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/* Implementation of the MATMUL intrinsic
Copyright (C) 2002-2021 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_10)
/* 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_10 *, const GFC_COMPLEX_10 *,
const int *, const GFC_COMPLEX_10 *, const int *,
const GFC_COMPLEX_10 *, GFC_COMPLEX_10 *, 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_c10 (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm);
export_proto(matmul_c10);
/* 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_c10_avx (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm) __attribute__((__target__("avx")));
static void
matmul_c10_avx (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm)
{
const GFC_COMPLEX_10 * restrict abase;
const GFC_COMPLEX_10 * restrict bbase;
GFC_COMPLEX_10 * 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_10));
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_10 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_COMPLEX_10 *a, *b;
GFC_COMPLEX_10 *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_10 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_10 *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_10)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_10));
/* 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_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 0;
for (n = 0; n < count; n++)
s += abase_x[n] * bbase_y[n];
dest_y[x] = s;
}
}
}
else
{
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10)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_COMPLEX_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 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_c10_avx2 (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm) __attribute__((__target__("avx2,fma")));
static void
matmul_c10_avx2 (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm)
{
const GFC_COMPLEX_10 * restrict abase;
const GFC_COMPLEX_10 * restrict bbase;
GFC_COMPLEX_10 * 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_10));
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_10 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_COMPLEX_10 *a, *b;
GFC_COMPLEX_10 *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_10 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_10 *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_10)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_10));
/* 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_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 0;
for (n = 0; n < count; n++)
s += abase_x[n] * bbase_y[n];
dest_y[x] = s;
}
}
}
else
{
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10)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_COMPLEX_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 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_c10_avx512f (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm) __attribute__((__target__("avx512f")));
static void
matmul_c10_avx512f (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm)
{
const GFC_COMPLEX_10 * restrict abase;
const GFC_COMPLEX_10 * restrict bbase;
GFC_COMPLEX_10 * 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_10));
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_10 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_COMPLEX_10 *a, *b;
GFC_COMPLEX_10 *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_10 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_10 *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_10)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_10));
/* 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_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 0;
for (n = 0; n < count; n++)
s += abase_x[n] * bbase_y[n];
dest_y[x] = s;
}
}
}
else
{
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 s;
for (y = 0; y < ycount; y++)
{
bbase_y = &bbase[y*bystride];
s = (GFC_COMPLEX_10) 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_COMPLEX_10)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_COMPLEX_10 *restrict abase_x;
const GFC_COMPLEX_10 *restrict bbase_y;
GFC_COMPLEX_10 *restrict dest_y;
GFC_COMPLEX_10 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_10) 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_c10_avx128_fma3 (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma")));
internal_proto(matmul_c10_avx128_fma3);
#endif
#if defined(HAVE_AVX) && defined(HAVE_FMA4) && defined(HAVE_AVX128)
void
matmul_c10_avx128_fma4 (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm) __attribute__((__target__("avx,fma4")));
internal_proto(matmul_c10_avx128_fma4);
#endif
/* Function to fall back to if there is no special processor-specific version. */
static void
matmul_c10_vanilla (gfc_array_c10 * const restrict retarray,
gfc_array_c10 * const restrict a, gfc_array_c10 * const restrict b, int try_blas,
int blas_limit, blas_call gemm)
{
const GFC_COMPLEX_10 * restrict abase;
const GFC_COMPLEX_10 * restrict bbase;
GFC_COMPLEX_10 * 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_10));
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_10 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_COMPLEX_10 *a, *b;
GFC_COMPLEX_10 *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_10 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_10 *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_10)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_10));
/* 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;