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| author | Shinji KONO <kono@ie.u-ryukyu.ac.jp> |
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| date | Mon, 25 May 2020 18:13:55 +0900 |
| parents | 1830386684a0 |
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/* Implementation of the MATMUL intrinsic Copyright (C) 2002-2020 Free Software Foundation, Inc. Contributed by Paul Brook <paul@nowt.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> #if defined (HAVE_GFC_COMPLEX_8) /* 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_COMPLEX_8 *, const GFC_COMPLEX_8 *, const int *, const GFC_COMPLEX_8 *, const int *, const GFC_COMPLEX_8 *, GFC_COMPLEX_8 *, const int *, int, int); /* The order of loops is different in the case of plain matrix multiplication C=MATMUL(A,B), and in the frequent special case where the argument A is the temporary result of a TRANSPOSE intrinsic: C=MATMUL(TRANSPOSE(A),B). Transposed temporaries are detected by looking at their strides. The equivalent Fortran pseudo-code is: DIMENSION A(M,COUNT), B(COUNT,N), C(M,N) IF (.NOT.IS_TRANSPOSED(A)) THEN C = 0 DO J=1,N DO K=1,COUNT DO I=1,M C(I,J) = C(I,J)+A(I,K)*B(K,J) ELSE DO J=1,N DO I=1,M S = 0 DO K=1,COUNT S = S+A(I,K)*B(K,J) C(I,J) = S ENDIF */ /* If try_blas is set to a nonzero value, then the matmul function will see if there is a way to perform the matrix multiplication by a call to the BLAS gemm function. */ extern void matmul_c8 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm); export_proto(matmul_c8); /* Put exhaustive list of possible architectures here here, ORed together. */ #if defined(HAVE_AVX) || defined(HAVE_AVX2) || defined(HAVE_AVX512F) #ifdef HAVE_AVX static void matmul_c8_avx (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) __attribute__((__target__("avx"))); static void matmul_c8_avx (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { const GFC_COMPLEX_8 * restrict abase; const GFC_COMPLEX_8 * restrict bbase; GFC_COMPLEX_8 * 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_COMPLEX_8)); 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_COMPLEX_8 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) { /* 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_COMPLEX_8 *a, *b; GFC_COMPLEX_8 *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_COMPLEX_8 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_COMPLEX_8 *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_COMPLEX_8)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_COMPLEX_8)); /* 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_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase_x[n] * bbase_y[n]; dest_y[x] = s; } } } else { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n]; dest[y*rystride] = s; } } } else if (axstride < aystride) { for (y = 0; y < ycount; y++) for (x = 0; x < xcount; x++) dest[x*rxstride + y*rystride] = (GFC_COMPLEX_8)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 if (GFC_DESCRIPTOR_RANK (a) == 1) { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n*bxstride]; dest[y*rxstride] = s; } } else { const GFC_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 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 /* HAVE_AVX */ #ifdef HAVE_AVX2 static void matmul_c8_avx2 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) __attribute__((__target__("avx2,fma"))); static void matmul_c8_avx2 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { const GFC_COMPLEX_8 * restrict abase; const GFC_COMPLEX_8 * restrict bbase; GFC_COMPLEX_8 * 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_COMPLEX_8)); 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_COMPLEX_8 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) { /* 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_COMPLEX_8 *a, *b; GFC_COMPLEX_8 *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_COMPLEX_8 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_COMPLEX_8 *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_COMPLEX_8)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_COMPLEX_8)); /* 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_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase_x[n] * bbase_y[n]; dest_y[x] = s; } } } else { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n]; dest[y*rystride] = s; } } } else if (axstride < aystride) { for (y = 0; y < ycount; y++) for (x = 0; x < xcount; x++) dest[x*rxstride + y*rystride] = (GFC_COMPLEX_8)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 if (GFC_DESCRIPTOR_RANK (a) == 1) { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n*bxstride]; dest[y*rxstride] = s; } } else { const GFC_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 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 /* HAVE_AVX2 */ #ifdef HAVE_AVX512F static void matmul_c8_avx512f (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) __attribute__((__target__("avx512f"))); static void matmul_c8_avx512f (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { const GFC_COMPLEX_8 * restrict abase; const GFC_COMPLEX_8 * restrict bbase; GFC_COMPLEX_8 * 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_COMPLEX_8)); 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_COMPLEX_8 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) { /* 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_COMPLEX_8 *a, *b; GFC_COMPLEX_8 *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_COMPLEX_8 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_COMPLEX_8 *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_COMPLEX_8)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_COMPLEX_8)); /* 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_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase_x[n] * bbase_y[n]; dest_y[x] = s; } } } else { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n]; dest[y*rystride] = s; } } } else if (axstride < aystride) { for (y = 0; y < ycount; y++) for (x = 0; x < xcount; x++) dest[x*rxstride + y*rystride] = (GFC_COMPLEX_8)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 if (GFC_DESCRIPTOR_RANK (a) == 1) { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n*bxstride]; dest[y*rxstride] = s; } } else { const GFC_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 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 /* HAVE_AVX512F */ /* AMD-specifix funtions with AVX128 and FMA3/FMA4. */ #if defined(HAVE_AVX) && defined(HAVE_FMA3) && defined(HAVE_AVX128) void matmul_c8_avx128_fma3 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma"))); internal_proto(matmul_c8_avx128_fma3); #endif #if defined(HAVE_AVX) && defined(HAVE_FMA4) && defined(HAVE_AVX128) void matmul_c8_avx128_fma4 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma4"))); internal_proto(matmul_c8_avx128_fma4); #endif /* Function to fall back to if there is no special processor-specific version. */ static void matmul_c8_vanilla (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { const GFC_COMPLEX_8 * restrict abase; const GFC_COMPLEX_8 * restrict bbase; GFC_COMPLEX_8 * 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_COMPLEX_8)); 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_COMPLEX_8 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) { /* 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_COMPLEX_8 *a, *b; GFC_COMPLEX_8 *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_COMPLEX_8 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_COMPLEX_8 *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_COMPLEX_8)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_COMPLEX_8)); /* 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_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase_x[n] * bbase_y[n]; dest_y[x] = s; } } } else { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n]; dest[y*rystride] = s; } } } else if (axstride < aystride) { for (y = 0; y < ycount; y++) for (x = 0; x < xcount; x++) dest[x*rxstride + y*rystride] = (GFC_COMPLEX_8)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 if (GFC_DESCRIPTOR_RANK (a) == 1) { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n*bxstride]; dest[y*rxstride] = s; } } else { const GFC_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 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 /* Compiling main function, with selection code for the processor. */ /* Currently, this is i386 only. Adjust for other architectures. */ #include <config/i386/cpuinfo.h> void matmul_c8 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { static void (*matmul_p) (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm); void (*matmul_fn) (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm); matmul_fn = __atomic_load_n (&matmul_p, __ATOMIC_RELAXED); if (matmul_fn == NULL) { matmul_fn = matmul_c8_vanilla; if (__cpu_model.__cpu_vendor == VENDOR_INTEL) { /* Run down the available processors in order of preference. */ #ifdef HAVE_AVX512F if (__cpu_model.__cpu_features[0] & (1 << FEATURE_AVX512F)) { matmul_fn = matmul_c8_avx512f; goto store; } #endif /* HAVE_AVX512F */ #ifdef HAVE_AVX2 if ((__cpu_model.__cpu_features[0] & (1 << FEATURE_AVX2)) && (__cpu_model.__cpu_features[0] & (1 << FEATURE_FMA))) { matmul_fn = matmul_c8_avx2; goto store; } #endif #ifdef HAVE_AVX if (__cpu_model.__cpu_features[0] & (1 << FEATURE_AVX)) { matmul_fn = matmul_c8_avx; goto store; } #endif /* HAVE_AVX */ } else if (__cpu_model.__cpu_vendor == VENDOR_AMD) { #if defined(HAVE_AVX) && defined(HAVE_FMA3) && defined(HAVE_AVX128) if ((__cpu_model.__cpu_features[0] & (1 << FEATURE_AVX)) && (__cpu_model.__cpu_features[0] & (1 << FEATURE_FMA))) { matmul_fn = matmul_c8_avx128_fma3; goto store; } #endif #if defined(HAVE_AVX) && defined(HAVE_FMA4) && defined(HAVE_AVX128) if ((__cpu_model.__cpu_features[0] & (1 << FEATURE_AVX)) && (__cpu_model.__cpu_features[0] & (1 << FEATURE_FMA4))) { matmul_fn = matmul_c8_avx128_fma4; goto store; } #endif } store: __atomic_store_n (&matmul_p, matmul_fn, __ATOMIC_RELAXED); } (*matmul_fn) (retarray, a, b, try_blas, blas_limit, gemm); } #else /* Just the vanilla function. */ void matmul_c8 (gfc_array_c8 * const restrict retarray, gfc_array_c8 * const restrict a, gfc_array_c8 * const restrict b, int try_blas, int blas_limit, blas_call gemm) { const GFC_COMPLEX_8 * restrict abase; const GFC_COMPLEX_8 * restrict bbase; GFC_COMPLEX_8 * 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_COMPLEX_8)); 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_COMPLEX_8 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) { /* 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_COMPLEX_8 *a, *b; GFC_COMPLEX_8 *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_COMPLEX_8 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_COMPLEX_8 *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_COMPLEX_8)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_COMPLEX_8)); /* 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_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase_x[n] * bbase_y[n]; dest_y[x] = s; } } } else { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n]; dest[y*rystride] = s; } } } else if (axstride < aystride) { for (y = 0; y < ycount; y++) for (x = 0; x < xcount; x++) dest[x*rxstride + y*rystride] = (GFC_COMPLEX_8)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 if (GFC_DESCRIPTOR_RANK (a) == 1) { const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 s; for (y = 0; y < ycount; y++) { bbase_y = &bbase[y*bystride]; s = (GFC_COMPLEX_8) 0; for (n = 0; n < count; n++) s += abase[n*axstride] * bbase_y[n*bxstride]; dest[y*rxstride] = s; } } else { const GFC_COMPLEX_8 *restrict abase_x; const GFC_COMPLEX_8 *restrict bbase_y; GFC_COMPLEX_8 *restrict dest_y; GFC_COMPLEX_8 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_COMPLEX_8) 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