -- always write 3x3 double
+    header.floating_point = std::string("IEEE64BIG");
+    header.data_type      = std::string("4D_SU3_GAUGE_3x3");
+    GaugeSimpleUnmunger<fobj3D,sobj> munge;
+	if ( grid->IsBoss() ) { 
+	  truncate(file);
+    offset = writeHeader(header,file);
+	}
+	grid->Broadcast(0,(void *)&offset,sizeof(offset));
+
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+    BinaryIO::writeLatticeObject<vobj,fobj3D>(Umu,file,munge,offset,header.floating_point,
+					      nersc_csum,scidac_csuma,scidac_csumb);
+    header.checksum = nersc_csum;
+	if ( grid->IsBoss() ) { 
+    writeHeader(header,file);
+	}
+
+    std::cout<<GridLogMessage <<"Written NERSC Configuration on "<< file << " checksum "
+	     <<std::hex<<header.checksum
+	     <<std::dec<<" plaq "<< header.plaquette <<std::endl;
+
+  }
+  ///////////////////////////////
+  // RNG state
+  ///////////////////////////////
+  static inline void writeRNGState(GridSerialRNG &serial,GridParallelRNG &parallel,std::string file)
+  {
+    typedef typename GridParallelRNG::RngStateType RngStateType;
+
+    // Following should become arguments
+    FieldMetaData header;
+    header.sequence_number = 1;
+    header.ensemble_id     = "UKQCD";
+    header.ensemble_label  = "DWF";
+
+    GridBase *grid = parallel.Grid();
+
+    GridMetaData(grid,header);
+    assert(header.nd==4);
+    header.link_trace=0.0;
+    header.plaquette=0.0;
+    MachineCharacteristics(header);
+
+	uint64_t offset;
+  
+#ifdef RNG_RANLUX
+    header.floating_point = std::string("UINT64");
+    header.data_type      = std::string("RANLUX48");
+#endif
+#ifdef RNG_MT19937
+    header.floating_point = std::string("UINT32");
+    header.data_type      = std::string("MT19937");
+#endif
+#ifdef RNG_SITMO
+    header.floating_point = std::string("UINT64");
+    header.data_type      = std::string("SITMO");
+#endif
+
+	if ( grid->IsBoss() ) { 
+    truncate(file);
+    offset = writeHeader(header,file);
+	}
+	grid->Broadcast(0,(void *)&offset,sizeof(offset));
+	
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+    BinaryIO::writeRNG(serial,parallel,file,offset,nersc_csum,scidac_csuma,scidac_csumb);
+    header.checksum = nersc_csum;
+	if ( grid->IsBoss() ) { 
+    offset = writeHeader(header,file);
+	}
+
+    std::cout<<GridLogMessage 
+	     <<"Written NERSC RNG STATE "<<file<< " checksum "
+	     <<std::hex<<header.checksum
+	     <<std::dec<<std::endl;
+
+  }
+    
+  static inline void readRNGState(GridSerialRNG &serial,GridParallelRNG & parallel,FieldMetaData& header,std::string file)
+  {
+    typedef typename GridParallelRNG::RngStateType RngStateType;
+
+    GridBase *grid = parallel.Grid();
+
+	uint64_t offset = readHeader(file,grid,header);
+
+    FieldMetaData clone(header);
+
+    std::string format(header.floating_point);
+    std::string data_type(header.data_type);
+
+#ifdef RNG_RANLUX
+    assert(format == std::string("UINT64"));
+    assert(data_type == std::string("RANLUX48"));
+#endif
+#ifdef RNG_MT19937
+    assert(format == std::string("UINT32"));
+    assert(data_type == std::string("MT19937"));
+#endif
+#ifdef RNG_SITMO
+    assert(format == std::string("UINT64"));
+    assert(data_type == std::string("SITMO"));
+#endif
+
+    // depending on datatype, set up munger;
+    // munger is a function of <floating point, Real, data_type>
+    uint32_t nersc_csum,scidac_csuma,scidac_csumb;
+    BinaryIO::readRNG(serial,parallel,file,offset,nersc_csum,scidac_csuma,scidac_csumb);
+
+    if ( nersc_csum != header.checksum ) { 
+      std::cerr << "checksum mismatch "<<std::hex<< nersc_csum <<" "<<header.checksum<<std::dec<<std::endl;
+      exit(0);
+    }
+    assert(nersc_csum == header.checksum );
+
+    std::cout<<GridLogMessage <<"Read NERSC RNG file "<<file<< " format "<< data_type <<std::endl;
+  }
+};
+
+NAMESPACE_END(QCD);
+
+#endif

Grid/perfmon/PerfCount.cc

@@ -0,0 +1,76 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/PerfCount.cc
+
+    Copyright (C) 2015
+
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+
+#include <Grid/GridCore.h>
+#include <Grid/perfmon/PerfCount.h>
+
+NAMESPACE_BEGIN(Grid);
+
+#define CacheControl(L,O,R) ((PERF_COUNT_HW_CACHE_##L)|(PERF_COUNT_HW_CACHE_OP_##O<<8)| (PERF_COUNT_HW_CACHE_RESULT_##R<<16))
+#define RawConfig(A,B) (A<<8|B)
+const PerformanceCounter::PerformanceCounterConfig PerformanceCounter::PerformanceCounterConfigs [] = {
+#ifdef __linux__
+  { PERF_TYPE_HARDWARE, PERF_COUNT_HW_CACHE_REFERENCES    ,  "CACHE_REFERENCES..." , INSTRUCTIONS},
+  { PERF_TYPE_HARDWARE, PERF_COUNT_HW_CACHE_MISSES        ,  "CACHE_MISSES......." , CACHE_REFERENCES},
+  { PERF_TYPE_HARDWARE, PERF_COUNT_HW_CPU_CYCLES          ,  "CPUCYCLES.........." , INSTRUCTIONS},
+  { PERF_TYPE_HARDWARE, PERF_COUNT_HW_INSTRUCTIONS        ,  "INSTRUCTIONS......." , CPUCYCLES   },
+  // 4
+#ifdef KNL
+  { PERF_TYPE_RAW, RawConfig(0x40,0x04), "ALL_LOADS..........", CPUCYCLES    },
+  { PERF_TYPE_RAW, RawConfig(0x01,0x04), "L1_MISS_LOADS......", L1D_READ_ACCESS },
+  { PERF_TYPE_RAW, RawConfig(0x40,0x04), "ALL_LOADS..........", L1D_READ_ACCESS },
+  { PERF_TYPE_RAW, RawConfig(0x02,0x04), "L2_HIT_LOADS.......", L1D_READ_ACCESS },
+  { PERF_TYPE_RAW, RawConfig(0x04,0x04), "L2_MISS_LOADS......", L1D_READ_ACCESS },
+  { PERF_TYPE_RAW, RawConfig(0x10,0x04), "UTLB_MISS_LOADS....", L1D_READ_ACCESS },
+  { PERF_TYPE_RAW, RawConfig(0x08,0x04), "DTLB_MISS_LOADS....", L1D_READ_ACCESS },
+  // 11
+#else
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,READ,ACCESS)     ,  "L1D_READ_ACCESS....",INSTRUCTIONS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,READ,MISS)       ,  "L1D_READ_MISS......",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,WRITE,MISS)      ,  "L1D_WRITE_MISS.....",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,WRITE,ACCESS)    ,  "L1D_WRITE_ACCESS...",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,PREFETCH,MISS)   ,  "L1D_PREFETCH_MISS..",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,PREFETCH,ACCESS) ,  "L1D_PREFETCH_ACCESS",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1D,PREFETCH,ACCESS) ,  "L1D_PREFETCH_ACCESS",L1D_READ_ACCESS},
+   // 11
+#endif
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,READ,MISS)        ,  "LL_READ_MISS.......",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,READ,ACCESS)      ,  "LL_READ_ACCESS.....",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,WRITE,MISS)       ,  "LL_WRITE_MISS......",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,WRITE,ACCESS)     ,  "LL_WRITE_ACCESS....",L1D_READ_ACCESS},
+  //15
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,PREFETCH,MISS)    ,  "LL_PREFETCH_MISS...",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(LL,PREFETCH,ACCESS)  ,  "LL_PREFETCH_ACCESS.",L1D_READ_ACCESS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1I,READ,MISS)       ,  "L1I_READ_MISS......",INSTRUCTIONS},
+  { PERF_TYPE_HW_CACHE, CacheControl(L1I,READ,ACCESS)     ,  "L1I_READ_ACCESS....",INSTRUCTIONS}
+  //19
+  //  { PERF_TYPE_HARDWARE, PERF_COUNT_HW_STALLED_CYCLES_FRONTEND, "STALL_CYCLES" },
+#endif
+};
+NAMESPACE_END(Grid);
+

