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

166 lines
4.7 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) 2011 Fredrik Johansson
******************************************************************************/
#include "arith.h"
static void
__ramanujan_even_common_denom(fmpz * num, fmpz * den, slong start, slong n)
{
fmpz_t t, c, d, cden;
slong j, k, m, mcase;
int prodsize;
if (start >= n)
return;
fmpz_init(t);
fmpz_init(c);
fmpz_init(d);
fmpz_init(cden);
/* Common denominator */
arith_primorial(cden, n + 1);
start += start % 2;
/* Convert initial values to common denominator */
for (k = 0; k < start; k += 2)
{
fmpz_divexact(t, cden, den + k);
fmpz_mul(num + k, num + k, t);
}
/* Ramanujan's recursive formula */
for (m = start; m < n; m += 2)
{
mcase = m % 6;
fmpz_mul_ui(num + m, cden, m + UWORD(3));
fmpz_divexact_ui(num + m, num + m, UWORD(3));
if (mcase == 4)
{
fmpz_neg(num + m, num + m);
fmpz_divexact_ui(num + m, num + m, UWORD(2));
}
/* All factors are strictly smaller than m + 4; choose prodsize such
that (m + 4)^prodsize fits in an slong. */
{
#if FLINT64
if (m < WORD(1444)) prodsize = 6;
else if (m < WORD(2097148)) prodsize = 3;
else if (m < WORD(3037000495)) prodsize = 2; /* not very likely... */
else abort();
#else
if (m < WORD(32)) prodsize = 6;
else if (m < WORD(1286)) prodsize = 3;
else if (m < WORD(46336)) prodsize = 2;
else abort();
#endif
}
/* c = t = binomial(m+3, m) */
fmpz_set_ui(t, m + UWORD(1));
fmpz_mul_ui(t, t, m + UWORD(2));
fmpz_mul_ui(t, t, m + UWORD(3));
fmpz_divexact_ui(t, t, UWORD(6));
fmpz_set(c, t);
for (j = 6; j <= m; j += 6)
{
slong r = m - j;
/* c = binomial(m+3, m-j); */
switch (prodsize)
{
case 2:
fmpz_mul_ui(c, c, (r+6)*(r+5));
fmpz_mul_ui(c, c, (r+4)*(r+3));
fmpz_mul_ui(c, c, (r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3));
fmpz_mul_ui(d, d, (j-2)*(j+2));
fmpz_mul_ui(d, d, (j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 3:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4));
fmpz_mul_ui(c, c, (r+3)*(r+2)*(r+1));
fmpz_set_ui(d, (j+0)*(j+3)*(j-2));
fmpz_mul_ui(d, d, (j+2)*(j-1)*(j+1));
fmpz_divexact(c, c, d);
break;
case 6:
fmpz_mul_ui(c, c, (r+6)*(r+5)*(r+4)*(r+3)*(r+2)*(r+1));
fmpz_divexact_ui(c, c, (j+0)*(j+3)*(j-2)*(j+2)*(j-1)*(j+1));
break;
}
fmpz_submul(num + m, c, num + (m - j));
}
fmpz_divexact(num + m, num + m, t);
}
/* Convert to separate denominators */
for (k = 0; k < n; k += 2)
{
arith_bernoulli_number_denom(den + k, k);
fmpz_divexact(t, cden, den + k);
fmpz_divexact(num + k, num + k, t);
}
fmpz_clear(t);
fmpz_clear(c);
fmpz_clear(d);
fmpz_clear(cden);
}
void _arith_bernoulli_number_vec_recursive(fmpz * num, fmpz * den, slong n)
{
slong i, start;
fmpz_t t;
fmpz_t d;
fmpz_init(t);
fmpz_init(d);
start = FLINT_MIN(BERNOULLI_SMALL_NUMER_LIMIT, n);
/* Initial values */
for (i = 0; i < start; i += 2)
_arith_bernoulli_number(num + i, den + i, i);
__ramanujan_even_common_denom(num, den, start, n);
/* Odd values */
for (i = 1; i < n; i += 2)
_arith_bernoulli_number(num + i, den + i, i);
fmpz_clear(d);
fmpz_clear(t);
}