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- /* Implementation of the MATMUL intrinsic
- Copyright (C) 2002-2022 Free Software Foundation, Inc.
- Contributed by Thomas Koenig <tkoenig@gcc.gnu.org>.
- This file is part of the GNU Fortran runtime library (libgfortran).
- Libgfortran is free software; you can redistribute it and/or
- modify it under the terms of the GNU General Public
- License as published by the Free Software Foundation; either
- version 3 of the License, or (at your option) any later version.
- Libgfortran is distributed in the hope that it will be useful,
- but WITHOUT ANY WARRANTY; without even the implied warranty of
- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- GNU General Public License for more details.
- Under Section 7 of GPL version 3, you are granted additional
- permissions described in the GCC Runtime Library Exception, version
- 3.1, as published by the Free Software Foundation.
- You should have received a copy of the GNU General Public License and
- a copy of the GCC Runtime Library Exception along with this program;
- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
- <http://www.gnu.org/licenses/>. */
- #include "libgfortran.h"
- #include <string.h>
- #include <assert.h>
- /* These are the specific versions of matmul with -mprefer-avx128. */
- #if defined (HAVE_GFC_REAL_4)
- /* Prototype for the BLAS ?gemm subroutine, a pointer to which can be
- passed to us by the front-end, in which case we call it for large
- matrices. */
- typedef void (*blas_call)(const char *, const char *, const int *, const int *,
- const int *, const GFC_REAL_4 *, const GFC_REAL_4 *,
- const int *, const GFC_REAL_4 *, const int *,
- const GFC_REAL_4 *, GFC_REAL_4 *, const int *,
- int, int);
- #if defined(HAVE_AVX) && defined(HAVE_FMA3) && defined(HAVE_AVX128)
- void
- matmul_r4_avx128_fma3 (gfc_array_r4 * const restrict retarray,
- gfc_array_r4 * const restrict a, gfc_array_r4 * const restrict b, int try_blas,
- int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma")));
- internal_proto(matmul_r4_avx128_fma3);
- void
- matmul_r4_avx128_fma3 (gfc_array_r4 * const restrict retarray,
- gfc_array_r4 * const restrict a, gfc_array_r4 * const restrict b, int try_blas,
- int blas_limit, blas_call gemm)
- {
- const GFC_REAL_4 * restrict abase;
- const GFC_REAL_4 * restrict bbase;
- GFC_REAL_4 * restrict dest;
- index_type rxstride, rystride, axstride, aystride, bxstride, bystride;
- index_type x, y, n, count, xcount, ycount;
- assert (GFC_DESCRIPTOR_RANK (a) == 2
- || GFC_DESCRIPTOR_RANK (b) == 2);
- /* C[xcount,ycount] = A[xcount, count] * B[count,ycount]
- Either A or B (but not both) can be rank 1:
- o One-dimensional argument A is implicitly treated as a row matrix
- dimensioned [1,count], so xcount=1.
- o One-dimensional argument B is implicitly treated as a column matrix
- dimensioned [count, 1], so ycount=1.
- */
- if (retarray->base_addr == NULL)
- {
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(b,1) - 1, 1);
- }
- else if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
- }
- else
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
- GFC_DIMENSION_SET(retarray->dim[1], 0,
- GFC_DESCRIPTOR_EXTENT(b,1) - 1,
- GFC_DESCRIPTOR_EXTENT(retarray,0));
- }
- retarray->base_addr
- = xmallocarray (size0 ((array_t *) retarray), sizeof (GFC_REAL_4));
- retarray->offset = 0;
- }
- else if (unlikely (compile_options.bounds_check))
- {
- index_type ret_extent, arg_extent;
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- else if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- else
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,1);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 2 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- }
- if (GFC_DESCRIPTOR_RANK (retarray) == 1)
- {
- /* One-dimensional result may be addressed in the code below
- either as a row or a column matrix. We want both cases to
- work. */
- rxstride = rystride = GFC_DESCRIPTOR_STRIDE(retarray,0);
- }
- else
- {
- rxstride = GFC_DESCRIPTOR_STRIDE(retarray,0);
- rystride = GFC_DESCRIPTOR_STRIDE(retarray,1);
- }
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- /* Treat it as a a row matrix A[1,count]. */
- axstride = GFC_DESCRIPTOR_STRIDE(a,0);
- aystride = 1;
- xcount = 1;
- count = GFC_DESCRIPTOR_EXTENT(a,0);
- }
- else
- {
- axstride = GFC_DESCRIPTOR_STRIDE(a,0);
- aystride = GFC_DESCRIPTOR_STRIDE(a,1);
- count = GFC_DESCRIPTOR_EXTENT(a,1);
- xcount = GFC_DESCRIPTOR_EXTENT(a,0);
- }
- if (count != GFC_DESCRIPTOR_EXTENT(b,0))
- {
- if (count > 0 || GFC_DESCRIPTOR_EXTENT(b,0) > 0)
- runtime_error ("Incorrect extent in argument B in MATMUL intrinsic "
- "in dimension 1: is %ld, should be %ld",
- (long int) GFC_DESCRIPTOR_EXTENT(b,0), (long int) count);
- }
- if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- /* Treat it as a column matrix B[count,1] */
- bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
- /* bystride should never be used for 1-dimensional b.
