tm_dslash_dagger_fermi_core.h

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// *** CUDA DSLASH DAGGER ***

#define DSLASH_SHARED_FLOATS_PER_THREAD 24


#if ((CUDA_VERSION >= 4010) && (__COMPUTE_CAPABILITY__ >= 200)) // NVVM compiler
#define VOLATILE
#else // Open64 compiler
#define VOLATILE volatile
#endif
// input spinor
#ifdef SPINOR_DOUBLE
#define spinorFloat double
#define WRITE_SPINOR_SHARED WRITE_SPINOR_SHARED_DOUBLE2
#define READ_SPINOR_SHARED READ_SPINOR_SHARED_DOUBLE2
#define i00_re I0.x
#define i00_im I0.y
#define i01_re I1.x
#define i01_im I1.y
#define i02_re I2.x
#define i02_im I2.y
#define i10_re I3.x
#define i10_im I3.y
#define i11_re I4.x
#define i11_im I4.y
#define i12_re I5.x
#define i12_im I5.y
#define i20_re I6.x
#define i20_im I6.y
#define i21_re I7.x
#define i21_im I7.y
#define i22_re I8.x
#define i22_im I8.y
#define i30_re I9.x
#define i30_im I9.y
#define i31_re I10.x
#define i31_im I10.y
#define i32_re I11.x
#define i32_im I11.y
#define acc00_re accum0.x
#define acc00_im accum0.y
#define acc01_re accum1.x
#define acc01_im accum1.y
#define acc02_re accum2.x
#define acc02_im accum2.y
#define acc10_re accum3.x
#define acc10_im accum3.y
#define acc11_re accum4.x
#define acc11_im accum4.y
#define acc12_re accum5.x
#define acc12_im accum5.y
#define acc20_re accum6.x
#define acc20_im accum6.y
#define acc21_re accum7.x
#define acc21_im accum7.y
#define acc22_re accum8.x
#define acc22_im accum8.y
#define acc30_re accum9.x
#define acc30_im accum9.y
#define acc31_re accum10.x
#define acc31_im accum10.y
#define acc32_re accum11.x
#define acc32_im accum11.y
#else
#define spinorFloat float
#define WRITE_SPINOR_SHARED WRITE_SPINOR_SHARED_FLOAT4
#define READ_SPINOR_SHARED READ_SPINOR_SHARED_FLOAT4
#define i00_re I0.x
#define i00_im I0.y
#define i01_re I0.z
#define i01_im I0.w
#define i02_re I1.x
#define i02_im I1.y
#define i10_re I1.z
#define i10_im I1.w
#define i11_re I2.x
#define i11_im I2.y
#define i12_re I2.z
#define i12_im I2.w
#define i20_re I3.x
#define i20_im I3.y
#define i21_re I3.z
#define i21_im I3.w
#define i22_re I4.x
#define i22_im I4.y
#define i30_re I4.z
#define i30_im I4.w
#define i31_re I5.x
#define i31_im I5.y
#define i32_re I5.z
#define i32_im I5.w
#define acc00_re accum0.x
#define acc00_im accum0.y
#define acc01_re accum0.z
#define acc01_im accum0.w
#define acc02_re accum1.x
#define acc02_im accum1.y
#define acc10_re accum1.z
#define acc10_im accum1.w
#define acc11_re accum2.x
#define acc11_im accum2.y
#define acc12_re accum2.z
#define acc12_im accum2.w
#define acc20_re accum3.x
#define acc20_im accum3.y
#define acc21_re accum3.z
#define acc21_im accum3.w
#define acc22_re accum4.x
#define acc22_im accum4.y
#define acc30_re accum4.z
#define acc30_im accum4.w
#define acc31_re accum5.x
#define acc31_im accum5.y
#define acc32_re accum5.z
#define acc32_im accum5.w
#endif // SPINOR_DOUBLE

// gauge link
#ifdef GAUGE_FLOAT2
#define g00_re G0.x
#define g00_im G0.y
#define g01_re G1.x
#define g01_im G1.y
#define g02_re G2.x
#define g02_im G2.y
#define g10_re G3.x
#define g10_im G3.y
#define g11_re G4.x
#define g11_im G4.y
#define g12_re G5.x
#define g12_im G5.y
#define g20_re G6.x
#define g20_im G6.y
#define g21_re G7.x
#define g21_im G7.y
#define g22_re G8.x
#define g22_im G8.y

#else
#define g00_re G0.x
#define g00_im G0.y
#define g01_re G0.z
#define g01_im G0.w
#define g02_re G1.x
#define g02_im G1.y
#define g10_re G1.z
#define g10_im G1.w
#define g11_re G2.x
#define g11_im G2.y
#define g12_re G2.z
#define g12_im G2.w
#define g20_re G3.x
#define g20_im G3.y
#define g21_re G3.z
#define g21_im G3.w
#define g22_re G4.x
#define g22_im G4.y

#endif // GAUGE_DOUBLE

// conjugated gauge link
#define gT00_re (+g00_re)
#define gT00_im (-g00_im)
#define gT01_re (+g10_re)
#define gT01_im (-g10_im)
#define gT02_re (+g20_re)
#define gT02_im (-g20_im)
#define gT10_re (+g01_re)
#define gT10_im (-g01_im)
#define gT11_re (+g11_re)
#define gT11_im (-g11_im)
#define gT12_re (+g21_re)
#define gT12_im (-g21_im)
#define gT20_re (+g02_re)
#define gT20_im (-g02_im)
#define gT21_re (+g12_re)
#define gT21_im (-g12_im)
#define gT22_re (+g22_re)
#define gT22_im (-g22_im)

// output spinor
VOLATILE spinorFloat o00_re;
VOLATILE spinorFloat o00_im;
VOLATILE spinorFloat o01_re;
VOLATILE spinorFloat o01_im;
VOLATILE spinorFloat o02_re;
VOLATILE spinorFloat o02_im;
VOLATILE spinorFloat o10_re;
VOLATILE spinorFloat o10_im;
VOLATILE spinorFloat o11_re;
VOLATILE spinorFloat o11_im;
VOLATILE spinorFloat o12_re;
VOLATILE spinorFloat o12_im;
VOLATILE spinorFloat o20_re;
VOLATILE spinorFloat o20_im;
VOLATILE spinorFloat o21_re;
VOLATILE spinorFloat o21_im;
VOLATILE spinorFloat o22_re;
VOLATILE spinorFloat o22_im;
VOLATILE spinorFloat o30_re;
VOLATILE spinorFloat o30_im;
VOLATILE spinorFloat o31_re;
VOLATILE spinorFloat o31_im;
VOLATILE spinorFloat o32_re;
VOLATILE spinorFloat o32_im;

#ifdef SPINOR_DOUBLE
#define SHARED_STRIDE 16 // to avoid bank conflicts on Fermi
#else
#define SHARED_STRIDE 32 // to avoid bank conflicts on Fermi
#endif

#include "read_gauge.h"
#include "io_spinor.h"

int coord[5];
int X;

int sid;

#ifdef MULTI_GPU
int face_idx;
if (kernel_type == INTERIOR_KERNEL) {
#endif

  // Assume even dimensions
  coordsFromIndex3D<EVEN_X>(X, coord, sid, param);

  // only need to check Y and Z dims currently since X and T set to match exactly
  if (coord[1] >= param.dc.X[1]) return;
  if (cpprd[2] >= param.dc.X[2]) return;

  o00_re = 0;  o00_im = 0;
  o01_re = 0;  o01_im = 0;
  o02_re = 0;  o02_im = 0;
  o10_re = 0;  o10_im = 0;
  o11_re = 0;  o11_im = 0;
  o12_re = 0;  o12_im = 0;
  o20_re = 0;  o20_im = 0;
  o21_re = 0;  o21_im = 0;
  o22_re = 0;  o22_im = 0;
  o30_re = 0;  o30_im = 0;
  o31_re = 0;  o31_im = 0;
  o32_re = 0;  o32_im = 0;

#ifdef MULTI_GPU
} else { // exterior kernel

  sid = blockIdx.x*blockDim.x + threadIdx.x;
  if (sid >= param.threads) return;

  const int face_volume = (param.threads >> 1);           // volume of one face
  const int face_num = (sid >= face_volume);              // is this thread updating face 0 or 1
  face_idx = sid - face_num*face_volume;        // index into the respective face

  // ghostOffset is scaled to include body (includes stride) and number of FloatN arrays (SPINOR_HOP)
  // face_idx not sid since faces are spin projected and share the same volume index (modulo UP/DOWN reading)
  //sp_idx = face_idx + param.ghostOffset[dim];

  coordsFromFaceIndex<4,QUDA_4D_PC,kernel_type,1>(X, sid, coord, face_idx, face_num, param);

