sixstep.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 <stdio.h>

#include "bits.h"
#include "constants.h"
#include "difradix2.h"
#include "numbertheory.h"
#include "sixstep.h"
#include "transpose.h"
#include "umodarith.h"


/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
   form 2**n (See literature/six-step.txt). */


/* forward transform with sign = -1 */
int
six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
    struct fnt_params *tparams;
    mpd_size_t log2n, C, R;
    mpd_uint_t kernel;
    mpd_uint_t umod;
#ifdef PPRO
    double dmod;
    uint32_t dinvmod[3];
#endif
    mpd_uint_t *x, w0, w1, wstep;
    mpd_size_t i, k;


    assert(ispower2(n));
    assert(n >= 16);
    assert(n <= MPD_MAXTRANSFORM_2N);

    log2n = mpd_bsr(n);
    C = ((mpd_size_t)1) << (log2n / 2);  /* number of columns */
    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */


    /* Transpose the matrix. */
    if (!transpose_pow2(a, R, C)) {
        return 0;
    }

    /* Length R transform on the rows. */
    if ((tparams = _mpd_init_fnt_params(R, -1, modnum)) == NULL) {
        return 0;
    }
    for (x = a; x < a+n; x += R) {
        fnt_dif2(x, R, tparams);
    }

    /* Transpose the matrix. */
    if (!transpose_pow2(a, C, R)) {
        mpd_free(tparams);
        return 0;
    }

    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
    SETMODULUS(modnum);
    kernel = _mpd_getkernel(n, -1, modnum);
    for (i = 1; i < R; i++) {
        w0 = 1;                  /* r**(i*0): initial value for k=0 */
        w1 = POWMOD(kernel, i);  /* r**(i*1): initial value for k=1 */
        wstep = MULMOD(w1, w1);  /* r**(2*i) */
        for (k = 0; k < C; k += 2) {
            mpd_uint_t x0 = a[i*C+k];
            mpd_uint_t x1 = a[i*C+k+1];
            MULMOD2(&x0, w0, &x1, w1);
            MULMOD2C(&w0, &w1, wstep);  /* r**(i*(k+2)) = r**(i*k) * r**(2*i) */
            a[i*C+k] = x0;
            a[i*C+k+1] = x1;
        }
    }

    /* Length C transform on the rows. */
    if (C != R) {
        mpd_free(tparams);
        if ((tparams = _mpd_init_fnt_params(C, -1, modnum)) == NULL) {
            return 0;
        }
    }
    for (x = a; x < a+n; x += C) {
        fnt_dif2(x, C, tparams);
    }
    mpd_free(tparams);

#if 0
    /* An unordered transform is sufficient for convolution. */
    /* Transpose the matrix. */
    if (!transpose_pow2(a, R, C)) {
        return 0;
    }
#endif

    return 1;
}


/* reverse transform, sign = 1 */
int
inv_six_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
    struct fnt_params *tparams;
    mpd_size_t log2n, C, R;
    mpd_uint_t kernel;
    mpd_uint_t umod;
#ifdef PPRO
    double dmod;
    uint32_t dinvmod[3];
#endif
    mpd_uint_t *x, w0, w1, wstep;
    mpd_size_t i, k;


    assert(ispower2(n));
    assert(n >= 16);
    assert(n <= MPD_MAXTRANSFORM_2N);

    log2n = mpd_bsr(n);
    C = ((mpd_size_t)1) << (log2n / 2); /* number of columns */
    R = ((mpd_size_t)1) << (log2n - (log2n / 2)); /* number of rows */


#if 0
    /* An unordered transform is sufficient for convolution. */
    /* Transpose the matrix, producing an R*C matrix. */
    if (!transpose_pow2(a, C, R)) {
        return 0;
    }
#endif

    /* Length C transform on the rows. */
    if ((tparams = _mpd_init_fnt_params(C, 1, modnum)) == NULL) {
        return 0;
    }
    for (x = a; x < a+n; x += C) {
        fnt_dif2(x, C, tparams);
    }

    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
    SETMODULUS(modnum);
    kernel = _mpd_getkernel(n, 1, modnum);
    for (i = 1; i < R; i++) {
        w0 = 1;
        w1 = POWMOD(kernel, i);
        wstep = MULMOD(w1, w1);
        for (k = 0; k < C; k += 2) {
            mpd_uint_t x0 = a[i*C+k];
            mpd_uint_t x1 = a[i*C+k+1];
            MULMOD2(&x0, w0, &x1, w1);
            MULMOD2C(&w0, &w1, wstep);
            a[i*C+k] = x0;
            a[i*C+k+1] = x1;
        }
    }

    /* Transpose the matrix. */
    if (!transpose_pow2(a, R, C)) {
        mpd_free(tparams);
        return 0;
    }

    /* Length R transform on the rows. */
    if (R != C) {
        mpd_free(tparams);
        if ((tparams = _mpd_init_fnt_params(R, 1, modnum)) == NULL) {
            return 0;
        }
    }
    for (x = a; x < a+n; x += R) {
        fnt_dif2(x, R, tparams);
    }
    mpd_free(tparams);

    /* Transpose the matrix. */
    if (!transpose_pow2(a, C, R)) {
        return 0;
    }

    return 1;
}