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/*
* Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include "mpdecimal.h"
#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "bits.h"
#include "constants.h"
#include "transpose.h"
#include "typearith.h"
#define BUFSIZE 4096
#define SIDE 128
/* Bignum: The transpose functions are used for very large transforms
in sixstep.c and fourstep.c. */
/* Definition of the matrix transpose */
void
std_trans(mpd_uint_t dest[], mpd_uint_t src[], mpd_size_t rows, mpd_size_t cols)
{
mpd_size_t idest, isrc;
mpd_size_t r, c;
for (r = 0; r < rows; r++) {
isrc = r * cols;
idest = r;
for (c = 0; c < cols; c++) {
dest[idest] = src[isrc];
isrc += 1;
idest += rows;
}
}
}
/*
* Swap half-rows of 2^n * (2*2^n) matrix.
* FORWARD_CYCLE: even/odd permutation of the halfrows.
* BACKWARD_CYCLE: reverse the even/odd permutation.
*/
static int
swap_halfrows_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols, int dir)
{
mpd_uint_t buf1[BUFSIZE];
mpd_uint_t buf2[BUFSIZE];
mpd_uint_t *readbuf, *writebuf, *hp;
mpd_size_t *done, dbits;
mpd_size_t b = BUFSIZE, stride;
mpd_size_t hn, hmax; /* halfrow number */
mpd_size_t m, r=0;
mpd_size_t offset;
mpd_size_t next;
assert(cols == mul_size_t(2, rows));
if (dir == FORWARD_CYCLE) {
r = rows;
}
else if (dir == BACKWARD_CYCLE) {
r = 2;
}
else {
abort(); /* GCOV_NOT_REACHED */
}
m = cols - 1;
hmax = rows; /* cycles start at odd halfrows */
dbits = 8 * sizeof *done;
if ((done = mpd_calloc(hmax/(sizeof *done) + 1, sizeof *done)) == NULL) {
return 0;
}
for (hn = 1; hn <= hmax; hn += 2) {
if (done[hn/dbits] & mpd_bits[hn%dbits]) {
continue;
}
readbuf = buf1; writebuf = buf2;
for (offset = 0; offset < cols/2; offset += b) {
stride = (offset + b < cols/2) ? b : cols/2-offset;
hp = matrix + hn*cols/2;
memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
pointerswap(&readbuf, &writebuf);
next = mulmod_size_t(hn, r, m);
hp = matrix + next*cols/2;
while (next != hn) {
memcpy(readbuf, hp+offset, stride*(sizeof *readbuf));
memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
pointerswap(&readbuf, &writebuf);
done[next/dbits] |= mpd_bits[next%dbits];
next = mulmod_size_t(next, r, m);
hp = matrix + next*cols/2;
}
memcpy(hp+offset, writebuf, stride*(sizeof *writebuf));
done[hn/dbits] |= mpd_bits[hn%dbits];
}
}
mpd_free(done);
return 1;
}
/* In-place transpose of a square matrix */
static inline void
squaretrans(mpd_uint_t *buf, mpd_size_t cols)
{
mpd_uint_t tmp;
mpd_size_t idest, isrc;
mpd_size_t r, c;
for (r = 0; r < cols; r++) {
c = r+1;
isrc = r*cols + c;
idest = c*cols + r;
for (c = r+1; c < cols; c++) {
tmp = buf[isrc];
buf[isrc] = buf[idest];
buf[idest] = tmp;
isrc += 1;
idest += cols;
}
}
}
/*
* Transpose 2^n * 2^n matrix. For cache efficiency, the matrix is split into
* square blocks with side length 'SIDE'. First, the blocks are transposed,
* then a square transposition is done on each individual block.
*/
static void
squaretrans_pow2(mpd_uint_t *matrix, mpd_size_t size)
{
mpd_uint_t buf1[SIDE*SIDE];
mpd_uint_t buf2[SIDE*SIDE];
mpd_uint_t *to, *from;
mpd_size_t b = size;
mpd_size_t r, c;
mpd_size_t i;
while (b > SIDE) b >>= 1;
for (r = 0; r < size; r += b) {
for (c = r; c < size; c += b) {
from = matrix + r*size + c;
to = buf1;
for (i = 0; i < b; i++) {
memcpy(to, from, b*(sizeof *to));
from += size;
to += b;
}
squaretrans(buf1, b);
if (r == c) {
to = matrix + r*size + c;
from = buf1;
for (i = 0; i < b; i++) {
memcpy(to, from, b*(sizeof *to));
from += b;
to += size;
}
continue;
}
else {
from = matrix + c*size + r;
to = buf2;
for (i = 0; i < b; i++) {
memcpy(to, from, b*(sizeof *to));
from += size;
to += b;
}
squaretrans(buf2, b);
to = matrix + c*size + r;
from = buf1;
for (i = 0; i < b; i++) {
memcpy(to, from, b*(sizeof *to));
from += b;
to += size;
}
to = matrix + r*size + c;
from = buf2;
for (i = 0; i < b; i++) {
memcpy(to, from, b*(sizeof *to));
from += b;
to += size;
}
}
}
}
}
/*
* In-place transposition of a 2^n x 2^n or a 2^n x (2*2^n)
* or a (2*2^n) x 2^n matrix.
*/
int
transpose_pow2(mpd_uint_t *matrix, mpd_size_t rows, mpd_size_t cols)
{
mpd_size_t size = mul_size_t(rows, cols);
assert(ispower2(rows));
assert(ispower2(cols));
if (cols == rows) {
squaretrans_pow2(matrix, rows);
}
else if (cols == mul_size_t(2, rows)) {
if (!swap_halfrows_pow2(matrix, rows, cols, FORWARD_CYCLE)) {
return 0;
}
squaretrans_pow2(matrix, rows);
squaretrans_pow2(matrix+(size/2), rows);
}
else if (rows == mul_size_t(2, cols)) {
squaretrans_pow2(matrix, cols);
squaretrans_pow2(matrix+(size/2), cols);
if (!swap_halfrows_pow2(matrix, cols, rows, BACKWARD_CYCLE)) {
return 0;
}
}
else {
abort(); /* GCOV_NOT_REACHED */
}
return 1;
}
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