Grid/perfmon/PerfCount.h

@@ -0,0 +1,249 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/PerfCount.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <peterboyle@MacBook-Pro.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_PERFCOUNT_H
+#define GRID_PERFCOUNT_H
+
+#include <sys/time.h>
+#include <ctime>
+#include <chrono>
+#include <string.h>
+#include <unistd.h>
+#include <sys/ioctl.h>
+
+#ifdef __linux__
+#include <syscall.h>
+#include <linux/perf_event.h>
+#else
+#include <sys/syscall.h>
+#endif
+#ifdef __x86_64__
+#include <x86intrin.h>
+#endif
+
+NAMESPACE_BEGIN(Grid);
+
+#ifdef __linux__
+static long perf_event_open(struct perf_event_attr *hw_event, pid_t pid,
+			    int cpu, int group_fd, unsigned long flags)
+{
+  int ret=0;
+
+  ret = syscall(__NR_perf_event_open, hw_event, pid, cpu,
+		group_fd, flags);
+  return ret;
+}
+#endif
+
+#ifdef TIMERS_OFF
+
+
+inline uint64_t cyclecount(void){ 
+  return 0;
+}
+#define __SSC_MARK(mark) __asm__ __volatile__ ("movl %0, %%ebx; .byte 0x64, 0x67, 0x90 " ::"i"(mark):"%ebx")
+#define __SSC_STOP  __SSC_MARK(0x110)
+#define __SSC_START __SSC_MARK(0x111)
+
+
+#else
+
+#define __SSC_MARK(mark) 
+#define __SSC_STOP  
+#define __SSC_START 
+
+/*
+ * cycle counters arch dependent
+ */
+
+#ifdef __bgq__
+inline uint64_t cyclecount(void){ 
+  uint64_t tmp;
+  asm volatile ("mfspr %0,0x10C" : "=&r" (tmp)  );
+  return tmp;
+}
+#elif defined __x86_64__
+#ifdef GRID_NVCC
+accelerator_inline uint64_t __rdtsc(void) {  return 0; }
+#endif
+inline uint64_t cyclecount(void){ 
+  return __rdtsc();
+  //  unsigned int dummy;
+  // return __rdtscp(&dummy);
+}
+#else
+
+inline uint64_t cyclecount(void){ 
+  return 0;
+}
+
+#endif
+
+#endif
+
+class PerformanceCounter {
+private:
+
+  typedef struct { 
+  public:
+    uint32_t type;
+    uint64_t config;
+    const char *name;
+    int normalisation;
+  } PerformanceCounterConfig; 
+  
+  static const PerformanceCounterConfig PerformanceCounterConfigs [];
+
+public:
+
+  enum PerformanceCounterType {
+    CACHE_REFERENCES=0,
+    CACHE_MISSES=1,
+    CPUCYCLES=2,
+    INSTRUCTIONS=3,
+    L1D_READ_ACCESS=4,
+    PERFORMANCE_COUNTER_NUM_TYPES=19
+  };
+
+public:
+    
+  int PCT;
+
+  long long count;
+  long long cycles;
+  int fd;
+  int cyclefd;
+  unsigned long long elapsed;
+  uint64_t begin;
+
+  static int NumTypes(void){ 
+    return PERFORMANCE_COUNTER_NUM_TYPES;
+  }
+
+  PerformanceCounter(int _pct) {
+#ifdef __linux__
+    assert(_pct>=0);
+    assert(_pct<PERFORMANCE_COUNTER_NUM_TYPES);
+    fd=-1;
+    cyclefd=-1;
+    count=0;
+    cycles=0;
+    PCT =_pct;
+    Open();
+#endif
+  }
+  void Open(void) 
+  {
+#ifdef __linux__
+    struct perf_event_attr pe;
+    memset(&pe, 0, sizeof(struct perf_event_attr));
+    pe.size = sizeof(struct perf_event_attr);
+
+    pe.disabled = 1;
+    pe.exclude_kernel = 1;
+    pe.exclude_hv = 1;
+    pe.inherit    = 1;
+
+    pe.type  = PerformanceCounterConfigs[PCT].type;
+    pe.config= PerformanceCounterConfigs[PCT].config;
+    const char * name = PerformanceCounterConfigs[PCT].name;
+    fd = perf_event_open(&pe, 0, -1, -1, 0); // pid 0, cpu -1 current process any cpu. group -1
+    if (fd == -1) {
+      fprintf(stderr, "Error opening leader %llx for event %s\n",(long long) pe.config,name);
+      perror("Error is");
+    }
+    int norm = PerformanceCounterConfigs[PCT].normalisation;
+    pe.type  = PerformanceCounterConfigs[norm].type;
+    pe.config= PerformanceCounterConfigs[norm].config;
+    name = PerformanceCounterConfigs[norm].name;
+    cyclefd = perf_event_open(&pe, 0, -1, -1, 0); // pid 0, cpu -1 current process any cpu. group -1
+    if (cyclefd == -1) {
+      fprintf(stderr, "Error opening leader %llx for event %s\n",(long long) pe.config,name);
+      perror("Error is");
+    }
+#endif
+  }
+
+  void Start(void)
+  {
+#ifdef __linux__
+    if ( fd!= -1) {
+      ::ioctl(fd, PERF_EVENT_IOC_RESET, 0);
+      ::ioctl(fd, PERF_EVENT_IOC_ENABLE, 0);
+      ::ioctl(cyclefd, PERF_EVENT_IOC_RESET, 0);
+      ::ioctl(cyclefd, PERF_EVENT_IOC_ENABLE, 0);
+    }
+    begin  =cyclecount();
+#else
+    begin = 0;
+#endif
+  }
+
+  void Stop(void) {
+    count=0;
+    cycles=0;
+#ifdef __linux__
+    ssize_t ign;
+    if ( fd!= -1) {
+      ::ioctl(fd, PERF_EVENT_IOC_DISABLE, 0);
+      ::ioctl(cyclefd, PERF_EVENT_IOC_DISABLE, 0);
+      ign=::read(fd, &count, sizeof(long long));
+      ign+=::read(cyclefd, &cycles, sizeof(long long));
+      assert(ign==2*sizeof(long long));
+    }
+    elapsed = cyclecount() - begin;
+#else
+    elapsed = 0;
+#endif
+
+  }
+  void Report(void) {
+#ifdef __linux__
+    int N = PerformanceCounterConfigs[PCT].normalisation;
+    const char * sn = PerformanceCounterConfigs[N].name ;
+    const char * sc = PerformanceCounterConfigs[PCT].name;
+    std::printf("tsc = %llu %s = %llu  %s = %20llu\n (%s/%s) rate = %lf\n", elapsed,sn ,cycles, 
+		sc, count, sc,sn, (double)count/(double)cycles);
+#else
+    std::printf("%llu cycles \n", elapsed );
+#endif
+  }
+
+  ~PerformanceCounter()
+  {
+#ifdef __linux__
+    ::close(fd);    ::close(cyclefd);
+#endif
+  }
+
+};
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/perfmon/Stat.cc