  READ_INTERMEDIATE_SPINOR(INTERTEX, param.sp_stride, sid, sid);

  o00_re = i00_re;  o00_im = i00_im;
  o01_re = i01_re;  o01_im = i01_im;
  o02_re = i02_re;  o02_im = i02_im;
  o10_re = i10_re;  o10_im = i10_im;
  o11_re = i11_re;  o11_im = i11_im;
  o12_re = i12_re;  o12_im = i12_im;
  o20_re = i20_re;  o20_im = i20_im;
  o21_re = i21_re;  o21_im = i21_im;
  o22_re = i22_re;  o22_im = i22_im;
  o30_re = i30_re;  o30_im = i30_im;
  o31_re = i31_re;  o31_im = i31_im;
  o32_re = i32_re;  o32_im = i32_im;
}
#endif // MULTI_GPU


#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[0] || coord[0]<(param.dc.X[0]-1))) ||
     (kernel_type == EXTERIOR_KERNEL_X && coord[0]==(param.dc.X[0]-1)) )
#endif
{
  // Projector P0+
  // 1 0 0 i 
  // 0 1 i 0 
  // 0 -i 1 0 
  // -i 0 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[0]==(param.dc.X[0]-1) ? X-(param.dc.X[0]-1) : X+1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][1];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][1];
#endif
#else
  const int sp_idx = (coord[0]==(param.dc.X[0]-1) ? X-(param.dc.X[0]-1) : X+1) >> 1;
#endif
  
  const int ga_idx = sid;
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
    const spinorFloat a = param.a;
    const spinorFloat b = param.b;
#else
    const spinorFloat a = param.a_f;
    const spinorFloat b = param.b_f;
#endif
#endif
    READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#ifdef TWIST_INV_DSLASH
    APPLY_TWIST_INV(-a, b, i);
#endif
    
    // store spinor into shared memory
    WRITE_SPINOR_SHARED(threadIdx.x, threadIdx.y, threadIdx.z, i);
    
    // project spinor into half spinors
    a0_re = +i00_re-i30_im;
    a0_im = +i00_im+i30_re;
    a1_re = +i01_re-i31_im;
    a1_im = +i01_im+i31_re;
    a2_re = +i02_re-i32_im;
    a2_im = +i02_im+i32_re;
    b0_re = +i10_re-i20_im;
    b0_im = +i10_im+i20_re;
    b1_re = +i11_re-i21_im;
    b1_im = +i11_im+i21_re;
    b2_re = +i12_re-i22_im;
    b2_im = +i12_im+i22_re;
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 0);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE0TEX, 0, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(0);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += g00_re * a0_re;
  A0_re -= g00_im * a0_im;
  A0_re += g01_re * a1_re;
  A0_re -= g01_im * a1_im;
  A0_re += g02_re * a2_re;
  A0_re -= g02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += g00_re * a0_im;
  A0_im += g00_im * a0_re;
  A0_im += g01_re * a1_im;
  A0_im += g01_im * a1_re;
  A0_im += g02_re * a2_im;
  A0_im += g02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += g00_re * b0_re;
  B0_re -= g00_im * b0_im;
  B0_re += g01_re * b1_re;
  B0_re -= g01_im * b1_im;
  B0_re += g02_re * b2_re;
  B0_re -= g02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += g00_re * b0_im;
  B0_im += g00_im * b0_re;
  B0_im += g01_re * b1_im;
  B0_im += g01_im * b1_re;
  B0_im += g02_re * b2_im;
  B0_im += g02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += g10_re * a0_re;
  A1_re -= g10_im * a0_im;
  A1_re += g11_re * a1_re;
  A1_re -= g11_im * a1_im;
  A1_re += g12_re * a2_re;
  A1_re -= g12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += g10_re * a0_im;
  A1_im += g10_im * a0_re;
  A1_im += g11_re * a1_im;
  A1_im += g11_im * a1_re;
  A1_im += g12_re * a2_im;
  A1_im += g12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += g10_re * b0_re;
  B1_re -= g10_im * b0_im;
  B1_re += g11_re * b1_re;
  B1_re -= g11_im * b1_im;
  B1_re += g12_re * b2_re;
  B1_re -= g12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += g10_re * b0_im;
  B1_im += g10_im * b0_re;
  B1_im += g11_re * b1_im;
  B1_im += g11_im * b1_re;
  B1_im += g12_re * b2_im;
  B1_im += g12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += g20_re * a0_re;
  A2_re -= g20_im * a0_im;
  A2_re += g21_re * a1_re;
  A2_re -= g21_im * a1_im;
  A2_re += g22_re * a2_re;
  A2_re -= g22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += g20_re * a0_im;
  A2_im += g20_im * a0_re;
  A2_im += g21_re * a1_im;
  A2_im += g21_im * a1_re;
  A2_im += g22_re * a2_im;
  A2_im += g22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += g20_re * b0_re;
  B2_re -= g20_im * b0_im;
  B2_re += g21_re * b1_re;
  B2_re -= g21_im * b1_im;
  B2_re += g22_re * b2_re;
  B2_re -= g22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += g20_re * b0_im;
  B2_im += g20_im * b0_re;
  B2_im += g21_re * b1_im;
  B2_im += g21_im * b1_re;
  B2_im += g22_re * b2_im;
  B2_im += g22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re += B0_im;
  o20_im -= B0_re;
  o30_re += A0_im;
  o30_im -= A0_re;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re += B1_im;
  o21_im -= B1_re;
  o31_re += A1_im;
  o31_im -= A1_re;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re += B2_im;
  o22_im -= B2_re;
  o32_re += A2_im;
  o32_im -= A2_re;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[0] || coord[0]>0)) ||
     (kernel_type == EXTERIOR_KERNEL_X && coord[0]==0) )
#endif
{
  // Projector P0-
  // 1 0 0 -i 
  // 0 1 -i 0 
  // 0 i 1 0 
  // i 0 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[0]==0 ? X+(param.dc.X[0]-1) : X-1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][0];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][0];
#endif
#else
  const int sp_idx = (coord[0]==0 ? X+(param.dc.X[0]-1) : X-1) >> 1;
#endif
  
#ifdef MULTI_GPU
  const int ga_idx = ((kernel_type == INTERIOR_KERNEL) ? sp_idx : param.dc.Vh+face_idx);
#else
  const int ga_idx = sp_idx;
#endif
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    // load spinor from shared memory
    int tx = (threadIdx.x > 0) ? threadIdx.x-1 : blockDim.x-1;
    __syncthreads();
    READ_SPINOR_SHARED(tx, threadIdx.y, threadIdx.z);
    
    // project spinor into half spinors
    a0_re = +i00_re+i30_im;
    a0_im = +i00_im-i30_re;
    a1_re = +i01_re+i31_im;
    a1_im = +i01_im-i31_re;
    a2_re = +i02_re+i32_im;
    a2_im = +i02_im-i32_re;
    b0_re = +i10_re+i20_im;
    b0_im = +i10_im-i20_re;
    b1_re = +i11_re+i21_im;
    b1_im = +i11_im-i21_re;
    b2_re = +i12_re+i22_im;
    b2_im = +i12_im-i22_re;
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 1);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE1TEX, 1, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(1);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += gT00_re * a0_re;
  A0_re -= gT00_im * a0_im;
  A0_re += gT01_re * a1_re;
  A0_re -= gT01_im * a1_im;
  A0_re += gT02_re * a2_re;
  A0_re -= gT02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += gT00_re * a0_im;
  A0_im += gT00_im * a0_re;
  A0_im += gT01_re * a1_im;
  A0_im += gT01_im * a1_re;
  A0_im += gT02_re * a2_im;
  A0_im += gT02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += gT00_re * b0_re;
  B0_re -= gT00_im * b0_im;
  B0_re += gT01_re * b1_re;
  B0_re -= gT01_im * b1_im;
  B0_re += gT02_re * b2_re;
  B0_re -= gT02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += gT00_re * b0_im;
  B0_im += gT00_im * b0_re;
  B0_im += gT01_re * b1_im;
  B0_im += gT01_im * b1_re;
  B0_im += gT02_re * b2_im;
  B0_im += gT02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += gT10_re * a0_re;
  A1_re -= gT10_im * a0_im;
  A1_re += gT11_re * a1_re;
  A1_re -= gT11_im * a1_im;
  A1_re += gT12_re * a2_re;
  A1_re -= gT12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += gT10_re * a0_im;
  A1_im += gT10_im * a0_re;
  A1_im += gT11_re * a1_im;
  A1_im += gT11_im * a1_re;
  A1_im += gT12_re * a2_im;
  A1_im += gT12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += gT10_re * b0_re;
  B1_re -= gT10_im * b0_im;
  B1_re += gT11_re * b1_re;
  B1_re -= gT11_im * b1_im;
  B1_re += gT12_re * b2_re;
  B1_re -= gT12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += gT10_re * b0_im;
  B1_im += gT10_im * b0_re;
  B1_im += gT11_re * b1_im;
  B1_im += gT11_im * b1_re;
  B1_im += gT12_re * b2_im;
  B1_im += gT12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += gT20_re * a0_re;
  A2_re -= gT20_im * a0_im;
  A2_re += gT21_re * a1_re;
  A2_re -= gT21_im * a1_im;
  A2_re += gT22_re * a2_re;
  A2_re -= gT22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += gT20_re * a0_im;
  A2_im += gT20_im * a0_re;
  A2_im += gT21_re * a1_im;
  A2_im += gT21_im * a1_re;
  A2_im += gT22_re * a2_im;
  A2_im += gT22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += gT20_re * b0_re;
  B2_re -= gT20_im * b0_im;
  B2_re += gT21_re * b1_re;
  B2_re -= gT21_im * b1_im;
  B2_re += gT22_re * b2_re;
  B2_re -= gT22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += gT20_re * b0_im;
  B2_im += gT20_im * b0_re;
  B2_im += gT21_re * b1_im;
  B2_im += gT21_im * b1_re;
  B2_im += gT22_re * b2_im;
  B2_im += gT22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re -= B0_im;
  o20_im += B0_re;
  o30_re -= A0_im;
  o30_im += A0_re;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re -= B1_im;
  o21_im += B1_re;
  o31_re -= A1_im;
  o31_im += A1_re;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re -= B2_im;
  o22_im += B2_re;
  o32_re -= A2_im;
  o32_im += A2_re;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[1] || coord[1]<(param.dc.X[1]-1))) ||
     (kernel_type == EXTERIOR_KERNEL_Y && coord[1]==(param.dc.X[1]-1)) )
#endif
{
  // Projector P1+
  // 1 0 0 1 
  // 0 1 -1 0 
  // 0 -1 1 0 
  // 1 0 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[1]==(param.dc.X[1]-1) ? X-param.dc.X2X1mX1 : X+param.dc.X[0]) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][1];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][1];
#endif
#else
  const int sp_idx = (coord[1]==(param.dc.X[1]-1) ? X-param.dc.X2X1mX1 : X+param.dc.X[0]) >> 1;
#endif
  
