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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 "bits.h"
33 #include "numbertheory.h"
34 #include "umodarith.h"
35 #include "difradix2.h"
36
37
38 /* Bignum: The actual transform routine (decimation in frequency). */
39
40
41 /*
42 * Generate index pairs (x, bitreverse(x)) and carry out the permutation.
43 * n must be a power of two.
44 * Algorithm due to Brent/Lehmann, see Joerg Arndt, "Matters Computational",
45 * Chapter 1.14.4. [http://www.jjj.de/fxt/]
46 */
47 static inline void
48 bitreverse_permute(mpd_uint_t a[], mpd_size_t n)
49 {
50 mpd_size_t x = 0;
51 mpd_size_t r = 0;
52 mpd_uint_t t;
53
54 do { /* Invariant: r = bitreverse(x) */
55 if (r > x) {
56 t = a[x];
57 a[x] = a[r];
58 a[r] = t;
59 }
60 /* Flip trailing consecutive 1 bits and the first zero bit
61 * that absorbs a possible carry. */
62 x += 1;
63 /* Mirror the operation on r: Flip n_trailing_zeros(x)+1
64 high bits of r. */
65 r ^= (n - (n >> (mpd_bsf(x)+1)));
66 /* The loop invariant is preserved. */
67 } while (x < n);
68 }
69
70
71 /* Fast Number Theoretic Transform, decimation in frequency. */
72 void
73 fnt_dif2(mpd_uint_t a[], mpd_size_t n, struct fnt_params *tparams)
74 {
75 mpd_uint_t *wtable = tparams->wtable;
76 mpd_uint_t umod;
77 #ifdef PPRO
78 double dmod;
79 uint32_t dinvmod[3];
80 #endif
81 mpd_uint_t u0, u1, v0, v1;
82 mpd_uint_t w, w0, w1, wstep;
83 mpd_size_t m, mhalf;
84 mpd_size_t j, r;
85
86
87 assert(ispower2(n));
88 assert(n >= 4);
89
90 SETMODULUS(tparams->modnum);
91
92 /* m == n */
93 mhalf = n / 2;
94 for (j = 0; j < mhalf; j += 2) {
95
96 w0 = wtable[j];
97 w1 = wtable[j+1];
98
99 u0 = a[j];
100 v0 = a[j+mhalf];
101
102 u1 = a[j+1];
103 v1 = a[j+1+mhalf];
104
105 a[j] = addmod(u0, v0, umod);
106 v0 = submod(u0, v0, umod);
107
108 a[j+1] = addmod(u1, v1, umod);
109 v1 = submod(u1, v1, umod);
110
111 MULMOD2(&v0, w0, &v1, w1);
112
113 a[j+mhalf] = v0;
114 a[j+1+mhalf] = v1;
115
116 }
117
118 wstep = 2;
119 for (m = n/2; m >= 2; m>>=1, wstep<<=1) {
120
121 mhalf = m / 2;
122
123 /* j == 0 */
124 for (r = 0; r < n; r += 2*m) {
125
126 u0 = a[r];
127 v0 = a[r+mhalf];
128
129 u1 = a[m+r];
130 v1 = a[m+r+mhalf];
131
132 a[r] = addmod(u0, v0, umod);
133 v0 = submod(u0, v0, umod);
134
135 a[m+r] = addmod(u1, v1, umod);
136 v1 = submod(u1, v1, umod);
137
138 a[r+mhalf] = v0;
139 a[m+r+mhalf] = v1;
140 }
141
142 for (j = 1; j < mhalf; j++) {
143
144 w = wtable[j*wstep];
145
146 for (r = 0; r < n; r += 2*m) {
147
148 u0 = a[r+j];
149 v0 = a[r+j+mhalf];
150
151 u1 = a[m+r+j];
152 v1 = a[m+r+j+mhalf];
153
154 a[r+j] = addmod(u0, v0, umod);
155 v0 = submod(u0, v0, umod);
156
157 a[m+r+j] = addmod(u1, v1, umod);
158 v1 = submod(u1, v1, umod);
159
160 MULMOD2C(&v0, &v1, w);
161
162 a[r+j+mhalf] = v0;
163 a[m+r+j+mhalf] = v1;
164 }
165
166 }
167
168 }
169
170 bitreverse_permute(a, n);
171 }
172
173
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