@@ -0,0 +1,246 @@
+#include <Grid/GridCore.h>
+#include <Grid/perfmon/PerfCount.h>
+#include <Grid/perfmon/Stat.h>
+
+NAMESPACE_BEGIN(Grid); 
+
+bool PmuStat::pmu_initialized=false;
+
+
+void PmuStat::init(const char *regname)
+{
+#ifdef __x86_64__
+  name = regname;
+  if (!pmu_initialized)
+    {
+      std::cout<<"initialising pmu"<<std::endl;
+      pmu_initialized = true;
+      pmu_init();
+    }
+  clear();
+#endif
+}
+void PmuStat::clear(void)
+{
+#ifdef __x86_64__
+  count = 0;
+  tregion = 0;
+  pmc0 = 0;
+  pmc1 = 0;
+  inst = 0;
+  cyc = 0;
+  ref = 0;
+  tcycles = 0;
+  reads = 0;
+  writes = 0;
+#endif
+}
+void PmuStat::print(void)
+{
+#ifdef __x86_64__
+  std::cout <<"Reg "<<std::string(name)<<":\n";
+  std::cout <<"  region "<<tregion<<std::endl;
+  std::cout <<"  cycles "<<tcycles<<std::endl;
+  std::cout <<"  inst   "<<inst   <<std::endl;
+  std::cout <<"  cyc    "<<cyc    <<std::endl;
+  std::cout <<"  ref    "<<ref    <<std::endl;
+  std::cout <<"  pmc0   "<<pmc0   <<std::endl;
+  std::cout <<"  pmc1   "<<pmc1   <<std::endl;
+  std::cout <<"  count  "<<count  <<std::endl;
+  std::cout <<"  reads  "<<reads  <<std::endl;
+  std::cout <<"  writes "<<writes <<std::endl;
+#endif
+}
+void PmuStat::start(void)
+{
+#ifdef __x86_64__
+  pmu_start();
+  ++count;
+  xmemctrs(&mrstart, &mwstart);
+  tstart = __rdtsc();
+#endif
+}
+void PmuStat::enter(int t)
+{
+#ifdef __x86_64__
+  counters[0][t] = __rdpmc(0);
+  counters[1][t] = __rdpmc(1);
+  counters[2][t] = __rdpmc((1<<30)|0);
+  counters[3][t] = __rdpmc((1<<30)|1);
+  counters[4][t] = __rdpmc((1<<30)|2);
+  counters[5][t] = __rdtsc();
+#endif
+}
+void PmuStat::exit(int t)
+{
+#ifdef __x86_64__
+  counters[0][t] = __rdpmc(0) - counters[0][t];
+  counters[1][t] = __rdpmc(1) - counters[1][t];
+  counters[2][t] = __rdpmc((1<<30)|0) - counters[2][t];
+  counters[3][t] = __rdpmc((1<<30)|1) - counters[3][t];
+  counters[4][t] = __rdpmc((1<<30)|2) - counters[4][t];
+  counters[5][t] = __rdtsc() - counters[5][t];
+#endif
+}
+void PmuStat::accum(int nthreads)
+{
+#ifdef __x86_64__
+  tend = __rdtsc();
+  xmemctrs(&mrend, &mwend);
+  pmu_stop();
+  for (int t = 0; t < nthreads; ++t) {
+    pmc0 += counters[0][t];
+    pmc1 += counters[1][t];
+    inst += counters[2][t];
+    cyc += counters[3][t];
+    ref += counters[4][t];
+    tcycles += counters[5][t];
+  }
+  uint64_t region = tend - tstart;
+  tregion += region;
+  uint64_t mreads = mrend - mrstart;
+  reads += mreads;
+  uint64_t mwrites = mwend - mwstart;
+  writes += mwrites;
+#endif
+}
+
+
+void PmuStat::pmu_fini(void) {}
+void PmuStat::pmu_start(void) {};
+void PmuStat::pmu_stop(void) {};
+void PmuStat::pmu_init(void)
+{
+#ifdef _KNIGHTS_LANDING_
+  KNLsetup();
+#endif
+}
+void PmuStat::xmemctrs(uint64_t *mr, uint64_t *mw)
+{
+#ifdef _KNIGHTS_LANDING_
+  ctrs c;
+  KNLreadctrs(c);
+  uint64_t emr = 0, emw = 0;
+  for (int i = 0; i < NEDC; ++i)
+    {
+      emr += c.edcrd[i];
+      emw += c.edcwr[i];
+    }
+  *mr = emr;
+  *mw = emw;
+#else
+  *mr = *mw = 0;
+#endif
+}
+
+#ifdef _KNIGHTS_LANDING_
+
+struct knl_gbl_ PmuStat::gbl;
+
+#define PMU_MEM
+
+void PmuStat::KNLevsetup(const char *ename, int &fd, int event, int umask)
+{
+  char fname[1024];
+  snprintf(fname, sizeof(fname), "%s/type", ename);
+  FILE *fp = fopen(fname, "r");
+  if (fp == 0) {
+    ::printf("open %s", fname);
+    ::exit(0);
+  }
+  int type;
+  int ret = fscanf(fp, "%d", &type);
+  assert(ret == 1);
+  fclose(fp);
+  //  std::cout << "Using PMU type "<<type<<" from " << std::string(ename) <<std::endl;
+
+  struct perf_event_attr hw = {};
+  hw.size = sizeof(hw);
+  hw.type = type;
+  // see /sys/devices/uncore_*/format/*
+  // All of the events we are interested in are configured the same way, but
+  // that isn't always true. Proper code would parse the format files
+  hw.config = event | (umask << 8);
+  //hw.read_format = PERF_FORMAT_GROUP;
+  // unfortunately the above only works within a single PMU; might
+  // as well just read them one at a time
+  int cpu = 0;
+  fd = perf_event_open(&hw, -1, cpu, -1, 0);
+  if (fd == -1) {
+    ::printf("CPU %d, box %s, event 0x%lx", cpu, ename, hw.config);
+    ::exit(0);
+  } else { 
+    //    std::cout << "event "<<std::string(ename)<<" set up for fd "<<fd<<" hw.config "<<hw.config <<std::endl;
+  }
+}
+
+
+void PmuStat::KNLsetup(void){
+
+  int ret;
+  char fname[1024];
+
+  // MC RPQ inserts and WPQ inserts (reads & writes)
+  for (int mc = 0; mc < NMC; ++mc)
+    {
+      ::snprintf(fname, sizeof(fname), "/sys/devices/uncore_imc_%d",mc);
+      // RPQ Inserts
+      KNLevsetup(fname, gbl.mc_rd[mc], 0x1, 0x1);
+      // WPQ Inserts
+      KNLevsetup(fname, gbl.mc_wr[mc], 0x2, 0x1);
+    }
+  // EDC RPQ inserts and WPQ inserts
+  for (int edc=0; edc < NEDC; ++edc)
+    {
+      ::snprintf(fname, sizeof(fname), "/sys/devices/uncore_edc_eclk_%d",edc);
+      // RPQ inserts
+      KNLevsetup(fname, gbl.edc_rd[edc], 0x1, 0x1);
+      // WPQ inserts
+      KNLevsetup(fname, gbl.edc_wr[edc], 0x2, 0x1);
+    }
+  // EDC HitE, HitM, MissE, MissM
+  for (int edc=0; edc < NEDC; ++edc)
+    {
+      ::snprintf(fname, sizeof(fname), "/sys/devices/uncore_edc_uclk_%d", edc);
+      KNLevsetup(fname, gbl.edc_hite[edc], 0x2, 0x1);
+      KNLevsetup(fname, gbl.edc_hitm[edc], 0x2, 0x2);
+      KNLevsetup(fname, gbl.edc_misse[edc], 0x2, 0x4);
+      KNLevsetup(fname, gbl.edc_missm[edc], 0x2, 0x8);
+    }
+}
+
+uint64_t PmuStat::KNLreadctr(int fd)
+{
+  uint64_t data;
+  size_t s = ::read(fd, &data, sizeof(data));
+  if (s != sizeof(uint64_t)){
+    ::printf("read counter %lu", s);
+    ::exit(0);
+  }
+  return data;
+}
+
+void PmuStat::KNLreadctrs(ctrs &c)
+{
+  for (int i = 0; i < NMC; ++i)
+    {
+      c.mcrd[i] = KNLreadctr(gbl.mc_rd[i]);
+      c.mcwr[i] = KNLreadctr(gbl.mc_wr[i]);
+    }
+  for (int i = 0; i < NEDC; ++i)
+    {
+      c.edcrd[i] = KNLreadctr(gbl.edc_rd[i]);
+      c.edcwr[i] = KNLreadctr(gbl.edc_wr[i]);
+    }
+  for (int i = 0; i < NEDC; ++i)
+    {
+      c.edchite[i] = KNLreadctr(gbl.edc_hite[i]);
+      c.edchitm[i] = KNLreadctr(gbl.edc_hitm[i]);
+      c.edcmisse[i] = KNLreadctr(gbl.edc_misse[i]);
+      c.edcmissm[i] = KNLreadctr(gbl.edc_missm[i]);
+    }
+}
+
+#endif
+NAMESPACE_END(Grid); 
+