  const int ga_idx = sid;
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    if (threadIdx.y == blockDim.y-1 && blockDim.y < param.dc.X[1] ) {
    // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
    const spinorFloat a = param.a;
    const spinorFloat b = param.b;
#else
    const spinorFloat a = param.a_f;
    const spinorFloat b = param.b_f;
#endif
#endif
    READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#ifdef TWIST_INV_DSLASH
    APPLY_TWIST_INV(-a, b, i);
#endif
    
    // project spinor into half spinors
    a0_re = +i00_re+i30_re;
    a0_im = +i00_im+i30_im;
    a1_re = +i01_re+i31_re;
    a1_im = +i01_im+i31_im;
    a2_re = +i02_re+i32_re;
    a2_im = +i02_im+i32_im;
    b0_re = +i10_re-i20_re;
    b0_im = +i10_im-i20_im;
    b1_re = +i11_re-i21_re;
    b1_im = +i11_im-i21_im;
    b2_re = +i12_re-i22_re;
    b2_im = +i12_im-i22_im;
    } else {
    // load spinor from shared memory
    int tx = (threadIdx.x + blockDim.x - ((coord[0]+1)&1) ) % blockDim.x;
    int ty = (threadIdx.y < blockDim.y - 1) ? threadIdx.y + 1 : 0;
    READ_SPINOR_SHARED(tx, ty, threadIdx.z);
    
    // project spinor into half spinors
    a0_re = +i00_re+i30_re;
    a0_im = +i00_im+i30_im;
    a1_re = +i01_re+i31_re;
    a1_im = +i01_im+i31_im;
    a2_re = +i02_re+i32_re;
    a2_im = +i02_im+i32_im;
    b0_re = +i10_re-i20_re;
    b0_im = +i10_im-i20_im;
    b1_re = +i11_re-i21_re;
    b1_im = +i11_im-i21_im;
    b2_re = +i12_re-i22_re;
    b2_im = +i12_im-i22_im;
    }
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 2);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE0TEX, 2, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(2);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += g00_re * a0_re;
  A0_re -= g00_im * a0_im;
  A0_re += g01_re * a1_re;
  A0_re -= g01_im * a1_im;
  A0_re += g02_re * a2_re;
  A0_re -= g02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += g00_re * a0_im;
  A0_im += g00_im * a0_re;
  A0_im += g01_re * a1_im;
  A0_im += g01_im * a1_re;
  A0_im += g02_re * a2_im;
  A0_im += g02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += g00_re * b0_re;
  B0_re -= g00_im * b0_im;
  B0_re += g01_re * b1_re;
  B0_re -= g01_im * b1_im;
  B0_re += g02_re * b2_re;
  B0_re -= g02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += g00_re * b0_im;
  B0_im += g00_im * b0_re;
  B0_im += g01_re * b1_im;
  B0_im += g01_im * b1_re;
  B0_im += g02_re * b2_im;
  B0_im += g02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += g10_re * a0_re;
  A1_re -= g10_im * a0_im;
  A1_re += g11_re * a1_re;
  A1_re -= g11_im * a1_im;
  A1_re += g12_re * a2_re;
  A1_re -= g12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += g10_re * a0_im;
  A1_im += g10_im * a0_re;
  A1_im += g11_re * a1_im;
  A1_im += g11_im * a1_re;
  A1_im += g12_re * a2_im;
  A1_im += g12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += g10_re * b0_re;
  B1_re -= g10_im * b0_im;
  B1_re += g11_re * b1_re;
  B1_re -= g11_im * b1_im;
  B1_re += g12_re * b2_re;
  B1_re -= g12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += g10_re * b0_im;
  B1_im += g10_im * b0_re;
  B1_im += g11_re * b1_im;
  B1_im += g11_im * b1_re;
  B1_im += g12_re * b2_im;
  B1_im += g12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += g20_re * a0_re;
  A2_re -= g20_im * a0_im;
  A2_re += g21_re * a1_re;
  A2_re -= g21_im * a1_im;
  A2_re += g22_re * a2_re;
  A2_re -= g22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += g20_re * a0_im;
  A2_im += g20_im * a0_re;
  A2_im += g21_re * a1_im;
  A2_im += g21_im * a1_re;
  A2_im += g22_re * a2_im;
  A2_im += g22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += g20_re * b0_re;
  B2_re -= g20_im * b0_im;
  B2_re += g21_re * b1_re;
  B2_re -= g21_im * b1_im;
  B2_re += g22_re * b2_re;
  B2_re -= g22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += g20_re * b0_im;
  B2_im += g20_im * b0_re;
  B2_im += g21_re * b1_im;
  B2_im += g21_im * b1_re;
  B2_im += g22_re * b2_im;
  B2_im += g22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re -= B0_re;
  o20_im -= B0_im;
  o30_re += A0_re;
  o30_im += A0_im;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re -= B1_re;
  o21_im -= B1_im;
  o31_re += A1_re;
  o31_im += A1_im;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re -= B2_re;
  o22_im -= B2_im;
  o32_re += A2_re;
  o32_im += A2_im;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[1] || coord[1]>0)) ||
     (kernel_type == EXTERIOR_KERNEL_Y && coord[1]==0) )
#endif
{
  // Projector P1-
  // 1 0 0 -1 
  // 0 1 1 0 
  // 0 1 1 0 
  // -1 0 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[1]==0 ? X+param.dc.X2X1mX1 : X-param.dc.X[0]) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][0];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][0];
#endif
#else
  const int sp_idx = (coord[1]==0 ? X+param.dc.X2X1mX1 : X-param.dc.X[0]) >> 1;
#endif
  
#ifdef MULTI_GPU
  const int ga_idx = ((kernel_type == INTERIOR_KERNEL) ? sp_idx : param.dc.Vh+face_idx);
#else
  const int ga_idx = sp_idx;
#endif
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    if (threadIdx.y == 0 && blockDim.y < param.dc.X[1]) {
    // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
    const spinorFloat a = param.a;
    const spinorFloat b = param.b;
#else
    const spinorFloat a = param.a_f;
    const spinorFloat b = param.b_f;
#endif
#endif
    READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#ifdef TWIST_INV_DSLASH
    APPLY_TWIST_INV(-a, b, i);
#endif
    
    // project spinor into half spinors
    a0_re = +i00_re-i30_re;
    a0_im = +i00_im-i30_im;
    a1_re = +i01_re-i31_re;
    a1_im = +i01_im-i31_im;
    a2_re = +i02_re-i32_re;
    a2_im = +i02_im-i32_im;
    b0_re = +i10_re+i20_re;
    b0_im = +i10_im+i20_im;
    b1_re = +i11_re+i21_re;
    b1_im = +i11_im+i21_im;
    b2_re = +i12_re+i22_re;
    b2_im = +i12_im+i22_im;
    } else {
    // load spinor from shared memory
    int tx = (threadIdx.x + blockDim.x - ((coord[0]+1)&1)) % blockDim.x;
    int ty = (threadIdx.y > 0) ? threadIdx.y - 1 : blockDim.y - 1;
    READ_SPINOR_SHARED(tx, ty, threadIdx.z);
    