- The value is only used for calculation of the
- memory by the buffer. */
- bystride = 256;
- ycount = 1;
- }
- else
- {
- bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
- bystride = GFC_DESCRIPTOR_STRIDE(b,1);
- ycount = GFC_DESCRIPTOR_EXTENT(b,1);
- }
- abase = a->base_addr;
- bbase = b->base_addr;
- dest = retarray->base_addr;
- /* Now that everything is set up, we perform the multiplication
- itself. */
- #define POW3(x) (((float) (x)) * ((float) (x)) * ((float) (x)))
- #define min(a,b) ((a) <= (b) ? (a) : (b))
- #define max(a,b) ((a) >= (b) ? (a) : (b))
- if (try_blas && rxstride == 1 && (axstride == 1 || aystride == 1)
- && (bxstride == 1 || bystride == 1)
- && (((float) xcount) * ((float) ycount) * ((float) count)
- > POW3(blas_limit)))
- {
- const int m = xcount, n = ycount, k = count, ldc = rystride;
- const GFC_REAL_4 one = 1, zero = 0;
- const int lda = (axstride == 1) ? aystride : axstride,
- ldb = (bxstride == 1) ? bystride : bxstride;
- if (lda > 0 && ldb > 0 && ldc > 0 && m > 1 && n > 1 && k > 1)
- {
- assert (gemm != NULL);
- const char *transa, *transb;
- if (try_blas & 2)
- transa = "C";
- else
- transa = axstride == 1 ? "N" : "T";
- if (try_blas & 4)
- transb = "C";
- else
- transb = bxstride == 1 ? "N" : "T";
- gemm (transa, transb , &m,
- &n, &k, &one, abase, &lda, bbase, &ldb, &zero, dest,
- &ldc, 1, 1);
- return;
- }
- }
- if (rxstride == 1 && axstride == 1 && bxstride == 1
- && GFC_DESCRIPTOR_RANK (b) != 1)
- {
- /* This block of code implements a tuned matmul, derived from
- Superscalar GEMM-based level 3 BLAS, Beta version 0.1
- Bo Kagstrom and Per Ling
- Department of Computing Science
- Umea University
- S-901 87 Umea, Sweden
- from netlib.org, translated to C, and modified for matmul.m4. */
- const GFC_REAL_4 *a, *b;
- GFC_REAL_4 *c;
- const index_type m = xcount, n = ycount, k = count;
- /* System generated locals */
- index_type a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset,
- i1, i2, i3, i4, i5, i6;
- /* Local variables */
- GFC_REAL_4 f11, f12, f21, f22, f31, f32, f41, f42,
- f13, f14, f23, f24, f33, f34, f43, f44;
- index_type i, j, l, ii, jj, ll;
- index_type isec, jsec, lsec, uisec, ujsec, ulsec;
- GFC_REAL_4 *t1;
- a = abase;
- b = bbase;
- c = retarray->base_addr;
- /* Parameter adjustments */
- c_dim1 = rystride;
- c_offset = 1 + c_dim1;
- c -= c_offset;
- a_dim1 = aystride;
- a_offset = 1 + a_dim1;
- a -= a_offset;
- b_dim1 = bystride;
- b_offset = 1 + b_dim1;
- b -= b_offset;
- /* Empty c first. */
- for (j=1; j<=n; j++)
- for (i=1; i<=m; i++)
- c[i + j * c_dim1] = (GFC_REAL_4)0;
- /* Early exit if possible */
- if (m == 0 || n == 0 || k == 0)
- return;
- /* Adjust size of t1 to what is needed. */
- index_type t1_dim, a_sz;
- if (aystride == 1)
- a_sz = rystride;
- else
- a_sz = a_dim1;
- t1_dim = a_sz * 256 + b_dim1;
- if (t1_dim > 65536)
- t1_dim = 65536;
- t1 = malloc (t1_dim * sizeof(GFC_REAL_4));
- /* Start turning the crank. */
- i1 = n;
- for (jj = 1; jj <= i1; jj += 512)
- {
- /* Computing MIN */
- i2 = 512;
- i3 = n - jj + 1;
- jsec = min(i2,i3);
- ujsec = jsec - jsec % 4;
- i2 = k;
- for (ll = 1; ll <= i2; ll += 256)
- {
- /* Computing MIN */
- i3 = 256;
- i4 = k - ll + 1;
- lsec = min(i3,i4);
- ulsec = lsec - lsec % 2;
- i3 = m;
- for (ii = 1; ii <= i3; ii += 256)
- {
- /* Computing MIN */
- i4 = 256;
- i5 = m - ii + 1;
- isec = min(i4,i5);
