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Issue 7652: Merge C version of decimal into py3k.
Patch Set: Created 7 years, 5 months ago
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1 /*
2 * Copyright (c) 2008-2010 Stefan Krah. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 *
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 *
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28
29 #include "mpdecimal.h"
30 #include <stdio.h>
31 #include <assert.h>
32 #include "numbertheory.h"
33 #include "umodarith.h"
34 #include "crt.h"
35
36
37 /* Bignum: Chinese Remainder Theorem, extends the maximum transform length. */
38
39
40 /* Multiply P1P2 by v, store result in w. */
41 static inline void
42 _crt_mulP1P2_3(mpd_uint_t w[3], mpd_uint_t v)
43 {
44 mpd_uint_t hi1, hi2, lo;
45
46 _mpd_mul_words(&hi1, &lo, LH_P1P2, v);
47 w[0] = lo;
48
49 _mpd_mul_words(&hi2, &lo, UH_P1P2, v);
50 lo = hi1 + lo;
51 if (lo < hi1) hi2++;
52
53 w[1] = lo;
54 w[2] = hi2;
55 }
56
57 /* Add 3 words from v to w. The result is known to fit in w. */
58 static inline void
59 _crt_add3(mpd_uint_t w[3], mpd_uint_t v[3])
60 {
61 mpd_uint_t carry;
62 mpd_uint_t s;
63
64 s = w[0] + v[0];
65 carry = (s < w[0]);
66 w[0] = s;
67
68 s = w[1] + (v[1] + carry);
69 carry = (s < w[1]);
70 w[1] = s;
71
72 w[2] = w[2] + (v[2] + carry);
73 }
74
75 /* Divide 3 words in u by v, store result in w, return remainder. */
76 static inline mpd_uint_t
77 _crt_div3(mpd_uint_t *w, const mpd_uint_t *u, mpd_uint_t v)
78 {
79 mpd_uint_t r1 = u[2];
80 mpd_uint_t r2;
81
82 if (r1 < v) {
83 w[2] = 0;
84 }
85 else {
86 _mpd_div_word(&w[2], &r1, u[2], v); /* GCOV_NOT_REACHED */
87 }
88
89 _mpd_div_words(&w[1], &r2, r1, u[1], v);
90 _mpd_div_words(&w[0], &r1, r2, u[0], v);
91
92 return r1;
93 }
94
95
96 /*
97 * Chinese Remainder Theorem:
98 * Algorithm from Joerg Arndt, "Matters Computational",
99 * Chapter 37.4.1 [http://www.jjj.de/fxt/]
100 *
101 * See also Knuth, TAOCP, Volume 2, 4.3.2, exercise 7.
102 */
103
104 /*
105 * CRT with carry: x1, x2, x3 contain numbers modulo p1, p2, p3. For each
106 * triple of members of the arrays, find the unique z modulo p1*p2*p3, with
107 * zmax = p1*p2*p3 - 1.
108 *
109 * In each iteration of the loop, split z into result[i] = z % MPD_RADIX
110 * and carry = z / MPD_RADIX. Let N be the size of carry[] and cmax the
111 * maximum carry.
112 *
113 * Limits for the 32-bit build:
114 *
115 * N = 2**96
116 * cmax = 7711435591312380274
117 *
118 * Limits for the 64 bit build:
119 *
120 * N = 2**192
121 * cmax = 627710135393475385904124401220046371710
122 *
123 * The following statements hold for both versions:
124 *
125 * 1) cmax + zmax < N, so the addition does not overflow.
126 *
127 * 2) (cmax + zmax) / MPD_RADIX == cmax.
128 *
129 * 3) If c <= cmax, then c_next = (c + zmax) / MPD_RADIX <= cmax.
130 */
131 void
132 crt3(mpd_uint_t *x1, mpd_uint_t *x2, mpd_uint_t *x3, mpd_size_t rsize)
133 {
134 mpd_uint_t p1 = mpd_moduli[P1];
135 mpd_uint_t umod;
136 #ifdef PPRO
137 double dmod;
138 uint32_t dinvmod[3];
139 #endif
140 mpd_uint_t a1, a2, a3;
141 mpd_uint_t s;
142 mpd_uint_t z[3], t[3];
143 mpd_uint_t carry[3] = {0,0,0};
144 mpd_uint_t hi, lo;
145 mpd_size_t i;
146
147 for (i = 0; i < rsize; i++) {
148
149 a1 = x1[i];
150 a2 = x2[i];
151 a3 = x3[i];
152
153 SETMODULUS(P2);
154 s = ext_submod(a2, a1, umod);
155 s = MULMOD(s, INV_P1_MOD_P2);
156
157 _mpd_mul_words(&hi, &lo, s, p1);
158 lo = lo + a1;
159 if (lo < a1) hi++;
160
161 SETMODULUS(P3);
162 s = dw_submod(a3, hi, lo, umod);
163 s = MULMOD(s, INV_P1P2_MOD_P3);
164
165 z[0] = lo;
166 z[1] = hi;
167 z[2] = 0;
168
169 _crt_mulP1P2_3(t, s);
170 _crt_add3(z, t);
171 _crt_add3(carry, z);
172
173 x1[i] = _crt_div3(carry, carry, MPD_RADIX);
174 }
175
176 assert(carry[0] == 0 && carry[1] == 0 && carry[2] == 0);
177 }
178
179
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