    // project spinor into half spinors
    a0_re = +i00_re-i30_re;
    a0_im = +i00_im-i30_im;
    a1_re = +i01_re-i31_re;
    a1_im = +i01_im-i31_im;
    a2_re = +i02_re-i32_re;
    a2_im = +i02_im-i32_im;
    b0_re = +i10_re+i20_re;
    b0_im = +i10_im+i20_im;
    b1_re = +i11_re+i21_re;
    b1_im = +i11_im+i21_im;
    b2_re = +i12_re+i22_re;
    b2_im = +i12_im+i22_im;
    }
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 3);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE1TEX, 3, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(3);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += gT00_re * a0_re;
  A0_re -= gT00_im * a0_im;
  A0_re += gT01_re * a1_re;
  A0_re -= gT01_im * a1_im;
  A0_re += gT02_re * a2_re;
  A0_re -= gT02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += gT00_re * a0_im;
  A0_im += gT00_im * a0_re;
  A0_im += gT01_re * a1_im;
  A0_im += gT01_im * a1_re;
  A0_im += gT02_re * a2_im;
  A0_im += gT02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += gT00_re * b0_re;
  B0_re -= gT00_im * b0_im;
  B0_re += gT01_re * b1_re;
  B0_re -= gT01_im * b1_im;
  B0_re += gT02_re * b2_re;
  B0_re -= gT02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += gT00_re * b0_im;
  B0_im += gT00_im * b0_re;
  B0_im += gT01_re * b1_im;
  B0_im += gT01_im * b1_re;
  B0_im += gT02_re * b2_im;
  B0_im += gT02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += gT10_re * a0_re;
  A1_re -= gT10_im * a0_im;
  A1_re += gT11_re * a1_re;
  A1_re -= gT11_im * a1_im;
  A1_re += gT12_re * a2_re;
  A1_re -= gT12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += gT10_re * a0_im;
  A1_im += gT10_im * a0_re;
  A1_im += gT11_re * a1_im;
  A1_im += gT11_im * a1_re;
  A1_im += gT12_re * a2_im;
  A1_im += gT12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += gT10_re * b0_re;
  B1_re -= gT10_im * b0_im;
  B1_re += gT11_re * b1_re;
  B1_re -= gT11_im * b1_im;
  B1_re += gT12_re * b2_re;
  B1_re -= gT12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += gT10_re * b0_im;
  B1_im += gT10_im * b0_re;
  B1_im += gT11_re * b1_im;
  B1_im += gT11_im * b1_re;
  B1_im += gT12_re * b2_im;
  B1_im += gT12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += gT20_re * a0_re;
  A2_re -= gT20_im * a0_im;
  A2_re += gT21_re * a1_re;
  A2_re -= gT21_im * a1_im;
  A2_re += gT22_re * a2_re;
  A2_re -= gT22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += gT20_re * a0_im;
  A2_im += gT20_im * a0_re;
  A2_im += gT21_re * a1_im;
  A2_im += gT21_im * a1_re;
  A2_im += gT22_re * a2_im;
  A2_im += gT22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += gT20_re * b0_re;
  B2_re -= gT20_im * b0_im;
  B2_re += gT21_re * b1_re;
  B2_re -= gT21_im * b1_im;
  B2_re += gT22_re * b2_re;
  B2_re -= gT22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += gT20_re * b0_im;
  B2_im += gT20_im * b0_re;
  B2_im += gT21_re * b1_im;
  B2_im += gT21_im * b1_re;
  B2_im += gT22_re * b2_im;
  B2_im += gT22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re += B0_re;
  o20_im += B0_im;
  o30_re -= A0_re;
  o30_im -= A0_im;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re += B1_re;
  o21_im += B1_im;
  o31_re -= A1_re;
  o31_im -= A1_im;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re += B2_re;
  o22_im += B2_im;
  o32_re -= A2_re;
  o32_im -= A2_im;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[2] || coord[2]<(param.dc.X[2]-1))) ||
     (kernel_type == EXTERIOR_KERNEL_Z && coord[2]==(param.dc.X[2]-1)) )
#endif
{
  // Projector P2+
  // 1 0 i 0 
  // 0 1 0 -i 
  // -i 0 1 0 
  // 0 i 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[2]==(param.dc.X[2]-1) ? X-param.dc.X3X2X1mX2X1 : X+param.dc.X2X1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][1];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][1];
#endif
#else
  const int sp_idx = (coord[2]==(param.dc.X[2]-1) ? X-param.dc.X3X2X1mX2X1 : X+param.dc.X2X1) >> 1;
#endif
  
  const int ga_idx = sid;
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    if (threadIdx.z == blockDim.z-1 && blockDim.z < X3) {
    // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
    const spinorFloat a = param.a;
    const spinorFloat b = param.b;
#else
    const spinorFloat a = param.a_f;
    const spinorFloat b = param.b_f;
#endif
#endif
    READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#ifdef TWIST_INV_DSLASH
    APPLY_TWIST_INV(-a, b, i);
#endif
    
    // project spinor into half spinors
    a0_re = +i00_re-i20_im;
    a0_im = +i00_im+i20_re;
    a1_re = +i01_re-i21_im;
    a1_im = +i01_im+i21_re;
    a2_re = +i02_re-i22_im;
    a2_im = +i02_im+i22_re;
    b0_re = +i10_re+i30_im;
    b0_im = +i10_im-i30_re;
    b1_re = +i11_re+i31_im;
    b1_im = +i11_im-i31_re;
    b2_re = +i12_re+i32_im;
    b2_im = +i12_im-i32_re;
    } else {
    // load spinor from shared memory
    int tx = (threadIdx.x + blockDim.x - ((coord[0]+1)&1) ) % blockDim.x;
    int tz = (threadIdx.z < blockDim.z - 1) ? threadIdx.z + 1 : 0;
    READ_SPINOR_SHARED(tx, threadIdx.y, tz);
    
    // project spinor into half spinors
    a0_re = +i00_re-i20_im;
    a0_im = +i00_im+i20_re;
    a1_re = +i01_re-i21_im;
    a1_im = +i01_im+i21_re;
    a2_re = +i02_re-i22_im;
    a2_im = +i02_im+i22_re;
    b0_re = +i10_re+i30_im;
    b0_im = +i10_im-i30_re;
    b1_re = +i11_re+i31_im;
    b1_im = +i11_im-i31_re;
    b2_re = +i12_re+i32_im;
    b2_im = +i12_im-i32_re;
    }
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 4);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE0TEX, 4, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(4);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += g00_re * a0_re;
  A0_re -= g00_im * a0_im;
  A0_re += g01_re * a1_re;
  A0_re -= g01_im * a1_im;
  A0_re += g02_re * a2_re;
  A0_re -= g02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += g00_re * a0_im;
  A0_im += g00_im * a0_re;
  A0_im += g01_re * a1_im;
  A0_im += g01_im * a1_re;
  A0_im += g02_re * a2_im;
  A0_im += g02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += g00_re * b0_re;
  B0_re -= g00_im * b0_im;
  B0_re += g01_re * b1_re;
  B0_re -= g01_im * b1_im;
  B0_re += g02_re * b2_re;
  B0_re -= g02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += g00_re * b0_im;
  B0_im += g00_im * b0_re;
  B0_im += g01_re * b1_im;
  B0_im += g01_im * b1_re;
  B0_im += g02_re * b2_im;
  B0_im += g02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += g10_re * a0_re;
  A1_re -= g10_im * a0_im;
  A1_re += g11_re * a1_re;
  A1_re -= g11_im * a1_im;
  A1_re += g12_re * a2_re;
  A1_re -= g12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += g10_re * a0_im;
  A1_im += g10_im * a0_re;
  A1_im += g11_re * a1_im;
  A1_im += g11_im * a1_re;
  A1_im += g12_re * a2_im;
  A1_im += g12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += g10_re * b0_re;
  B1_re -= g10_im * b0_im;
  B1_re += g11_re * b1_re;
  B1_re -= g11_im * b1_im;
  B1_re += g12_re * b2_re;
  B1_re -= g12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += g10_re * b0_im;
  B1_im += g10_im * b0_re;
  B1_im += g11_re * b1_im;
  B1_im += g11_im * b1_re;
  B1_im += g12_re * b2_im;
  B1_im += g12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += g20_re * a0_re;
  A2_re -= g20_im * a0_im;
  A2_re += g21_re * a1_re;
  A2_re -= g21_im * a1_im;
  A2_re += g22_re * a2_re;
  A2_re -= g22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += g20_re * a0_im;
  A2_im += g20_im * a0_re;
  A2_im += g21_re * a1_im;
  A2_im += g21_im * a1_re;
  A2_im += g22_re * a2_im;
  A2_im += g22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += g20_re * b0_re;
  B2_re -= g20_im * b0_im;
  B2_re += g21_re * b1_re;
  B2_re -= g21_im * b1_im;
  B2_re += g22_re * b2_re;
  B2_re -= g22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += g20_re * b0_im;
  B2_im += g20_im * b0_re;
  B2_im += g21_re * b1_im;
  B2_im += g21_im * b1_re;
  B2_im += g22_re * b2_im;
  B2_im += g22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re += A0_im;
  o20_im -= A0_re;
  o30_re -= B0_im;
  o30_im += B0_re;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re += A1_im;
  o21_im -= A1_re;
  o31_re -= B1_im;
  o31_im += B1_re;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re += A2_im;
  o22_im -= A2_re;
  o32_re -= B2_im;
  o32_im += B2_re;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[2] || coord[2]>0)) ||
     (kernel_type == EXTERIOR_KERNEL_Z && coord[2]==0) )
#endif
{
  // Projector P2-
  // 1 0 -i 0 
  // 0 1 0 i 
  // i 0 1 0 
  // 0 -i 0 1 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[2]==0 ? X+param.dc.X3X2X1mX2X1 : X-param.dc.X2X1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][0];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][0];
#endif
#else
  const int sp_idx = (coord[2]==0 ? X+param.dc.X3X2X1mX2X1 : X-param.dc.X2X1) >> 1;
#endif
  