- uisec = isec - isec % 2;
- i4 = ll + ulsec - 1;
- for (l = ll; l <= i4; l += 2)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 2)
- {
- t1[l - ll + 1 + ((i - ii + 1) << 8) - 257] =
- a[i + l * a_dim1];
- t1[l - ll + 2 + ((i - ii + 1) << 8) - 257] =
- a[i + (l + 1) * a_dim1];
- t1[l - ll + 1 + ((i - ii + 2) << 8) - 257] =
- a[i + 1 + l * a_dim1];
- t1[l - ll + 2 + ((i - ii + 2) << 8) - 257] =
- a[i + 1 + (l + 1) * a_dim1];
- }
- if (uisec < isec)
- {
- t1[l - ll + 1 + (isec << 8) - 257] =
- a[ii + isec - 1 + l * a_dim1];
- t1[l - ll + 2 + (isec << 8) - 257] =
- a[ii + isec - 1 + (l + 1) * a_dim1];
- }
- }
- if (ulsec < lsec)
- {
- i4 = ii + isec - 1;
- for (i = ii; i<= i4; ++i)
- {
- t1[lsec + ((i - ii + 1) << 8) - 257] =
- a[i + (ll + lsec - 1) * a_dim1];
- }
- }
- uisec = isec - isec % 4;
- i4 = jj + ujsec - 1;
- for (j = jj; j <= i4; j += 4)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 4)
- {
- f11 = c[i + j * c_dim1];
- f21 = c[i + 1 + j * c_dim1];
- f12 = c[i + (j + 1) * c_dim1];
- f22 = c[i + 1 + (j + 1) * c_dim1];
- f13 = c[i + (j + 2) * c_dim1];
- f23 = c[i + 1 + (j + 2) * c_dim1];
- f14 = c[i + (j + 3) * c_dim1];
- f24 = c[i + 1 + (j + 3) * c_dim1];
- f31 = c[i + 2 + j * c_dim1];
- f41 = c[i + 3 + j * c_dim1];
- f32 = c[i + 2 + (j + 1) * c_dim1];
- f42 = c[i + 3 + (j + 1) * c_dim1];
- f33 = c[i + 2 + (j + 2) * c_dim1];
- f43 = c[i + 3 + (j + 2) * c_dim1];
- f34 = c[i + 2 + (j + 3) * c_dim1];
- f44 = c[i + 3 + (j + 3) * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + j * b_dim1];
- f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + j * b_dim1];
- f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f22 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f23 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f24 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + j * b_dim1];
- f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + j * b_dim1];
- f32 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f42 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f33 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f43 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f34 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f44 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + 1 + j * c_dim1] = f21;
- c[i + (j + 1) * c_dim1] = f12;
- c[i + 1 + (j + 1) * c_dim1] = f22;
- c[i + (j + 2) * c_dim1] = f13;
- c[i + 1 + (j + 2) * c_dim1] = f23;
- c[i + (j + 3) * c_dim1] = f14;
- c[i + 1 + (j + 3) * c_dim1] = f24;
- c[i + 2 + j * c_dim1] = f31;
- c[i + 3 + j * c_dim1] = f41;
- c[i + 2 + (j + 1) * c_dim1] = f32;
- c[i + 3 + (j + 1) * c_dim1] = f42;
- c[i + 2 + (j + 2) * c_dim1] = f33;
- c[i + 3 + (j + 2) * c_dim1] = f43;
- c[i + 2 + (j + 3) * c_dim1] = f34;
- c[i + 3 + (j + 3) * c_dim1] = f44;
- }
- if (uisec < isec)
- {
- i5 = ii + isec - 1;
- for (i = ii + uisec; i <= i5; ++i)
- {
- f11 = c[i + j * c_dim1];
- f12 = c[i + (j + 1) * c_dim1];
- f13 = c[i + (j + 2) * c_dim1];
- f14 = c[i + (j + 3) * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 1) * b_dim1];
- f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 2) * b_dim1];
- f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 3) * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + (j + 1) * c_dim1] = f12;
- c[i + (j + 2) * c_dim1] = f13;
- c[i + (j + 3) * c_dim1] = f14;
- }
- }
- }
- if (ujsec < jsec)
- {
- i4 = jj + jsec - 1;
