cpython/Modules/_decimal/libmpdec/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)
{ … }
#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)
{ … }

/* backward transform, sign = 1; transform length = 3 * 2**n */
int
inv_four_step_fnt(mpd_uint_t *a, mpd_size_t n, int modnum)
{ … }