6 return [complex(x)
for x
in a]
10 if a ==
int(a):
return `
int(a)`
14 if a == 0:
return "0i" 15 elif a == -1:
return "-i" 16 elif a == 1:
return "i" 17 else:
return fltToString(a)+
"i" 21 if re == 0
and im == 0:
return "0" 22 elif re == 0:
return imToString(im)
23 elif im == 0:
return fltToString(re)
25 im_str =
"-"+imToString(-im)
if im < 0
else "+"+imToString(im)
26 return fltToString(re)+im_str
75 return [x+y
for (x,y)
in zip(g1,g2)]
78 return [x-y
for (x,y)
in zip(g1,g2)]
98 def indentline(line):
return (
" "+line
if (line.count(
"#", 0, 1) == 0)
else line)
99 return ''.join([indentline(line)+
"\n" for line
in code.splitlines()])
102 return "{\n"+
indent(code)+
"}" 106 elif x==-1:
return "-" 107 elif x==+2:
return "+2*" 108 elif x==-2:
return "-2*" 111 return `(n/4)` +
"." + [
"x",
"y",
"z",
"w"][n%4]
114 return `(n/2)` +
"." + [
"x",
"y"][n%2]
117 def in_re(s, c):
return "i"+`s`+`c`+
"_re" 118 def in_im(s, c):
return "i"+`s`+`c`+
"_im" 119 def g_re(d, m, n):
return (
"g" if (d%2==0)
else "gT")+`m`+`n`+
"_re" 120 def g_im(d, m, n):
return (
"g" if (d%2==0)
else "gT")+`m`+`n`+
"_im" 121 def out_re(s, c):
return "o"+`s`+`c`+
"_re" 122 def out_im(s, c):
return "o"+`s`+`c`+
"_im" 123 def h1_re(h, c):
return [
"a",
"b"][h]+`c`+
"_re" 124 def h1_im(h, c):
return [
"a",
"b"][h]+`c`+
"_im" 125 def h2_re(h, c):
return [
"A",
"B"][h]+`c`+
"_re" 126 def h2_im(h, c):
return [
"A",
"B"][h]+`c`+
"_im" 127 def a_re(b, s, c):
return "a"+`(s+2*b)`+`c`+
"_re" 128 def a_im(b, s, c):
return "a"+`(s+2*b)`+`c`+
"_im" 130 def acc_re(s, c):
return "acc"+`s`+`c`+
"_re" 131 def acc_im(s, c):
return "acc"+`s`+`c`+
"_im" 133 def tmp_re(s, c):
return "tmp"+`s`+`c`+
"_re" 134 def tmp_im(s, c):
return "tmp"+`s`+`c`+
"_im" 137 if z==0:
return name+`s`+`c`+
"_re" 138 else:
return name+`s`+`c`+
"_im" 142 str +=
"// input spinor\n" 143 str +=
"#ifdef SPINOR_DOUBLE\n" 144 str +=
"#define spinorFloat double\n" 146 str +=
"#define WRITE_SPINOR_SHARED WRITE_SPINOR_SHARED_DOUBLE2\n" 147 str +=
"#define READ_SPINOR_SHARED READ_SPINOR_SHARED_DOUBLE2\n" 154 if dslash
and not pack:
161 str +=
"#define spinorFloat float\n" 163 str +=
"#define WRITE_SPINOR_SHARED WRITE_SPINOR_SHARED_FLOAT4\n" 164 str +=
"#define READ_SPINOR_SHARED READ_SPINOR_SHARED_FLOAT4\n" 170 if dslash
and not pack:
176 str +=
"#endif // SPINOR_DOUBLE\n\n" 182 str =
"// gauge link\n" 183 str +=
"#ifdef GAUGE_FLOAT2\n" 199 str +=
"#endif // GAUGE_DOUBLE\n\n" 201 str +=
"// conjugated gauge link\n" 205 str +=
"#define "+
g_re(1,m,n)+
" (+"+
g_re(0,n,m)+
")\n" 206 str +=
"#define "+
g_im(1,m,n)+
" (-"+
g_im(0,n,m)+
")\n" 216 str =