- for (j = jj + ujsec; j <= i4; ++j)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 4)
- {
- f11 = c[i + j * c_dim1];
- f21 = c[i + 1 + j * c_dim1];
- f31 = c[i + 2 + j * c_dim1];
- f41 = c[i + 3 + j * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) -
- 257] * b[l + j * b_dim1];
- f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) -
- 257] * b[l + j * b_dim1];
- f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) -
- 257] * b[l + j * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + 1 + j * c_dim1] = f21;
- c[i + 2 + j * c_dim1] = f31;
- c[i + 3 + j * c_dim1] = f41;
- }
- i5 = ii + isec - 1;
- for (i = ii + uisec; i <= i5; ++i)
- {
- f11 = c[i + j * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- }
- }
- }
- }
- }
- }
- free(t1);
- return;
- }
- else if (rxstride == 1 && aystride == 1 && bxstride == 1)
- {
- if (GFC_DESCRIPTOR_RANK (a) != 1)
- {
- const GFC_REAL_4 *restrict abase_x;
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 *restrict dest_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- dest_y = &dest[y*rystride];
- for (x = 0; x < xcount; x++)
- {
- abase_x = &abase[x*axstride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase_x[n] * bbase_y[n];
- dest_y[x] = s;
- }
- }
- }
- else
- {
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase[n*axstride] * bbase_y[n];
- dest[y*rystride] = s;
- }
- }
- }
- else if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase[n*axstride] * bbase_y[n*bxstride];
- dest[y*rxstride] = s;
- }
- }
- else if (axstride < aystride)
- {
- for (y = 0; y < ycount; y++)
- for (x = 0; x < xcount; x++)
- dest[x*rxstride + y*rystride] = (GFC_REAL_4)0;
- for (y = 0; y < ycount; y++)
- for (n = 0; n < count; n++)
- for (x = 0; x < xcount; x++)
- /* dest[x,y] += a[x,n] * b[n,y] */
- dest[x*rxstride + y*rystride] +=
- abase[x*axstride + n*aystride] *
- bbase[n*bxstride + y*bystride];
- }
- else
- {
- const GFC_REAL_4 *restrict abase_x;
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 *restrict dest_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- dest_y = &dest[y*rystride];
- for (x = 0; x < xcount; x++)
- {
- abase_x = &abase[x*axstride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase_x[n*aystride] * bbase_y[n*bxstride];
- dest_y[x*rxstride] = s;
- }
- }
- }
- }
- #undef POW3
- #undef min
- #undef max
- #endif
- #if defined(HAVE_AVX) && defined(HAVE_FMA4) && defined(HAVE_AVX128)
- void
- matmul_r4_avx128_fma4 (gfc_array_r4 * const restrict retarray,
- gfc_array_r4 * const restrict a, gfc_array_r4 * const restrict b, int try_blas,
- int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma4")));
- internal_proto(matmul_r4_avx128_fma4);
- void
- matmul_r4_avx128_fma4 (gfc_array_r4 * const restrict retarray,
- gfc_array_r4 * const restrict a, gfc_array_r4 * const restrict b, int try_blas,
- int blas_limit, blas_call gemm)
- {
- const GFC_REAL_4 * restrict abase;
- const GFC_REAL_4 * restrict bbase;
- GFC_REAL_4 * restrict dest;
- index_type rxstride, rystride, axstride, aystride, bxstride, bystride;
- index_type x, y, n, count, xcount, ycount;
- assert (GFC_DESCRIPTOR_RANK (a) == 2
- || GFC_DESCRIPTOR_RANK (b) == 2);
- /* C[xcount,ycount] = A[xcount, count] * B[count,ycount]
- Either A or B (but not both) can be rank 1:
- o One-dimensional argument A is implicitly treated as a row matrix
- dimensioned [1,count], so xcount=1.