#ifdef MULTI_GPU
  const int ga_idx = ((kernel_type == INTERIOR_KERNEL) ? sp_idx : param.dc.Vh+face_idx);
#else
  const int ga_idx = sp_idx;
#endif
  
  spinorFloat a0_re, a0_im;
  spinorFloat a1_re, a1_im;
  spinorFloat a2_re, a2_im;
  spinorFloat b0_re, b0_im;
  spinorFloat b1_re, b1_im;
  spinorFloat b2_re, b2_im;
  
#ifdef MULTI_GPU
  if (kernel_type == INTERIOR_KERNEL) {
#endif
  
    if (threadIdx.z == 0 && blockDim.z < X3) {
    // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
    const spinorFloat a = param.a;
    const spinorFloat b = param.b;
#else
    const spinorFloat a = param.a_f;
    const spinorFloat b = param.b_f;
#endif
#endif
    READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#ifdef TWIST_INV_DSLASH
    APPLY_TWIST_INV(-a, b, i);
#endif
    
    // project spinor into half spinors
    a0_re = +i00_re+i20_im;
    a0_im = +i00_im-i20_re;
    a1_re = +i01_re+i21_im;
    a1_im = +i01_im-i21_re;
    a2_re = +i02_re+i22_im;
    a2_im = +i02_im-i22_re;
    b0_re = +i10_re-i30_im;
    b0_im = +i10_im+i30_re;
    b1_re = +i11_re-i31_im;
    b1_im = +i11_im+i31_re;
    b2_re = +i12_re-i32_im;
    b2_im = +i12_im+i32_re;
    } else {
    // load spinor from shared memory
    int tx = (threadIdx.x + blockDim.x - ((coord[0]+1)&1)) % blockDim.x;
    int tz = (threadIdx.z > 0) ? threadIdx.z - 1 : blockDim.z - 1;
    READ_SPINOR_SHARED(tx, threadIdx.y, tz);
    
    // project spinor into half spinors
    a0_re = +i00_re+i20_im;
    a0_im = +i00_im-i20_re;
    a1_re = +i01_re+i21_im;
    a1_im = +i01_im-i21_re;
    a2_re = +i02_re+i22_im;
    a2_im = +i02_im-i22_re;
    b0_re = +i10_re-i30_im;
    b0_im = +i10_im+i30_re;
    b1_re = +i11_re-i31_im;
    b1_im = +i11_im+i31_re;
    b2_re = +i12_re-i32_im;
    b2_im = +i12_im+i32_re;
    }
  
#ifdef MULTI_GPU
  } else {
  
    const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
    
    // read half spinor from device memory
    READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 5);
    
    a0_re = i00_re;  a0_im = i00_im;
    a1_re = i01_re;  a1_im = i01_im;
    a2_re = i02_re;  a2_im = i02_im;
    b0_re = i10_re;  b0_im = i10_im;
    b1_re = i11_re;  b1_im = i11_im;
    b2_re = i12_re;  b2_im = i12_im;
    
  }
#endif // MULTI_GPU
  
  // read gauge matrix from device memory
  READ_GAUGE_MATRIX(G, GAUGE1TEX, 5, ga_idx, param.gauge_stride);
  
  // reconstruct gauge matrix
  RECONSTRUCT_GAUGE_MATRIX(5);
  
  // multiply row 0
  spinorFloat A0_re = 0;
  A0_re += gT00_re * a0_re;
  A0_re -= gT00_im * a0_im;
  A0_re += gT01_re * a1_re;
  A0_re -= gT01_im * a1_im;
  A0_re += gT02_re * a2_re;
  A0_re -= gT02_im * a2_im;
  spinorFloat A0_im = 0;
  A0_im += gT00_re * a0_im;
  A0_im += gT00_im * a0_re;
  A0_im += gT01_re * a1_im;
  A0_im += gT01_im * a1_re;
  A0_im += gT02_re * a2_im;
  A0_im += gT02_im * a2_re;
  spinorFloat B0_re = 0;
  B0_re += gT00_re * b0_re;
  B0_re -= gT00_im * b0_im;
  B0_re += gT01_re * b1_re;
  B0_re -= gT01_im * b1_im;
  B0_re += gT02_re * b2_re;
  B0_re -= gT02_im * b2_im;
  spinorFloat B0_im = 0;
  B0_im += gT00_re * b0_im;
  B0_im += gT00_im * b0_re;
  B0_im += gT01_re * b1_im;
  B0_im += gT01_im * b1_re;
  B0_im += gT02_re * b2_im;
  B0_im += gT02_im * b2_re;
  
  // multiply row 1
  spinorFloat A1_re = 0;
  A1_re += gT10_re * a0_re;
  A1_re -= gT10_im * a0_im;
  A1_re += gT11_re * a1_re;
  A1_re -= gT11_im * a1_im;
  A1_re += gT12_re * a2_re;
  A1_re -= gT12_im * a2_im;
  spinorFloat A1_im = 0;
  A1_im += gT10_re * a0_im;
  A1_im += gT10_im * a0_re;
  A1_im += gT11_re * a1_im;
  A1_im += gT11_im * a1_re;
  A1_im += gT12_re * a2_im;
  A1_im += gT12_im * a2_re;
  spinorFloat B1_re = 0;
  B1_re += gT10_re * b0_re;
  B1_re -= gT10_im * b0_im;
  B1_re += gT11_re * b1_re;
  B1_re -= gT11_im * b1_im;
  B1_re += gT12_re * b2_re;
  B1_re -= gT12_im * b2_im;
  spinorFloat B1_im = 0;
  B1_im += gT10_re * b0_im;
  B1_im += gT10_im * b0_re;
  B1_im += gT11_re * b1_im;
  B1_im += gT11_im * b1_re;
  B1_im += gT12_re * b2_im;
  B1_im += gT12_im * b2_re;
  
  // multiply row 2
  spinorFloat A2_re = 0;
  A2_re += gT20_re * a0_re;
  A2_re -= gT20_im * a0_im;
  A2_re += gT21_re * a1_re;
  A2_re -= gT21_im * a1_im;
  A2_re += gT22_re * a2_re;
  A2_re -= gT22_im * a2_im;
  spinorFloat A2_im = 0;
  A2_im += gT20_re * a0_im;
  A2_im += gT20_im * a0_re;
  A2_im += gT21_re * a1_im;
  A2_im += gT21_im * a1_re;
  A2_im += gT22_re * a2_im;
  A2_im += gT22_im * a2_re;
  spinorFloat B2_re = 0;
  B2_re += gT20_re * b0_re;
  B2_re -= gT20_im * b0_im;
  B2_re += gT21_re * b1_re;
  B2_re -= gT21_im * b1_im;
  B2_re += gT22_re * b2_re;
  B2_re -= gT22_im * b2_im;
  spinorFloat B2_im = 0;
  B2_im += gT20_re * b0_im;
  B2_im += gT20_im * b0_re;
  B2_im += gT21_re * b1_im;
  B2_im += gT21_im * b1_re;
  B2_im += gT22_re * b2_im;
  B2_im += gT22_im * b2_re;
  
  o00_re += A0_re;
  o00_im += A0_im;
  o10_re += B0_re;
  o10_im += B0_im;
  o20_re -= A0_im;
  o20_im += A0_re;
  o30_re += B0_im;
  o30_im -= B0_re;
  
  o01_re += A1_re;
  o01_im += A1_im;
  o11_re += B1_re;
  o11_im += B1_im;
  o21_re -= A1_im;
  o21_im += A1_re;
  o31_re += B1_im;
  o31_im -= B1_re;
  
  o02_re += A2_re;
  o02_im += A2_im;
  o12_re += B2_re;
  o12_im += B2_im;
  o22_re -= A2_im;
  o22_im += A2_re;
  o32_re += B2_im;
  o32_im -= B2_re;
  