"// output spinor\n" 220 if 2*i < sharedFloats
and not sharedDslash:
221 str +=
"#define "+
out_re(s,c)+
" s["+`(2*i+0)`+
"*SHARED_STRIDE]\n" 223 str +=
"VOLATILE spinorFloat "+
out_re(s,c)+
";\n" 224 if 2*i+1 < sharedFloats
and not sharedDslash:
225 str +=
"#define "+
out_im(s,c)+
" s["+`(2*i+1)`+
"*SHARED_STRIDE]\n" 227 str +=
"VOLATILE spinorFloat "+
out_im(s,c)+
";\n" 235 prolog_str = (
"#ifdef MULTI_GPU\n\n")
238 prolog_str+= (
"// *** CUDA DSLASH ***\n\n" if not dagger
else "// *** CUDA DSLASH DAGGER ***\n\n")
239 prolog_str+=
"#define DSLASH_SHARED_FLOATS_PER_THREAD "+str(sharedFloats)+
"\n\n" 241 print "Undefined prolog" 246 #if ((CUDA_VERSION >= 4010) && (__COMPUTE_CAPABILITY__ >= 200)) // NVVM compiler 248 #else // Open64 compiler 249 #define VOLATILE volatile 254 if dslash ==
True: prolog_str+=
def_gauge()
257 if (sharedFloats > 0):
262 #define SHARED_STRIDE 16 // to avoid bank conflicts on Fermi 264 #define SHARED_STRIDE 32 // to avoid bank conflicts on Fermi 271 #define SHARED_STRIDE 8 // to avoid bank conflicts on G80 and GT200 273 #define SHARED_STRIDE 16 // to avoid bank conflicts on G80 and GT200 279 if sharedFloats > 0
and not sharedDslash:
282 extern __shared__ char s_data[]; 288 VOLATILE spinorFloat *s = (spinorFloat*)s_data + DSLASH_SHARED_FLOATS_PER_THREAD*SHARED_STRIDE*(threadIdx.x/SHARED_STRIDE) 289 + (threadIdx.x % SHARED_STRIDE); 296 #include "read_gauge.h" 297 #include "io_spinor.h" 302 #if (DD_PREC==2) // half precision 304 #endif // half precision 312 sid = blockIdx.x*blockDim.x + threadIdx.x; 313 if (sid >= param.threads) return; 316 int dim = dimFromFaceIndex(sid, param); // sid is also modified 318 const int face_volume = ((param.threadDimMapUpper[dim] - param.threadDimMapLower[dim]) >> 1); 319 const int face_num = (sid >= face_volume); // is this thread updating face 0 or 1 320 int face_idx = sid - face_num*face_volume; // index into the respective face 324 coordsFromFaceIndex<4,QUDA_4D_PC,0,1>(X, sid, coord, face_idx, face_num, param); 327 coordsFromFaceIndex<4,QUDA_4D_PC,1,1>(X, sid, coord, face_idx, face_num, param); 330 coordsFromFaceIndex<4,QUDA_4D_PC,2,1>(X, sid, coord, face_idx, face_num, param); 333 coordsFromFaceIndex<4,QUDA_4D_PC,3,1>(X, sid, coord, face_idx, face_num, param); 339 for(int dir=0; dir<4; ++dir){ 340 active = active || isActive(dim,dir,+1,coord,param.commDim,param.dc.X); 345 READ_INTERMEDIATE_SPINOR(INTERTEX, param.sp_stride, sid, sid); 361 def gen(dir, pack_only=False):
362 projIdx = dir
if not dagger
else dir + (1 - 2*(dir%2))
365 return projectors[projIdx][4*i+j]
372 return (1, proj(i,1))