- o One-dimensional argument B is implicitly treated as a column matrix
- dimensioned [count, 1], so ycount=1.
- */
- if (retarray->base_addr == NULL)
- {
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(b,1) - 1, 1);
- }
- else if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
- }
- else
- {
- GFC_DIMENSION_SET(retarray->dim[0], 0,
- GFC_DESCRIPTOR_EXTENT(a,0) - 1, 1);
- GFC_DIMENSION_SET(retarray->dim[1], 0,
- GFC_DESCRIPTOR_EXTENT(b,1) - 1,
- GFC_DESCRIPTOR_EXTENT(retarray,0));
- }
- retarray->base_addr
- = xmallocarray (size0 ((array_t *) retarray), sizeof (GFC_REAL_4));
- retarray->offset = 0;
- }
- else if (unlikely (compile_options.bounds_check))
- {
- index_type ret_extent, arg_extent;
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- else if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- else
- {
- arg_extent = GFC_DESCRIPTOR_EXTENT(a,0);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,0);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 1 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- arg_extent = GFC_DESCRIPTOR_EXTENT(b,1);
- ret_extent = GFC_DESCRIPTOR_EXTENT(retarray,1);
- if (arg_extent != ret_extent)
- runtime_error ("Array bound mismatch for dimension 2 of "
- "array (%ld/%ld) ",
- (long int) ret_extent, (long int) arg_extent);
- }
- }
- if (GFC_DESCRIPTOR_RANK (retarray) == 1)
- {
- /* One-dimensional result may be addressed in the code below
- either as a row or a column matrix. We want both cases to
- work. */
- rxstride = rystride = GFC_DESCRIPTOR_STRIDE(retarray,0);
- }
- else
- {
- rxstride = GFC_DESCRIPTOR_STRIDE(retarray,0);
- rystride = GFC_DESCRIPTOR_STRIDE(retarray,1);
- }
- if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- /* Treat it as a a row matrix A[1,count]. */
- axstride = GFC_DESCRIPTOR_STRIDE(a,0);
- aystride = 1;
- xcount = 1;
- count = GFC_DESCRIPTOR_EXTENT(a,0);
- }
- else
- {
- axstride = GFC_DESCRIPTOR_STRIDE(a,0);
- aystride = GFC_DESCRIPTOR_STRIDE(a,1);
- count = GFC_DESCRIPTOR_EXTENT(a,1);
- xcount = GFC_DESCRIPTOR_EXTENT(a,0);
- }
- if (count != GFC_DESCRIPTOR_EXTENT(b,0))
- {
- if (count > 0 || GFC_DESCRIPTOR_EXTENT(b,0) > 0)
- runtime_error ("Incorrect extent in argument B in MATMUL intrinsic "
- "in dimension 1: is %ld, should be %ld",
- (long int) GFC_DESCRIPTOR_EXTENT(b,0), (long int) count);
- }
- if (GFC_DESCRIPTOR_RANK (b) == 1)
- {
- /* Treat it as a column matrix B[count,1] */
- bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
- /* bystride should never be used for 1-dimensional b.
