/*
* 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;
}
}
}