libgfortran/m4/matmul_internal.m4

   1 `void
   2 'matmul_name` ('rtype` * const restrict retarray,
   3         'rtype` * const restrict a, 'rtype` * const restrict b, int try_blas,
   4         int blas_limit, blas_call gemm)
   5 {
   6   const 'rtype_name` * restrict abase;
   7   const 'rtype_name` * restrict bbase;
   8   'rtype_name` * restrict dest;
   9
  10   index_type rxstride, rystride, axstride, aystride, bxstride, bystride;
  11   index_type x, y, n, count, xcount, ycount;
  12
  13   assert (GFC_DESCRIPTOR_RANK (a) == 2
  14           || GFC_DESCRIPTOR_RANK (b) == 2);
  15
  16 /* C[xcount,ycount] = A[xcount, count] * B[count,ycount]
  17
  18    Either A or B (but not both) can be rank 1:
  19
  20    o One-dimensional argument A is implicitly treated as a row matrix
  21      dimensioned [1,count], so xcount=1.
  22
  23    o One-dimensional argument B is implicitly treated as a column matrix
  24      dimensioned [count, 1], so ycount=1.
  25 */
  26
  27   if (retarray->base_addr == NULL)
  28     {
  29       if (GFC_DESCRIPTOR_RANK (a) == 1)
  30         {
  31           GFC_DIMENSION_SET(retarray->dim[0], 0,
  32                             GFC_DESCRIPTOR_EXTENT(b,1) - 1, 1);
  33         }
  34       else if (GFC_DESCRIPTOR_RANK (b) == 1)
  35         {
  36           GFC_DIMENSION_SET(retarray->dim[0], 0,
  37                             GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
  38         }
  39       else
  40         {
  41           GFC_DIMENSION_SET(retarray->dim[0], 0,
  42                             GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
  43
  44           GFC_DIMENSION_SET(retarray->dim[1], 0,
  45                             GFC_DESCRIPTOR_EXTENT(b,1) - 1,
  46                             GFC_DESCRIPTOR_EXTENT(retarray,0));
  47         }
  48
  49       retarray->base_addr
  50         = xmallocarray (size0 ((array_t *) retarray), sizeof ('rtype_name`));
  51       retarray->offset = 0;
  52     }
  53   else if (unlikely (compile_options.bounds_check))
  54     {
  55       index_type ret_extent, arg_extent;
  56
  57       if (GFC_DESCRIPTOR_RANK (a) == 1)
  58         {
  59           arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
  60           ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
  61           if (arg_extent != ret_extent)
  62             runtime_error ("Incorrect extent in return array in"
  63                            " MATMUL intrinsic: is %ld, should be %ld",
  64                            (long int) ret_extent, (long int) arg_extent);
  65         }
  66       else if (GFC_DESCRIPTOR_RANK (b) == 1)
  67         {
  68           arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
  69           ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
  70           if (arg_extent != ret_extent)
  71             runtime_error ("Incorrect extent in return array in"
  72                            " MATMUL intrinsic: is %ld, should be %ld",
  73                            (long int) ret_extent, (long int) arg_extent);
  74         }
  75       else
  76         {
  77           arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
  78           ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
  79           if (arg_extent != ret_extent)
  80             runtime_error ("Incorrect extent in return array in"
  81                            " MATMUL intrinsic for dimension 1:"
  82                            " is %ld, should be %ld",
  83                            (long int) ret_extent, (long int) arg_extent);
  84
  85           arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
  86           ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,1);
  87           if (arg_extent != ret_extent)
  88             runtime_error ("Incorrect extent in return array in"
  89                            " MATMUL intrinsic for dimension 2:"
  90                            " is %ld, should be %ld",
  91                            (long int) ret_extent, (long int) arg_extent);
  92         }
  93     }
  94 '
  95 sinclude(`matmul_asm_'rtype_code`.m4')dnl
  96 `
  97   if (GFC_DESCRIPTOR_RANK (retarray) == 1)
  98     {
  99       /* One-dimensional result may be addressed in the code below
 100          either as a row or a column matrix. We want both cases to
 101          work. */
 102       rxstride = rystride = GFC_DESCRIPTOR_STRIDE(retarray,0);
 103     }
 104   else
 105     {
 106       rxstride = GFC_DESCRIPTOR_STRIDE(retarray,0);
 107       rystride = GFC_DESCRIPTOR_STRIDE(retarray,1);
 108     }
 109
 110
 111   if (GFC_DESCRIPTOR_RANK (a) == 1)
 112     {
 113       /* Treat it as a a row matrix A[1,count]. */
 114       axstride = GFC_DESCRIPTOR_STRIDE(a,0);
 115       aystride = 1;
 116
 117       xcount = 1;
 118       count = GFC_DESCRIPTOR_EXTENT(a,0);
 119     }
 120   else
 121     {
 122       axstride = GFC_DESCRIPTOR_STRIDE(a,0);
 123       aystride = GFC_DESCRIPTOR_STRIDE(a,1);
 124
 125       count = GFC_DESCRIPTOR_EXTENT(a,1);
 126       xcount = GFC_DESCRIPTOR_EXTENT(a,0);
 127     }
 128
 129   if (count != GFC_DESCRIPTOR_EXTENT(b,0))
 130     {
 131       if (count > 0 || GFC_DESCRIPTOR_EXTENT(b,0) > 0)
 132         runtime_error ("dimension of array B incorrect in MATMUL intrinsic");
 133     }
 134
 135   if (GFC_DESCRIPTOR_RANK (b) == 1)
 136     {
 137       /* Treat it as a column matrix B[count,1] */
 138       bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
 139
 140       /* bystride should never be used for 1-dimensional b.
