fourstep.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 "constants.h"
#include "fourstep.h"
#include "numbertheory.h"
#include "sixstep.h"
#include "umodarith.h"


/* Bignum: Cache efficient Matrix Fourier Transform for arrays of the
   form 3 * 2**n (See literature/matrix-transform.txt). */


#ifndef PPRO
static inline void
std_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3,
              mpd_uint_t w3table[3], mpd_uint_t umod)
{
    mpd_uint_t r1, r2;
    mpd_uint_t w;
    mpd_uint_t s, tmp;


    /* k = 0 -> w = 1 */
    s = *x1;
    s = addmod(s, *x2, umod);
    s = addmod(s, *x3, umod);

    r1 = s;

    /* k = 1 */
    s = *x1;

    w = w3table[1];
    tmp = MULMOD(*x2, w);
    s = addmod(s, tmp, umod);

    w = w3table[2];
    tmp = MULMOD(*x3, w);
    s = addmod(s, tmp, umod);

    r2 = s;

    /* k = 2 */
    s = *x1;

    w = w3table[2];
    tmp = MULMOD(*x2, w);
    s = addmod(s, tmp, umod);

    w = w3table[1];
    tmp = MULMOD(*x3, w);
    s = addmod(s, tmp, umod);

    *x3 = s;
    *x2 = r2;
    *x1 = r1;
}
#else /* PPRO */
static inline void
ppro_size3_ntt(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_uint_t w3table[3],
               mpd_uint_t umod, double *dmod, uint32_t dinvmod[3])
{
    mpd_uint_t r1, r2;
    mpd_uint_t w;
    mpd_uint_t s, tmp;


    /* k = 0 -> w = 1 */
    s = *x1;
    s = addmod(s, *x2, umod);
    s = addmod(s, *x3, umod);

    r1 = s;

    /* k = 1 */
    s = *x1;

    w = w3table[1];
    tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
    s = addmod(s, tmp, umod);

    w = w3table[2];
    tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
    s = addmod(s, tmp, umod);

    r2 = s;

    /* k = 2 */
    s = *x1;

    w = w3table[2];
    tmp = ppro_mulmod(*x2, w, dmod, dinvmod);
    s = addmod(s, tmp, umod);

    w = w3table[1];
    tmp = ppro_mulmod(*x3, w, dmod, dinvmod);
    s = addmod(s, tmp, umod);

    *x3 = s;
    *x2 = r2;
    *x1 = r1;
}
#endif


/* forward transform, sign = -1; transform length = 3 * 2**n */
int
four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
    mpd_size_t R = 3; /* number of rows */
    mpd_size_t C = n / 3; /* number of columns */
    mpd_uint_t w3table[3];
    mpd_uint_t kernel, w0, w1, wstep;
    mpd_uint_t *s, *p0, *p1, *p2;
    mpd_uint_t umod;
#ifdef PPRO
    double dmod;
    uint32_t dinvmod[3];
#endif
    mpd_size_t i, k;


    assert(n >= 48);
    assert(n <= 3*MPD_MAXTRANSFORM_2N);


    /* Length R transform on the columns. */
    SETMODULUS(modnum);
    _mpd_init_w3table(w3table, -1, modnum);
    for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {

        SIZE3_NTT(p0, p1, p2, w3table);
    }

    /* Multiply each matrix element (addressed by i*C+k) by r**(i*k). */
    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-1; 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. */
    for (s = a; s < a+n; s += C) {
        if (!six_step_fnt(s, C, modnum)) {
            return 0;
        }
    }

#if 0
    /* An unordered transform is sufficient for convolution. */
    /* Transpose the matrix. */
    #include "transpose.h"
    transpose_3xpow2(a, R, C);
#endif

    return 1;
}

/* backward transform, sign = 1; transform length = 3 * 2**n */
int
inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{
    mpd_size_t R = 3; /* number of rows */
    mpd_size_t C = n / 3; /* number of columns */
    mpd_uint_t w3table[3];
    mpd_uint_t kernel, w0, w1, wstep;
    mpd_uint_t *s, *p0, *p1, *p2;
    mpd_uint_t umod;
#ifdef PPRO
    double dmod;
    uint32_t dinvmod[3];
#endif
    mpd_size_t i, k;


    assert(n >= 48);
    assert(n <= 3*MPD_MAXTRANSFORM_2N);


#if 0
    /* An unordered transform is sufficient for convolution. */
    /* Transpose the matrix, producing an R*C matrix. */
    #include "transpose.h"
    transpose_3xpow2(a, C, R);
#endif

    /* Length C transform on the rows. */
    for (s = a; s < a+n; s += C) {
        if (!inv_six_step_fnt(s, C, modnum)) {
            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;
        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;
        }
    }

    /* Length R transform on the columns. */
    _mpd_init_w3table(w3table, 1, modnum);
    for (p0=a, p1=p0+C, p2=p0+2*C; p0<a+C; p0++,p1++,p2++) {

        SIZE3_NTT(p0, p1, p2, w3table);
    }

    return 1;
}