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-rw-r--r--src/fftw3/kernel/transpose.c430
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diff --git a/src/fftw3/kernel/transpose.c b/src/fftw3/kernel/transpose.c
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--- a/src/fftw3/kernel/transpose.c
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-/*
- * Copyright (c) 2003 Matteo Frigo
- * Copyright (c) 2003 Massachusetts Institute of Technology
- *
- * This program 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 2 of the License, or
- * (at your option) any later version.
- *
- * This program 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.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- *
- */
-
-/* transposes of unit-stride arrays, including arrays of N-tuples and
- non-square matrices, using cache-oblivious recursive algorithms */
-
-#include "ifftw.h"
-#include <string.h> /* memcpy */
-
-#define CUTOFF 8 /* size below which we do a naive transpose */
-
-/*************************************************************************/
-/* some utilities for the solvers */
-
-static int Ntuple_transposable(const iodim *a, const iodim *b,
- int vl, int s, R *ri, R *ii)
-{
- return(2 == s && (ii == ri + 1 || ri == ii + 1)
- &&
- ((a->is == b->os && a->is == (vl*2)
- && a->os == b->n * (vl*2) && b->is == a->n * (vl*2))
- ||
- (a->os == b->is && a->os == (vl*2)
- && a->is == b->n * (vl*2) && b->os == a->n * (vl*2))));
-}
-
-
-/* our solvers' transpose routines work for square matrices of arbitrary
- stride, or for non-square matrices of a given vl*vl2 corresponding
- to the N of the Ntuple with vl2 == s. */
-int X(transposable)(const iodim *a, const iodim *b,
- int vl, int s, R *ri, R *ii)
-{
- return ((a->n == b->n && a->os == b->is && a->is == b->os)
- || Ntuple_transposable(a, b, vl, s, ri, ii));
-}
-
-static int gcd(int a, int b)
-{
- int r;
- do {
- r = a % b;
- a = b;
- b = r;
- } while (r != 0);
-
- return a;
-}
-
-/* all of the solvers need to extract n, m, d, n/d, and m/d from the
- two iodims, so we put it here to save code space */
-void X(transpose_dims)(const iodim *a, const iodim *b,
- int *n, int *m, int *d, int *nd, int *md)
-{
- int n0, m0, d0;
- /* matrix should be n x m, row-major */
- if (a->is < b->is) {
- *n = n0 = b->n;
- *m = m0 = a->n;
- }
- else {
- *n = n0 = a->n;
- *m = m0 = b->n;
- }
- *d = d0 = gcd(n0, m0);
- *nd = n0 / d0;
- *md = m0 / d0;
-}
-
-/* use the simple square transpose in the solver for square matrices
- that aren't too big or which have the wrong stride */
-int X(transpose_simplep)(const iodim *a, const iodim *b, int vl, int s,
- R *ri, R *ii)
-{
- return (a->n == b->n &&
- (a->n*(vl*2) < CUTOFF
- || !Ntuple_transposable(a, b, vl, s, ri, ii)));
-}
-
-/* use the slow general transpose if the buffer would be more than 1/8
- the whole transpose and the transpose is fairly big.
- (FIXME: use the CONSERVE_MEMORY flag?) */
-int X(transpose_slowp)(const iodim *a, const iodim *b, int N)
-{
- int d = gcd(a->n, b->n);
- return (d < 8 && (a->n * b->n * N) / d > 65536);
-}
-
-/*************************************************************************/
-/* Out-of-place transposes: */
-
-/* Transpose A (n x m) to B (m x n), where A and B are stored
- as n x fda and m x fda arrays, respectively, operating on N-tuples: */
-static void rec_transpose_Ntuple(R *A, R *B, int n, int m, int fda, int fdb,
- int N)
-{
- if (n == 1 || m == 1 || (n + m) * N < CUTOFF*2) {
- int i, j, k;
- for (i = 0; i < n; ++i) {
- for (j = 0; j < m; ++j) {
- for (k = 0; k < N; ++k) { /* FIXME: unroll */
- B[(j*fdb + i) * N + k] = A[(i*fda + j) * N + k];
- }
- }
- }
- }
- else if (n > m) {
- int n2 = n / 2;
- rec_transpose_Ntuple(A, B, n2, m, fda, fdb, N);
- rec_transpose_Ntuple(A + n2*N*fda, B + n2*N, n - n2, m, fda, fdb, N);
- }
- else {
- int m2 = m / 2;
- rec_transpose_Ntuple(A, B, n, m2, fda, fdb, N);
- rec_transpose_Ntuple(A + m2*N, B + m2*N*fdb, n, m - m2, fda, fdb, N);
- }
-}
-
-/*************************************************************************/
-/* In-place transposes of square matrices of N-tuples: */
-
-/* Transpose both A and B, where A is n x m and B is m x n, storing
- the transpose of A in B and the transpose of B in A. A and B
- are actually stored as n x fda and m x fda arrays. */
