| /* |
| * Copyright (c) 2008-2016 Stefan Krah. All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| |
| #include mpdecimal_header |
| #include <stdlib.h> |
| #include <assert.h> |
| #include "bits.h" |
| #include "umodarith.h" |
| #include "numbertheory.h" |
| |
| |
| /* Bignum: Initialize the Number Theoretic Transform. */ |
| |
| |
| /* |
| * Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n) |
| * in the Fourier transform. We have w**n == 1 (mod p). |
| * n := transform length. |
| * sign := -1 for forward transform, 1 for backward transform. |
| * modnum := one of {P1, P2, P3}. |
| */ |
| mpd_uint_t |
| _mpd_getkernel(mpd_uint_t n, int sign, int modnum) |
| { |
| mpd_uint_t umod, p, r, xi; |
| #ifdef PPRO |
| double dmod; |
| uint32_t dinvmod[3]; |
| #endif |
| |
| SETMODULUS(modnum); |
| r = mpd_roots[modnum]; /* primitive root of F(p) */ |
| p = umod; |
| xi = (p-1) / n; |
| |
| if (sign == -1) |
| return POWMOD(r, (p-1-xi)); |
| else |
| return POWMOD(r, xi); |
| } |
| |
| /* |
| * Initialize and return transform parameters. |
| * n := transform length. |
| * sign := -1 for forward transform, 1 for backward transform. |
| * modnum := one of {P1, P2, P3}. |
| */ |
| struct fnt_params * |
| _mpd_init_fnt_params(mpd_size_t n, int sign, int modnum) |
| { |
| struct fnt_params *tparams; |
| mpd_uint_t umod; |
| #ifdef PPRO |
| double dmod; |
| uint32_t dinvmod[3]; |
| #endif |
| mpd_uint_t kernel, w; |
| mpd_uint_t i; |
| mpd_size_t nhalf; |
| |
| assert(ispower2(n)); |
| assert(sign == -1 || sign == 1); |
| assert(P1 <= modnum && modnum <= P3); |
| |
| nhalf = n/2; |
| tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t)); |
| if (tparams == NULL) { |
| return NULL; |
| } |
| |
| SETMODULUS(modnum); |
| kernel = _mpd_getkernel(n, sign, modnum); |
| |
| tparams->modnum = modnum; |
| tparams->modulus = umod; |
| tparams->kernel = kernel; |
| |
| /* wtable[] := w**0, w**1, ..., w**(nhalf-1) */ |
| w = 1; |
| for (i = 0; i < nhalf; i++) { |
| tparams->wtable[i] = w; |
| w = MULMOD(w, kernel); |
| } |
| |
| return tparams; |
| } |
| |
| /* Initialize wtable of size three. */ |
| void |
| _mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum) |
| { |
| mpd_uint_t umod; |
| #ifdef PPRO |
| double dmod; |
| uint32_t dinvmod[3]; |
| #endif |
| mpd_uint_t kernel; |
| |
| SETMODULUS(modnum); |
| kernel = _mpd_getkernel(3, sign, modnum); |
| |
| w3table[0] = 1; |
| w3table[1] = kernel; |
| w3table[2] = POWMOD(kernel, 2); |
| } |
| |
| |