diff --git a/Grid/lattice/Lattice_reduction.h b/Grid/lattice/Lattice_reduction.h
index a6bbcf15..66788a4c 100644
--- a/Grid/lattice/Lattice_reduction.h
+++ b/Grid/lattice/Lattice_reduction.h
@@ -31,6 +31,7 @@ Author: Christoph Lehner <christoph@lhnr.de>
 #if defined(GRID_SYCL)
 #include <Grid/lattice/Lattice_reduction_sycl.h>
 #endif
+#include <Grid/lattice/Lattice_slicesum_core.h>
 
 NAMESPACE_BEGIN(Grid);
 
@@ -448,19 +449,10 @@ template<class vobj> inline void sliceSum(const Lattice<vobj> &Data,std::vector<
   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
-  autoView( Data_v, Data, CpuRead);
-  thread_for( r,rd, {
-    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];
-      }
-    }
-  });
+  int ostride=grid->_ostride[orthogdim];
+  
+  //Reduce Data down to lvSum
+  sliceSumReduction(Data,lvSum,rd, e1,e2,stride,ostride,Nsimd);
 
   // Sum across simd lanes in the plane, breaking out orthog dir.
   Coordinate icoor(Nd);
@@ -504,6 +496,7 @@ sliceSum(const Lattice<vobj> &Data,int orthogdim)
   return result;
 }
 
+
 template<class vobj>
 static void sliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim) 
 {
diff --git a/Grid/lattice/Lattice_slicesum_core.h b/Grid/lattice/Lattice_slicesum_core.h
new file mode 100644
index 00000000..7c3518cd
--- /dev/null
+++ b/Grid/lattice/Lattice_slicesum_core.h
@@ -0,0 +1,218 @@
+#pragma once
+#include <type_traits>
+#if defined(GRID_CUDA)
+
+#include <cub/cub.cuh>
+#define gpucub cub
+#define gpuError_t cudaError_t
+#define gpuSuccess cudaSuccess
+
+#elif defined(GRID_HIP)
+
+#include <hipcub/hipcub.hpp>
+#define gpucub hipcub
+#define gpuError_t hipError_t
+#define gpuSuccess hipSuccess
+
+#endif
+
+
+NAMESPACE_BEGIN(Grid);
+
+
+#if defined(GRID_CUDA) || defined(GRID_HIP)
+template<class vobj> inline void sliceSumReduction_cub_small(const vobj *Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd) {
+  size_t subvol_size = e1*e2;
+  commVector<vobj> reduction_buffer(rd*subvol_size);
+  auto rb_p = &reduction_buffer[0];
+  vobj zero_init;
+  zeroit(zero_init);
+
+  
+  void *temp_storage_array = NULL;
+  size_t temp_storage_bytes = 0;
+  vobj *d_out;
+  int* d_offsets;
+
+  std::vector<int> offsets(rd+1,0);
+
+  for (int i = 0; i < offsets.size(); i++) {
+    offsets[i] = i*subvol_size;
+  }
+  
+  //Allocate memory for output and offset arrays on device
+  d_out = static_cast<vobj*>(acceleratorAllocDevice(rd*sizeof(vobj)));
+  
+  d_offsets = static_cast<int*>(acceleratorAllocDevice((rd+1)*sizeof(int)));
+  
+  //copy offsets to device
+  acceleratorCopyToDeviceAsync(&offsets[0],d_offsets,sizeof(int)*(rd+1),computeStream);
+  
+  
+  gpuError_t gpuErr = gpucub::DeviceSegmentedReduce::Reduce(temp_storage_array, temp_storage_bytes, rb_p,d_out, rd, d_offsets, d_offsets+1, ::gpucub::Sum(), zero_init, computeStream);
+  if (gpuErr!=gpuSuccess) {
+    std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce (setup)! Error: " << gpuErr <<std::endl;
+    exit(EXIT_FAILURE);
+  }
+
+  //allocate memory for temp_storage_array  
+  temp_storage_array = acceleratorAllocDevice(temp_storage_bytes);
+  
+  //prepare buffer for reduction
+  //use non-blocking accelerator_for to avoid syncs (ok because we submit to same computeStream)
+  //use 2d accelerator_for to avoid launch latencies found when serially looping over rd 