 141          The value is only used for calculation of the
 142          memory by the buffer.  */
 143       bystride = 256;
 144       ycount = 1;
 145     }
 146   else
 147     {
 148       bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
 149       bystride = GFC_DESCRIPTOR_STRIDE(b,1);
 150       ycount = GFC_DESCRIPTOR_EXTENT(b,1);
 151     }
 152
 153   abase = a->base_addr;
 154   bbase = b->base_addr;
 155   dest = retarray->base_addr;
 156
 157   /* Now that everything is set up, we perform the multiplication
 158      itself.  */
 159
 160 #define POW3(x) (((float) (x)) * ((float) (x)) * ((float) (x)))
 161 #define min(a,b) ((a) <= (b) ? (a) : (b))
 162 #define max(a,b) ((a) >= (b) ? (a) : (b))
 163
 164   if (try_blas && rxstride == 1 && (axstride == 1 || aystride == 1)
 165       && (bxstride == 1 || bystride == 1)
 166       && (((float) xcount) * ((float) ycount) * ((float) count)
 167           > POW3(blas_limit)))
 168     {
 169       const int m = xcount, n = ycount, k = count, ldc = rystride;
 170       const 'rtype_name` one = 1, zero = 0;
 171       const int lda = (axstride == 1) ? aystride : axstride,
 172                 ldb = (bxstride == 1) ? bystride : bxstride;
 173
 174       if (lda > 0 && ldb > 0 && ldc > 0 && m > 1 && n > 1 && k > 1)
 175         {
 176           assert (gemm != NULL);
 177           gemm (axstride == 1 ? "N" : "T", bxstride == 1 ? "N" : "T", &m,
 178                 &n, &k, &one, abase, &lda, bbase, &ldb, &zero, dest,
 179                 &ldc, 1, 1);
 180           return;
 181         }
 182     }
 183
 184   if (rxstride == 1 && axstride == 1 && bxstride == 1)
 185     {
 186       /* This block of code implements a tuned matmul, derived from
 187          Superscalar GEMM-based level 3 BLAS,  Beta version 0.1
 188
 189                Bo Kagstrom and Per Ling
 190                Department of Computing Science
 191                Umea University
 192                S-901 87 Umea, Sweden
 193
 194          from netlib.org, translated to C, and modified for matmul.m4.  */
 195
 196       const 'rtype_name` *a, *b;
 197       'rtype_name` *c;
 198       const index_type m = xcount, n = ycount, k = count;
 199
 200       /* System generated locals */
 201       index_type a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset,
 202                  i1, i2, i3, i4, i5, i6;
 203
 204       /* Local variables */
 205       'rtype_name` f11, f12, f21, f22, f31, f32, f41, f42,
 206                  f13, f14, f23, f24, f33, f34, f43, f44;
 207       index_type i, j, l, ii, jj, ll;
 208       index_type isec, jsec, lsec, uisec, ujsec, ulsec;
 209       'rtype_name` *t1;
 210
 211       a = abase;
 212       b = bbase;
 213       c = retarray->base_addr;
 214
 215       /* Parameter adjustments */
 216       c_dim1 = rystride;
 217       c_offset = 1 + c_dim1;
 218       c -= c_offset;
 219       a_dim1 = aystride;
 220       a_offset = 1 + a_dim1;
 221       a -= a_offset;
 222       b_dim1 = bystride;
 223       b_offset = 1 + b_dim1;
 224       b -= b_offset;
 225
 226       /* Empty c first.  */
 227       for (j=1; j<=n; j++)
 228         for (i=1; i<=m; i++)
 229           c[i + j * c_dim1] = ('rtype_name`)0;
 230
 231       /* Early exit if possible */
 232       if (m == 0 || n == 0 || k == 0)
 233         return;
 234
 235       /* Adjust size of t1 to what is needed.  */
 236       index_type t1_dim;
 237       t1_dim = (a_dim1 - (ycount > 1)) * 256 + b_dim1;
 238       if (t1_dim > 65536)
 239         t1_dim = 65536;
 240
 241       t1 = malloc (t1_dim * sizeof('rtype_name`));
 242
 243       /* Start turning the crank. */
 244       i1 = n;
 245       for (jj = 1; jj <= i1; jj += 512)
 246         {
 247           /* Computing MIN */
 248           i2 = 512;
 249           i3 = n - jj + 1;
 250           jsec = min(i2,i3);
 251           ujsec = jsec - jsec % 4;
 252           i2 = k;
 253           for (ll = 1; ll <= i2; ll += 256)
 254             {
 255               /* Computing MIN */
 256               i3 = 256;
 257               i4 = k - ll + 1;
 258               lsec = min(i3,i4);
 259               ulsec = lsec - lsec % 2;
 260
 261               i3 = m;
 262               for (ii = 1; ii <= i3; ii += 256)
 263                 {
 264                   /* Computing MIN */
 265                   i4 = 256;
 266                   i5 = m - ii + 1;
 267                   isec = min(i4,i5);
 268                   uisec = isec - isec % 2;
 269                   i4 = ll + ulsec - 1;
 270                   for (l = ll; l <= i4; l += 2)
 271                     {
 272                       i5 = ii + uisec - 1;