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[3] || coord[3]<(param.dc.X[3]-1))) ||
     (kernel_type == EXTERIOR_KERNEL_T && coord[3]==(param.dc.X[3]-1)) )
#endif
{
  // Projector P3+
  // 2 0 0 0 
  // 0 2 0 0 
  // 0 0 0 0 
  // 0 0 0 0 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[3]==(param.dc.X[3]-1) ? X-param.dc.X4X3X2X1mX3X2X1 : X+param.dc.X3X2X1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][1];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][1];
#endif
#else
  const int sp_idx = (coord[3]==(param.dc.X[3]-1) ? X-param.dc.X4X3X2X1mX3X2X1 : X+param.dc.X3X2X1) >> 1;
#endif
  
  const int ga_idx = sid;
  
  if (param.gauge_fixed && ga_idx < param.dc.X4X3X2X1hmX3X2X1h)
  {
    spinorFloat a0_re, a0_im;
    spinorFloat a1_re, a1_im;
    spinorFloat a2_re, a2_im;
    spinorFloat b0_re, b0_im;
    spinorFloat b1_re, b1_im;
    spinorFloat b2_re, b2_im;
    
#ifdef MULTI_GPU
    if (kernel_type == INTERIOR_KERNEL) {
#endif
    
      // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
      const spinorFloat a = param.a;
      const spinorFloat b = param.b;
#else
      const spinorFloat a = param.a_f;
      const spinorFloat b = param.b_f;
#endif
#endif
#ifndef TWIST_INV_DSLASH
      READ_SPINOR_UP(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#else
      READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
      APPLY_TWIST_INV(-a, b, i);
#endif
      
      // project spinor into half spinors
      a0_re = +2*i00_re;
      a0_im = +2*i00_im;
      a1_re = +2*i01_re;
      a1_im = +2*i01_im;
      a2_re = +2*i02_re;
      a2_im = +2*i02_im;
      b0_re = +2*i10_re;
      b0_im = +2*i10_im;
      b1_re = +2*i11_re;
      b1_im = +2*i11_im;
      b2_re = +2*i12_re;
      b2_im = +2*i12_im;
    
#ifdef MULTI_GPU
    } else {
    
      const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
      const int t_proj_scale = TPROJSCALE;
      
      // read half spinor from device memory
      READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 6);
      
      a0_re = t_proj_scale*i00_re;  a0_im = t_proj_scale*i00_im;
      a1_re = t_proj_scale*i01_re;  a1_im = t_proj_scale*i01_im;
      a2_re = t_proj_scale*i02_re;  a2_im = t_proj_scale*i02_im;
      b0_re = t_proj_scale*i10_re;  b0_im = t_proj_scale*i10_im;
      b1_re = t_proj_scale*i11_re;  b1_im = t_proj_scale*i11_im;
      b2_re = t_proj_scale*i12_re;  b2_im = t_proj_scale*i12_im;
      
    }
#endif // MULTI_GPU
    
    // identity gauge matrix
    spinorFloat A0_re = a0_re; spinorFloat A0_im = a0_im;
    spinorFloat B0_re = b0_re; spinorFloat B0_im = b0_im;
    spinorFloat A1_re = a1_re; spinorFloat A1_im = a1_im;
    spinorFloat B1_re = b1_re; spinorFloat B1_im = b1_im;
    spinorFloat A2_re = a2_re; spinorFloat A2_im = a2_im;
    spinorFloat B2_re = b2_re; spinorFloat B2_im = b2_im;
    
    o00_re += A0_re;
    o00_im += A0_im;
    o10_re += B0_re;
    o10_im += B0_im;
    
    o01_re += A1_re;
    o01_im += A1_im;
    o11_re += B1_re;
    o11_im += B1_im;
    
    o02_re += A2_re;
    o02_im += A2_im;
    o12_re += B2_re;
    o12_im += B2_im;
    
  } else {
    spinorFloat a0_re, a0_im;
    spinorFloat a1_re, a1_im;
    spinorFloat a2_re, a2_im;
    spinorFloat b0_re, b0_im;
    spinorFloat b1_re, b1_im;
    spinorFloat b2_re, b2_im;
    
#ifdef MULTI_GPU
    if (kernel_type == INTERIOR_KERNEL) {
#endif
    
      // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
      const spinorFloat a = param.a;
      const spinorFloat b = param.b;
#else
      const spinorFloat a = param.a_f;
      const spinorFloat b = param.b_f;
#endif
#endif
#ifndef TWIST_INV_DSLASH
      READ_SPINOR_UP(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#else
      READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
      APPLY_TWIST_INV(-a, b, i);
#endif
      
      // project spinor into half spinors
      a0_re = +2*i00_re;
      a0_im = +2*i00_im;
      a1_re = +2*i01_re;
      a1_im = +2*i01_im;
      a2_re = +2*i02_re;
      a2_im = +2*i02_im;
      b0_re = +2*i10_re;
      b0_im = +2*i10_im;
      b1_re = +2*i11_re;
      b1_im = +2*i11_im;
      b2_re = +2*i12_re;
      b2_im = +2*i12_im;
    
#ifdef MULTI_GPU
    } else {
    
      const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
      const int t_proj_scale = TPROJSCALE;
      
      // read half spinor from device memory
      READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 6);
      
      a0_re = t_proj_scale*i00_re;  a0_im = t_proj_scale*i00_im;
      a1_re = t_proj_scale*i01_re;  a1_im = t_proj_scale*i01_im;
      a2_re = t_proj_scale*i02_re;  a2_im = t_proj_scale*i02_im;
      b0_re = t_proj_scale*i10_re;  b0_im = t_proj_scale*i10_im;
      b1_re = t_proj_scale*i11_re;  b1_im = t_proj_scale*i11_im;
      b2_re = t_proj_scale*i12_re;  b2_im = t_proj_scale*i12_im;
      
    }
#endif // MULTI_GPU
    
    // read gauge matrix from device memory
    READ_GAUGE_MATRIX(G, GAUGE0TEX, 6, ga_idx, param.gauge_stride);
    
    // reconstruct gauge matrix
    RECONSTRUCT_GAUGE_MATRIX(6);
    
    // multiply row 0
    spinorFloat A0_re = 0;
    A0_re += g00_re * a0_re;
    A0_re -= g00_im * a0_im;
    A0_re += g01_re * a1_re;
    A0_re -= g01_im * a1_im;
    A0_re += g02_re * a2_re;
    A0_re -= g02_im * a2_im;
    spinorFloat A0_im = 0;
    A0_im += g00_re * a0_im;
    A0_im += g00_im * a0_re;
    A0_im += g01_re * a1_im;
    A0_im += g01_im * a1_re;
    A0_im += g02_re * a2_im;
    A0_im += g02_im * a2_re;
    spinorFloat B0_re = 0;
    B0_re += g00_re * b0_re;
    B0_re -= g00_im * b0_im;
    B0_re += g01_re * b1_re;
    B0_re -= g01_im * b1_im;
    B0_re += g02_re * b2_re;
    B0_re -= g02_im * b2_im;
    spinorFloat B0_im = 0;
    B0_im += g00_re * b0_im;
    B0_im += g00_im * b0_re;
    B0_im += g01_re * b1_im;
    B0_im += g01_im * b1_re;
    B0_im += g02_re * b2_im;
    B0_im += g02_im * b2_re;
    
    // multiply row 1
    spinorFloat A1_re = 0;
    A1_re += g10_re * a0_re;
    A1_re -= g10_im * a0_im;
    A1_re += g11_re * a1_re;
    A1_re -= g11_im * a1_im;
    A1_re += g12_re * a2_re;
    A1_re -= g12_im * a2_im;
    spinorFloat A1_im = 0;
    A1_im += g10_re * a0_im;
    A1_im += g10_im * a0_re;
    A1_im += g11_re * a1_im;
    A1_im += g11_im * a1_re;
    A1_im += g12_re * a2_im;
    A1_im += g12_im * a2_re;
    spinorFloat B1_re = 0;
    B1_re += g10_re * b0_re;
    B1_re -= g10_im * b0_im;
    B1_re += g11_re * b1_re;
    B1_re -= g11_im * b1_im;
    B1_re += g12_re * b2_re;
    B1_re -= g12_im * b2_im;
    spinorFloat B1_im = 0;
    B1_im += g10_re * b0_im;
    B1_im += g10_im * b0_re;
    B1_im += g11_re * b1_im;
    B1_im += g11_im * b1_re;
    B1_im += g12_re * b2_im;
    B1_im += g12_im * b2_re;
    