+  accelerator_for2dNB( s,subvol_size, r,rd, Nsimd,{ 
+  
+    int n = s / e2;
+    int b = s % e2;
+    int so=r*ostride; // base offset for start of plane 
+    int ss= so+n*stride+b;
+
+    coalescedWrite(rb_p[r*subvol_size+s], coalescedRead(Data[ss]));
+
+  });
+  
+  //issue segmented reductions in computeStream
+  gpuErr = gpucub::DeviceSegmentedReduce::Reduce(temp_storage_array, temp_storage_bytes, rb_p, d_out, rd, d_offsets, d_offsets+1,::gpucub::Sum(), zero_init, computeStream);
+  if (gpuErr!=gpuSuccess) {
+    std::cout << GridLogError << "Lattice_slicesum_gpu.h: Encountered error during gpucub::DeviceSegmentedReduce::Reduce! Error: " << gpuErr <<std::endl;
+    exit(EXIT_FAILURE);
+  }
+  
+  acceleratorCopyFromDeviceAsync(d_out,&lvSum[0],rd*sizeof(vobj),computeStream);
+  
+  //sync after copy
+  accelerator_barrier();
+ 
+  acceleratorFreeDevice(temp_storage_array);
+  acceleratorFreeDevice(d_out);
+  acceleratorFreeDevice(d_offsets);
+  
+
+}
+
+template<class vobj> inline void sliceSumReduction_cub_large(const vobj *Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd) {
+  typedef typename vobj::vector_type vector;
+  const int words = sizeof(vobj)/sizeof(vector);
+  const int osites = rd*e1*e2;
+  commVector<vector>buffer(osites);
+  vector *dat = (vector *)Data;
+  vector *buf = &buffer[0];
+  Vector<vector> lvSum_small(rd);
+  vector *lvSum_ptr = (vector *)&lvSum[0];
+
+  for (int w = 0; w < words; w++) {
+    accelerator_for(ss,osites,1,{
+	    buf[ss] = dat[ss*words+w];
+    });
+
+    sliceSumReduction_cub_small(buf,lvSum_small,rd,e1,e2,stride, ostride,Nsimd);
+      
+    for (int r = 0; r < rd; r++) {
+      lvSum_ptr[w+words*r]=lvSum_small[r];
+    }
+
+  }
+
+  
+}
+
+template<class vobj> inline void sliceSumReduction_cub(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int rd, const int e1, const int e2, const int stride, const int ostride, const int Nsimd)
+{
+  autoView(Data_v, Data, AcceleratorRead);
+  #if defined(GRID_CUDA)
+    sliceSumReduction_cub_small(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+
+  #elif defined (GRID_HIP) //hipcub cannot deal with large vobjs that don't fit in shared memory, therefore separate into _small/_large. 
+    if constexpr (sizeof(vobj) <= 256) {
+      sliceSumReduction_cub_small(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+    }
+    else {
+      sliceSumReduction_cub_large(&Data_v[0], lvSum, rd, e1, e2, stride, ostride, Nsimd);
+    }
+  #endif
+}
+#endif
+
+
+#if defined(GRID_SYCL)
+template<class vobj> inline void sliceSumReduction_sycl(const Lattice<vobj> &Data, Vector <vobj> &lvSum, const int  &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd)
+{
+  typedef typename vobj::scalar_object sobj;
+  size_t subvol_size = e1*e2;
+
+  vobj *mysum = (vobj *) malloc_shared(sizeof(vobj),*theGridAccelerator);
+  vobj vobj_zero;
+  zeroit(vobj_zero);
+    
+  commVector<vobj> reduction_buffer(rd*subvol_size);    
+
+  auto rb_p = &reduction_buffer[0];
+
+  autoView(Data_v, Data, AcceleratorRead);
+
+  //prepare reduction buffer 
+  accelerator_for2d( s,subvol_size, r,rd, (size_t)Nsimd,{ 
+  
+      int n = s / e2;
+      int b = s % e2;
+      int so=r*ostride; // base offset for start of plane 
+      int ss= so+n*stride+b;
+
+      coalescedWrite(rb_p[r*subvol_size+s], coalescedRead(Data_v[ss]));
+
+  });
+
+  for (int r = 0; r < rd; r++) {
