mirror of
https://github.com/vale981/arb
synced 2025-03-05 17:31:38 -05:00
127 lines
3.1 KiB
C
127 lines
3.1 KiB
C
/*=============================================================================
|
|
|
|
This file is part of ARB.
|
|
|
|
ARB 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.
|
|
|
|
ARB 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 ARB; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
|
|
=============================================================================*/
|
|
/******************************************************************************
|
|
|
|
Copyright (C) 2013 Fredrik Johansson
|
|
|
|
******************************************************************************/
|
|
|
|
#include "gamma.h"
|
|
|
|
/* x(x+1)...(x+7) = (28 + 98x + 63x^2 + 14x^3 + x^4)^2 - 16 (7+2x)^2 */
|
|
static void
|
|
rfac_eight(fmprb_t t, const fmprb_t x, long prec)
|
|
{
|
|
fmprb_t u, v;
|
|
|
|
fmprb_init(u);
|
|
fmprb_init(v);
|
|
|
|
/* t = x^2, v = x^3, u = x^4 */
|
|
fmprb_mul(t, x, x, prec);
|
|
fmprb_mul(v, x, t, prec);
|
|
fmprb_mul(u, t, t, prec);
|
|
|
|
/* u = (28 + ...)^2 */
|
|
fmprb_addmul_ui(u, v, 14UL, prec);
|
|
fmprb_addmul_ui(u, t, 63UL, prec);
|
|
fmprb_addmul_ui(u, x, 98UL, prec);
|
|
fmprb_add_ui(u, u, 28UL, prec);
|
|
fmprb_mul(u, u, u, prec);
|
|
|
|
/* 16 (7+2x)^2 = 784 + 448x + 64x^2 */
|
|
fmprb_sub_ui(u, u, 784UL, prec);
|
|
fmprb_submul_ui(u, x, 448UL, prec);
|
|
fmprb_mul_2exp_si(t, t, 6);
|
|
fmprb_sub(t, u, t, prec);
|
|
|
|
fmprb_clear(u);
|
|
fmprb_clear(v);
|
|
}
|
|
|
|
/* assumes y and x not aliased, the length is a positive multiple of 8 */
|
|
static void
|
|
bsplit(fmprb_t y, const fmprb_t x, ulong a, ulong b, long prec)
|
|
{
|
|
fmprb_t t;
|
|
fmprb_init(t);
|
|
|
|
if (b - a == 8)
|
|
{
|
|
fmprb_add_ui(t, x, a, prec);
|
|
rfac_eight(y, t, prec);
|
|
}
|
|
else
|
|
{
|
|
ulong m = a + ((b - a) / 16) * 8;
|
|
bsplit(y, x, a, m, prec);
|
|
bsplit(t, x, m, b, prec);
|
|
fmprb_mul(y, y, t, prec);
|
|
}
|
|
|
|
fmprb_clear(t);
|
|
}
|
|
|
|
void
|
|
gamma_rising_fmprb_ui_bsplit_eight(fmprb_t y, const fmprb_t x, ulong n, long prec)
|
|
{
|
|
if (n == 0)
|
|
{
|
|
fmprb_one(y);
|
|
}
|
|
else if (n == 1)
|
|
{
|
|
fmprb_set_round(y, x, prec);
|
|
}
|
|
else
|
|
{
|
|
ulong k, a;
|
|
long wp;
|
|
fmprb_t t, u;
|
|
|
|
wp = FMPR_PREC_ADD(prec, FLINT_BIT_COUNT(n));
|
|
|
|
fmprb_init(t);
|
|
fmprb_init(u);
|
|
|
|
if (n >= 8)
|
|
{
|
|
bsplit(t, x, 0, (n / 8) * 8, wp);
|
|
a = (n / 8) * 8;
|
|
}
|
|
else
|
|
{
|
|
fmprb_set(t, x);
|
|
a = 1;
|
|
}
|
|
|
|
for (k = a; k < n; k++)
|
|
{
|
|
fmprb_add_ui(u, x, k, wp);
|
|
fmprb_mul(t, t, u, wp);
|
|
}
|
|
|
|
fmprb_set_round(y, t, prec);
|
|
|
|
fmprb_clear(t);
|
|
fmprb_clear(u);
|
|
}
|
|
}
|
|
|