/*

 * Copyright (c) 2008-2024 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 <assert.h>

#include "constants.h"

#include "fourstep.h"

#include "mpdecimal.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;

        }

    }

    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);

    /* 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;

}