+      mysum[0] = vobj_zero; //dirty hack: cannot pass vobj_zero as identity to sycl::reduction as its not device_copyable
+      theGridAccelerator->submit([&](cl::sycl::handler &cgh) {
+          auto Reduction = cl::sycl::reduction(mysum,std::plus<>());
+          cgh.parallel_for(cl::sycl::range<1>{subvol_size},
+          Reduction,
+          [=](cl::sycl::id<1> item, auto &sum) {
+              auto s = item[0];
+              sum += rb_p[r*subvol_size+s];
+          });
+      });
+      theGridAccelerator->wait();
+      lvSum[r] = mysum[0];
+  }
+  
+  free(mysum,*theGridAccelerator);
+}
+#endif
+
+template<class vobj> inline void sliceSumReduction_cpu(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd)
+{
+  // sum over reduced dimension planes, breaking out orthog dir
+  // Parallel over orthog direction
+  autoView( Data_v, Data, CpuRead);
+  thread_for( r,rd, {
+    int so=r*ostride; // 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];
+      }
+    }
+  });
+}
+
+template<class vobj> inline void sliceSumReduction(const Lattice<vobj> &Data, Vector<vobj> &lvSum, const int &rd, const int &e1, const int &e2, const int &stride, const int &ostride, const int &Nsimd) 
+{
+  #if defined(GRID_CUDA) || defined(GRID_HIP)
+  
+  sliceSumReduction_cub(Data, lvSum, rd, e1, e2, stride, ostride, Nsimd);
+  
+  #elif defined(GRID_SYCL)
+  
+  sliceSumReduction_sycl(Data, lvSum, rd, e1, e2, stride, ostride, Nsimd);
+  
+  #else
+  sliceSumReduction_cpu(Data, lvSum, rd, e1, e2, stride, ostride, Nsimd);
+
+  #endif
+}
+
+
+NAMESPACE_END(Grid);
\ No newline at end of file
diff --git a/Grid/perfmon/Tracing.h b/Grid/perfmon/Tracing.h
index 5000cef4..10b638dc 100644
--- a/Grid/perfmon/Tracing.h
+++ b/Grid/perfmon/Tracing.h
@@ -34,7 +34,7 @@ class GridTracer {
 };
 inline void tracePush(const char *name) { roctxRangePushA(name); }
 inline void tracePop(const char *name) { roctxRangePop(); }
-inline int  traceStart(const char *name) { roctxRangeStart(name); }
+inline int  traceStart(const char *name) { return roctxRangeStart(name); }
 inline void traceStop(int ID) { roctxRangeStop(ID); }
 #endif
 
diff --git a/Grid/threads/Accelerator.h b/Grid/threads/Accelerator.h
index ff5ccd7a..d4407fad 100644
--- a/Grid/threads/Accelerator.h
+++ b/Grid/threads/Accelerator.h
@@ -225,6 +225,8 @@ inline void acceleratorFreeShared(void *ptr){ cudaFree(ptr);};
 inline void acceleratorFreeDevice(void *ptr){ cudaFree(ptr);};
 inline void acceleratorCopyToDevice(void *from,void *to,size_t bytes)  { cudaMemcpy(to,from,bytes, cudaMemcpyHostToDevice);}
 inline void acceleratorCopyFromDevice(void *from,void *to,size_t bytes){ cudaMemcpy(to,from,bytes, cudaMemcpyDeviceToHost);}
+inline void acceleratorCopyToDeviceAsync(void *from, void *to, size_t bytes, cudaStream_t stream = copyStream) { cudaMemcpyAsync(to,from,bytes, cudaMemcpyHostToDevice, stream);}
+inline void acceleratorCopyFromDeviceAsync(void *from, void *to, size_t bytes, cudaStream_t stream = copyStream) { cudaMemcpyAsync(to,from,bytes, cudaMemcpyDeviceToHost, stream);}
 inline void acceleratorMemSet(void *base,int value,size_t bytes) { cudaMemset(base,value,bytes);}
 inline void acceleratorCopyDeviceToDeviceAsynch(void *from,void *to,size_t bytes) // Asynch
 {
@@ -442,6 +444,8 @@ inline void acceleratorFreeShared(void *ptr){ auto r=hipFree(ptr);};
