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/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* i0.c
*
* Modified Bessel function of order zero
*
*
*
* SYNOPSIS:
*
* double x, y, i0();
*
* y = i0( x );
*
*
*
* DESCRIPTION:
*
* Returns modified Bessel function of order zero of the
* argument.
*
* The function is defined as i0(x) = j0( ix ).
*
* The range is partitioned into the two intervals [0,8] and
* (8, infinity). Chebyshev polynomial expansions are employed
* in each interval.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 30000 5.8e-16 1.4e-16
*
*/
/* i0e.c
*
* Modified Bessel function of order zero,
* exponentially scaled
*
*
*
* SYNOPSIS:
*
* double x, y, i0e();
*
* y = i0e( x );
*
*
*
* DESCRIPTION:
*
* Returns exponentially scaled modified Bessel function
* of order zero of the argument.
*
* The function is defined as i0e(x) = exp(-|x|) j0( ix ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,30 30000 5.4e-16 1.2e-16
* See i0().
*
*/
/* i0.c */
/*
* Cephes Math Library Release 2.8: June, 2000
* Copyright 1984, 1987, 2000 by Stephen L. Moshier
*/
#pragma once
#include "../config.h"
#include "chbevl.h"
namespace xsf {
namespace cephes {
namespace detail {
/* Chebyshev coefficients for exp(-x) I0(x)
* in the interval [0,8].
*
* lim(x->0){ exp(-x) I0(x) } = 1.
*/
constexpr double i0_A[] = {
-4.41534164647933937950E-18, 3.33079451882223809783E-17, -2.43127984654795469359E-16,
1.71539128555513303061E-15, -1.16853328779934516808E-14, 7.67618549860493561688E-14,
-4.85644678311192946090E-13, 2.95505266312963983461E-12, -1.72682629144155570723E-11,
9.67580903537323691224E-11, -5.18979560163526290666E-10, 2.65982372468238665035E-9,
-1.30002500998624804212E-8, 6.04699502254191894932E-8, -2.67079385394061173391E-7,
1.11738753912010371815E-6, -4.41673835845875056359E-6, 1.64484480707288970893E-5,
-5.75419501008210370398E-5, 1.88502885095841655729E-4, -5.76375574538582365885E-4,
1.63947561694133579842E-3, -4.32430999505057594430E-3, 1.05464603945949983183E-2,
-2.37374148058994688156E-2, 4.93052842396707084878E-2, -9.49010970480476444210E-2,
1.71620901522208775349E-1, -3.04682672343198398683E-1, 6.76795274409476084995E-1};
/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
* in the inverted interval [8,infinity].
*
* lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
*/
constexpr double i0_B[] = {
-7.23318048787475395456E-18, -4.83050448594418207126E-18, 4.46562142029675999901E-17,
3.46122286769746109310E-17, -2.82762398051658348494E-16, -3.42548561967721913462E-16,
1.77256013305652638360E-15, 3.81168066935262242075E-15, -9.55484669882830764870E-15,
-4.15056934728722208663E-14, 1.54008621752140982691E-14, 3.85277838274214270114E-13,
7.18012445138366623367E-13, -1.79417853150680611778E-12, -1.32158118404477131188E-11,
-3.14991652796324136454E-11, 1.18891471078464383424E-11, 4.94060238822496958910E-10,
3.39623202570838634515E-9, 2.26666899049817806459E-8, 2.04891858946906374183E-7,
2.89137052083475648297E-6, 6.88975834691682398426E-5, 3.36911647825569408990E-3,
8.04490411014108831608E-1};
} // namespace detail
XSF_HOST_DEVICE inline double i0(double x) {
double y;
if (x < 0)
x = -x;
if (x <= 8.0) {
y = (x / 2.0) - 2.0;
return (std::exp(x) * chbevl(y, detail::i0_A, 30));
}
return (std::exp(x) * chbevl(32.0 / x - 2.0, detail::i0_B, 25) / sqrt(x));
}
XSF_HOST_DEVICE inline double i0e(double x) {
double y;
if (x < 0)
x = -x;
if (x <= 8.0) {
y = (x / 2.0) - 2.0;
return (chbevl(y, detail::i0_A, 30));
}
return (chbevl(32.0 / x - 2.0, detail::i0_B, 25) / std::sqrt(x));
}
} // namespace cephes
} // namespace xsf
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