/*

 * 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 "crt.h"

#include "numbertheory.h"

#include "mpdecimal.h"

#include "typearith.h"

#include "umodarith.h"

/* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */

/* Multiply P1P2 by v, store result in w. */

static inline void

_crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)

{

    mpd_uint_t hi1, hi2, lo;

    _mpd_mul_words(&hi1, &lo, LH_P1P2, v);

    w[0] = lo;

    _mpd_mul_words(&hi2, &lo, UH_P1P2, v);

    lo = hi1 + lo;

    if (lo < hi1) hi2++;

    w[1] = lo;

    w[2] = hi2;

}

/* Add 3 words from v to w. The result is known to fit in w. */

static inline void

_crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])

{

    mpd_uint_t carry;

    w[0] = w[0] + v[0];

    carry = (w[0] < v[0]);

    w[1] = w[1] + v[1];

    if (w[1] < v[1]) w[2]++;

    w[1] = w[1] + carry;

    if (w[1] < carry) w[2]++;

    w[2] += v[2];

}

/* Divide 3 words in u by v, store result in w, return remainder. */

static inline mpd_uint_t

_crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)

{

    mpd_uint_t r1 = u[2];

    mpd_uint_t r2;

    if (r1 < v) {

        w[2] = 0;

    }

    else {

        _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */

    }

    _mpd_div_words(&w[1], &r2, r1, u[1], v);

    _mpd_div_words(&w[0], &r1, r2, u[0], v);

    return r1;

}

/*

 * Chinese Remainder Theorem:

 * Algorithm from Joerg Arndt, "Matters Computational",

 * Chapter 37.4.1 [http://www.jjj.de/fxt/]

 *

 * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7.

 */

/*

 * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each

 * triple of members of the arrays, find the unique z modulo p1*p2*p3, with

 * zmax = p1*p2*p3 - 1.

 *

 * In each iteration of the loop, split z into result[i] = z % MPD_RADIX

 * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the

 * maximum carry.

 *

 * Limits for the 32-bit build:

 *

 *   N    = 2**96

 *   cmax = 7711435591312380274

 *

 * Limits for the 64 bit build:

 *

 *   N    = 2**192

 *   cmax = 627710135393475385904124401220046371710

 *

 * The following statements hold for both versions:

 *

 *   1) cmax + zmax < N, so the addition does not overflow.

 *

 *   2) (cmax + zmax) / MPD_RADIX == cmax.

 *

 *   3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax.

 */

void

crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)

{

    mpd_uint_t p1 = mpd_moduli[P1];

    mpd_uint_t umod;

#ifdef PPRO

    double dmod;

    uint32_t dinvmod[3];

#endif

    mpd_uint_t a1, a2, a3;

    mpd_uint_t s;

    mpd_uint_t z[3], t[3];

    mpd_uint_t carry[3] = {0,0,0};

    mpd_uint_t hi, lo;

    mpd_size_t i;

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

        a1 = x1[i];

        a2 = x2[i];

        a3 = x3[i];

        SETMODULUS(P2);

        s = ext_submod(a2, a1, umod);

        s = MULMOD(s, INV_P1_MOD_P2);

        _mpd_mul_words(&hi, &lo, s, p1);

        lo = lo + a1;

        if (lo < a1) hi++;

        SETMODULUS(P3);

        s = dw_submod(a3, hi, lo, umod);

        s = MULMOD(s, INV_P1P2_MOD_P3);

        z[0] = lo;

        z[1] = hi;

        z[2] = 0;

        _crt_mulP1P2_3(t, s);

        _crt_add3(z, t);

        _crt_add3(carry, z);

        x1[i] = _crt_div3(carry, carry, MPD_RADIX);

    }

    assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);

}