- The value is only used for calculation of the
- memory by the buffer. */
- bystride = 256;
- ycount = 1;
- }
- else
- {
- bxstride = GFC_DESCRIPTOR_STRIDE(b,0);
- bystride = GFC_DESCRIPTOR_STRIDE(b,1);
- ycount = GFC_DESCRIPTOR_EXTENT(b,1);
- }
- abase = a->base_addr;
- bbase = b->base_addr;
- dest = retarray->base_addr;
- /* Now that everything is set up, we perform the multiplication
- itself. */
- #define POW3(x) (((float) (x)) * ((float) (x)) * ((float) (x)))
- #define min(a,b) ((a) <= (b) ? (a) : (b))
- #define max(a,b) ((a) >= (b) ? (a) : (b))
- if (try_blas && rxstride == 1 && (axstride == 1 || aystride == 1)
- && (bxstride == 1 || bystride == 1)
- && (((float) xcount) * ((float) ycount) * ((float) count)
- > POW3(blas_limit)))
- {
- const int m = xcount, n = ycount, k = count, ldc = rystride;
- const GFC_REAL_4 one = 1, zero = 0;
- const int lda = (axstride == 1) ? aystride : axstride,
- ldb = (bxstride == 1) ? bystride : bxstride;
- if (lda > 0 && ldb > 0 && ldc > 0 && m > 1 && n > 1 && k > 1)
- {
- assert (gemm != NULL);
- const char *transa, *transb;
- if (try_blas & 2)
- transa = "C";
- else
- transa = axstride == 1 ? "N" : "T";
- if (try_blas & 4)
- transb = "C";
- else
- transb = bxstride == 1 ? "N" : "T";
- gemm (transa, transb , &m,
- &n, &k, &one, abase, &lda, bbase, &ldb, &zero, dest,
- &ldc, 1, 1);
- return;
- }
- }
- if (rxstride == 1 && axstride == 1 && bxstride == 1
- && GFC_DESCRIPTOR_RANK (b) != 1)
- {
- /* This block of code implements a tuned matmul, derived from
- Superscalar GEMM-based level 3 BLAS, Beta version 0.1
- Bo Kagstrom and Per Ling
- Department of Computing Science
- Umea University
- S-901 87 Umea, Sweden
- from netlib.org, translated to C, and modified for matmul.m4. */
- const GFC_REAL_4 *a, *b;
- GFC_REAL_4 *c;
- const index_type m = xcount, n = ycount, k = count;
- /* System generated locals */
- index_type a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset,
- i1, i2, i3, i4, i5, i6;
- /* Local variables */
- GFC_REAL_4 f11, f12, f21, f22, f31, f32, f41, f42,
- f13, f14, f23, f24, f33, f34, f43, f44;
- index_type i, j, l, ii, jj, ll;
- index_type isec, jsec, lsec, uisec, ujsec, ulsec;
- GFC_REAL_4 *t1;
- a = abase;
- b = bbase;
- c = retarray->base_addr;
- /* Parameter adjustments */
- c_dim1 = rystride;
- c_offset = 1 + c_dim1;
- c -= c_offset;
- a_dim1 = aystride;
- a_offset = 1 + a_dim1;
- a -= a_offset;
- b_dim1 = bystride;
- b_offset = 1 + b_dim1;
- b -= b_offset;
- /* Empty c first. */
- for (j=1; j<=n; j++)
- for (i=1; i<=m; i++)
- c[i + j * c_dim1] = (GFC_REAL_4)0;
- /* Early exit if possible */
- if (m == 0 || n == 0 || k == 0)
- return;
- /* Adjust size of t1 to what is needed. */
- index_type t1_dim, a_sz;
- if (aystride == 1)
- a_sz = rystride;
- else
- a_sz = a_dim1;
- t1_dim = a_sz * 256 + b_dim1;
- if (t1_dim > 65536)
- t1_dim = 65536;
- t1 = malloc (t1_dim * sizeof(GFC_REAL_4));
- /* Start turning the crank. */
- i1 = n;
- for (jj = 1; jj <= i1; jj += 512)
- {
- /* Computing MIN */
- i2 = 512;
- i3 = n - jj + 1;
- jsec = min(i2,i3);
- ujsec = jsec - jsec % 4;
- i2 = k;
- for (ll = 1; ll <= i2; ll += 256)
- {
- /* Computing MIN */
- i3 = 256;
- i4 = k - ll + 1;
- lsec = min(i3,i4);
