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/* Translated into C++ by SciPy developers in 2024.
* Original header with Copyright information appears below.
*/
/* j1.c
*
* Bessel function of order one
*
*
*
* SYNOPSIS:
*
* double x, y, j1();
*
* y = j1( x );
*
*
*
* DESCRIPTION:
*
* Returns Bessel function of order one of the argument.
*
* The domain is divided into the intervals [0, 8] and
* (8, infinity). In the first interval a 24 term Chebyshev
* expansion is used. In the second, the asymptotic
* trigonometric representation is employed using two
* rational functions of degree 5/5.
*
*
*
* ACCURACY:
*
* Absolute error:
* arithmetic domain # trials peak rms
* IEEE 0, 30 30000 2.6e-16 1.1e-16
*
*
*/
/* y1.c
*
* Bessel function of second kind of order one
*
*
*
* SYNOPSIS:
*
* double x, y, y1();
*
* y = y1( x );
*
*
*
* DESCRIPTION:
*
* Returns Bessel function of the second kind of order one
* of the argument.
*
* The domain is divided into the intervals [0, 8] and
* (8, infinity). In the first interval a 25 term Chebyshev
* expansion is used, and a call to j1() is required.
* In the second, the asymptotic trigonometric representation
* is employed using two rational functions of degree 5/5.
*
*
*
* ACCURACY:
*
* Absolute error:
* arithmetic domain # trials peak rms
* IEEE 0, 30 30000 1.0e-15 1.3e-16
*
* (error criterion relative when |y1| > 1).
*
*/
/*
* Cephes Math Library Release 2.8: June, 2000
* Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
*/
/*
* #define PIO4 .78539816339744830962
* #define THPIO4 2.35619449019234492885
* #define SQ2OPI .79788456080286535588
*/
#pragma once
#include "../config.h"
#include "../error.h"
#include "const.h"
#include "polevl.h"
namespace xsf {
namespace cephes {
namespace detail {
constexpr double j1_RP[4] = {
-8.99971225705559398224E8,
4.52228297998194034323E11,
-7.27494245221818276015E13,
3.68295732863852883286E15,
};
constexpr double j1_RQ[8] = {
/* 1.00000000000000000000E0, */
6.20836478118054335476E2, 2.56987256757748830383E5, 8.35146791431949253037E7, 2.21511595479792499675E10,
4.74914122079991414898E12, 7.84369607876235854894E14, 8.95222336184627338078E16, 5.32278620332680085395E18,
};
constexpr double j1_PP[7] = {
7.62125616208173112003E-4, 7.31397056940917570436E-2, 1.12719608129684925192E0, 5.11207951146807644818E0,
8.42404590141772420927E0, 5.21451598682361504063E0, 1.00000000000000000254E0,
};
constexpr double j1_PQ[7] = {
5.71323128072548699714E-4, 6.88455908754495404082E-2, 1.10514232634061696926E0, 5.07386386128601488557E0,
8.39985554327604159757E0, 5.20982848682361821619E0, 9.99999999999999997461E-1,
};
constexpr double j1_QP[8] = {
5.10862594750176621635E-2, 4.98213872951233449420E0, 7.58238284132545283818E1, 3.66779609360150777800E2,
7.10856304998926107277E2, 5.97489612400613639965E2, 2.11688757100572135698E2, 2.52070205858023719784E1,
};
constexpr double j1_QQ[7] = {
/* 1.00000000000000000000E0, */
7.42373277035675149943E1, 1.05644886038262816351E3, 4.98641058337653607651E3, 9.56231892404756170795E3,
7.99704160447350683650E3, 2.82619278517639096600E3, 3.36093607810698293419E2,
};
constexpr double j1_YP[6] = {
1.26320474790178026440E9, -6.47355876379160291031E11, 1.14509511541823727583E14,
-8.12770255501325109621E15, 2.02439475713594898196E17, -7.78877196265950026825E17,
};
constexpr double j1_YQ[8] = {
/* 1.00000000000000000000E0, */
5.94301592346128195359E2, 2.35564092943068577943E5, 7.34811944459721705660E7, 1.87601316108706159478E10,
3.88231277496238566008E12, 6.20557727146953693363E14, 6.87141087355300489866E16, 3.97270608116560655612E18,
};
constexpr double j1_Z1 = 1.46819706421238932572E1;
constexpr double j1_Z2 = 4.92184563216946036703E1;
} // namespace detail
XSF_HOST_DEVICE inline double j1(double x) {
double w, z, p, q, xn;
w = x;
if (x < 0) {
return -j1(-x);
}
if (w <= 5.0) {
z = x * x;
w = polevl(z, detail::j1_RP, 3) / p1evl(z, detail::j1_RQ, 8);
w = w * x * (z - detail::j1_Z1) * (z - detail::j1_Z2);
return (w);
}
w = 5.0 / x;
z = w * w;
p = polevl(z, detail::j1_PP, 6) / polevl(z, detail::j1_PQ, 6);
q = polevl(z, detail::j1_QP, 7) / p1evl(z, detail::j1_QQ, 7);
xn = x - detail::THPIO4;
p = p * std::cos(xn) - w * q * std::sin(xn);
return (p * detail::SQRT2OPI / std::sqrt(x));
}
XSF_HOST_DEVICE inline double y1(double x) {
double w, z, p, q, xn;
if (x <= 5.0) {
if (x == 0.0) {
set_error("y1", SF_ERROR_SINGULAR, NULL);
return -std::numeric_limits<double>::infinity();
} else if (x <= 0.0) {
set_error("y1", SF_ERROR_DOMAIN, NULL);
return std::numeric_limits<double>::quiet_NaN();
}
z = x * x;
w = x * (polevl(z, detail::j1_YP, 5) / p1evl(z, detail::j1_YQ, 8));
w += M_2_PI * (j1(x) * std::log(x) - 1.0 / x);
return (w);
}
w = 5.0 / x;
z = w * w;
p = polevl(z, detail::j1_PP, 6) / polevl(z, detail::j1_PQ, 6);
q = polevl(z, detail::j1_QP, 7) / p1evl(z, detail::j1_QQ, 7);
xn = x - detail::THPIO4;
p = p * std::sin(xn) + w * q * std::cos(xn);
return (p * detail::SQRT2OPI / std::sqrt(x));
}
} // namespace cephes
} // namespace xsf
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