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/* rgamma.c
*
* Reciprocal Gamma function
*
*
*
* SYNOPSIS:
*
* double x, y, rgamma();
*
* y = rgamma( x );
*
*
*
* DESCRIPTION:
*
* Returns one divided by the Gamma function of the argument.
*
* The function is approximated by a Chebyshev expansion in
* the interval [0,1]. Range reduction is by recurrence
* for arguments between -34.034 and +34.84425627277176174.
* 0 is returned for positive arguments outside this
* range. For arguments less than -34.034 the cosecant
* reflection formula is applied; lograrithms are employed
* to avoid unnecessary overflow.
*
* The reciprocal Gamma function has no singularities,
* but overflow and underflow may occur for large arguments.
* These conditions return either INFINITY or 0 with
* appropriate sign.
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -30,+30 30000 1.1e-15 2.0e-16
* For arguments less than -34.034 the peak error is on the
* order of 5e-15 (DEC), excepting overflow or underflow.
*/
/*
* Cephes Math Library Release 2.0: April, 1987
* Copyright 1985, 1987 by Stephen L. Moshier
* Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#pragma once
#include "../config.h"
#include "../error.h"
#include "chbevl.h"
#include "const.h"
#include "gamma.h"
#include "trig.h"
namespace xsf {
namespace cephes {
namespace detail {
/* Chebyshev coefficients for reciprocal Gamma function
* in interval 0 to 1. Function is 1/(x Gamma(x)) - 1
*/
constexpr double rgamma_R[] = {
3.13173458231230000000E-17, -6.70718606477908000000E-16, 2.20039078172259550000E-15,
2.47691630348254132600E-13, -6.60074100411295197440E-12, 5.13850186324226978840E-11,
1.08965386454418662084E-9, -3.33964630686836942556E-8, 2.68975996440595483619E-7,
2.96001177518801696639E-6, -8.04814124978471142852E-5, 4.16609138709688864714E-4,
5.06579864028608725080E-3, -6.41925436109158228810E-2, -4.98558728684003594785E-3,
1.27546015610523951063E-1};
} // namespace detail
XSF_HOST_DEVICE double rgamma(double x) {
double w, y, z;
if (x == 0) {
// This case is separate from below to get correct sign for zero.
return x;
}
if (x < 0 && x == std::floor(x)) {
// Gamma poles.
return 0.0;
}
if (std::abs(x) > 4.0) {
return 1.0 / Gamma(x);
}
z = 1.0;
w = x;
while (w > 1.0) { /* Downward recurrence */
w -= 1.0;
z *= w;
}
while (w < 0.0) { /* Upward recurrence */
z /= w;
w += 1.0;
}
if (w == 0.0) /* Nonpositive integer */
return (0.0);
if (w == 1.0) /* Other integer */
return (1.0 / z);
y = w * (1.0 + chbevl(4.0 * w - 2.0, detail::rgamma_R, 16)) / z;
return (y);
}
} // namespace cephes
} // namespace xsf
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