374 return (0, proj(i,0))
376 boundary = [
"coord[0]==(param.dc.X[0]-1)",
"coord[0]==0",
"coord[1]==(param.dc.X[1]-1)",
"coord[1]==0",
"coord[2]==(param.dc.X[2]-1)",
"coord[2]==0",
"coord[3]==(param.dc.X[3]-1)",
"coord[3]==0"]
377 interior = [
"coord[0]<(param.dc.X[0]-1)",
"coord[0]>0",
"coord[1]<(param.dc.X[1]-1)",
"coord[1]>0",
"coord[2]<(param.dc.X[2]-1)",
"coord[2]>0",
"coord[3]<(param.dc.X[3]-1)",
"coord[3]>0"]
378 offset = [
"+1",
"-1",
"+1",
"-1",
"+1",
"-1",
"+1",
"-1"];
379 dim = [
"X",
"Y",
"Z",
"T"]
382 sp_idx = [
"X+1",
"X-1",
"X+param.dc.X[0]",
"X-param.dc.X[0]",
"X+param.dc.X2X1",
"X-param.dc.X2X1",
"X+param.dc.X3X2X1",
"X-param.dc.X3X2X1"]
385 sp_idx_wrap = [
"X-(param.dc.X[0]-1)",
"X+(param.dc.X[0]-1)",
"X-param.dc.X2X1mX1",
"X+param.dc.X2X1mX1",
"X-param.dc.X3X2X1mX2X1",
"X+param.dc.X3X2X1mX2X1",
386 "X-param.dc.X4X3X2X1mX3X2X1",
"X+param.dc.X4X3X2X1mX3X2X1"]
390 cond +=
"if (isActive(dim," + `dir/2` +
"," + offset[dir] +
",coord,param.commDim,param.dc.X) && " +boundary[dir]+
" )\n" 395 projName =
"P"+`dir/2`+[
"-",
"+"][projIdx%2]
396 str +=
"// Projector "+projName+
"\n" 397 for l
in projStr.splitlines():
401 str +=
"faceIndexFromCoords<4,1>(face_idx,coord," + `dir/2` +
",param);\n" 402 str +=
"const int sp_idx = face_idx + param.ghostOffset[" + `dir/2` +
"][" + `1-dir%2` +
"];\n" 405 str +=
"#if (DD_PREC==2)\n" 406 str +=
" sp_norm_idx = face_idx + " 407 str +=
"param.ghostNormOffset[" + `dir/2` +
"][" + `1-dir%2` +
"];\n" 414 str +=
"const int ga_idx = sid;\n" 416 str +=
"const int ga_idx = param.dc.Vh+face_idx;\n" 420 row_cnt = ([0,0,0,0])
425 if re != 0
or im != 0:
427 row_cnt[0] += row_cnt[1]
428 row_cnt[2] += row_cnt[3]
431 for h
in range(0, 2):
432 for c
in range(0, 3):
433 decl_half +=
"spinorFloat "+
h1_re(h,c)+
", "+
h1_im(h,c)+
";\n";
436 load_spinor =
"// read spinor from device memory\n" 438 load_spinor +=
"#ifdef TWIST_INV_DSLASH\n" 439 load_spinor +=
"#ifdef SPINOR_DOUBLE\n" 440 load_spinor +=
"const spinorFloat a = param.a;\n" 441 load_spinor +=
"const spinorFloat b = param.b;\n" 442 load_spinor +=
"#else\n" 443 load_spinor +=
"const spinorFloat a = param.a_f;\n" 444 load_spinor +=
"const spinorFloat b = param.b_f;\n" 445 load_spinor +=
"#endif\n" 446 load_spinor +=
"#endif\n" 450 load_spinor +=
"#ifndef TWIST_INV_DSLASH\n" 451 load_spinor +=
"READ_SPINOR_DOWN(SPINORTEX, param.sp_stride, sp_idx, sp_idx);\n" 452 load_spinor +=
"#else\n" 453 load_spinor +=
"READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);\n" 455 load_spinor +=
"APPLY_TWIST_INV( a, b, i);\n" 457 load_spinor +=
"APPLY_TWIST_INV(-a, b, i);\n" 459 load_spinor +=