 273                       for (i = ii; i <= i5; i += 2)
 274                         {
 275                           t1[l - ll + 1 + ((i - ii + 1) << 8) - 257] =
 276                                         a[i + l * a_dim1];
 277                           t1[l - ll + 2 + ((i - ii + 1) << 8) - 257] =
 278                                         a[i + (l + 1) * a_dim1];
 279                           t1[l - ll + 1 + ((i - ii + 2) << 8) - 257] =
 280                                         a[i + 1 + l * a_dim1];
 281                           t1[l - ll + 2 + ((i - ii + 2) << 8) - 257] =
 282                                         a[i + 1 + (l + 1) * a_dim1];
 283                         }
 284                       if (uisec < isec)
 285                         {
 286                           t1[l - ll + 1 + (isec << 8) - 257] =
 287                                     a[ii + isec - 1 + l * a_dim1];
 288                           t1[l - ll + 2 + (isec << 8) - 257] =
 289                                     a[ii + isec - 1 + (l + 1) * a_dim1];
 290                         }
 291                     }
 292                   if (ulsec < lsec)
 293                     {
 294                       i4 = ii + isec - 1;
 295                       for (i = ii; i<= i4; ++i)
 296                         {
 297                           t1[lsec + ((i - ii + 1) << 8) - 257] =
 298                                     a[i + (ll + lsec - 1) * a_dim1];
 299                         }
 300                     }
 301
 302                   uisec = isec - isec % 4;
 303                   i4 = jj + ujsec - 1;
 304                   for (j = jj; j <= i4; j += 4)
 305                     {
 306                       i5 = ii + uisec - 1;
 307                       for (i = ii; i <= i5; i += 4)
 308                         {
 309                           f11 = c[i + j * c_dim1];
 310                           f21 = c[i + 1 + j * c_dim1];
 311                           f12 = c[i + (j + 1) * c_dim1];
 312                           f22 = c[i + 1 + (j + 1) * c_dim1];
 313                           f13 = c[i + (j + 2) * c_dim1];
 314                           f23 = c[i + 1 + (j + 2) * c_dim1];
 315                           f14 = c[i + (j + 3) * c_dim1];
 316                           f24 = c[i + 1 + (j + 3) * c_dim1];
 317                           f31 = c[i + 2 + j * c_dim1];
 318                           f41 = c[i + 3 + j * c_dim1];
 319                           f32 = c[i + 2 + (j + 1) * c_dim1];
 320                           f42 = c[i + 3 + (j + 1) * c_dim1];
 321                           f33 = c[i + 2 + (j + 2) * c_dim1];
 322                           f43 = c[i + 3 + (j + 2) * c_dim1];
 323                           f34 = c[i + 2 + (j + 3) * c_dim1];
 324                           f44 = c[i + 3 + (j + 3) * c_dim1];
 325                           i6 = ll + lsec - 1;
 326                           for (l = ll; l <= i6; ++l)
 327                             {
 328                               f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
 329                                       * b[l + j * b_dim1];
 330                               f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
 331                                       * b[l + j * b_dim1];
 332                               f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
 333                                       * b[l + (j + 1) * b_dim1];
 334                               f22 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
 335                                       * b[l + (j + 1) * b_dim1];
 336                               f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
 337                                       * b[l + (j + 2) * b_dim1];
 338                               f23 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
 339                                       * b[l + (j + 2) * b_dim1];
 340                               f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
 341                                       * b[l + (j + 3) * b_dim1];
 342                               f24 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
 343                                       * b[l + (j + 3) * b_dim1];
 344                               f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
 345                                       * b[l + j * b_dim1];
 346                               f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
 347                                       * b[l + j * b_dim1];
 348                               f32 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