- ulsec = lsec - lsec % 2;
- i3 = m;
- for (ii = 1; ii <= i3; ii += 256)
- {
- /* Computing MIN */
- i4 = 256;
- i5 = m - ii + 1;
- isec = min(i4,i5);
- uisec = isec - isec % 2;
- i4 = ll + ulsec - 1;
- for (l = ll; l <= i4; l += 2)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 2)
- {
- t1[l - ll + 1 + ((i - ii + 1) << 8) - 257] =
- a[i + l * a_dim1];
- t1[l - ll + 2 + ((i - ii + 1) << 8) - 257] =
- a[i + (l + 1) * a_dim1];
- t1[l - ll + 1 + ((i - ii + 2) << 8) - 257] =
- a[i + 1 + l * a_dim1];
- t1[l - ll + 2 + ((i - ii + 2) << 8) - 257] =
- a[i + 1 + (l + 1) * a_dim1];
- }
- if (uisec < isec)
- {
- t1[l - ll + 1 + (isec << 8) - 257] =
- a[ii + isec - 1 + l * a_dim1];
- t1[l - ll + 2 + (isec << 8) - 257] =
- a[ii + isec - 1 + (l + 1) * a_dim1];
- }
- }
- if (ulsec < lsec)
- {
- i4 = ii + isec - 1;
- for (i = ii; i<= i4; ++i)
- {
- t1[lsec + ((i - ii + 1) << 8) - 257] =
- a[i + (ll + lsec - 1) * a_dim1];
- }
- }
- uisec = isec - isec % 4;
- i4 = jj + ujsec - 1;
- for (j = jj; j <= i4; j += 4)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 4)
- {
- f11 = c[i + j * c_dim1];
- f21 = c[i + 1 + j * c_dim1];
- f12 = c[i + (j + 1) * c_dim1];
- f22 = c[i + 1 + (j + 1) * c_dim1];
- f13 = c[i + (j + 2) * c_dim1];
- f23 = c[i + 1 + (j + 2) * c_dim1];
- f14 = c[i + (j + 3) * c_dim1];
- f24 = c[i + 1 + (j + 3) * c_dim1];
- f31 = c[i + 2 + j * c_dim1];
- f41 = c[i + 3 + j * c_dim1];
- f32 = c[i + 2 + (j + 1) * c_dim1];
- f42 = c[i + 3 + (j + 1) * c_dim1];
- f33 = c[i + 2 + (j + 2) * c_dim1];
- f43 = c[i + 3 + (j + 2) * c_dim1];
- f34 = c[i + 2 + (j + 3) * c_dim1];
- f44 = c[i + 3 + (j + 3) * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + j * b_dim1];
- f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + j * b_dim1];
- f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f22 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f23 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f24 += t1[l - ll + 1 + ((i - ii + 2) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + j * b_dim1];
- f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + j * b_dim1];
- f32 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f42 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 1) * b_dim1];
- f33 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f43 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 2) * b_dim1];
- f34 += t1[l - ll + 1 + ((i - ii + 3) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- f44 += t1[l - ll + 1 + ((i - ii + 4) << 8) - 257]
- * b[l + (j + 3) * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + 1 + j * c_dim1] = f21;
- c[i + (j + 1) * c_dim1] = f12;
- c[i + 1 + (j + 1) * c_dim1] = f22;
- c[i + (j + 2) * c_dim1] = f13;
- c[i + 1 + (j + 2) * c_dim1] = f23;
- c[i + (j + 3) * c_dim1] = f14;
- c[i + 1 + (j + 3) * c_dim1] = f24;
- c[i + 2 + j * c_dim1] = f31;
- c[i + 3 + j * c_dim1] = f41;
- c[i + 2 + (j + 1) * c_dim1] = f32;
- c[i + 3 + (j + 1) * c_dim1] = f42;
- c[i + 2 + (j + 2) * c_dim1] = f33;
- c[i + 3 + (j + 2) * c_dim1] = f43;
- c[i + 2 + (j + 3) * c_dim1] = f34;
- c[i + 3 + (j + 3) * c_dim1] = f44;
- }
- if (uisec < isec)
- {
- i5 = ii + isec - 1;
- for (i = ii + uisec; i <= i5; ++i)
- {
- f11 = c[i + j * c_dim1];