-static void rec_transpose_swap_Ntuple(R *A, R *B, int n, int m, int fda, int N)
-{
- if (n == 1 || m == 1 || (n + m) * N <= CUTOFF*2) {
- switch (N) {
- case 1: {
- int i, j;
- for (i = 0; i < n; ++i) {
- for (j = 0; j < m; ++j) {
- R a = A[(i*fda + j)];
- A[(i*fda + j)] = B[(j*fda + i)];
- B[(j*fda + i)] = a;
- }
- }
- break;
- }
- case 2: {
- int i, j;
- for (i = 0; i < n; ++i) {
- for (j = 0; j < m; ++j) {
- R a0 = A[(i*fda + j) * 2 + 0];
- R a1 = A[(i*fda + j) * 2 + 1];
- A[(i*fda + j) * 2 + 0] = B[(j*fda + i) * 2 + 0];
- A[(i*fda + j) * 2 + 1] = B[(j*fda + i) * 2 + 1];
- B[(j*fda + i) * 2 + 0] = a0;
- B[(j*fda + i) * 2 + 1] = a1;
- }
- }
- break;
- }
- default: {
- int i, j, k;
- for (i = 0; i < n; ++i) {
- for (j = 0; j < m; ++j) {
- for (k = 0; k < N; ++k) {
- R a = A[(i*fda + j) * N + k];
- A[(i*fda + j) * N + k] =
- B[(j*fda + i) * N + k];
- B[(j*fda + i) * N + k] = a;
- }
- }
- }
- }
- }
- } else if (n > m) {
- int n2 = n / 2;
- rec_transpose_swap_Ntuple(A, B, n2, m, fda, N);
- rec_transpose_swap_Ntuple(A + n2*N*fda, B + n2*N, n - n2, m, fda, N);
- }
- else {
- int m2 = m / 2;
- rec_transpose_swap_Ntuple(A, B, n, m2, fda, N);
- rec_transpose_swap_Ntuple(A + m2*N, B + m2*N*fda, n, m - m2, fda, N);
- }
-}
-
-/* Transpose A, an n x n matrix (stored as n x fda), in-place. */
-static void rec_transpose_sq_ip_Ntuple(R *A, int n, int fda, int N)
-{
- if (n == 1)
- return;
- else if (n*N <= CUTOFF) {
- switch (N) {
- case 1: {
- int i, j;
- for (i = 0; i < n; ++i) {
- for (j = i + 1; j < n; ++j) {
- R a = A[(i*fda + j)];
- A[(i*fda + j)] = A[(j*fda + i)];
- A[(j*fda + i)] = a;
- }
- }
- break;
- }
- case 2: {
- int i, j;
- for (i = 0; i < n; ++i) {
- for (j = i + 1; j < n; ++j) {
- R a0 = A[(i*fda + j) * 2 + 0];
- R a1 = A[(i*fda + j) * 2 + 1];
- A[(i*fda + j) * 2 + 0] = A[(j*fda + i) * 2 + 0];
- A[(i*fda + j) * 2 + 1] = A[(j*fda + i) * 2 + 1];
- A[(j*fda + i) * 2 + 0] = a0;
- A[(j*fda + i) * 2 + 1] = a1;
- }
- }
- break;
- }
- default: {
- int i, j, k;
- for (i = 0; i < n; ++i) {
- for (j = i + 1; j < n; ++j) {
- for (k = 0; k < N; ++k) {
- R a = A[(i*fda + j) * N + k];
- A[(i*fda + j) * N + k] =
- A[(j*fda + i) * N + k];
- A[(j*fda + i) * N + k] = a;
- }
- }
- }
- }
- }
- } else {
- int n2 = n / 2;
- rec_transpose_sq_ip_Ntuple(A, n2, fda, N);
- rec_transpose_sq_ip_Ntuple((A + n2*N) + n2*N*fda, n - n2, fda, N);
- rec_transpose_swap_Ntuple(A + n2*N, A + n2*N*fda, n2, n - n2, fda,N);
- }
-}
-
-/*************************************************************************/
-/* In-place transposes of non-square matrices: */
-
-/* Transpose the matrix A in-place, where A is an (n*d) x (m*d) matrix
- of N-tuples and buf contains at least n*m*d*N elements. In
- general, to transpose a p x q matrix, you should call this routine
- with d = gcd(p, q), n = p/d, and m = q/d. */
-void X(transpose)(R *A, int n, int m, int d, int N, R *buf)
-{
- A(n > 0 && m > 0 && N > 0 && d > 0);
- if (d == 1) {
- rec_transpose_Ntuple(A, buf, n,m, m,n, N);
- memcpy(A, buf, m*n*N*sizeof(R));
- }
- else if (n*m == 1) {
- rec_transpose_sq_ip_Ntuple(A, d, d, N);
- }
- else {
- int i, num_el = n*m*d*N;
-
- /* treat as (d x n) x (d' x m) matrix. (d' = d) */
-
- /* First, transpose d x (n x d') x m to d x (d' x n) x m,
- using the buf matrix. This consists of d transposes
- of contiguous n x d' matrices of m-tuples. */
- if (n > 1) {
- for (i = 0; i < d; ++i) {
- rec_transpose_Ntuple(A + i*num_el, buf,
- n,d, d,n, m*N);
- memcpy(A + i*num_el, buf, num_el*sizeof(R));
- }
- }
-
- /* Now, transpose (d x d') x (n x m) to (d' x d) x (n x m), which
- is a square in-place transpose of n*m-tuples: */
- rec_transpose_sq_ip_Ntuple(A, d, d, n*m*N);
-
- /* Finally, transpose d' x ((d x n) x m) to d' x (m x (d x n)),
- using the buf matrix. This consists of d' transposes
- of contiguous d*n x m matrices. */
- if (m > 1) {
- for (i = 0; i < d; ++i) {
- rec_transpose_Ntuple(A + i*num_el, buf,
- d*n,m, m,d*n, N);
- memcpy(A + i*num_el, buf, num_el*sizeof(R));
- }
- }
- }
-}
-
-/*************************************************************************/
-/* In-place transpose routine from TOMS. This routine is much slower
- than the cache-oblivious algorithm above, but is has the advantage
- of requiring less buffer space for the case of gcd(nx,ny) small. */
-
-/*
- * TOMS Transpose. Revised version of algorithm 380.
