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/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* i1.c
*
* Modified Bessel function of order one
*
*
*
* SYNOPSIS:
*
* double x, y, i1();
*
* y = i1( x );
*
*
*
* DESCRIPTION:
*
* Returns modified Bessel function of order one of the
* argument.
*
* The function is defined as i1(x) = -i j1( 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 1.9e-15 2.1e-16
*
*
*/
/* i1e.c
*
* Modified Bessel function of order one,
* exponentially scaled
*
*
*
* SYNOPSIS:
*
* double x, y, i1e();
*
* y = i1e( x );
*
*
*
* DESCRIPTION:
*
* Returns exponentially scaled modified Bessel function
* of order one of the argument.
*
* The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0, 30 30000 2.0e-15 2.0e-16
* See i1().
*
*/
/* i1.c 2 */
/*
* Cephes Math Library Release 2.8: June, 2000
* Copyright 1985, 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) I1(x) / x
* in the interval [0,8].
*
* lim(x->0){ exp(-x) I1(x) / x } = 1/2.
*/
constexpr double i1_A[] = {
2.77791411276104639959E-18, -2.11142121435816608115E-17, 1.55363195773620046921E-16,
-1.10559694773538630805E-15, 7.60068429473540693410E-15, -5.04218550472791168711E-14,
3.22379336594557470981E-13, -1.98397439776494371520E-12, 1.17361862988909016308E-11,
-6.66348972350202774223E-11, 3.62559028155211703701E-10, -1.88724975172282928790E-9,
9.38153738649577178388E-9, -4.44505912879632808065E-8, 2.00329475355213526229E-7,
-8.56872026469545474066E-7, 3.47025130813767847674E-6, -1.32731636560394358279E-5,
4.78156510755005422638E-5, -1.61760815825896745588E-4, 5.12285956168575772895E-4,
-1.51357245063125314899E-3, 4.15642294431288815669E-3, -1.05640848946261981558E-2,
2.47264490306265168283E-2, -5.29459812080949914269E-2, 1.02643658689847095384E-1,
-1.76416518357834055153E-1, 2.52587186443633654823E-1};
/* Chebyshev coefficients for exp(-x) sqrt(x) I1(x)
* in the inverted interval [8,infinity].
*
* lim(x->inf){ exp(-x) sqrt(x) I1(x) } = 1/sqrt(2pi).
*/
constexpr double i1_B[] = {
7.51729631084210481353E-18, 4.41434832307170791151E-18, -4.65030536848935832153E-17,
-3.20952592199342395980E-17, 2.96262899764595013876E-16, 3.30820231092092828324E-16,
-1.88035477551078244854E-15, -3.81440307243700780478E-15, 1.04202769841288027642E-14,
4.27244001671195135429E-14, -2.10154184277266431302E-14, -4.08355111109219731823E-13,
-7.19855177624590851209E-13, 2.03562854414708950722E-12, 1.41258074366137813316E-11,
3.25260358301548823856E-11, -1.89749581235054123450E-11, -5.58974346219658380687E-10,
-3.83538038596423702205E-9, -2.63146884688951950684E-8, -2.51223623787020892529E-7,
-3.88256480887769039346E-6, -1.10588938762623716291E-4, -9.76109749136146840777E-3,
7.78576235018280120474E-1};
} // namespace detail
XSF_HOST_DEVICE inline double i1(double x) {
double y, z;
z = std::abs(x);
if (z <= 8.0) {
y = (z / 2.0) - 2.0;
z = chbevl(y, detail::i1_A, 29) * z * std::exp(z);
} else {
z = std::exp(z) * chbevl(32.0 / z - 2.0, detail::i1_B, 25) / std::sqrt(z);
}
if (x < 0.0)
z = -z;
return (z);
}
/* i1e() */
XSF_HOST_DEVICE inline double i1e(double x) {
double y, z;
z = std::abs(x);
if (z <= 8.0) {
y = (z / 2.0) - 2.0;
z = chbevl(y, detail::i1_A, 29) * z;
} else {
z = chbevl(32.0 / z - 2.0, detail::i1_B, 25) / std::sqrt(z);
}
if (x < 0.0)
z = -z;
return (z);
}
} // namespace cephes
} // namespace xsf
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