pqc/external/flint-2.4.3/nmod_poly/exp_series.c
2014-05-24 23:16:06 +02:00

216 lines
6.0 KiB
C

/*=============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2011 Fredrik Johansson
******************************************************************************/
#include <gmp.h>
#include "flint.h"
#include "ulong_extras.h"
#include "nmod_vec.h"
#include "nmod_poly.h"
#define NMOD_POLY_NEWTON_EXP_CUTOFF 200
/* with inverse=1 simultaneously computes g = exp(-x) to length n
with inverse=0 uses g as scratch space, computing
g = exp(-x) only to length (n+1)/2 */
static void
_nmod_poly_exp_series_newton(mp_ptr f, mp_ptr g,
mp_srcptr h, slong n, nmod_t mod, int inverse)
{
slong a[FLINT_BITS];
slong i, m, m2, l;
mp_ptr T, U, hprime;
T = _nmod_vec_init(n);
U = _nmod_vec_init(n);
hprime = _nmod_vec_init(n);
_nmod_poly_derivative(hprime, h, n, mod);
hprime[n-1] = UWORD(0);
for (i = 1; (WORD(1) << i) < n; i++);
a[i = 0] = n;
while (n >= NMOD_POLY_NEWTON_EXP_CUTOFF)
a[++i] = (n = (n + 1) / 2);
/* f := exp(h) + O(x^m), g := exp(-h) + O(x^m2) */
_nmod_poly_exp_series_basecase(f, h, n, n, mod);
_nmod_poly_inv_series_basecase(g, f, (n + 1) / 2, mod);
for (i--; i >= 0; i--)
{
m = n; /* previous length */
n = a[i]; /* new length */
m2 = (m + 1) / 2;
l = m - 1; /* shifted for derivative */
/* g := exp(-h) + O(x^m) */
_nmod_poly_mullow(T, f, m, g, m2, m, mod);
_nmod_poly_mullow(g + m2, g, m2, T + m2, m - m2, m - m2, mod);
_nmod_vec_neg(g + m2, g + m2, m - m2, mod);
/* U := h' + g (f' - f h') + O(x^(n-1))
Note: should replace h' by h' mod x^(m-1) */
_nmod_vec_zero(f + m, n - m);
_nmod_poly_mullow(T, f, n, hprime, n, n, mod); /* should be mulmid */
_nmod_poly_derivative(U, f, n, mod); U[n - 1] = 0; /* should skip low terms */
_nmod_vec_sub(U + l, U + l, T + l, n - l, mod);
_nmod_poly_mullow(T + l, g, n - m, U + l, n - m, n - m, mod);
_nmod_vec_add(U + l, hprime + l, T + l, n - m, mod);
/* f := f + f * (h - int U) + O(x^n) = exp(h) + O(x^n) */
_nmod_poly_integral(U, U, n, mod); /* should skip low terms */
_nmod_vec_sub(U + m, h + m, U + m, n - m, mod);
_nmod_poly_mullow(f + m, f, n - m, U + m, n - m, n - m, mod);
/* g := exp(-h) + O(x^n) */
/* not needed if we only want exp(x) */
if (i == 0 && inverse)
{
_nmod_poly_mullow(T, f, n, g, m, n, mod);
_nmod_poly_mullow(g + m, g, m, T + m, n - m, n - m, mod);
_nmod_vec_neg(g + m, g + m, n - m, mod);
}
}
_nmod_vec_clear(hprime);
_nmod_vec_clear(T);
_nmod_vec_clear(U);
}
void
_nmod_poly_exp_expinv_series(mp_ptr f, mp_ptr g, mp_srcptr h, slong n, nmod_t mod)
{
if (n < NMOD_POLY_NEWTON_EXP_CUTOFF)
{
_nmod_poly_exp_series_basecase(f, h, n, n, mod);
_nmod_poly_inv_series(g, f, n, mod);
}
else
{
_nmod_poly_exp_series_newton(f, g, h, n, mod, 1);
}
}
void
_nmod_poly_exp_series(mp_ptr f, mp_srcptr h, slong n, nmod_t mod)
{
if (n < NMOD_POLY_NEWTON_EXP_CUTOFF)
{
_nmod_poly_exp_series_basecase(f, h, n, n, mod);
}
else
{
mp_ptr g = _nmod_vec_init((n + 1) / 2);
_nmod_poly_exp_series_newton(f, g, h, n, mod, 0);
_nmod_vec_clear(g);
}
}
void
nmod_poly_exp_series(nmod_poly_t f, const nmod_poly_t h, slong n)
{
mp_ptr f_coeffs, h_coeffs;
nmod_poly_t t1;
slong hlen, k;
nmod_poly_fit_length(f, n);
hlen = h->length;
if (hlen > 0 && h->coeffs[0] != UWORD(0))
{
flint_printf("Exception (nmod_poly_exp_series). Constant term != 0.\n");
abort();
}
if (n <= 1 || hlen == 0)
{
if (n == 0)
{
nmod_poly_zero(f);
}
else
{
f->coeffs[0] = UWORD(1);
f->length = 1;
}
return;
}
/* Handle monomials */
for (k = 0; h->coeffs[k] == UWORD(0) && k < n - 1; k++);
if (k == hlen - 1 || k == n - 1)
{
hlen = FLINT_MIN(hlen, n);
_nmod_poly_exp_series_monomial_ui(f->coeffs,
h->coeffs[hlen-1], hlen - 1, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (n < NMOD_POLY_NEWTON_EXP_CUTOFF)
{
_nmod_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (hlen < n)
{
h_coeffs = _nmod_vec_init(n);
flint_mpn_copyi(h_coeffs, h->coeffs, hlen);
flint_mpn_zero(h_coeffs + hlen, n - hlen);
}
else
h_coeffs = h->coeffs;
if (h == f && hlen >= n)
{
nmod_poly_init2(t1, h->mod.n, n);
f_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(f, n);
f_coeffs = f->coeffs;
}
_nmod_poly_exp_series(f_coeffs, h_coeffs, n, f->mod);
if (h == f && hlen >= n)
{
nmod_poly_swap(f, t1);
nmod_poly_clear(t1);
}
f->length = n;
if (hlen < n)
_nmod_vec_clear(h_coeffs);
_nmod_poly_normalise(f);
}