Grid/perfmon/Stat.h

@@ -0,0 +1,105 @@
+#ifndef _GRID_STAT_H
+#define _GRID_STAT_H
+
+#ifdef AVX512
+#define _KNIGHTS_LANDING_ROOTONLY
+#endif
+
+NAMESPACE_BEGIN(Grid); 
+
+///////////////////////////////////////////////////////////////////////////////
+// Extra KNL counters from MCDRAM
+///////////////////////////////////////////////////////////////////////////////
+#ifdef _KNIGHTS_LANDING_
+#define NMC 6
+#define NEDC 8
+struct ctrs
+{
+  uint64_t mcrd[NMC];
+  uint64_t mcwr[NMC];
+  uint64_t edcrd[NEDC]; 
+  uint64_t edcwr[NEDC];
+  uint64_t edchite[NEDC];
+  uint64_t edchitm[NEDC];
+  uint64_t edcmisse[NEDC];
+  uint64_t edcmissm[NEDC];
+};
+// Peter/Azusa:
+// Our modification of a code provided by Larry Meadows from Intel
+// Verified by email exchange non-NDA, ok for github. Should be as uses /sys/devices/ FS
+// so is already public and in the linux kernel for KNL.
+struct knl_gbl_
+{
+  int mc_rd[NMC];
+  int mc_wr[NMC];
+  int edc_rd[NEDC];
+  int edc_wr[NEDC];
+  int edc_hite[NEDC];
+  int edc_hitm[NEDC];
+  int edc_misse[NEDC];
+  int edc_missm[NEDC];
+};
+#endif
+///////////////////////////////////////////////////////////////////////////////
+
+class PmuStat
+{
+  uint64_t counters[8][256];
+#ifdef _KNIGHTS_LANDING_
+  static struct knl_gbl_ gbl;
+#endif
+  const char *name;
+
+  uint64_t reads;     // memory reads
+  uint64_t writes;    // memory writes
+  uint64_t mrstart;   // memory read counter at start of parallel region
+  uint64_t mrend;     // memory read counter at end of parallel region
+  uint64_t mwstart;   // memory write counter at start of parallel region
+  uint64_t mwend;     // memory write counter at end of parallel region
+
+  // cumulative counters
+  uint64_t count;     // number of invocations
+  uint64_t tregion;   // total time in parallel region (from thread 0)
+  uint64_t tcycles;   // total cycles inside parallel region
+  uint64_t inst, ref, cyc;   // fixed counters
+  uint64_t pmc0, pmc1;// pmu
+  // add memory counters here
+  // temp variables
+  uint64_t tstart;    // tsc at start of parallel region
+  uint64_t tend;      // tsc at end of parallel region
+  // map for ctrs values
+  // 0 pmc0 start
+  // 1 pmc0 end
+  // 2 pmc1 start
+  // 3 pmc1 end
+  // 4 tsc start
+  // 5 tsc end
+  static bool pmu_initialized;
+public:
+  static bool is_init(void){ return pmu_initialized;}
+  static void pmu_init(void);
+  static void pmu_fini(void);
+  static void pmu_start(void);
+  static void pmu_stop(void);
+  void accum(int nthreads);
+  static void xmemctrs(uint64_t *mr, uint64_t *mw);
+  void start(void);
+  void enter(int t);
+  void exit(int t);
+  void print(void);
+  void init(const char *regname);
+  void clear(void);
+#ifdef _KNIGHTS_LANDING_
+  static void     KNLsetup(void);
+  static uint64_t KNLreadctr(int fd);
+  static void     KNLreadctrs(ctrs &c);
+  static void     KNLevsetup(const char *ename, int &fd, int event, int umask);
+#endif
+    
+};
+
+NAMESPACE_END(Grid); 
+
+#endif
+
+

Grid/perfmon/Timer.h

@@ -0,0 +1,128 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/Timer.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_TIME_H
+#define GRID_TIME_H
+
+#include <sys/time.h>
+#include <ctime>
+#include <chrono>
+
+NAMESPACE_BEGIN(Grid)
+
+// Dress the output; use std::chrono
+// C++11 time facilities better?
+inline double usecond(void) {
+  struct timeval tv;
+#ifdef TIMERS_ON
+  gettimeofday(&tv,NULL);
+#endif
+  return 1.0*tv.tv_usec + 1.0e6*tv.tv_sec;
+}
+
+typedef  std::chrono::system_clock          GridClock;
+typedef  std::chrono::time_point<GridClock> GridTimePoint;
+
+typedef  std::chrono::seconds               GridSecs;
+typedef  std::chrono::milliseconds          GridMillisecs;
+typedef  std::chrono::microseconds          GridUsecs;
+typedef  std::chrono::microseconds          GridTime;
+
+inline std::ostream& operator<< (std::ostream & stream, const GridSecs & time)
+{
+  stream << time.count()<<" s";
+  return stream;
+}
+inline std::ostream& operator<< (std::ostream & stream, const GridMillisecs & now)
+{
+  GridSecs second(1);
+  auto     secs       = now/second ; 
+  auto     subseconds = now%second ;
+  auto     fill       = stream.fill();
+  stream << secs<<"."<<std::setw(3)<<std::setfill('0')<<subseconds.count()<<" s";
+  stream.fill(fill);
+  return stream;
+}
+inline std::ostream& operator<< (std::ostream & stream, const GridUsecs & now)
+{
+  GridSecs second(1);
+  auto     seconds    = now/second ; 
+  auto     subseconds = now%second ;
+  auto     fill       = stream.fill();
+  stream << seconds<<"."<<std::setw(6)<<std::setfill('0')<<subseconds.count()<<" s";
+  stream.fill(fill);
+  return stream;
+}
+ 
+
+class GridStopWatch {
+private:
+  bool running;
+  GridTimePoint start;
+  GridUsecs accumulator;
+public:
+  GridStopWatch () { 
+    Reset();
+  }
+  void     Start(void) { 
+    assert(running == false);
+#ifdef TIMERS_ON
+    start = GridClock::now(); 
+#endif
+    running = true;
+  }
+  void     Stop(void)  { 
+    assert(running == true);
+#ifdef TIMERS_ON
+    accumulator+= std::chrono::duration_cast<GridUsecs>(GridClock::now()-start); 
+#endif
+    running = false; 
+  };
+  void     Reset(void){
+    running = false;
+#ifdef TIMERS_ON
+    start = GridClock::now();
+#endif
+    accumulator = std::chrono::duration_cast<GridUsecs>(start-start); 
+  }
+  GridTime Elapsed(void) {
+    assert(running == false);
+    return std::chrono::duration_cast<GridTime>( accumulator );
+  }
+  uint64_t useconds(void){
+    assert(running == false);
+    return (uint64_t) accumulator.count();
+  }
+  bool isRunning(void){
+    return running;
+  }
+};
+
+NAMESPACE_END(Grid)
+
+#endif

Grid/pugixml/pugiconfig.hpp

@@ -0,0 +1,74 @@
+/**
+ * pugixml parser - version 1.9
+ * --------------------------------------------------------
+ * Copyright (C) 2006-2018, by Arseny Kapoulkine (arseny.kapoulkine@gmail.com)
+ * Report bugs and download new versions at http://pugixml.org/
+ *
+ * This library is distributed under the MIT License. See notice at the end
+ * of this file.
+ *
+ * This work is based on the pugxml parser, which is:
+ * Copyright (C) 2003, by Kristen Wegner (kristen@tima.net)
+ */
+
+#ifndef HEADER_PUGICONFIG_HPP
+#define HEADER_PUGICONFIG_HPP
+
+// Uncomment this to enable wchar_t mode
+// #define PUGIXML_WCHAR_MODE
+
+// Uncomment this to enable compact mode
+// #define PUGIXML_COMPACT
+
+// Uncomment this to disable XPath
+// #define PUGIXML_NO_XPATH
+
+// Uncomment this to disable STL
+// #define PUGIXML_NO_STL
+
+// Uncomment this to disable exceptions
+// #define PUGIXML_NO_EXCEPTIONS
+
+// Set this to control attributes for public classes/functions, i.e.:
+// #define PUGIXML_API __declspec(dllexport) // to export all public symbols from DLL
+// #define PUGIXML_CLASS __declspec(dllimport) // to import all classes from DLL
+// #define PUGIXML_FUNCTION __fastcall // to set calling conventions to all public functions to fastcall
+// In absence of PUGIXML_CLASS/PUGIXML_FUNCTION definitions PUGIXML_API is used instead
+
+// Tune these constants to adjust memory-related behavior
+// #define PUGIXML_MEMORY_PAGE_SIZE 32768
+// #define PUGIXML_MEMORY_OUTPUT_STACK 10240
+// #define PUGIXML_MEMORY_XPATH_PAGE_SIZE 4096
+
+// Uncomment this to switch to header-only version
+// #define PUGIXML_HEADER_ONLY
+
+// Uncomment this to enable long long support
+// #define PUGIXML_HAS_LONG_LONG
+
+#endif
+
+/**
+ * Copyright (c) 2006-2018 Arseny Kapoulkine
+ *
+ * Permission is hereby granted, free of charge, to any person
+ * obtaining a copy of this software and associated documentation
+ * files (the "Software"), to deal in the Software without
+ * restriction, including without limitation the rights to use,
+ * copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following
+ * conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+ * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+ * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+ * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+ * OTHER DEALINGS IN THE SOFTWARE.
+ */