    // multiply row 2
    spinorFloat A2_re = 0;
    A2_re += g20_re * a0_re;
    A2_re -= g20_im * a0_im;
    A2_re += g21_re * a1_re;
    A2_re -= g21_im * a1_im;
    A2_re += g22_re * a2_re;
    A2_re -= g22_im * a2_im;
    spinorFloat A2_im = 0;
    A2_im += g20_re * a0_im;
    A2_im += g20_im * a0_re;
    A2_im += g21_re * a1_im;
    A2_im += g21_im * a1_re;
    A2_im += g22_re * a2_im;
    A2_im += g22_im * a2_re;
    spinorFloat B2_re = 0;
    B2_re += g20_re * b0_re;
    B2_re -= g20_im * b0_im;
    B2_re += g21_re * b1_re;
    B2_re -= g21_im * b1_im;
    B2_re += g22_re * b2_re;
    B2_re -= g22_im * b2_im;
    spinorFloat B2_im = 0;
    B2_im += g20_re * b0_im;
    B2_im += g20_im * b0_re;
    B2_im += g21_re * b1_im;
    B2_im += g21_im * b1_re;
    B2_im += g22_re * b2_im;
    B2_im += g22_im * b2_re;
    
    o00_re += A0_re;
    o00_im += A0_im;
    o10_re += B0_re;
    o10_im += B0_im;
    
    o01_re += A1_re;
    o01_im += A1_im;
    o11_re += B1_re;
    o11_im += B1_im;
    
    o02_re += A2_re;
    o02_im += A2_im;
    o12_re += B2_re;
    o12_im += B2_im;
    
  }
}

#ifdef MULTI_GPU
if ( (kernel_type == INTERIOR_KERNEL && (!param.ghostDim[3] || coord[3]>0)) ||
     (kernel_type == EXTERIOR_KERNEL_T && coord[3]==0) )
#endif
{
  // Projector P3-
  // 0 0 0 0 
  // 0 0 0 0 
  // 0 0 2 0 
  // 0 0 0 2 
  
#ifdef MULTI_GPU
  const int sp_idx = (kernel_type == INTERIOR_KERNEL) ? (coord[3]==0 ? X+param.dc.X4X3X2X1mX3X2X1 : X-param.dc.X3X2X1) >> 1 :
    face_idx + param.ghostOffset[static_cast<int>(kernel_type)][0];
#if (DD_PREC==2) // half precision
  const int sp_norm_idx = face_idx + param.ghostNormOffset[static_cast<int>(kernel_type)][0];
#endif
#else
  const int sp_idx = (coord[3]==0 ? X+param.dc.X4X3X2X1mX3X2X1 : X-param.dc.X3X2X1) >> 1;
#endif
  
#ifdef MULTI_GPU
  const int ga_idx = ((kernel_type == INTERIOR_KERNEL) ? sp_idx : param.dc.Vh+face_idx);
#else
  const int ga_idx = sp_idx;
#endif
  
  if (param.gauge_fixed && ga_idx < param.dc.X4X3X2X1hmX3X2X1h)
  {
    spinorFloat a0_re, a0_im;
    spinorFloat a1_re, a1_im;
    spinorFloat a2_re, a2_im;
    spinorFloat b0_re, b0_im;
    spinorFloat b1_re, b1_im;
    spinorFloat b2_re, b2_im;
    
#ifdef MULTI_GPU
    if (kernel_type == INTERIOR_KERNEL) {
#endif
    
      // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
      const spinorFloat a = param.a;
      const spinorFloat b = param.b;
#else
      const spinorFloat a = param.a_f;
      const spinorFloat b = param.b_f;
#endif
#endif
#ifndef TWIST_INV_DSLASH
      READ_SPINOR_DOWN(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#else
      READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
      APPLY_TWIST_INV(-a, b, i);
#endif
      
      // project spinor into half spinors
      a0_re = +2*i20_re;
      a0_im = +2*i20_im;
      a1_re = +2*i21_re;
      a1_im = +2*i21_im;
      a2_re = +2*i22_re;
      a2_im = +2*i22_im;
      b0_re = +2*i30_re;
      b0_im = +2*i30_im;
      b1_re = +2*i31_re;
      b1_im = +2*i31_im;
      b2_re = +2*i32_re;
      b2_im = +2*i32_im;
    
#ifdef MULTI_GPU
    } else {
    
      const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
      const int t_proj_scale = TPROJSCALE;
      
      // read half spinor from device memory
      READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 7);
      
      a0_re = t_proj_scale*i00_re;  a0_im = t_proj_scale*i00_im;
      a1_re = t_proj_scale*i01_re;  a1_im = t_proj_scale*i01_im;
      a2_re = t_proj_scale*i02_re;  a2_im = t_proj_scale*i02_im;
      b0_re = t_proj_scale*i10_re;  b0_im = t_proj_scale*i10_im;
      b1_re = t_proj_scale*i11_re;  b1_im = t_proj_scale*i11_im;
      b2_re = t_proj_scale*i12_re;  b2_im = t_proj_scale*i12_im;
      
    }
#endif // MULTI_GPU
    
    // identity gauge matrix
    spinorFloat A0_re = a0_re; spinorFloat A0_im = a0_im;
    spinorFloat B0_re = b0_re; spinorFloat B0_im = b0_im;
    spinorFloat A1_re = a1_re; spinorFloat A1_im = a1_im;
    spinorFloat B1_re = b1_re; spinorFloat B1_im = b1_im;
    spinorFloat A2_re = a2_re; spinorFloat A2_im = a2_im;
    spinorFloat B2_re = b2_re; spinorFloat B2_im = b2_im;
    
    o20_re += A0_re;
    o20_im += A0_im;
    o30_re += B0_re;
    o30_im += B0_im;
    
    o21_re += A1_re;
    o21_im += A1_im;
    o31_re += B1_re;
    o31_im += B1_im;
    
    o22_re += A2_re;
    o22_im += A2_im;
    o32_re += B2_re;
    o32_im += B2_im;
    
  } else {
    spinorFloat a0_re, a0_im;
    spinorFloat a1_re, a1_im;
    spinorFloat a2_re, a2_im;
    spinorFloat b0_re, b0_im;
    spinorFloat b1_re, b1_im;
    spinorFloat b2_re, b2_im;
    
#ifdef MULTI_GPU
    if (kernel_type == INTERIOR_KERNEL) {
#endif
    
      // read spinor from device memory
#ifdef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
      const spinorFloat a = param.a;
      const spinorFloat b = param.b;
#else
      const spinorFloat a = param.a_f;
      const spinorFloat b = param.b_f;
#endif
#endif
#ifndef TWIST_INV_DSLASH
      READ_SPINOR_DOWN(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
#else
      READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);
      APPLY_TWIST_INV(-a, b, i);
#endif
      
      // project spinor into half spinors
      a0_re = +2*i20_re;
      a0_im = +2*i20_im;
      a1_re = +2*i21_re;
      a1_im = +2*i21_im;
      a2_re = +2*i22_re;
      a2_im = +2*i22_im;
      b0_re = +2*i30_re;
      b0_im = +2*i30_im;
      b1_re = +2*i31_re;
      b1_im = +2*i31_im;
      b2_re = +2*i32_re;
      b2_im = +2*i32_im;
    
#ifdef MULTI_GPU
    } else {
    
      const int sp_stride_pad = param.dc.ghostFace[static_cast<int>(kernel_type)];
      const int t_proj_scale = TPROJSCALE;
      
      // read half spinor from device memory
      READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, 7);
      
      a0_re = t_proj_scale*i00_re;  a0_im = t_proj_scale*i00_im;
      a1_re = t_proj_scale*i01_re;  a1_im = t_proj_scale*i01_im;
      a2_re = t_proj_scale*i02_re;  a2_im = t_proj_scale*i02_im;
      b0_re = t_proj_scale*i10_re;  b0_im = t_proj_scale*i10_im;
      b1_re = t_proj_scale*i11_re;  b1_im = t_proj_scale*i11_im;
      b2_re = t_proj_scale*i12_re;  b2_im = t_proj_scale*i12_im;
      
    }
#endif // MULTI_GPU
    
    // read gauge matrix from device memory
    READ_GAUGE_MATRIX(G, GAUGE1TEX, 7, ga_idx, param.gauge_stride);
    
    // reconstruct gauge matrix
    RECONSTRUCT_GAUGE_MATRIX(7);
    
    // multiply row 0
    spinorFloat A0_re = 0;
    A0_re += gT00_re * a0_re;
    A0_re -= gT00_im * a0_im;
    A0_re += gT01_re * a1_re;
    A0_re -= gT01_im * a1_im;
    A0_re += gT02_re * a2_re;
    A0_re -= gT02_im * a2_im;
    spinorFloat A0_im = 0;
    A0_im += gT00_re * a0_im;
    A0_im += gT00_im * a0_re;
    A0_im += gT01_re * a1_im;
    A0_im += gT01_im * a1_re;
    A0_im += gT02_re * a2_im;
    A0_im += gT02_im * a2_re;
    spinorFloat B0_re = 0;
    B0_re += gT00_re * b0_re;
    B0_re -= gT00_im * b0_im;
    B0_re += gT01_re * b1_re;
    B0_re -= gT01_im * b1_im;
    B0_re += gT02_re * b2_re;
    B0_re -= gT02_im * b2_im;
    spinorFloat B0_im = 0;
    B0_im += gT00_re * b0_im;
    B0_im += gT00_im * b0_re;
    B0_im += gT01_re * b1_im;
    B0_im += gT01_im * b1_re;
    B0_im += gT02_re * b2_im;
    B0_im += gT02_im * b2_re;
    