"#endif\n" 460 elif row_cnt[2] == 0:
462 load_spinor +=
"#ifndef TWIST_INV_DSLASH\n" 463 load_spinor +=
"READ_SPINOR_UP(SPINORTEX, param.sp_stride, sp_idx, sp_idx);\n" 464 load_spinor +=
"#else\n" 465 load_spinor +=
"READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);\n" 467 load_spinor +=
"APPLY_TWIST_INV( a, b, i);\n" 469 load_spinor +=
"APPLY_TWIST_INV(-a, b, i);\n" 471 load_spinor +=
"#endif\n" 473 load_spinor +=
"READ_SPINOR(SPINORTEX, param.sp_stride, sp_idx, sp_idx);\n" 475 load_spinor +=
"#ifdef TWIST_INV_DSLASH\n" 477 load_spinor +=
"APPLY_TWIST_INV( a, b, i);\n" 479 load_spinor +=
"APPLY_TWIST_INV(-a, b, i);\n" 481 load_spinor +=
"#endif\n" 485 load_half +=
"const int sp_stride_pad = param.dc.ghostFace[" + `dir/2` +
"];\n" 490 if dir >= 6: load_half +=
"const int t_proj_scale = TPROJSCALE;\n" 493 load_half +=
"// read half spinor from device memory\n" 497 load_half +=
"READ_SPINOR_GHOST(GHOSTSPINORTEX, sp_stride_pad, sp_idx, sp_norm_idx, "+`dir`+
");\n\n" 500 load_gauge =
"// read gauge matrix from device memory\n" 501 load_gauge +=
"READ_GAUGE_MATRIX(G, GAUGE"+`dir%2`+
"TEX, "+`dir`+
", ga_idx, param.gauge_stride);\n\n" 503 reconstruct_gauge =
"// reconstruct gauge matrix\n" 504 reconstruct_gauge +=
"RECONSTRUCT_GAUGE_MATRIX("+`dir`+
");\n\n" 506 project =
"// project spinor into half spinors\n" 507 for h
in range(0, 2):
508 for c
in range(0, 3):
511 for s
in range(0, 4):
514 if re==0
and im==0: ()
522 for s
in range(0, 4):
523 re = proj(h+2,s).real
524 im = proj(h+2,s).imag
525 if re==0
and im==0: ()
533 project +=
h1_re(h,c)+
" = "+strRe+
";\n" 534 project +=
h1_im(h,c)+
" = "+strIm+
";\n" 537 """// store spinor into shared memory 538 WRITE_SPINOR_SHARED(threadIdx.x, threadIdx.y, threadIdx.z, i);\n 542 """// load spinor from shared memory 543 int tx = (threadIdx.x > 0) ? threadIdx.x-1 : blockDim.x-1; 545 READ_SPINOR_SHARED(tx, threadIdx.y, threadIdx.z);\n 549 """// load spinor from shared memory 550 int tx = (threadIdx.x + blockDim.x - ((x1+1)&1) ) % blockDim.x; 551 int ty = (threadIdx.y < blockDim.y - 1) ? threadIdx.y + 1 : 0; 552 READ_SPINOR_SHARED(tx, ty, threadIdx.z);\n 556 """// load spinor from shared memory 557 int tx = (threadIdx.x + blockDim.x - ((x1+1)&1)) % blockDim.x; 558 int ty = (threadIdx.y > 0) ? threadIdx.y - 1 : blockDim.y - 1; 559 READ_SPINOR_SHARED(tx, ty, threadIdx.z);\n 563 """// load spinor from shared memory 564 int tx = (threadIdx.x + blockDim.x - ((x1+1)&1) ) % blockDim.x; 565 int tz = (threadIdx.z < blockDim.z - 1) ? threadIdx.z + 1 : 0; 566 READ_SPINOR_SHARED(tx, threadIdx.y, tz);\n 570 """// load spinor from shared memory 571 int tx = (threadIdx.x + blockDim.x - ((x1+1)&1)) % blockDim.x; 572 int tz = (threadIdx.z > 0) ? threadIdx.z - 1 : blockDim.z - 1; 573 READ_SPINOR_SHARED(tx, threadIdx.y, tz);\n 578 for h
