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/* * 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.h" #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); }