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132 lines
3.5 KiB
C
132 lines
3.5 KiB
C
/*
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* Copyright (c) 2008-2020 Stefan Krah. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS "AS IS" AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include "mpdecimal.h"
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#include <assert.h>
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#include <stdlib.h>
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#include "bits.h"
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#include "numbertheory.h"
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#include "umodarith.h"
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/* Bignum: Initialize the Number Theoretic Transform. */
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/*
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* Return the nth root of unity in F(p). This corresponds to e**((2*pi*i)/n)
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* in the Fourier transform. We have w**n == 1 (mod p).
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* n := transform length.
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* sign := -1 for forward transform, 1 for backward transform.
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* modnum := one of {P1, P2, P3}.
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*/
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mpd_uint_t
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_mpd_getkernel(mpd_uint_t n, int sign, int modnum)
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{
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mpd_uint_t umod, p, r, xi;
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#ifdef PPRO
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double dmod;
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uint32_t dinvmod[3];
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#endif
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SETMODULUS(modnum);
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r = mpd_roots[modnum]; /* primitive root of F(p) */
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p = umod;
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xi = (p-1) / n;
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if (sign == -1)
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return POWMOD(r, (p-1-xi));
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else
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return POWMOD(r, xi);
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}
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/*
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* Initialize and return transform parameters.
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* n := transform length.
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* sign := -1 for forward transform, 1 for backward transform.
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* modnum := one of {P1, P2, P3}.
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*/
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struct fnt_params *
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_mpd_init_fnt_params(mpd_size_t n, int sign, int modnum)
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{
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struct fnt_params *tparams;
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mpd_uint_t umod;
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#ifdef PPRO
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double dmod;
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uint32_t dinvmod[3];
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#endif
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mpd_uint_t kernel, w;
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mpd_uint_t i;
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mpd_size_t nhalf;
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assert(ispower2(n));
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assert(sign == -1 || sign == 1);
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assert(P1 <= modnum && modnum <= P3);
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nhalf = n/2;
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tparams = mpd_sh_alloc(sizeof *tparams, nhalf, sizeof (mpd_uint_t));
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if (tparams == NULL) {
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return NULL;
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}
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SETMODULUS(modnum);
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kernel = _mpd_getkernel(n, sign, modnum);
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tparams->modnum = modnum;
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tparams->modulus = umod;
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tparams->kernel = kernel;
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/* wtable[] := w**0, w**1, ..., w**(nhalf-1) */
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w = 1;
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for (i = 0; i < nhalf; i++) {
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tparams->wtable[i] = w;
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w = MULMOD(w, kernel);
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}
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return tparams;
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}
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/* Initialize wtable of size three. */
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void
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_mpd_init_w3table(mpd_uint_t w3table[3], int sign, int modnum)
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{
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mpd_uint_t umod;
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#ifdef PPRO
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double dmod;
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uint32_t dinvmod[3];
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#endif
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mpd_uint_t kernel;
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SETMODULUS(modnum);
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kernel = _mpd_getkernel(3, sign, modnum);
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w3table[0] = 1;
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w3table[1] = kernel;
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w3table[2] = POWMOD(kernel, 2);
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}
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