- f12 = c[i + (j + 1) * c_dim1];
- f13 = c[i + (j + 2) * c_dim1];
- f14 = c[i + (j + 3) * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- f12 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 1) * b_dim1];
- f13 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 2) * b_dim1];
- f14 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + (j + 3) * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + (j + 1) * c_dim1] = f12;
- c[i + (j + 2) * c_dim1] = f13;
- c[i + (j + 3) * c_dim1] = f14;
- }
- }
- }
- if (ujsec < jsec)
- {
- i4 = jj + jsec - 1;
- for (j = jj + ujsec; j <= i4; ++j)
- {
- i5 = ii + uisec - 1;
- for (i = ii; i <= i5; i += 4)
- {
- f11 = c[i + j * c_dim1];
- f21 = c[i + 1 + j * c_dim1];
- f31 = c[i + 2 + j * c_dim1];
- f41 = c[i + 3 + j * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- f21 += t1[l - ll + 1 + ((i - ii + 2) << 8) -
- 257] * b[l + j * b_dim1];
- f31 += t1[l - ll + 1 + ((i - ii + 3) << 8) -
- 257] * b[l + j * b_dim1];
- f41 += t1[l - ll + 1 + ((i - ii + 4) << 8) -
- 257] * b[l + j * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- c[i + 1 + j * c_dim1] = f21;
- c[i + 2 + j * c_dim1] = f31;
- c[i + 3 + j * c_dim1] = f41;
- }
- i5 = ii + isec - 1;
- for (i = ii + uisec; i <= i5; ++i)
- {
- f11 = c[i + j * c_dim1];
- i6 = ll + lsec - 1;
- for (l = ll; l <= i6; ++l)
- {
- f11 += t1[l - ll + 1 + ((i - ii + 1) << 8) -
- 257] * b[l + j * b_dim1];
- }
- c[i + j * c_dim1] = f11;
- }
- }
- }
- }
- }
- }
- free(t1);
- return;
- }
- else if (rxstride == 1 && aystride == 1 && bxstride == 1)
- {
- if (GFC_DESCRIPTOR_RANK (a) != 1)
- {
- const GFC_REAL_4 *restrict abase_x;
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 *restrict dest_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- dest_y = &dest[y*rystride];
- for (x = 0; x < xcount; x++)
- {
- abase_x = &abase[x*axstride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase_x[n] * bbase_y[n];
- dest_y[x] = s;
- }
- }
- }
- else
- {
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase[n*axstride] * bbase_y[n];
- dest[y*rystride] = s;
- }
- }
- }
- else if (GFC_DESCRIPTOR_RANK (a) == 1)
- {
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase[n*axstride] * bbase_y[n*bxstride];
- dest[y*rxstride] = s;
- }
- }
- else if (axstride < aystride)
- {
- for (y = 0; y < ycount; y++)
- for (x = 0; x < xcount; x++)
- dest[x*rxstride + y*rystride] = (GFC_REAL_4)0;
- for (y = 0; y < ycount; y++)
- for (n = 0; n < count; n++)
- for (x = 0; x < xcount; x++)
- /* dest[x,y] += a[x,n] * b[n,y] */
- dest[x*rxstride + y*rystride] +=
- abase[x*axstride + n*aystride] *
- bbase[n*bxstride + y*bystride];
- }
- else
- {
- const GFC_REAL_4 *restrict abase_x;
- const GFC_REAL_4 *restrict bbase_y;
- GFC_REAL_4 *restrict dest_y;
- GFC_REAL_4 s;
- for (y = 0; y < ycount; y++)
- {
- bbase_y = &bbase[y*bystride];
- dest_y = &dest[y*rystride];
- for (x = 0; x < xcount; x++)
- {
- abase_x = &abase[x*axstride];
- s = (GFC_REAL_4) 0;
- for (n = 0; n < count; n++)
- s += abase_x[n*aystride] * bbase_y[n*bxstride];
- dest_y[x*rxstride] = s;
- }
- }
- }
- }
- #undef POW3
- #undef min
- #undef max
- #endif
- #endif
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