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fast gamma for rational and integer arguments

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This commit is contained in:
Fredrik Johansson 2013-03-22 23:48:18 +01:00
parent 8c4081ee78
commit fb6e85669c
4 changed files with 115 additions and 0 deletions
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2
doc/source/fmprb.rst
View file

@ -698,6 +698,8 @@ Gamma function
.. function:: void fmprb_gamma(fmprb_t y, const fmprb_t x, long prec)
.. function:: void fmprb_gamma_fmpq(fmprb_t y, const fmpq_t x, long prec)
Sets `y = \Gamma(x)`, the gamma function.
.. function:: void fmprb_rgamma(fmprb_t y, const fmprb_t x, long prec)

1
fmprb.h
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@ -321,6 +321,7 @@ void fmprb_agm(fmprb_t z, const fmprb_t x, const fmprb_t y, long prec);
void fmprb_lgamma(fmprb_t y, const fmprb_t x, long prec);
void fmprb_rgamma(fmprb_t y, const fmprb_t x, long prec);
void fmprb_gamma(fmprb_t y, const fmprb_t x, long prec);
void fmprb_gamma_fmpq(fmprb_t y, const fmpq_t x, long prec);
void fmprb_digamma(fmprb_t y, const fmprb_t x, long prec);

42
fmprb/gamma.c
View file

@ -33,6 +33,48 @@ _fmprb_gamma(fmprb_t y, const fmprb_t x, long prec, int inverse)
long r, n, wp;
fmprb_t t, u, v;
if (fmprb_is_exact(x))
{
const fmpr_struct * mid = fmprb_midref(x);
if (fmpr_is_special(mid))
{
if (!inverse && fmpr_is_pos_inf(mid))
{
fmprb_set(y, x);
}
else if (fmpr_is_nan(mid) || fmpr_is_neg_inf(mid) || !inverse)
{
fmpr_nan(fmprb_midref(y));
fmpr_pos_inf(fmprb_radref(y));
}
else
{
fmprb_zero(y);
}
return;
}
else
{
const fmpz exp = *fmpr_expref(mid);
const fmpz man = *fmpr_manref(mid);
/* fast gamma(n), gamma(n/2) or gamma(n/4) */
if (!COEFF_IS_MPZ(exp) && (exp >= -2) &&
((double) fmpz_bits(&man) + exp < prec))
{
fmpq_t a;
fmpq_init(a);
fmpr_get_fmpq(a, mid);
fmprb_gamma_fmpq(y, a, prec + 2 * inverse);
if (inverse)
fmprb_ui_div(y, 1, y, prec);
fmpq_clear(a);
return;
}
}
}
wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 1, 0, wp);

70
fmprb/gamma_fmpq.c Normal file
View file

@ -0,0 +1,70 @@
/*=============================================================================
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 "fmprb.h"
#include "gamma.h"
void
fmprb_gamma_fmpq(fmprb_t y, const fmpq_t x, long prec)
{
fmpz p, q;
p = *fmpq_numref(x);
q = *fmpq_denref(x);
if ((q == 1 || q == 2 || q == 3 || q == 4 || q == 6) && !COEFF_IS_MPZ(p))
{
if (q == 1)
{
if (p <= 0)
{
fmpr_nan(fmprb_midref(y));
fmpr_pos_inf(fmprb_radref(y));
return;
}
if (p < 1200 || 1.44265 * (p*log(p) - p) < 15.0 * prec)
{
fmpz_t t;
fmpz_init(t);
fmpz_fac_ui(t, p - 1);
fmprb_set_round_fmpz(y, t, prec);
fmpz_clear(t);
return;
}
}
p = FLINT_ABS(p);
if (p < q * 500.0 || p < q * (500.0 + 0.1 * prec * sqrt(prec)))
{
gamma_fmpq_outward(y, x, prec);
return;
}
}
gamma_fmpq_stirling(y, x, prec);
}