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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 | 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 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x 1x | /**
* @license Apache-2.0
*
* Copyright (c) 2022 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 following copyright, license, and long comment were part of the original implementation available as part of [SciPy]{@link https://github.com/scipy/scipy/blob/ed14bf0a66440a4d164581499fda662121963a56/scipy/special/Faddeeva.cc}. The implementation follows the original, but has been modified for JavaScript.
*
* ```text
* Copyright (c) 2012 Massachusetts Institute of Technology
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
* ```
*/
'use strict';
// MODULES //
var exp = require( '@stdlib/math/base/special/exp' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var erfcxY100 = require( './erfcx_y100.js' );
// VARIABLES //
var INV_SQRT_PI = 0.56418958354775628694807945156; // 1 / sqrt(pi)
// MAIN //
/**
* Evaluates the scaled complementary error function.
*
* ```tex
* \operatorname{erfcx}(x) = \exp{x^2} \cdot \operatorname{erfc}(x)
* ```
*
* ## Notes
*
* - Use this function to replace expressions containing `exp{x^2} erfc(x)` in order to avoid errors due to underflow or overflow.
* - For expressions of the form `\exp{-x^2} erfcx(x)`, use the complementary error function `erfc(x)` instead, as this substitution maintains accuracy by avoiding roundoff errors for large values of `x`.
*
* @param {number} x - input value
* @returns {number} evaluated scaled complementary error function
*
* @example
* var y = erfcx( 0.0 );
* // returns 1.0
*
* @example
* var y = erfcx( 1.0 );
* // returns ~0.4276
*
* @example
* var y = erfcx( -1.0 );
* // returns ~5.01
*
* @example
* var y = erfcx( 50.0 );
* // returns ~0.011
*
* @example
* var y = erfcx( -50.0 );
* // returns +Infinity
*
* @example
* var y = erfcx( NaN );
* // returns NaN
*/
function erfcx( x ) {
var x2;
if ( isnan( x ) ) {
return x;
}
if ( x >= 0.0 ) {
if ( x > 50.0 ) { // continued-fraction expansion is faster
if ( x > 5.0e7 ) { // 1-term expansion, important to avoid overflow
return INV_SQRT_PI / x;
}
x2 = x * x;
// 5-term expansion (rely on compiler for CSE), simplified from: INV_SQRT_PI / (x+0.5/(x+1/(x+1.5/(x+2/x))))
return INV_SQRT_PI * ( ( x2 * (x2+4.5) ) + 2.0 ) / ( x * ( ( x2*(x2+5.0) ) + 3.75 ) ); // eslint-disable-line max-len
}
return erfcxY100( 400.0/(4.0+x) );
}
if ( x < -26.7 ) {
return PINF;
}
x2 = x * x;
if ( x < -6.1 ) {
return 2.0 * exp( x2 );
}
return ( 2.0*exp( x2 ) ) - erfcxY100( 400.0/(4.0-x) );
}
// EXPORTS //
module.exports = erfcx;
|