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Diffstat (limited to 'Modules/_decimal/libmpdec/crt.c')
| -rw-r--r-- | Modules/_decimal/libmpdec/crt.c | 179 |
1 files changed, 179 insertions, 0 deletions
diff --git a/Modules/_decimal/libmpdec/crt.c b/Modules/_decimal/libmpdec/crt.c new file mode 100644 index 0000000..c71c4ee --- /dev/null +++ b/Modules/_decimal/libmpdec/crt.c @@ -0,0 +1,179 @@ +/* + * 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); +} + + |