in range(0, 2):
579 for c
in range(0, 3):
580 copy_half +=
h1_re(h,c)+
" = "+(
"t_proj_scale*" if (dir >= 6)
else "")+
in_re(h,c)+
"; " 581 copy_half +=
h1_im(h,c)+
" = "+(
"t_proj_scale*" if (dir >= 6)
else "")+
in_im(h,c)+
";\n" 586 prep_half += load_half
587 prep_half += copy_half
589 ident =
"// identity gauge matrix\n" 592 ident +=
"spinorFloat "+
h2_re(h,m)+
" = " +
h1_re(h,m) +
"; " 593 ident +=
"spinorFloat "+
h2_im(h,m)+
" = " +
h1_im(h,m) +
";\n" 598 mult +=
"// multiply row "+`m`+
"\n" 600 re =
"spinorFloat "+
h2_re(h,m)+
" = 0;\n" 601 im =
"spinorFloat "+
h2_im(h,m)+
" = 0;\n" 603 re +=
h2_re(h,m) +
" += " +
g_re(dir,m,c) +
" * "+
h1_re(h,c)+
";\n" 604 re +=
h2_re(h,m) +
" -= " +
g_im(dir,m,c) +
" * "+
h1_im(h,c)+
";\n" 605 im +=
h2_im(h,m) +
" += " +
g_re(dir,m,c) +
" * "+
h1_im(h,c)+
";\n" 606 im +=
h2_im(h,m) +
" += " +
g_im(dir,m,c) +
" * "+
h1_re(h,c)+
";\n" 618 reconstruct +=
out_re(h_out, m) +
" += " +
h2_re(h,m) +
";\n" 619 reconstruct +=
out_im(h_out, m) +
" += " +
h2_im(h,m) +
";\n" 625 if im == 0
and re == 0: ()
627 reconstruct +=
out_re(s, m) +
" " +
sign(re) +
"= " +
h2_re(h,m) +
";\n" 628 reconstruct +=
out_im(s, m) +
" " +
sign(re) +
"= " +
h2_im(h,m) +
";\n" 630 reconstruct +=
out_re(s, m) +
" " +
sign(-im) +
"= " +
h2_im(h,m) +
";\n" 631 reconstruct +=
out_im(s, m) +
" " +
sign(+im) +
"= " +
h2_re(h,m) +
";\n" 636 str +=
"if (param.gauge_fixed && ga_idx < param.dc.X4X3X2X1hmX3X2X1h)\n" 637 str +=
block(decl_half + prep_half + ident + reconstruct)
639 str +=
block(decl_half + prep_half + load_gauge + reconstruct_gauge + mult + reconstruct)
641 str += decl_half + prep_half + load_gauge + reconstruct_gauge + mult + reconstruct
644 out = load_spinor + decl_half + project
645 out = out.replace(
"sp_idx",
"idx")
648 return cond +
block(str)+
"\n\n" 654 if z==0:
return out_re(s,c)
657 if z==0:
return in_re(s,c)
658 else:
return in_im(s,c)
663 str +=
"#ifndef TWIST_INV_DSLASH\n" 664 str +=
"#ifdef SPINOR_DOUBLE\n" 665 str +=
"const spinorFloat a = param.a;\n" 666 str +=
"const spinorFloat b = param.b;\n" 668 str +=
"const spinorFloat a = param.a_f;\n" 669 str +=
"const spinorFloat b = param.b_f;\n" 673 str +=
"#ifdef DSLASH_XPAY\n" 674 str +=
"READ_ACCUM(ACCUMTEX, param.sp_stride)\n\n" 676 str +=
"#ifndef TWIST_XPAY\n" 677 str +=
"#ifndef TWIST_INV_DSLASH\n" 678 str +=
"//perform invert twist first:\n" 680 str +=
