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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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