 inline void acceleratorFreeDevice(void *ptr){ auto r=hipFree(ptr);};
 inline void acceleratorCopyToDevice(void *from,void *to,size_t bytes)  { auto r=hipMemcpy(to,from,bytes, hipMemcpyHostToDevice);}
 inline void acceleratorCopyFromDevice(void *from,void *to,size_t bytes){ auto r=hipMemcpy(to,from,bytes, hipMemcpyDeviceToHost);}
+inline void acceleratorCopyToDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) { auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyHostToDevice, stream);}
+inline void acceleratorCopyFromDeviceAsync(void *from, void *to, size_t bytes, hipStream_t stream = copyStream) { auto r = hipMemcpyAsync(to,from,bytes, hipMemcpyDeviceToHost, stream);}
 //inline void acceleratorCopyDeviceToDeviceAsynch(void *from,void *to,size_t bytes)  { hipMemcpy(to,from,bytes, hipMemcpyDeviceToDevice);}
 //inline void acceleratorCopySynchronise(void) {  }
 inline void acceleratorMemSet(void *base,int value,size_t bytes) { auto r=hipMemset(base,value,bytes);}
diff --git a/tests/core/Test_sliceSum.cc b/tests/core/Test_sliceSum.cc
new file mode 100644
index 00000000..e366f1f3
--- /dev/null
+++ b/tests/core/Test_sliceSum.cc
@@ -0,0 +1,321 @@
+#include <Grid/Grid.h>
+
+template<class vobj> inline void sliceSumCPU(const Grid::Lattice<vobj> &Data,std::vector<typename vobj::scalar_object> &result,int orthogdim)
+{
+  using namespace Grid;
+  ///////////////////////////////////////////////////////
+  // FIXME precision promoted summation
+  // may be important for correlation functions
+  // But easily avoided by using double precision fields
+  ///////////////////////////////////////////////////////
+  typedef typename vobj::scalar_object sobj;
+  typedef typename vobj::scalar_object::scalar_type scalar_type;
+  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];
+  int ostride=grid->_ostride[orthogdim];
+  
+  //Reduce Data down to lvSum
+  sliceSumReduction_cpu(Data,lvSum,rd, e1,e2,stride,ostride,Nsimd);
+
+  // 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.
+  for(int t=0;t<fd;t++){
+    int pt = t/ld; // processor plane
+    int lt = t%ld;
+    if ( pt == grid->_processor_coor[orthogdim] ) {
+      result[t]=lsSum[lt];
+    } else {
+      result[t]=Zero();
+    }
+
+  }
+  scalar_type * ptr = (scalar_type *) &result[0];
+  int words = fd*sizeof(sobj)/sizeof(scalar_type);
+  grid->GlobalSumVector(ptr, words);
+}
+
+
+int main (int argc, char ** argv) {
+    
+    using namespace Grid;
+
+    Grid_init(&argc,&argv);
+
+
+    Coordinate latt_size({64,64,64,16});
+    auto simd_layout = GridDefaultSimd(Nd, vComplexD::Nsimd());
+    auto mpi_layout = GridDefaultMpi();
+    GridCartesian Grid(latt_size, simd_layout, mpi_layout);
+
+    std::vector<int> seeds({1, 2, 3, 4});
+
+    GridParallelRNG pRNG(&Grid);
+    pRNG.SeedFixedIntegers(seeds);
+
+    LatticeComplexD test_data(&Grid);
+    gaussian(pRNG,test_data);
+
+    std::vector<TComplexD> reduction_reference;
+    std::vector<TComplexD> reduction_result;
+
+    //warmup
+    for (int sweeps = 0; sweeps < 5; sweeps++) {
+      reduction_result = sliceSum(test_data,0);
+    }
+
+    int trace_id = traceStart("sliceSum benchmark - ComplexD");
+    std::cout << GridLogMessage << "Testing ComplexD" << std::endl;
+    std::cout << GridLogMessage << "sizeof(ComplexD) = " << sizeof(ComplexD) << std::endl;
