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 <stdlib.h> 31 #include <assert.h> 32 #include "bits.h" 33 #include "umodarith.h" 34 #include "numbertheory.h" 35 36 37 /* Bignum: Initialize the Number Theoretic Transform. */ 38 39 40 /* 41 * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n) 42 * in the Fourier transform. We have w**n == 1 (mod p). 43 * n := transform length. 44 * sign := -1 for forward transform, 1 for backward transform. 45 * modnum := one of {P1, P2, P3}. 46 */ 47 mpd_uint_t 48 _mpd_getkernel(mpd_uint_t n, int sign, int modnum) 49 { 50 mpd_uint_t umod, p, r, xi; 51 #ifdef PPRO 52 double dmod; 53 uint32_t dinvmod[3]; 54 #endif 55 56 SETMODULUS(modnum); 57 r = mpd_roots[modnum]; /* primitive root of F(p) */ 58 p = umod; 59 xi = (p-1) / n; 60 61 if (sign == -1) 62 return POWMOD(r, (p-1-xi)); 63 else 64 return POWMOD(r, xi); 65 } 66 67 /* 68 * Initialize and return transform parameters. 69 * n := transform length. 70 * sign := -1 for forward transform, 1 for backward transform. 71 * modnum := one of {P1, P2, P3}. 72 */ 73 struct fnt_params * 74 _mpd_init_fnt_params(mpd_size_t n, int sign, int modnum) 75 { 76 struct fnt_params *tparams; 77 mpd_uint_t umod; 78 #ifdef PPRO 79 double dmod; 80 uint32_t dinvmod[3]; 81 #endif 82 mpd_uint_t kernel, w; 83 mpd_uint_t i; 84 mpd_size_t nhalf; 85 86 assert(ispower2(n)); 87 assert(sign == -1 || sign == 1); 88 assert(P1 <= modnum && modnum <= P3); 89 90 nhalf = n/2; 91 tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t)); 92 if (tparams == NULL) { 93 return NULL; 94 } 95 96 SETMODULUS(modnum); 97 kernel = _mpd_getkernel(n, sign, modnum); 98 99 tparams->modnum = modnum; 100 tparams->modulus = umod; 101 tparams->kernel = kernel; 102 103 /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */ 104 w = 1; 105 for (i = 0; i < nhalf; i++) { 106 tparams->wtable[i] = w; 107 w = MULMOD(w, kernel); 108 } 109 110 return tparams; 111 } 112 113 /* Initialize wtable of size three. */ 114 void 115 _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum) 116 { 117 mpd_uint_t umod; 118 #ifdef PPRO 119 double dmod; 120 uint32_t dinvmod[3]; 121 #endif 122 mpd_uint_t kernel; 123 124 SETMODULUS(modnum); 125 kernel = _mpd_getkernel(3, sign, modnum); 126 127 w3table[0] = 1; 128 w3table[1] = kernel; 129 w3table[2] = POWMOD(kernel, 2); 130 } 131 132 133