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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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