"APPLY_TWIST_INV( a, b, o);\n" 682 str +=
"APPLY_TWIST_INV(-a, b, o);\n" 691 str +=
"APPLY_TWIST( a, acc);\n" 693 str +=
"APPLY_TWIST(-a, acc);\n" 694 str +=
"//warning! b is unrelated to the twisted mass parameter in this case!\n\n" 700 str +=
"#endif//TWIST_XPAY\n" 701 str +=
"#else //no XPAY\n" 702 str +=
"#ifndef TWIST_INV_DSLASH\n" 704 str +=
" APPLY_TWIST_INV( a, b, o);\n" 706 str +=
" APPLY_TWIST_INV(-a, b, o);\n" 717 str +=
block( block_str )
720 str +=
"// write spinor field back to device memory\n" 721 str +=
"WRITE_SPINOR(param.sp_stride);\n\n" 723 str +=
"// undefine to prevent warning when precision is changed\n" 724 str +=
"#undef spinorFloat\n" 726 str +=
"#undef WRITE_SPINOR_SHARED\n" 727 str +=
"#undef READ_SPINOR_SHARED\n" 728 if sharedFloats > 0: str +=
"#undef SHARED_STRIDE\n\n" 734 str +=
"#undef "+
g_re(0,m,n)+
"\n" 735 str +=
"#undef "+
g_im(0,m,n)+
"\n" 741 str +=
"#undef "+
in_re(s,c)+
"\n" 742 str +=
"#undef "+
in_im(s,c)+
"\n" 749 str +=
"#undef "+
acc_re(s,c)+
"\n" 750 str +=
"#undef "+
acc_im(s,c)+
"\n" 758 if 2*i < sharedFloats:
759 str +=
"#undef "+
out_re(s,c)+
"\n" 760 if 2*i+1 < sharedFloats:
761 str +=
"#undef "+
out_im(s,c)+
"\n" 764 str +=
"#undef VOLATILE\n\n" 766 str +=
"#endif // MULTI_GPU\n" 774 str +=
"switch(dim) {\n" 775 for dim
in range(0,4):
776 str +=
"case "+`dim`+
":\n" 777 proj =
gen(2*dim+facenum, pack_only=
True)
779 proj +=
"// write half spinor back to device memory\n" 780 proj +=
"WRITE_HALF_SPINOR(face_volume, face_idx);\n" 787 assert (sharedFloats == 0)
790 str +=
"#include \"io_spinor.h\"\n\n" 792 str +=
"if (face_num) " 798 str +=
"// undefine to prevent warning when precision is changed\n" 799 str +=
"#undef spinorFloat\n" 800 str +=
"#undef SHARED_STRIDE\n\n" 805 str +=
"#undef "+
in_re(s,c)+
"\n" 806 str +=
"#undef "+
in_im(s,c)+
"\n" 818 print "Generating dslash kernel for sm" + str(arch/10)
841 print "Shared floats set to " + str(sharedFloats)
846 filename =
'dslash_core/tm_fused_exterior_dslash_' + name +
'_core.h' 847 print sys.argv[0] +
": generating " + filename;
848 f = open(filename,
'w')
853 filename =
'dslash_core/tm_fused_exterior_dslash_dagger_' + name +
'_core.h' 854 print sys.argv[0] +
": generating " + filename +
"\n";
855 f = open(filename,
'w')
def input_spinor(s, c, z)
def complexify(a)
complex numbers ######################################################################## ...
def gen(dir, pack_only=False)
def indent(code)
code generation ######################################################################## ...
def generate_dslash_kernels(arch)
def spinor(name, s, c, z)