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/*
* 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 "crt.h"
#include "numbertheory.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);
}
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