1/*
2 * Copyright (c) 2008-2016 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 */
47static inline void
48bitreverse_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. */
72void
73fnt_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
174