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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 6000x 210x 210x 210x 210x 210x 6000x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 5790x 6000x 3x 3x 3x 3x 3x | /**
* @license Apache-2.0
*
* Copyright (c) 2018 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 http://www.boost.org/doc/libs/1_64_0/boost/math/special_functions/gamma.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* Copyright John Maddock 2006-7, 2013-14.
* Copyright Paul A. Bristow 2007, 2013-14.
* Copyright Nikhar Agrawal 2013-14.
* Copyright Christopher Kormanyos 2013-14.
*
* 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 lanczosSumExpGScaled = require( '@stdlib/math/base/special/gamma-lanczos-sum-expg-scaled' );
var gammaln = require( '@stdlib/math/base/special/gammaln' );
var gamma = require( '@stdlib/math/base/special/gamma' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/abs' );
var exp = require( '@stdlib/math/base/special/exp' );
var pow = require( '@stdlib/math/base/special/pow' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
var ln = require( '@stdlib/math/base/special/ln' );
var MAX_LN = require( '@stdlib/constants/float64/max-ln' );
var MIN_LN = require( '@stdlib/constants/float64/min-ln' );
var G = require( '@stdlib/constants/float64/gamma-lanczos-g' );
var E = require( '@stdlib/constants/float64/e' );
// MAIN //
/**
* Computes `(z^a)*(e^-z) / gamma(a)`.
*
* @private
* @param {number} a - input value
* @param {number} z - input value
* @returns {number} function value
*/
function regularisedGammaPrefix( a, z ) {
var prefix;
var amza;
var agh;
var alz;
var amz;
var sq;
var d;
agh = a + G - 0.5;
d = ( (z - a) - G + 0.5 ) / agh;
if ( a < 1.0 ) {
// Treat a < 1 as a special case because our Lanczos approximations are optimized against the factorials with a > 1, and for high precision types very small values of `a` can give rather erroneous results for gamma:
if ( z <= MIN_LN ) {
// Use logs, so should be free of cancellation errors:
return exp( ( a * ln(z) ) - z - gammaln( a ) );
}
// No danger of overflow as gamma(a) < 1/a for small a, so direct calculation:
return pow( z, a ) * exp( -z ) / gamma( a );
}
if ( abs(d*d*a) <= 100.0 && a > 150.0 ) {
// Special case for large a and a ~ z:
prefix = ( a * ( log1p( d ) - d ) ) + ( z * ( 0.5-G ) / agh );
prefix = exp( prefix );
}
else {
// General case. Direct computation is most accurate, but use various fallbacks for different parts of the problem domain:
alz = a * ln(z / agh);
amz = a - z;
if (
min(alz, amz) <= MIN_LN ||
max(alz, amz) >= MAX_LN
) {
amza = amz / a;
if (
min(alz, amz)/2.0 > MIN_LN &&
max(alz, amz)/2.0 < MAX_LN
) {
// Compute square root of the result and then square it:
sq = pow( z / agh, a / 2.0 ) * exp( amz / 2.0 );
prefix = sq * sq;
}
else if (
min(alz, amz)/4.0 > MIN_LN &&
max(alz, amz)/4.0 < MAX_LN &&
z > a
) {
// Compute the 4th root of the result then square it twice:
sq = pow( z / agh, a / 4.0 ) * exp( amz / 4.0 );
prefix = sq * sq;
prefix *= prefix;
}
else if (
amza > MIN_LN &&
amza < MAX_LN
) {
prefix = pow( (z * exp(amza)) / agh, a );
}
else {
prefix = exp( alz + amz );
}
}
else
{
prefix = pow( z / agh, a ) * exp( amz );
}
}
prefix *= sqrt( agh / E ) / lanczosSumExpGScaled( a );
return prefix;
}
// EXPORTS //
module.exports = regularisedGammaPrefix;
|