Grid/pugixml/readme.txt

@@ -0,0 +1,52 @@
+pugixml 1.9 - an XML processing library
+
+Copyright (C) 2006-2018, by Arseny Kapoulkine (arseny.kapoulkine@gmail.com)
+Report bugs and download new versions at http://pugixml.org/
+
+This is the distribution of pugixml, which is a C++ XML processing library,
+which consists of a DOM-like interface with rich traversal/modification
+capabilities, an extremely fast XML parser which constructs the DOM tree from
+an XML file/buffer, and an XPath 1.0 implementation for complex data-driven
+tree queries. Full Unicode support is also available, with Unicode interface
+variants and conversions between different Unicode encodings (which happen
+automatically during parsing/saving).
+
+The distribution contains the following folders:
+
+	contrib/ - various contributions to pugixml
+
+	docs/ - documentation
+		docs/samples - pugixml usage examples
+		docs/quickstart.html - quick start guide
+		docs/manual.html - complete manual
+
+	scripts/ - project files for IDE/build systems
+
+	src/ - header and source files
+
+	readme.txt - this file.
+
+This library is distributed under the MIT License:
+
+Copyright (c) 2006-2018 Arseny Kapoulkine
+
+Permission is hereby granted, free of charge, to any person
+obtaining a copy of this software and associated documentation
+files (the "Software"), to deal in the Software without
+restriction, including without limitation the rights to use,
+copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the
+Software is furnished to do so, subject to the following
+conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.

Grid/qcd/LatticeTheories.h

@@ -0,0 +1,124 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/qcd/QCD.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: neo <cossu@post.kek.jp>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#ifndef GRID_LT_H
+#define GRID_LT_H
+namespace Grid{
+
+// First steps in the complete generalization of the Physics part
+// Design not final
+namespace LatticeTheories {
+
+template <int Dimensions>
+struct LatticeTheory {
+  static const int Nd = Dimensions;
+  static const int Nds = Dimensions * 2;  // double stored field
+  template <typename vtype>
+  using iSinglet = iScalar<iScalar<iScalar<vtype> > >;
+};
+
+template <int Dimensions, int Colours>
+struct LatticeGaugeTheory : public LatticeTheory<Dimensions> {
+  static const int Nds = Dimensions * 2;
+  static const int Nd = Dimensions;
+  static const int Nc = Colours;
+
+  template <typename vtype> 
+  using iColourMatrix = iScalar<iScalar<iMatrix<vtype, Nc> > >;
+  template <typename vtype>
+  using iLorentzColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nd>;
+  template <typename vtype>
+  using iDoubleStoredColourMatrix = iVector<iScalar<iMatrix<vtype, Nc> >, Nds>;
+  template <typename vtype>
+  using iColourVector = iScalar<iScalar<iVector<vtype, Nc> > >;
+};
+
+template <int Dimensions, int Colours, int Spin>
+struct FermionicLatticeGaugeTheory
+    : public LatticeGaugeTheory<Dimensions, Colours> {
+  static const int Nd = Dimensions;
+  static const int Nds = Dimensions * 2;
+  static const int Nc = Colours;
+  static const int Ns = Spin;
+
+  template <typename vtype>
+  using iSpinMatrix = iScalar<iMatrix<iScalar<vtype>, Ns> >;
+  template <typename vtype>
+  using iSpinColourMatrix = iScalar<iMatrix<iMatrix<vtype, Nc>, Ns> >;
+  template <typename vtype>
+  using iSpinVector = iScalar<iVector<iScalar<vtype>, Ns> >;
+  template <typename vtype>
+  using iSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Ns> >;
+  // These 2 only if Spin is a multiple of 2
+  static const int Nhs = Spin / 2;
+  template <typename vtype>
+  using iHalfSpinVector = iScalar<iVector<iScalar<vtype>, Nhs> >;
+  template <typename vtype>
+  using iHalfSpinColourVector = iScalar<iVector<iVector<vtype, Nc>, Nhs> >;
+
+  //tests
+  typedef iColourMatrix<Complex> ColourMatrix;
+  typedef iColourMatrix<ComplexF> ColourMatrixF;
+  typedef iColourMatrix<ComplexD> ColourMatrixD;
+
+
+};
+
+// Examples, not complete now.
+struct QCD : public FermionicLatticeGaugeTheory<4, 3, 4> {
+    static const int Xp = 0;
+    static const int Yp = 1;
+    static const int Zp = 2;
+    static const int Tp = 3;
+    static const int Xm = 4;
+    static const int Ym = 5;
+    static const int Zm = 6;
+    static const int Tm = 7;
+
+    typedef FermionicLatticeGaugeTheory FLGT;
+
+    typedef FLGT::iSpinMatrix<Complex  >          SpinMatrix;
+    typedef FLGT::iSpinMatrix<ComplexF >          SpinMatrixF;
+    typedef FLGT::iSpinMatrix<ComplexD >          SpinMatrixD;
+
+};
+struct QED : public FermionicLatticeGaugeTheory<4, 1, 4> {//fill
+};
+
+template <int Dimensions>
+struct Scalar : public LatticeTheory<Dimensions> {};
+
+};  // LatticeTheories
+
+} // Grid
+
+#endif