+    std::cout << GridLogMessage << "sizeof(vComplexD) = " << sizeof(vComplexD) << std::endl;
+    for (int i = 0; i < Nd; i++) {
+
+      RealD t=-usecond();
+
+      tracePush("sliceSum");
+      sliceSumCPU(test_data,reduction_reference,i);
+      tracePop("sliceSum");
+
+      t+=usecond();
+      std::cout << GridLogMessage << "Orthog. dir. = " << i << std::endl;
+      std::cout << GridLogMessage << "CPU sliceSum took "<<t<<" usecs"<<std::endl;
+      
+      
+      RealD tgpu=-usecond();
+
+      tracePush("sliceSumGpu");
+      reduction_result = sliceSum(test_data,i);
+      tracePop("sliceSumGpu");
+
+      tgpu+=usecond();
+
+      std::cout << GridLogMessage <<"GPU sliceSum took "<<tgpu<<" usecs"<<std::endl<<std::endl;;
+
+
+      for(int t=0;t<reduction_reference.size();t++) {
+
+        auto diff = reduction_reference[t]-reduction_result[t];
+        assert(abs(TensorRemove(diff)) < 1e-8 );
+
+      }
+
+    
+    }
+    traceStop(trace_id);
+
+    LatticeSpinVectorD test_data_cv(&Grid);
+    gaussian(pRNG,test_data_cv);
+
+    std::vector<SpinVectorD> reduction_reference_cv;
+    std::vector<SpinVectorD> reduction_result_cv;
+
+    //warmup
+    for (int sweeps = 0; sweeps < 5; sweeps++) {
+      reduction_result_cv = sliceSum(test_data_cv,0);
+    }
+    trace_id = traceStart("sliceSum benchmark - SpinVectorD");
+
+    std::cout << GridLogMessage << "Testing SpinVectorD" << std::endl;
+    std::cout << GridLogMessage << "sizeof(SpinVectorD) = " << sizeof(SpinVectorD) << std::endl;
+    std::cout << GridLogMessage << "sizeof(vSpinVectorD) = " << sizeof(vSpinVectorD) << std::endl;
+    for (int i = 0; i < Nd; i++) {
+
+      RealD t=-usecond();
+
+      tracePush("sliceSum");
+      sliceSumCPU(test_data_cv,reduction_reference_cv,i);
+      tracePop("sliceSum");
+
+      t+=usecond();
+      std::cout << GridLogMessage << "Orthog. dir. = " << i << std::endl;
+      std::cout << GridLogMessage << "CPU sliceSum took "<<t<<" usecs"<<std::endl;
+      
+      
+      RealD tgpu=-usecond();
+
+      tracePush("sliceSumGpu");
+      reduction_result_cv = sliceSum(test_data_cv,i);
+      tracePop("sliceSumGpu");
+
+      tgpu+=usecond();
+
+      std::cout << GridLogMessage <<"GPU sliceSum took "<<tgpu<<" usecs"<<std::endl<<std::endl;;
+
+
+      for(int t=0;t<reduction_reference_cv.size();t++) {
+
+        auto diff = reduction_reference_cv[t]-reduction_result_cv[t];
+        assert(abs(diff()(0)()) < 1e-8 );
+        assert(abs(diff()(1)()) < 1e-8 );
+        assert(abs(diff()(2)()) < 1e-8 );
+        assert(abs(diff()(3)()) < 1e-8 );
+
+      }
+
+    
+    }
+    traceStop(trace_id);
+
+    LatticeSpinColourVectorD test_data_scv(&Grid);
+    gaussian(pRNG,test_data_scv);
+
+    std::vector<SpinColourVectorD> reduction_reference_scv;
+    std::vector<SpinColourVectorD> reduction_result_scv;
+
+    //warmup
+    for (int sweeps = 0; sweeps < 5; sweeps++) {
+      reduction_result_scv = sliceSum(test_data_scv,0);
+    }
+    trace_id = traceStart("sliceSum benchmark - SpinColourVectorD");
+
+    std::cout << GridLogMessage << "Testing SpinColourVectorD" << std::endl;
+    std::cout << GridLogMessage << "sizeof(SpinColourVectorD) = " << sizeof(SpinColourVectorD) << std::endl;
+    std::cout << GridLogMessage << "sizeof(vSpinColourVectorD) = " << sizeof(vSpinColourVectorD) << std::endl;
+    for (int i = 0; i < Nd; i++) {
