transpose.c

/*
 * 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;
}