Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 | 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 21016x 21016x 21016x 21016x 21016x 1001x 1001x 21016x 1x 1x 21016x 1x 1x 20013x 20013x 21016x 5458x 5458x 5458x 5458x 5458x 14555x 14555x 21016x 14554x 14554x 14554x 1x 1x 1x 1x 1x 21016x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2026 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link https://www.boost.org/doc/libs/1_85_0/boost/math/special_functions/detail/bessel_k1.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright (c) 2006 Xiaogang Zhang
* Copyright (c) 2017 John Maddock
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var exp = require( '@stdlib/math/base/special/exp' );
var ln = require( '@stdlib/math/base/special/ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var poly1 = require( './rational_p1q1.js' );
var poly2 = require( './rational_p2q2.js' );
var poly3 = require( './rational_p3q3.js' );
// VARIABLES //
var Y_SMALL = 8.69547128677368164e-02;
var Y_LARGE = 1.45034217834472656;
var LOG_MAX = 709.782712893384;
// MAIN //
/**
* Computes the modified Bessel function of the second kind of order one.
*
* ## Notes
*
* - The function has a pole at `x = 0` (behaves like 1/x).
* - Accuracy for subnormal `x` is very poor. Full accuracy is achieved at approximately `1.0e-308` but degrades rapidly as `x → 0`.
*
* @param {number} x - input value
* @returns {number} evaluated Bessel function
*
* @example
* var v = k1( 0.0 );
* // returns Infinity
*
* @example
* var v = k1( 1.0 );
* // returns ~0.6019
*
* @example
* var v = k1( 5.0 );
* // returns ~0.004045
*
* @example
* var v = k1( -1.0 );
* // returns NaN
*
* @example
* var v = k1( Infinity );
* // returns 0.0
*/
function k1( x ) {
var ex;
var a;
if ( x < 0.0 ) {
return NaN;
}
if ( x === 0.0 ) {
return PINF;
}
if ( x === PINF ) {
return 0.0;
}
// x <= 1
if ( x <= 1.0 ) {
a = ( x * x ) * 0.25;
a = ( ( poly1( a ) + Y_SMALL ) * a * a ) + ( a * 0.5 ) + 1.0;
a = a * x * 0.5;
return ( poly2( x * x ) * x ) + ( 1.0 / x ) + ( ln( x ) * a );
}
// x > 1
if ( x < LOG_MAX ) {
return ( poly3( 1.0 / x ) + Y_LARGE ) *
exp( -x ) / sqrt( x );
}
// overflow-safe
ex = exp( -x * 0.5 );
return ( poly3( 1.0 / x ) + Y_LARGE ) *
ex / sqrt( x ) * ex;
}
// EXPORTS //
module.exports = k1;
|