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* @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.
*/
'use strict';
// MODULES //
var isNegativeInteger = require( '@stdlib/math/base/assert/is-negative-integer' );
var gamma1pm1 = require( '@stdlib/math/base/special/gamma1pm1' );
var gammaln = require( '@stdlib/math/base/special/gammaln' );
var log1p = require( '@stdlib/math/base/special/log1p' );
// MAIN //
/**
* Evaluates the natural logarithm of the factorial of `x`.
*
* ## Method
*
* For \\(-1 < x < 2\\), forming \\(x+1\\) can round away low-order bits of \\(x\\), which results in large relative errors near the zeros of \\(\ln \Gamma(x+1)\\) at \\(x = 0\\) and \\(x = 1\\). To avoid forming \\(x+1\\), we use the identity
*
* ```tex
* \ln \Gamma(x+1) = \operatorname{log1p}(\Gamma(x+1) - 1) = \operatorname{log1p}(\operatorname{gamma1pm1}(x))
* ```
*
* @param {number} x - input value
* @returns {number} natural logarithm of factorial of `x`
*
* @example
* var v = factorialln( 3.0 );
* // returns ~1.792
*
* @example
* var v = factorialln( 2.4 );
* // returns ~1.092
*
* @example
* var v = factorialln( -1.0 );
* // returns NaN
*
* @example
* var v = factorialln( -1.5 );
* // returns ~1.266
*
* @example
* var v = factorialln( NaN );
* // returns NaN
*/
function factorialln( x ) {
if ( isNegativeInteger( x ) ) {
return NaN;
}
if ( x > -1.0 && x < 2.0 ) {
return log1p( gamma1pm1( x ) );
}
return gammaln( x + 1.0 );
}
// EXPORTS //
module.exports = factorialln;
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