Grid/qcd/QCD.h

@@ -0,0 +1,529 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/qcd/QCD.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: neo <cossu@post.kek.jp>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+*************************************************************************************/
+/*  END LEGAL */
+#pragma once
+
+NAMESPACE_BEGIN(Grid);
+
+static constexpr int Xdir = 0;
+static constexpr int Ydir = 1;
+static constexpr int Zdir = 2;
+static constexpr int Tdir = 3;
+
+static constexpr int Xp = 0;
+static constexpr int Yp = 1;
+static constexpr int Zp = 2;
+static constexpr int Tp = 3;
+static constexpr int Xm = 4;
+static constexpr int Ym = 5;
+static constexpr int Zm = 6;
+static constexpr int Tm = 7;
+
+static constexpr int Nc=3;
+static constexpr int Ns=4;
+static constexpr int Nd=4;
+static constexpr int Nhs=2; // half spinor
+static constexpr int Nds=8; // double stored gauge field
+static constexpr int Ngp=2; // gparity index range
+
+//////////////////////////////////////////////////////////////////////////////
+// QCD iMatrix types
+// Index conventions:                            Lorentz x Spin x Colour
+// note: static constexpr int or constexpr will work for type deductions
+//       with the intel compiler (up to version 17)
+//////////////////////////////////////////////////////////////////////////////
+#define ColourIndex  (2)
+#define SpinIndex    (1)
+#define LorentzIndex (0)
+
+// Also should make these a named enum type
+static constexpr int DaggerNo=0;
+static constexpr int DaggerYes=1;
+static constexpr int InverseNo=0;
+static constexpr int InverseYes=1;
+
+// Useful traits is this a spin index
+//typename std::enable_if<matchGridTensorIndex<iVector<vtype,Ns>,SpinorIndex>::value,iVector<vtype,Ns> >::type *SFINAE;
+
+const int SpinorIndex = 2;
+template<typename T> struct isSpinor {
+  static constexpr bool value = (SpinorIndex==T::TensorLevel);
+};
+template <typename T> using IfSpinor    = Invoke<std::enable_if< isSpinor<T>::value,int> > ;
+template <typename T> using IfNotSpinor = Invoke<std::enable_if<!isSpinor<T>::value,int> > ;
+
+// ChrisK very keen to add extra space for Gparity doubling.
+//
+// Also add domain wall index, in a way where Wilson operator 
+// naturally distributes across the 5th dimensions.
+//
+// That probably makes for GridRedBlack4dCartesian grid.
+
+// s,sp,c,spc,lc
+
+template<typename vtype> using iSinglet                   = iScalar<iScalar<iScalar<vtype> > >;
+template<typename vtype> using iSpinMatrix                = iScalar<iMatrix<iScalar<vtype>, Ns> >;
+template<typename vtype> using iColourMatrix              = iScalar<iScalar<iMatrix<vtype, Nc> > > ;
+template<typename vtype> using iSpinColourMatrix          = iScalar<iMatrix<iMatrix<vtype, Nc>, Ns> >;
+template<typename vtype> using iLorentzColourMatrix       = iVector<iScalar<iMatrix<vtype, Nc> >, Nd > ;
+template<typename vtype> using iDoubleStoredColourMatrix  = iVector<iScalar<iMatrix<vtype, Nc> >, Nds > ;
+template<typename vtype> using iSpinVector                = iScalar<iVector<iScalar<vtype>, Ns> >;
+template<typename vtype> using iColourVector              = iScalar<iScalar<iVector<vtype, Nc> > >;
+template<typename vtype> using iSpinColourVector          = iScalar<iVector<iVector<vtype, Nc>, Ns> >;
+template<typename vtype> using iHalfSpinVector            = iScalar<iVector<iScalar<vtype>, Nhs> >;
+template<typename vtype> using iHalfSpinColourVector      = iScalar<iVector<iVector<vtype, Nc>, Nhs> >;
+    template<typename vtype> using iSpinColourSpinColourMatrix  = iScalar<iMatrix<iMatrix<iMatrix<iMatrix<vtype, Nc>, Ns>, Nc>, Ns> >;
+
+
+template<typename vtype> using iGparitySpinColourVector       = iVector<iVector<iVector<vtype, Nc>, Ns>, Ngp >;
+template<typename vtype> using iGparityHalfSpinColourVector   = iVector<iVector<iVector<vtype, Nc>, Nhs>, Ngp >;
+
+// Spin matrix
+typedef iSpinMatrix<Complex  >          SpinMatrix;
+typedef iSpinMatrix<ComplexF >          SpinMatrixF;
+typedef iSpinMatrix<ComplexD >          SpinMatrixD;
+
+typedef iSpinMatrix<vComplex >          vSpinMatrix;
+typedef iSpinMatrix<vComplexF>          vSpinMatrixF;
+typedef iSpinMatrix<vComplexD>          vSpinMatrixD;
+
+// Colour Matrix
+typedef iColourMatrix<Complex  >        ColourMatrix;
+typedef iColourMatrix<ComplexF >        ColourMatrixF;
+typedef iColourMatrix<ComplexD >        ColourMatrixD;
+
+typedef iColourMatrix<vComplex >        vColourMatrix;
+typedef iColourMatrix<vComplexF>        vColourMatrixF;
+typedef iColourMatrix<vComplexD>        vColourMatrixD;
+
+// SpinColour matrix
+typedef iSpinColourMatrix<Complex  >    SpinColourMatrix;
+typedef iSpinColourMatrix<ComplexF >    SpinColourMatrixF;
+typedef iSpinColourMatrix<ComplexD >    SpinColourMatrixD;
+
+typedef iSpinColourMatrix<vComplex >    vSpinColourMatrix;
+typedef iSpinColourMatrix<vComplexF>    vSpinColourMatrixF;
+typedef iSpinColourMatrix<vComplexD>    vSpinColourMatrixD;
+
+    // SpinColourSpinColour matrix
+    typedef iSpinColourSpinColourMatrix<Complex  >    SpinColourSpinColourMatrix;
+    typedef iSpinColourSpinColourMatrix<ComplexF >    SpinColourSpinColourMatrixF;
+    typedef iSpinColourSpinColourMatrix<ComplexD >    SpinColourSpinColourMatrixD;
+
+    typedef iSpinColourSpinColourMatrix<vComplex >    vSpinColourSpinColourMatrix;
+    typedef iSpinColourSpinColourMatrix<vComplexF>    vSpinColourSpinColourMatrixF;
+    typedef iSpinColourSpinColourMatrix<vComplexD>    vSpinColourSpinColourMatrixD;
+
+    // SpinColourSpinColour matrix
+    typedef iSpinColourSpinColourMatrix<Complex  >    SpinColourSpinColourMatrix;
+    typedef iSpinColourSpinColourMatrix<ComplexF >    SpinColourSpinColourMatrixF;
+    typedef iSpinColourSpinColourMatrix<ComplexD >    SpinColourSpinColourMatrixD;
+
+    typedef iSpinColourSpinColourMatrix<vComplex >    vSpinColourSpinColourMatrix;
+    typedef iSpinColourSpinColourMatrix<vComplexF>    vSpinColourSpinColourMatrixF;
+    typedef iSpinColourSpinColourMatrix<vComplexD>    vSpinColourSpinColourMatrixD;
+
+// LorentzColour
+typedef iLorentzColourMatrix<Complex  > LorentzColourMatrix;
+typedef iLorentzColourMatrix<ComplexF > LorentzColourMatrixF;
+typedef iLorentzColourMatrix<ComplexD > LorentzColourMatrixD;
+
+typedef iLorentzColourMatrix<vComplex > vLorentzColourMatrix;
+typedef iLorentzColourMatrix<vComplexF> vLorentzColourMatrixF;
+typedef iLorentzColourMatrix<vComplexD> vLorentzColourMatrixD;
+
+// DoubleStored gauge field
+typedef iDoubleStoredColourMatrix<Complex  > DoubleStoredColourMatrix;
+typedef iDoubleStoredColourMatrix<ComplexF > DoubleStoredColourMatrixF;
+typedef iDoubleStoredColourMatrix<ComplexD > DoubleStoredColourMatrixD;
+
+typedef iDoubleStoredColourMatrix<vComplex > vDoubleStoredColourMatrix;
+typedef iDoubleStoredColourMatrix<vComplexF> vDoubleStoredColourMatrixF;
+typedef iDoubleStoredColourMatrix<vComplexD> vDoubleStoredColourMatrixD;
+
+// Spin vector
+typedef iSpinVector<Complex >           SpinVector;
+typedef iSpinVector<ComplexF>           SpinVectorF;
+typedef iSpinVector<ComplexD>           SpinVectorD;
+
+typedef iSpinVector<vComplex >           vSpinVector;
+typedef iSpinVector<vComplexF>           vSpinVectorF;
+typedef iSpinVector<vComplexD>           vSpinVectorD;
+
+// Colour vector
+typedef iColourVector<Complex >         ColourVector;