 349                                       * b[l + (j + 1) * b_dim1];
 350                               f42 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
 351                                       * b[l + (j + 1) * b_dim1];
 352                               f33 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
 353                                       * b[l + (j + 2) * b_dim1];
 354                               f43 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
 355                                       * b[l + (j + 2) * b_dim1];
 356                               f34 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
 357                                       * b[l + (j + 3) * b_dim1];
 358                               f44 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
 359                                       * b[l + (j + 3) * b_dim1];
 360                             }
 361                           c[i + j * c_dim1] = f11;
 362                           c[i + 1 + j * c_dim1] = f21;
 363                           c[i + (j + 1) * c_dim1] = f12;
 364                           c[i + 1 + (j + 1) * c_dim1] = f22;
 365                           c[i + (j + 2) * c_dim1] = f13;
 366                           c[i + 1 + (j + 2) * c_dim1] = f23;
 367                           c[i + (j + 3) * c_dim1] = f14;
 368                           c[i + 1 + (j + 3) * c_dim1] = f24;
 369                           c[i + 2 + j * c_dim1] = f31;
 370                           c[i + 3 + j * c_dim1] = f41;
 371                           c[i + 2 + (j + 1) * c_dim1] = f32;
 372                           c[i + 3 + (j + 1) * c_dim1] = f42;
 373                           c[i + 2 + (j + 2) * c_dim1] = f33;
 374                           c[i + 3 + (j + 2) * c_dim1] = f43;
 375                           c[i + 2 + (j + 3) * c_dim1] = f34;
 376                           c[i + 3 + (j + 3) * c_dim1] = f44;
 377                         }
 378                       if (uisec < isec)
 379                         {
 380                           i5 = ii + isec - 1;
 381                           for (i = ii + uisec; i <= i5; ++i)
 382                             {
 383                               f11 = c[i + j * c_dim1];
 384                               f12 = c[i + (j + 1) * c_dim1];
 385                               f13 = c[i + (j + 2) * c_dim1];
 386                               f14 = c[i + (j + 3) * c_dim1];
 387                               i6 = ll + lsec - 1;
 388                               for (l = ll; l <= i6; ++l)
 389                                 {
 390                                   f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 391                                           257] * b[l + j * b_dim1];
 392                                   f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 393                                           257] * b[l + (j + 1) * b_dim1];
 394                                   f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 395                                           257] * b[l + (j + 2) * b_dim1];
 396                                   f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 397                                           257] * b[l + (j + 3) * b_dim1];
 398                                 }
 399                               c[i + j * c_dim1] = f11;
 400                               c[i + (j + 1) * c_dim1] = f12;
 401                               c[i + (j + 2) * c_dim1] = f13;
 402                               c[i + (j + 3) * c_dim1] = f14;
 403                             }
 404                         }
 405                     }
 406                   if (ujsec < jsec)
 407                     {
 408                       i4 = jj + jsec - 1;
 409                       for (j = jj + ujsec; j <= i4; ++j)
 410                         {
 411                           i5 = ii + uisec - 1;
 412                           for (i = ii; i <= i5; i += 4)
 413                             {
 414                               f11 = c[i + j * c_dim1];
 415                               f21 = c[i + 1 + j * c_dim1];
 416                               f31 = c[i + 2 + j * c_dim1];
 417                               f41 = c[i + 3 + j * c_dim1];
 418                               i6 = ll + lsec - 1;
 419                               for (l = ll; l <= i6; ++l)
 420                                 {
 421                                   f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 422                                           257] * b[l + j * b_dim1];
 423                                   f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) -