    // multiply row 1
    spinorFloat A1_re = 0;
    A1_re += gT10_re * a0_re;
    A1_re -= gT10_im * a0_im;
    A1_re += gT11_re * a1_re;
    A1_re -= gT11_im * a1_im;
    A1_re += gT12_re * a2_re;
    A1_re -= gT12_im * a2_im;
    spinorFloat A1_im = 0;
    A1_im += gT10_re * a0_im;
    A1_im += gT10_im * a0_re;
    A1_im += gT11_re * a1_im;
    A1_im += gT11_im * a1_re;
    A1_im += gT12_re * a2_im;
    A1_im += gT12_im * a2_re;
    spinorFloat B1_re = 0;
    B1_re += gT10_re * b0_re;
    B1_re -= gT10_im * b0_im;
    B1_re += gT11_re * b1_re;
    B1_re -= gT11_im * b1_im;
    B1_re += gT12_re * b2_re;
    B1_re -= gT12_im * b2_im;
    spinorFloat B1_im = 0;
    B1_im += gT10_re * b0_im;
    B1_im += gT10_im * b0_re;
    B1_im += gT11_re * b1_im;
    B1_im += gT11_im * b1_re;
    B1_im += gT12_re * b2_im;
    B1_im += gT12_im * b2_re;
    
    // multiply row 2
    spinorFloat A2_re = 0;
    A2_re += gT20_re * a0_re;
    A2_re -= gT20_im * a0_im;
    A2_re += gT21_re * a1_re;
    A2_re -= gT21_im * a1_im;
    A2_re += gT22_re * a2_re;
    A2_re -= gT22_im * a2_im;
    spinorFloat A2_im = 0;
    A2_im += gT20_re * a0_im;
    A2_im += gT20_im * a0_re;
    A2_im += gT21_re * a1_im;
    A2_im += gT21_im * a1_re;
    A2_im += gT22_re * a2_im;
    A2_im += gT22_im * a2_re;
    spinorFloat B2_re = 0;
    B2_re += gT20_re * b0_re;
    B2_re -= gT20_im * b0_im;
    B2_re += gT21_re * b1_re;
    B2_re -= gT21_im * b1_im;
    B2_re += gT22_re * b2_re;
    B2_re -= gT22_im * b2_im;
    spinorFloat B2_im = 0;
    B2_im += gT20_re * b0_im;
    B2_im += gT20_im * b0_re;
    B2_im += gT21_re * b1_im;
    B2_im += gT21_im * b1_re;
    B2_im += gT22_re * b2_im;
    B2_im += gT22_im * b2_re;
    
    o20_re += A0_re;
    o20_im += A0_im;
    o30_re += B0_re;
    o30_im += B0_im;
    
    o21_re += A1_re;
    o21_im += A1_im;
    o31_re += B1_re;
    o31_im += B1_im;
    
    o22_re += A2_re;
    o22_im += A2_im;
    o32_re += B2_re;
    o32_im += B2_im;
    
  }
}

#ifdef MULTI_GPU

int incomplete = 0; // Have all 8 contributions been computed for this site?

switch(kernel_type) { // intentional fall-through
case INTERIOR_KERNEL:
  incomplete = incomplete || (param.commDim[3] && (coord[3]==0 || coord[3]==(param.dc.X[3]-1)));
case EXTERIOR_KERNEL_T:
  incomplete = incomplete || (param.commDim[2] && (coord[2]==0 || coord[2]==(param.dc.X[2]-1)));
case EXTERIOR_KERNEL_Z:
  incomplete = incomplete || (param.commDim[1] && (coord[1]==0 || coord[1]==(param.dc.X[1]-1)));
case EXTERIOR_KERNEL_Y:
  incomplete = incomplete || (param.commDim[0] && (coord[0]==0 || coord[0]==(param.dc.X[0]-1)));
}

if (!incomplete)
#endif // MULTI_GPU
{
#ifndef TWIST_INV_DSLASH
#ifdef SPINOR_DOUBLE
  const spinorFloat a = param.a;
  const spinorFloat b = param.b;
#else
  const spinorFloat a = param.a_f;
  const spinorFloat b = param.b_f;
#endif
#endif
#ifdef DSLASH_XPAY
  READ_ACCUM(ACCUMTEX, param.sp_stride)
  
#ifndef TWIST_XPAY
#ifndef TWIST_INV_DSLASH
  //perform invert twist first:
  APPLY_TWIST_INV(-a, b, o);
#endif
  o00_re += acc00_re;
  o00_im += acc00_im;
  o01_re += acc01_re;
  o01_im += acc01_im;
  o02_re += acc02_re;
  o02_im += acc02_im;
  o10_re += acc10_re;
  o10_im += acc10_im;
  o11_re += acc11_re;
  o11_im += acc11_im;
  o12_re += acc12_re;
  o12_im += acc12_im;
  o20_re += acc20_re;
  o20_im += acc20_im;
  o21_re += acc21_re;
  o21_im += acc21_im;
  o22_re += acc22_re;
  o22_im += acc22_im;
  o30_re += acc30_re;
  o30_im += acc30_im;
  o31_re += acc31_re;
  o31_im += acc31_im;
  o32_re += acc32_re;
  o32_im += acc32_im;
#else
  APPLY_TWIST(-a, acc);
  //warning! b is unrelated to the twisted mass parameter in this case!
  
  o00_re = b*o00_re+acc00_re;
  o00_im = b*o00_im+acc00_im;
  o01_re = b*o01_re+acc01_re;
  o01_im = b*o01_im+acc01_im;
  o02_re = b*o02_re+acc02_re;
  o02_im = b*o02_im+acc02_im;
  o10_re = b*o10_re+acc10_re;
  o10_im = b*o10_im+acc10_im;
  o11_re = b*o11_re+acc11_re;
  o11_im = b*o11_im+acc11_im;
  o12_re = b*o12_re+acc12_re;
  o12_im = b*o12_im+acc12_im;
  o20_re = b*o20_re+acc20_re;
  o20_im = b*o20_im+acc20_im;
  o21_re = b*o21_re+acc21_re;
  o21_im = b*o21_im+acc21_im;
  o22_re = b*o22_re+acc22_re;
  o22_im = b*o22_im+acc22_im;
  o30_re = b*o30_re+acc30_re;
  o30_im = b*o30_im+acc30_im;
  o31_re = b*o31_re+acc31_re;
  o31_im = b*o31_im+acc31_im;
  o32_re = b*o32_re+acc32_re;
  o32_im = b*o32_im+acc32_im;
#endif//TWIST_XPAY
#else //no XPAY
#ifndef TWIST_INV_DSLASH
     APPLY_TWIST_INV(-a, b, o);
#endif
#endif
}

// write spinor field back to device memory
WRITE_SPINOR(param.sp_stride);

// undefine to prevent warning when precision is changed
#undef spinorFloat
#undef WRITE_SPINOR_SHARED
#undef READ_SPINOR_SHARED
#undef SHARED_STRIDE

#undef g00_re
#undef g00_im
#undef g01_re
#undef g01_im
#undef g02_re
#undef g02_im
#undef g10_re
#undef g10_im
#undef g11_re
#undef g11_im
#undef g12_re
#undef g12_im
#undef g20_re
#undef g20_im
#undef g21_re
#undef g21_im
#undef g22_re
#undef g22_im

#undef i00_re
#undef i00_im
#undef i01_re
#undef i01_im
#undef i02_re
#undef i02_im
#undef i10_re
#undef i10_im
#undef i11_re
#undef i11_im
#undef i12_re
#undef i12_im
#undef i20_re
#undef i20_im
#undef i21_re
#undef i21_im
#undef i22_re
#undef i22_im
#undef i30_re
#undef i30_im
#undef i31_re
#undef i31_im
#undef i32_re
#undef i32_im

#undef acc00_re
#undef acc00_im
#undef acc01_re
#undef acc01_im
#undef acc02_re
#undef acc02_im
#undef acc10_re
#undef acc10_im
#undef acc11_re
#undef acc11_im
#undef acc12_re
#undef acc12_im
#undef acc20_re
#undef acc20_im
#undef acc21_re
#undef acc21_im
#undef acc22_re
#undef acc22_im
#undef acc30_re
#undef acc30_im
#undef acc31_re
#undef acc31_im
#undef acc32_re
#undef acc32_im


#undef o00_re
#undef o00_im
#undef o01_re
#undef o01_im
#undef o02_re
#undef o02_im
#undef o10_re
#undef o10_im
#undef o11_re
#undef o11_im
#undef o12_re
#undef o12_im
#undef o20_re
#undef o20_im
#undef o21_re
#undef o21_im
#undef o22_re
#undef o22_im
#undef o30_re
#undef o30_im
#undef o31_re
#undef o31_im
#undef o32_re
#undef o32_im

#undef VOLATILE