+typedef iColourVector<ComplexF>         ColourVectorF;
+typedef iColourVector<ComplexD>         ColourVectorD;
+
+typedef iColourVector<vComplex >         vColourVector;
+typedef iColourVector<vComplexF>         vColourVectorF;
+typedef iColourVector<vComplexD>         vColourVectorD;
+
+// SpinColourVector
+typedef iSpinColourVector<Complex >     SpinColourVector;
+typedef iSpinColourVector<ComplexF>     SpinColourVectorF;
+typedef iSpinColourVector<ComplexD>     SpinColourVectorD;
+
+typedef iSpinColourVector<vComplex >     vSpinColourVector;
+typedef iSpinColourVector<vComplexF>     vSpinColourVectorF;
+typedef iSpinColourVector<vComplexD>     vSpinColourVectorD;
+
+// HalfSpin vector
+typedef iHalfSpinVector<Complex >       HalfSpinVector;
+typedef iHalfSpinVector<ComplexF>       HalfSpinVectorF;
+typedef iHalfSpinVector<ComplexD>       HalfSpinVectorD;
+
+typedef iHalfSpinVector<vComplex >       vHalfSpinVector;
+typedef iHalfSpinVector<vComplexF>       vHalfSpinVectorF;
+typedef iHalfSpinVector<vComplexD>       vHalfSpinVectorD;
+
+// HalfSpinColour vector
+typedef iHalfSpinColourVector<Complex > HalfSpinColourVector;
+typedef iHalfSpinColourVector<ComplexF> HalfSpinColourVectorF;
+typedef iHalfSpinColourVector<ComplexD> HalfSpinColourVectorD;
+    
+typedef iHalfSpinColourVector<vComplex > vHalfSpinColourVector;
+typedef iHalfSpinColourVector<vComplexF> vHalfSpinColourVectorF;
+typedef iHalfSpinColourVector<vComplexD> vHalfSpinColourVectorD;
+    
+// singlets
+typedef iSinglet<Complex >         TComplex;     // FIXME This is painful. Tensor singlet complex type.
+typedef iSinglet<ComplexF>         TComplexF;    // FIXME This is painful. Tensor singlet complex type.
+typedef iSinglet<ComplexD>         TComplexD;    // FIXME This is painful. Tensor singlet complex type.
+
+typedef iSinglet<vComplex >        vTComplex ;   // what if we don't know the tensor structure
+typedef iSinglet<vComplexF>        vTComplexF;   // what if we don't know the tensor structure
+typedef iSinglet<vComplexD>        vTComplexD;   // what if we don't know the tensor structure
+
+typedef iSinglet<Real >            TReal;        // Shouldn't need these; can I make it work without?
+typedef iSinglet<RealF>            TRealF;       // Shouldn't need these; can I make it work without?
+typedef iSinglet<RealD>            TRealD;       // Shouldn't need these; can I make it work without?
+
+typedef iSinglet<vReal >           vTReal;      
+typedef iSinglet<vRealF>           vTRealF;      
+typedef iSinglet<vRealD>           vTRealD;      
+
+typedef iSinglet<vInteger>         vTInteger;
+typedef iSinglet<Integer >         TInteger;
+
+
+// Lattices of these
+typedef Lattice<vColourMatrix>          LatticeColourMatrix;
+typedef Lattice<vColourMatrixF>         LatticeColourMatrixF;
+typedef Lattice<vColourMatrixD>         LatticeColourMatrixD;
+
+typedef Lattice<vSpinMatrix>            LatticeSpinMatrix;
+typedef Lattice<vSpinMatrixF>           LatticeSpinMatrixF;
+typedef Lattice<vSpinMatrixD>           LatticeSpinMatrixD;
+
+typedef Lattice<vSpinColourMatrix>      LatticeSpinColourMatrix;
+typedef Lattice<vSpinColourMatrixF>     LatticeSpinColourMatrixF;
+typedef Lattice<vSpinColourMatrixD>     LatticeSpinColourMatrixD;
+
+typedef Lattice<vSpinColourSpinColourMatrix>      LatticeSpinColourSpinColourMatrix;
+typedef Lattice<vSpinColourSpinColourMatrixF>     LatticeSpinColourSpinColourMatrixF;
+typedef Lattice<vSpinColourSpinColourMatrixD>     LatticeSpinColourSpinColourMatrixD;
+
+typedef Lattice<vLorentzColourMatrix>  LatticeLorentzColourMatrix;
+typedef Lattice<vLorentzColourMatrixF> LatticeLorentzColourMatrixF;
+typedef Lattice<vLorentzColourMatrixD> LatticeLorentzColourMatrixD;
+
+// DoubleStored gauge field
+typedef Lattice<vDoubleStoredColourMatrix>  LatticeDoubleStoredColourMatrix;
+typedef Lattice<vDoubleStoredColourMatrixF> LatticeDoubleStoredColourMatrixF;
+typedef Lattice<vDoubleStoredColourMatrixD> LatticeDoubleStoredColourMatrixD;
+
+typedef Lattice<vSpinVector>            LatticeSpinVector;
+typedef Lattice<vSpinVectorF>           LatticeSpinVectorF;
+typedef Lattice<vSpinVectorD>           LatticeSpinVectorD;
+
+typedef Lattice<vColourVector>          LatticeColourVector;
+typedef Lattice<vColourVectorF>         LatticeColourVectorF;
+typedef Lattice<vColourVectorD>         LatticeColourVectorD;
+
+typedef Lattice<vSpinColourVector>      LatticeSpinColourVector;
+typedef Lattice<vSpinColourVectorF>     LatticeSpinColourVectorF;
+typedef Lattice<vSpinColourVectorD>     LatticeSpinColourVectorD;
+
+typedef Lattice<vHalfSpinVector>        LatticeHalfSpinVector;
+typedef Lattice<vHalfSpinVectorF>       LatticeHalfSpinVectorF;
+typedef Lattice<vHalfSpinVectorD>       LatticeHalfSpinVectorD;
+
+typedef Lattice<vHalfSpinColourVector>  LatticeHalfSpinColourVector;
+typedef Lattice<vHalfSpinColourVectorF> LatticeHalfSpinColourVectorF;
+typedef Lattice<vHalfSpinColourVectorD> LatticeHalfSpinColourVectorD;
+
+typedef Lattice<vTReal>            LatticeReal;
+typedef Lattice<vTRealF>           LatticeRealF;
+typedef Lattice<vTRealD>           LatticeRealD;
+
+typedef Lattice<vTComplex>         LatticeComplex;
+typedef Lattice<vTComplexF>        LatticeComplexF;
+typedef Lattice<vTComplexD>        LatticeComplexD;
+
+typedef Lattice<vTInteger>         LatticeInteger; // Predicates for "where"
+
+
+///////////////////////////////////////////
+// Physical names for things
+///////////////////////////////////////////
+typedef LatticeHalfSpinColourVector  LatticeHalfFermion;
+typedef LatticeHalfSpinColourVectorF LatticeHalfFermionF;
+typedef LatticeHalfSpinColourVectorF LatticeHalfFermionD;
+
+typedef LatticeSpinColourVector      LatticeFermion;
+typedef LatticeSpinColourVectorF     LatticeFermionF;
+typedef LatticeSpinColourVectorD     LatticeFermionD;
+
+typedef LatticeSpinColourMatrix                LatticePropagator;
+typedef LatticeSpinColourMatrixF               LatticePropagatorF;
+typedef LatticeSpinColourMatrixD               LatticePropagatorD;
+
+typedef LatticeLorentzColourMatrix             LatticeGaugeField;
+typedef LatticeLorentzColourMatrixF            LatticeGaugeFieldF;
+typedef LatticeLorentzColourMatrixD            LatticeGaugeFieldD;
+
+typedef LatticeDoubleStoredColourMatrix        LatticeDoubledGaugeField;
+typedef LatticeDoubleStoredColourMatrixF       LatticeDoubledGaugeFieldF;
+typedef LatticeDoubleStoredColourMatrixD       LatticeDoubledGaugeFieldD;
+
+template<class GF> using LorentzScalar = Lattice<iScalar<typename GF::vector_object::element> >;
+
+// Uhgg... typing this hurt  ;)
+// (my keyboard got burning hot when I typed this, must be the anti-Fermion)
+typedef Lattice<vColourVector>          LatticeStaggeredFermion;    
+typedef Lattice<vColourVectorF>         LatticeStaggeredFermionF;    
+typedef Lattice<vColourVectorD>         LatticeStaggeredFermionD;    
+
+typedef Lattice<vColourMatrix>          LatticeStaggeredPropagator; 
+typedef Lattice<vColourMatrixF>         LatticeStaggeredPropagatorF; 
+typedef Lattice<vColourMatrixD>         LatticeStaggeredPropagatorD; 
+
+//////////////////////////////////////////////////////////////////////////////
+// Peek and Poke named after physics attributes
+//////////////////////////////////////////////////////////////////////////////
+
+//spin
+template<class vobj> auto peekSpin(const vobj &rhs,int i) -> decltype(PeekIndex<SpinIndex>(rhs,0))
