124 lines
3.2 KiB
C
124 lines
3.2 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) 2010 Sebastian Pancratz
|
||
|
|
|
||
|
|
******************************************************************************/
|
||
|
|
|
||
|
|
#include <stdlib.h>
|
||
|
|
#include <gmp.h>
|
||
|
|
#include "flint.h"
|
||
|
|
#include "fmpz.h"
|
||
|
|
#include "fmpz_vec.h"
|
||
|
|
#include "fmpz_poly.h"
|
||
|
|
|
||
|
|
void
|
||
|
|
_fmpz_poly_pow_binomial(fmpz * res, const fmpz * poly, ulong e)
|
||
|
|
{
|
||
|
|
ulong i, f;
|
||
|
|
fmpz_t a, b, c;
|
||
|
|
|
||
|
|
*a = WORD(1);
|
||
|
|
*b = WORD(1);
|
||
|
|
*c = WORD(1);
|
||
|
|
|
||
|
|
fmpz_one(res);
|
||
|
|
fmpz_one(res + e);
|
||
|
|
|
||
|
|
for (i = UWORD(1), f = e - UWORD(1); i <= (e - UWORD(1)) >> 1; i++, f--)
|
||
|
|
{
|
||
|
|
fmpz_mul(a, a, poly);
|
||
|
|
fmpz_mul(b, b, poly + 1);
|
||
|
|
fmpz_mul_ui(c, c, f + UWORD(1));
|
||
|
|
fmpz_divexact_ui(c, c, i);
|
||
|
|
|
||
|
|
fmpz_mul(res + i, b, c);
|
||
|
|
fmpz_mul(res + f, a, c);
|
||
|
|
}
|
||
|
|
|
||
|
|
if ((e & UWORD(1)) == UWORD(0))
|
||
|
|
{
|
||
|
|
fmpz_mul(a, a, poly);
|
||
|
|
fmpz_mul(b, b, poly + 1);
|
||
|
|
fmpz_mul_ui(c, c, f + UWORD(1));
|
||
|
|
fmpz_divexact_ui(c, c, i);
|
||
|
|
|
||
|
|
fmpz_mul(res + i, b, c);
|
||
|
|
fmpz_mul(res + i, res + i, a);
|
||
|
|
i++, f--;
|
||
|
|
}
|
||
|
|
|
||
|
|
for ( ; i <= e; i++, f--)
|
||
|
|
{
|
||
|
|
fmpz_mul(a, a, poly);
|
||
|
|
fmpz_mul(b, b, poly + 1);
|
||
|
|
|
||
|
|
fmpz_mul(res + i, res + i, b);
|
||
|
|
fmpz_mul(res + f, res + f, a);
|
||
|
|
}
|
||
|
|
|
||
|
|
fmpz_clear(a);
|
||
|
|
fmpz_clear(b);
|
||
|
|
fmpz_clear(c);
|
||
|
|
}
|
||
|
|
|
||
|
|
void
|
||
|
|
fmpz_poly_pow_binomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
|
||
|
|
{
|
||
|
|
const slong len = poly->length;
|
||
|
|
slong rlen;
|
||
|
|
|
||
|
|
if (len != 2)
|
||
|
|
{
|
||
|
|
flint_printf("Exception (fmpz_poly_pow_binomial). poly->length not equal to 2.\n");
|
||
|
|
abort();
|
||
|
|
}
|
||
|
|
|
||
|
|
if (e < UWORD(3))
|
||
|
|
{
|
||
|
|
if (e == UWORD(0))
|
||
|
|
fmpz_poly_set_ui(res, UWORD(1));
|
||
|
|
else if (e == UWORD(1))
|
||
|
|
fmpz_poly_set(res, poly);
|
||
|
|
else /* e == UWORD(2) */
|
||
|
|
fmpz_poly_sqr(res, poly);
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
rlen = (slong) e + 1;
|
||
|
|
|
||
|
|
if (res != poly)
|
||
|
|
{
|
||
|
|
fmpz_poly_fit_length(res, rlen);
|
||
|
|
_fmpz_poly_set_length(res, rlen);
|
||
|
|
_fmpz_poly_pow_binomial(res->coeffs, poly->coeffs, e);
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
fmpz_poly_t t;
|
||
|
|
fmpz_poly_init2(t, rlen);
|
||
|
|
_fmpz_poly_set_length(t, rlen);
|
||
|
|
_fmpz_poly_pow_binomial(t->coeffs, poly->coeffs, e);
|
||
|
|
fmpz_poly_swap(res, t);
|
||
|
|
fmpz_poly_clear(t);
|
||
|
|
}
|
||
|
|
}
|