 424                                           257] * b[l + j * b_dim1];
 425                                   f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) -
 426                                           257] * b[l + j * b_dim1];
 427                                   f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) -
 428                                           257] * b[l + j * b_dim1];
 429                                 }
 430                               c[i + j * c_dim1] = f11;
 431                               c[i + 1 + j * c_dim1] = f21;
 432                               c[i + 2 + j * c_dim1] = f31;
 433                               c[i + 3 + j * c_dim1] = f41;
 434                             }
 435                           i5 = ii + isec - 1;
 436                           for (i = ii + uisec; i <= i5; ++i)
 437                             {
 438                               f11 = c[i + j * c_dim1];
 439                               i6 = ll + lsec - 1;
 440                               for (l = ll; l <= i6; ++l)
 441                                 {
 442                                   f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
 443                                           257] * b[l + j * b_dim1];
 444                                 }
 445                               c[i + j * c_dim1] = f11;
 446                             }
 447                         }
 448                     }
 449                 }
 450             }
 451         }
 452       free(t1);
 453       return;
 454     }
 455   else if (rxstride == 1 && aystride == 1 && bxstride == 1)
 456     {
 457       if (GFC_DESCRIPTOR_RANK (a) != 1)
 458         {
 459           const 'rtype_name` *restrict abase_x;
 460           const 'rtype_name` *restrict bbase_y;
 461           'rtype_name` *restrict dest_y;
 462           'rtype_name` s;
 463
 464           for (y = 0; y < ycount; y++)
 465             {
 466               bbase_y = &bbase[y*bystride];
 467               dest_y = &dest[y*rystride];
 468               for (x = 0; x < xcount; x++)
 469                 {
 470                   abase_x = &abase[x*axstride];
 471                   s = ('rtype_name`) 0;
 472                   for (n = 0; n < count; n++)
 473                     s += abase_x[n] * bbase_y[n];
 474                   dest_y[x] = s;
 475                 }
 476             }
 477         }
 478       else
 479         {
 480           const 'rtype_name` *restrict bbase_y;
 481           'rtype_name` s;
 482
 483           for (y = 0; y < ycount; y++)
 484             {
 485               bbase_y = &bbase[y*bystride];
 486               s = ('rtype_name`) 0;
 487               for (n = 0; n < count; n++)
 488                 s += abase[n*axstride] * bbase_y[n];
 489               dest[y*rystride] = s;
 490             }
 491         }
 492     }
 493   else if (axstride < aystride)
 494     {
 495       for (y = 0; y < ycount; y++)
 496         for (x = 0; x < xcount; x++)
 497           dest[x*rxstride + y*rystride] = ('rtype_name`)0;
 498
 499       for (y = 0; y < ycount; y++)
 500         for (n = 0; n < count; n++)
 501           for (x = 0; x < xcount; x++)
 502             /* dest[x,y] += a[x,n] * b[n,y] */
 503             dest[x*rxstride + y*rystride] +=
 504                                         abase[x*axstride + n*aystride] *
 505                                         bbase[n*bxstride + y*bystride];
 506     }
 507   else if (GFC_DESCRIPTOR_RANK (a) == 1)
 508     {
 509       const 'rtype_name` *restrict bbase_y;
 510       'rtype_name` s;
 511
 512       for (y = 0; y < ycount; y++)
 513         {
 514           bbase_y = &bbase[y*bystride];
 515           s = ('rtype_name`) 0;
 516           for (n = 0; n < count; n++)
 517             s += abase[n*axstride] * bbase_y[n*bxstride];
 518           dest[y*rxstride] = s;
 519         }
 520     }
 521   else
 522     {
 523       const 'rtype_name` *restrict abase_x;
 524       const 'rtype_name` *restrict bbase_y;
 525       'rtype_name` *restrict dest_y;
 526       'rtype_name` s;
 527
 528       for (y = 0; y < ycount; y++)
 529         {
 530           bbase_y = &bbase[y*bystride];
 531           dest_y = &dest[y*rystride];
 532           for (x = 0; x < xcount; x++)
 533             {
 534               abase_x = &abase[x*axstride];
 535               s = ('rtype_name`) 0;
 536               for (n = 0; n < count; n++)
 537                 s += abase_x[n*aystride] * bbase_y[n*bxstride];
 538               dest_y[x*rxstride] = s;
 539             }
 540         }
 541     }
 542 }
 543 #undef POW3
 544 #undef min
 545 #undef max
 546 '