pqc/external/flint-2.4.3/arith/divisors.c

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2014-05-18 22:03:37 +00:00
/*=============================================================================
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 Fredrik Johansson
******************************************************************************/
#include "arith.h"
#include "fmpz.h"
#define FLINT_NUM_TINY_DIVISORS FLINT_BITS
const int FLINT_TINY_DIVISORS_SIZE[FLINT_NUM_TINY_DIVISORS] = {
0,1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,8,3,4,4,6,2,8,2,
#if FLINT64
6,4,4,4,9,2,4,4,8,2,8,2,6,6,4,2,10,3,6,4,6,2,8,4,8,4,4,2,12,2,4,6
#endif
};
const ulong FLINT_TINY_DIVISORS_LOOKUP[FLINT_NUM_TINY_DIVISORS] = {
UWORD(0x0),UWORD(0x2),UWORD(0x6),0xaUL,UWORD(0x16),UWORD(0x22),0x4eUL,UWORD(0x82),UWORD(0x116),0x20aUL,
UWORD(0x426),UWORD(0x802),0x105eUL,UWORD(0x2002),UWORD(0x4086),0x802aUL,UWORD(0x10116),UWORD(0x20002),
0x4024eUL,UWORD(0x80002),UWORD(0x100436),0x20008aUL,UWORD(0x400806),UWORD(0x800002),
0x100115eUL,UWORD(0x2000022),UWORD(0x4002006),0x800020aUL,UWORD(0x10004096),UWORD(0x20000002),
0x4000846eUL,UWORD(0x80000002),
#if FLINT64
UWORD(0x100010116),0x20000080aUL,UWORD(0x400020006),UWORD(0x8000000a2),0x100004125eUL,
UWORD(0x2000000002),UWORD(0x4000080006),0x800000200aUL,UWORD(0x10000100536),
UWORD(0x20000000002),0x400002040ceUL,UWORD(0x80000000002),UWORD(0x100000400816),
0x20000000822aUL,UWORD(0x400000800006),UWORD(0x800000000002),0x100000101115eUL,
UWORD(0x2000000000082),UWORD(0x4000002000426),0x800000002000aUL,UWORD(0x10000004002016),
UWORD(0x20000000000002),0x4000000804024eUL,UWORD(0x80000000000822),
UWORD(0x100000010004196),0x20000000008000aUL,UWORD(0x400000020000006),
UWORD(0x800000000000002),0x100000004010947eUL,UWORD(0x2000000000000002),
UWORD(0x4000000080000006),0x800000000020028aUL
#endif
};
void
_arith_divisors(fmpz *res, slong size, fmpz_factor_t factors)
{
slong i;
slong *exp = flint_malloc(sizeof(slong) * factors->num);
slong *exp_max = flint_malloc(sizeof(slong) * factors->num);
fmpz *powers = _fmpz_vec_init(factors->num);
fmpz_t d;
for (i = 0; i < factors->num; i++)
{
exp[i] = 0;
fmpz_set(powers + i, factors->p + i);
exp_max[i] = factors->exp[i];
fmpz_pow_ui(powers + i, powers + i, exp_max[i]);
}
fmpz_init(d);
fmpz_one(res);
fmpz_one(d);
res++;
i = 0;
while (1)
{
while (1)
{
if (i == factors->num)
goto all_done;
if (exp[i] < exp_max[i])
{
exp[i]++;
fmpz_mul(d, d, factors->p + i);
i = 0;
break;
}
else
{
exp[i] = 0;
fmpz_divexact(d, d, powers+i);
i += 1;
}
}
fmpz_set(res, d);
res++;
}
all_done:
fmpz_clear(d);
flint_free(exp);
flint_free(exp_max);
_fmpz_vec_clear(powers, factors->num);
}
void
_arith_divisors_tiny(fmpz_poly_t res, slong n)
{
slong size;
slong i, k;
size = FLINT_TINY_DIVISORS_SIZE[n];
fmpz_poly_fit_length(res, size);
i = 0;
for (k = 1; k <= n; k++)
{
if (FLINT_TINY_DIVISORS_LOOKUP[n] & (UWORD(1) << k))
{
fmpz_poly_set_coeff_si(res, i, k);
i++;
}
}
_fmpz_poly_set_length(res, size);
return;
}
void
arith_divisors(fmpz_poly_t res, const fmpz_t n)
{
slong i, size, m;
fmpz_factor_t factors;
if (!COEFF_IS_MPZ(*n))
{
m = fmpz_get_si(n);
if (-FLINT_NUM_TINY_DIVISORS < m && m < FLINT_NUM_TINY_DIVISORS)
{
_arith_divisors_tiny(res, FLINT_ABS(m));
return;
}
}
fmpz_factor_init(factors);
fmpz_factor(factors, n);
/* TODO: check for overflow for huge n */
size = 1;
for (i = 0; i < factors->num; i++)
size *= factors->exp[i] + 1;
fmpz_poly_fit_length(res, size);
_arith_divisors(res->coeffs, size, factors);
_fmpz_poly_set_length(res, size);
_fmpz_vec_sort(res->coeffs, size);
fmpz_factor_clear(factors);
}