- *
- * These routines do in-place transposes of arrays.
- *
- * [ Cate, E.G. and Twigg, D.W., ACM Transactions on Mathematical Software,
- * vol. 3, no. 1, 104-110 (1977) ]
- *
- * C version by Steven G. Johnson. February 1997.
- */
-
-/*
- * "a" is a 1D array of length ny*nx*N which constains the nx x ny
- * matrix of N-tuples to be transposed. "a" is stored in row-major
- * order (last index varies fastest). move is a 1D array of length
- * move_size used to store information to speed up the process. The
- * value move_size=(ny+nx)/2 is recommended. buf should be an array
- * of length 2*N.
- *
- */
-
-void X(transpose_slow)(R *a, int nx, int ny, int N,
- char *move, int move_size, R *buf)
-{
- int i, j, im, mn;
- R *b, *c, *d;
- int ncount;
- int k;
-
- /* check arguments and initialize: */
- A(ny > 0 && nx > 0 && N > 0 && move_size > 0);
-
- b = buf;
-
- if (ny == nx) {
- /*
- * if matrix is square, exchange elements a(i,j) and a(j,i):
- */
- for (i = 0; i < nx; ++i)
- for (j = i + 1; j < nx; ++j) {
- memcpy(b, &a[N * (i + j * nx)], N * sizeof(R));
- memcpy(&a[N * (i + j * nx)], &a[N * (j + i * nx)], N * sizeof(R));
- memcpy(&a[N * (j + i * nx)], b, N * sizeof(R));
- }
- return;
- }
- c = buf + N;
- ncount = 2; /* always at least 2 fixed points */
- k = (mn = ny * nx) - 1;
-
- for (i = 0; i < move_size; ++i)
- move[i] = 0;
-
- if (ny >= 3 && nx >= 3)
- ncount += gcd(ny - 1, nx - 1) - 1; /* # fixed points */
-
- i = 1;
- im = ny;
-
- while (1) {
- int i1, i2, i1c, i2c;
- int kmi;
-
- /** Rearrange the elements of a loop
- and its companion loop: **/
-
- i1 = i;
- kmi = k - i;
- memcpy(b, &a[N * i1], N * sizeof(R));
- i1c = kmi;
- memcpy(c, &a[N * i1c], N * sizeof(R));
-
- while (1) {
- i2 = ny * i1 - k * (i1 / nx);
- i2c = k - i2;
- if (i1 < move_size)
- move[i1] = 1;
- if (i1c < move_size)
- move[i1c] = 1;
- ncount += 2;
- if (i2 == i)
- break;
- if (i2 == kmi) {
- d = b;
- b = c;
- c = d;
- break;
- }
- memcpy(&a[N * i1], &a[N * i2],
- N * sizeof(R));
- memcpy(&a[N * i1c], &a[N * i2c],
- N * sizeof(R));
- i1 = i2;
- i1c = i2c;
- }
- memcpy(&a[N * i1], b, N * sizeof(R));
- memcpy(&a[N * i1c], c, N * sizeof(R));
-
- if (ncount >= mn)
- break; /* we've moved all elements */
-
- /** Search for loops to rearrange: **/
-
- while (1) {
- int max = k - i;
- ++i;
- A(i <= max);
- im += ny;
- if (im > k)
- im -= k;
- i2 = im;
- if (i == i2)
- continue;
- if (i >= move_size) {
- while (i2 > i && i2 < max) {
- i1 = i2;
- i2 = ny * i1 - k * (i1 / nx);
- }
- if (i2 == i)
- break;
- } else if (!move[i])
- break;
- }
- }
-}
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