pqc/external/flint-2.4.3/arith/stirling1.c
2014-05-24 23:16:06 +02:00

139 lines
3.7 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 Fredrik Johansson
******************************************************************************/
#include "arith.h"
static void
_rising_factorial(fmpz * res, slong a, slong b, slong trunc)
{
const slong span = b - a;
switch (span)
{
case 0:
fmpz_one(res);
break;
case 1:
fmpz_set_ui(res, a);
if (trunc > 1) fmpz_one(res+1);
break;
case 2:
fmpz_set_ui(res, a);
fmpz_mul_ui(res, res, a + UWORD(1));
if (trunc > 1)
{
fmpz_set_ui(res+1, 2*a + UWORD(1));
if (trunc > 2) fmpz_one(res+2);
}
break;
case 3:
fmpz_set_ui(res, a);
fmpz_mul_ui(res, res, a + UWORD(1));
fmpz_mul_ui(res, res, a + UWORD(2));
if (trunc > 1)
{
fmpz_set_ui(res+1, 3*a);
fmpz_mul_ui(res+1, res+1, a + UWORD(2));
fmpz_add_ui(res+1, res+1, 2);
if (trunc > 2)
{
fmpz_set_ui(res+2, 3*(a+1));
if (trunc > 3)
fmpz_one(res+3);
}
}
break;
default:
{
const slong mid = (a + b) / 2;
const int chk = (b - a + 1 < trunc); /* i.e. nprod < trunc */
const slong nleft = chk ? mid - a + 1 : trunc;
const slong nright = chk ? b - mid + 1 : trunc;
fmpz *left = _fmpz_vec_init(nleft);
fmpz *right = _fmpz_vec_init(nright);
_rising_factorial(left, a, mid, trunc);
_rising_factorial(right, mid, b, trunc);
if (chk)
_fmpz_poly_mul(res, right, nright, left, nleft);
else
_fmpz_poly_mullow(res, left, nleft, right, nright, trunc);
_fmpz_vec_clear(left, nleft);
_fmpz_vec_clear(right, nright);
}
}
}
void
arith_stirling_number_1u(fmpz_t s, slong n, slong k)
{
/* Various special cases
TODO: factorials, binomial coefficients, harmonic numbers ... */
if (k < 1)
{
fmpz_set_ui(s, (n == 0) & (k == 0));
}
if (k >= n)
{
fmpz_set_ui(s, n == k);
}
else
{
fmpz *tmp = _fmpz_vec_init(k+1);
_rising_factorial(tmp, 0, n, k+1);
fmpz_set(s, tmp+k);
_fmpz_vec_clear(tmp, k+1);
}
}
void
arith_stirling_number_1(fmpz_t s, slong n, slong k)
{
arith_stirling_number_1u(s, n, k);
if ((n + k) % 2)
fmpz_neg(s, s);
}
void
arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen)
{
if (klen > 0)
_rising_factorial(row, 0, n, klen);
}
void
arith_stirling_number_1_vec(fmpz * row, slong n, slong klen)
{
slong k;
arith_stirling_number_1u_vec(row, n, klen);
for (k = (n + 1) % 2; k < klen; k += 2)
fmpz_neg(row + k, row + k);
}