+{
+  return PeekIndex<SpinIndex>(rhs,i);
+}
+template<class vobj> auto peekSpin(const vobj &rhs,int i,int j) -> decltype(PeekIndex<SpinIndex>(rhs,0,0))
+{
+  return PeekIndex<SpinIndex>(rhs,i,j);
+}
+template<class vobj> auto peekSpin(const Lattice<vobj> &rhs,int i) -> decltype(PeekIndex<SpinIndex>(rhs,0))
+{
+  return PeekIndex<SpinIndex>(rhs,i);
+}
+template<class vobj> auto peekSpin(const Lattice<vobj> &rhs,int i,int j) -> decltype(PeekIndex<SpinIndex>(rhs,0,0))
+{
+  return PeekIndex<SpinIndex>(rhs,i,j);
+}
+//colour
+template<class vobj> auto peekColour(const vobj &rhs,int i) -> decltype(PeekIndex<ColourIndex>(rhs,0))
+{
+  return PeekIndex<ColourIndex>(rhs,i);
+}
+template<class vobj> auto peekColour(const vobj &rhs,int i,int j) -> decltype(PeekIndex<ColourIndex>(rhs,0,0))
+{
+  return PeekIndex<ColourIndex>(rhs,i,j);
+}
+template<class vobj> auto peekColour(const Lattice<vobj> &rhs,int i) -> decltype(PeekIndex<ColourIndex>(rhs,0))
+{
+  return PeekIndex<ColourIndex>(rhs,i);
+}
+template<class vobj> auto peekColour(const Lattice<vobj> &rhs,int i,int j) -> decltype(PeekIndex<ColourIndex>(rhs,0,0))
+{
+  return PeekIndex<ColourIndex>(rhs,i,j);
+}
+//lorentz
+template<class vobj> auto peekLorentz(const vobj &rhs,int i) -> decltype(PeekIndex<LorentzIndex>(rhs,0))
+{
+  return PeekIndex<LorentzIndex>(rhs,i);
+}
+template<class vobj> auto peekLorentz(const Lattice<vobj> &rhs,int i) -> decltype(PeekIndex<LorentzIndex>(rhs,0))
+{
+  return PeekIndex<LorentzIndex>(rhs,i);
+}
+
+//////////////////////////////////////////////
+// Poke lattice
+//////////////////////////////////////////////
+template<class vobj> 
+void pokeColour(Lattice<vobj> &lhs,
+		const Lattice<decltype(peekIndex<ColourIndex>(vobj(),0))> & rhs,
+		int i)
+{
+  PokeIndex<ColourIndex>(lhs,rhs,i);
+}
+template<class vobj> 
+void pokeColour(Lattice<vobj> &lhs,
+		const Lattice<decltype(peekIndex<ColourIndex>(vobj(),0,0))> & rhs,
+		int i,int j)
+{
+  PokeIndex<ColourIndex>(lhs,rhs,i,j);
+}
+template<class vobj> 
+void pokeSpin(Lattice<vobj> &lhs,
+              const Lattice<decltype(peekIndex<SpinIndex>(vobj(),0))> & rhs,
+              int i)
+{
+  PokeIndex<SpinIndex>(lhs,rhs,i);
+}
+template<class vobj> 
+void pokeSpin(Lattice<vobj> &lhs,
+              const Lattice<decltype(peekIndex<SpinIndex>(vobj(),0,0))> & rhs,
+              int i,int j)
+{
+  PokeIndex<SpinIndex>(lhs,rhs,i,j);
+}
+template<class vobj> 
+void pokeLorentz(Lattice<vobj> &lhs,
+		 const Lattice<decltype(peekIndex<LorentzIndex>(vobj(),0))> & rhs,
+		 int i)
+{
+  PokeIndex<LorentzIndex>(lhs,rhs,i);
+}
+
+//////////////////////////////////////////////
+// Poke scalars
+//////////////////////////////////////////////
+template<class vobj> void pokeSpin(vobj &lhs,const decltype(peekIndex<SpinIndex>(lhs,0)) & rhs,int i)
+{
+  pokeIndex<SpinIndex>(lhs,rhs,i);
+}
+template<class vobj> void pokeSpin(vobj &lhs,const decltype(peekIndex<SpinIndex>(lhs,0,0)) & rhs,int i,int j)
+{
+  pokeIndex<SpinIndex>(lhs,rhs,i,j);
+}
+
+template<class vobj> void pokeColour(vobj &lhs,const decltype(peekIndex<ColourIndex>(lhs,0)) & rhs,int i)
+{
+  pokeIndex<ColourIndex>(lhs,rhs,i);
+}
+template<class vobj> void pokeColour(vobj &lhs,const decltype(peekIndex<ColourIndex>(lhs,0,0)) & rhs,int i,int j)
+{
+  pokeIndex<ColourIndex>(lhs,rhs,i,j);
+}
+
+template<class vobj> void pokeLorentz(vobj &lhs,const decltype(peekIndex<LorentzIndex>(lhs,0)) & rhs,int i)
+{
+  pokeIndex<LorentzIndex>(lhs,rhs,i);
+}
+
+//////////////////////////////////////////////
+// Fermion <-> propagator assignements
+//////////////////////////////////////////////
+    //template <class Prop, class Ferm>
+    template <class Fimpl>
+      void FermToProp(typename Fimpl::PropagatorField &p, const typename Fimpl::FermionField &f, const int s, const int c)
+{
+  for(int j = 0; j < Ns; ++j)
+    {
+      auto pjs = peekSpin(p, j, s);
+      auto fj  = peekSpin(f, j);
+            
+            for(int i = 0; i < Fimpl::Dimension; ++i)
+	{
+	  pokeColour(pjs, peekColour(fj, i), i, c);
+	}
+      pokeSpin(p, pjs, j, s);
+    }
+}
+    
+    //template <class Prop, class Ferm>
+    template <class Fimpl>
+      void PropToFerm(typename Fimpl::FermionField &f, const typename Fimpl::PropagatorField &p, const int s, const int c)
+{
+  for(int j = 0; j < Ns; ++j)
+    {
+      auto pjs = peekSpin(p, j, s);
+      auto fj  = peekSpin(f, j);
+            
+            for(int i = 0; i < Fimpl::Dimension; ++i)
+	{
+	  pokeColour(fj, peekColour(pjs, i, c), i);
+	}
+      pokeSpin(f, fj, j);
+    }
+}
+    
+//////////////////////////////////////////////
+// transpose array and scalar
+//////////////////////////////////////////////
+template<int Index,class vobj> inline Lattice<vobj> transposeSpin(const Lattice<vobj> &lhs){
+  return transposeIndex<SpinIndex>(lhs);
+}
+template<int Index,class vobj> inline Lattice<vobj> transposeColour(const Lattice<vobj> &lhs){
+  return transposeIndex<ColourIndex>(lhs);
+}
+template<int Index,class vobj> inline vobj transposeSpin(const vobj &lhs){
+  return transposeIndex<SpinIndex>(lhs);
+}
+template<int Index,class vobj> inline vobj transposeColour(const vobj &lhs){
+  return transposeIndex<ColourIndex>(lhs);
+}
+
+//////////////////////////////////////////
+// Trace lattice and non-lattice
+//////////////////////////////////////////
+template<int Index,class vobj>
+inline auto traceSpin(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<SpinIndex>(vobj()))>
+{
+  return traceIndex<SpinIndex>(lhs);
+}
+template<int Index,class vobj>
+inline auto traceColour(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<ColourIndex>(vobj()))>
+{
+  return traceIndex<ColourIndex>(lhs);
+}
+template<int Index,class vobj>
+inline auto traceSpin(const vobj &lhs) -> Lattice<decltype(traceIndex<SpinIndex>(lhs))>
+{
+  return traceIndex<SpinIndex>(lhs);
+}
+template<int Index,class vobj>
+inline auto traceColour(const vobj &lhs) -> Lattice<decltype(traceIndex<ColourIndex>(lhs))>
+{
+  return traceIndex<ColourIndex>(lhs);
+}
+
+//////////////////////////////////////////
+// Current types
+//////////////////////////////////////////
+GRID_SERIALIZABLE_ENUM(Current, undef,
+		       Vector,  0,
+		       Axial,   1,
+		       Tadpole, 2);
+
+NAMESPACE_END(Grid);
+

Grid/qcd/action/Action.h

@@ -0,0 +1,54 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/qcd/action/Actions.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: neo <cossu@post.kek.jp>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#ifndef GRID_QCD_ACTION_H
+#define GRID_QCD_ACTION_H
+
+////////////////////////////////////////////
+// Abstract base interface
+////////////////////////////////////////////
+#include <Grid/qcd/action/ActionCore.h>
+NAMESPACE_CHECK(ActionCore);
+////////////////////////////////////////////////////////////////////////
+// Fermion actions; prevent coupling fermion.cc files to other headers
+////////////////////////////////////////////////////////////////////////
+#include <Grid/qcd/action/fermion/FermionCore.h>
+NAMESPACE_CHECK(FermionCore);
+#include <Grid/qcd/action/fermion/Fermion.h>
+NAMESPACE_CHECK(Fermion);
+////////////////////////////////////////
+// Pseudo fermion combinations for HMC
+////////////////////////////////////////
+#include <Grid/qcd/action/pseudofermion/PseudoFermion.h>
+NAMESPACE_CHECK(PseudoFermion);
+
+#endif