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/*
* Copyright (c) 2008-2020 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 <assert.h>
#include <stdlib.h>
#include "bits.h"
#include "numbertheory.h"
#include "umodarith.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);
}
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