To PeriodicBC and ConjugateBC, added a new function "CshiftLink" which performs a boundary-aware C-shift of links or products of links. For the latter, the links crossing the global boundary are complex-conjugated.

To the gauge implementations, added CshiftLink functions calling into the appropriate operation for the BC in a given direction.
GaugeTransform, FourierAcceleratedGaugeFixer and WilsonLoops::FieldStrength no longer implicitly assume periodic boundary conditions; instead the shifted link is obtained using CshiftLink and is aware of the gauge implementation.
Added an assert-check to ensure that the gauge fixing converges within the specified number of steps.
Added functionality to compute the timeslice averaged plaquette
Added functionality to compute the 5LI topological charge and timeslice topological charge
Added a check of the properties of the charge conjugation matrix C=-gamma_2 gamma_4 to Test_gamma
Fixed const correctness for Replicate
Modified Test_fft_gfix to support either conjugate or periodic BCs, optionally disabling Fourier-accelerated gauge fixing, and tuning of alpha using cmdline options

Grid/qcd/action/gauge/GaugeImplementations.h

@@ -69,6 +69,11 @@ public:
     return PeriodicBC::ShiftStaple(Link,mu);
   }
 
+  //Same as Cshift for periodic BCs
+  static inline GaugeLinkField CshiftLink(const GaugeLinkField &Link, int mu, int shift){
+    return PeriodicBC::CshiftLink(Link,mu,shift);
+  }
+
   static inline bool isPeriodicGaugeField(void) { return true; }
 };
 
@@ -110,6 +115,11 @@ public:
       return PeriodicBC::CovShiftBackward(Link, mu, field);
   }
 
+  //If mu is a conjugate BC direction
+  //Out(x) = U^dag_\mu(x-mu)  | x_\mu != 0
+  //       = U^T_\mu(L-1)  | x_\mu == 0
+  //else
+  //Out(x) = U^dag_\mu(x-mu mod L)
   static inline GaugeLinkField
   CovShiftIdentityBackward(const GaugeLinkField &Link, int mu)
   {
@@ -129,6 +139,13 @@ public:
       return PeriodicBC::CovShiftIdentityForward(Link,mu);
   }
 
+
+  //If mu is a conjugate BC direction
+  //Out(x) = S_\mu(x+mu)  | x_\mu != L-1
+  //       = S*_\mu(x+mu)  | x_\mu == L-1
+  //else
+  //Out(x) = S_\mu(x+mu mod L)
+  //Note: While this is used for Staples it is also applicable for shifting gauge links or gauge transformation matrices
   static inline GaugeLinkField ShiftStaple(const GaugeLinkField &Link, int mu)
   {
     assert(_conjDirs.size() == Nd);
@@ -138,6 +155,27 @@ public:
       return PeriodicBC::ShiftStaple(Link,mu);
   }
 
+  //Boundary-aware C-shift of gauge links / gauge transformation matrices
+  //For conjugate BC direction
+  //shift = 1
+  //Out(x) = U_\mu(x+\hat\mu)  | x_\mu != L-1
+  //       = U*_\mu(0)  | x_\mu == L-1
+  //shift = -1
+  //Out(x) = U_\mu(x-mu)  | x_\mu != 0
+  //       = U*_\mu(L-1)  | x_\mu == 0
+  //else
+  //shift = 1
+  //Out(x) = U_\mu(x+\hat\mu mod L)
+  //shift = -1
+  //Out(x) = U_\mu(x-\hat\mu mod L)
+  static inline GaugeLinkField CshiftLink(const GaugeLinkField &Link, int mu, int shift){
+    assert(_conjDirs.size() == Nd);
+    if(_conjDirs[mu]) 
+      return ConjugateBC::CshiftLink(Link,mu,shift);
+    else     
+      return PeriodicBC::CshiftLink(Link,mu,shift);
+  }
+
   static inline void       setDirections(std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
   static inline std::vector<int> getDirections(void) { return _conjDirs; }
   static inline bool isPeriodicGaugeField(void) { return false; }