+
+      RealD t=-usecond();
+
+      tracePush("sliceSum");
+      sliceSumCPU(test_data_scv,reduction_reference_scv,i);
+      tracePop("sliceSum");
+
+      t+=usecond();
+      std::cout << GridLogMessage << "Orthog. dir. = " << i << std::endl;
+      std::cout << GridLogMessage << "CPU sliceSum took "<<t<<" usecs"<<std::endl;
+      
+      
+      RealD tgpu=-usecond();
+
+      tracePush("sliceSumGpu");
+      reduction_result_scv = sliceSum(test_data_scv,i);
+      tracePop("sliceSumGpu");
+
+      tgpu+=usecond();
+
+      std::cout << GridLogMessage <<"GPU sliceSum took "<<tgpu<<" usecs"<<std::endl<<std::endl;;
+
+
+      for(int t=0;t<reduction_reference_scv.size();t++) {
+
+        auto diff = reduction_reference_scv[t]-reduction_result_scv[t];
+        // std::cout << diff <<std::endl;
+        assert(abs(diff()(0)(0)) < 1e-8 );
+        assert(abs(diff()(0)(1)) < 1e-8 );
+        assert(abs(diff()(0)(2)) < 1e-8 );
+        assert(abs(diff()(1)(0)) < 1e-8 );
+        assert(abs(diff()(1)(1)) < 1e-8 );
+        assert(abs(diff()(1)(2)) < 1e-8 );    
+        assert(abs(diff()(2)(0)) < 1e-8 );
+        assert(abs(diff()(2)(1)) < 1e-8 );
+        assert(abs(diff()(2)(2)) < 1e-8 );    
+        assert(abs(diff()(3)(0)) < 1e-8 );
+        assert(abs(diff()(3)(1)) < 1e-8 );
+        assert(abs(diff()(3)(2)) < 1e-8 );
+
+      }
+
+    
+    }
+    traceStop(trace_id);
+
+    LatticeSpinColourMatrixD test_data_scm(&Grid);
+    gaussian(pRNG,test_data_scm);
+
+    std::vector<SpinColourMatrixD> reduction_reference_scm;
+    std::vector<SpinColourMatrixD> reduction_result_scm;
+
+    //warmup
+    for (int sweeps = 0; sweeps < 5; sweeps++) {
+      reduction_result_scm = sliceSum(test_data_scm,0);
+    }
+    trace_id = traceStart("sliceSum benchmark - SpinColourMatrixD");
+
+    std::cout << GridLogMessage << "Testing SpinColourMatrixD" << std::endl;
+    std::cout << GridLogMessage << "sizeof(SpinColourMatrixD) = " << sizeof(SpinColourMatrixD) << std::endl;
+    std::cout << GridLogMessage << "sizeof(vSpinColourMatrixD) = " << sizeof(vSpinColourMatrixD) << std::endl;
+    for (int i = 0; i < Nd; i++) {
+
+      RealD t=-usecond();
+
+      tracePush("sliceSum");
+      sliceSumCPU(test_data_scm,reduction_reference_scm,i);
+      tracePop("sliceSum");
+
+      t+=usecond();
+      std::cout << GridLogMessage << "Orthog. dir. = " << i << std::endl;
+      std::cout << GridLogMessage << "CPU sliceSum took "<<t<<" usecs"<<std::endl;
+      
+      
+      RealD tgpu=-usecond();
+
+      tracePush("sliceSumGpu");
+      reduction_result_scm = sliceSum(test_data_scm,i);
+      tracePop("sliceSumGpu");
+
+      tgpu+=usecond();
+
+      std::cout << GridLogMessage <<"GPU sliceSum took "<<tgpu<<" usecs"<<std::endl<<std::endl;;
+
+
+      for(int t=0;t<reduction_reference_scm.size();t++) {
+
+        auto diff = reduction_reference_scm[t]-reduction_result_scm[t];
+        // std::cout << diff <<std::endl;
+        for (int is = 0; is < Ns; is++) {
+          for (int js = 0; js < Ns; js++) {
+            for (int ic = 0; ic < Nc; ic++) {
+              for (int jc = 0; jc < Nc; jc++) {
+                assert(abs(diff()(is,js)(ic,jc)) < 1e-8);
+              }
+            }
+          }
+        }
+
+      }
+
+    
+    }
+    traceStop(trace_id);
+
+    Grid_finalize();
+    return 0;
+}