/*

 * 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 <stdlib.h>

#include "bits.h"

#include "numbertheory.h"

#include "mpdecimal.h"

#include "umodarith.h"

/* Bignum: Initialize the Number Theoretic Transform. */

/*

 * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)

 * in the Fourier transform. We have w**n == 1 (mod p).

 *    n := transform length.

 *    sign := -1 for forward transform, 1 for backward transform.

 *    modnum := one of {P1, P2, P3}.

 */

mpd_uint_t

_mpd_getkernel(mpd_uint_t n, int sign, int modnum)

{

    mpd_uint_t umod, p, r, xi;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    SETMODULUS(modnum);

    r = mpd_roots[modnum]; /* primitive root of F(p) */

    p = umod;

    xi = (p-1) / n;

    if (sign == -1)

        return POWMOD(r, (p-1-xi));

    else

        return POWMOD(r, xi);

}

/*

 * Initialize and return transform parameters.

 *    n := transform length.

 *    sign := -1 for forward transform, 1 for backward transform.

 *    modnum := one of {P1, P2, P3}.

 */

struct fnt_params *

_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)

{

    struct fnt_params *tparams;

    mpd_uint_t umod;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    mpd_uint_t kernel, w;

    mpd_uint_t i;

    mpd_size_t nhalf;

    assert(ispower2(n));

    assert(sign == -1 || sign == 1);

    assert(P1 <= modnum && modnum <= P3);

    nhalf = n/2;

    tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));

    if (tparams == NULL) {

        return NULL;

    }

    SETMODULUS(modnum);

    kernel = _mpd_getkernel(n, sign, modnum);

    tparams->modnum = modnum;

    tparams->modulus = umod;

    tparams->kernel = kernel;

    /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */

    w = 1;

    for (i = 0; i < nhalf; i++) {

        tparams->wtable[i] = w;

        w = MULMOD(w, kernel);

    }

    return tparams;

}

/* Initialize wtable of size three. */

void

_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)

{

    mpd_uint_t umod;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    mpd_uint_t kernel;

    SETMODULUS(modnum);

    kernel = _mpd_getkernel(3, sign, modnum);

    w3table[0] = 1;

    w3table[1] = kernel;

    w3table[2] = POWMOD(kernel, 2);

}