| /* |
| * Copyright (c) 2008-2012 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 <stdio.h> |
| #include <assert.h> |
| #include "numbertheory.h" |
| #include "umodarith.h" |
| #include "crt.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; |
| mpd_uint_t s; |
| |
| s = w[0] + v[0]; |
| carry = (s < w[0]); |
| w[0] = s; |
| |
| s = w[1] + (v[1] + carry); |
| carry = (s < w[1]); |
| w[1] = s; |
| |
| w[2] = w[2] + (v[2] + carry); |
| } |
| |
| /* 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); |
| } |
| |
| |