time-to-botec

Benchmark sampling in different programming languages
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asymptotic_expansion.js (1605B)

      1 /**
      2 * @license Apache-2.0
      3 *
      4 * Copyright (c) 2018 The Stdlib Authors.
      5 *
      6 * Licensed under the Apache License, Version 2.0 (the "License");
      7 * you may not use this file except in compliance with the License.
      8 * You may obtain a copy of the License at
      9 *
     10 *    http://www.apache.org/licenses/LICENSE-2.0
     11 *
     12 * Unless required by applicable law or agreed to in writing, software
     13 * distributed under the License is distributed on an "AS IS" BASIS,
     14 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     15 * See the License for the specific language governing permissions and
     16 * limitations under the License.
     17 *
     18 *
     19 * ## Notice
     20 *
     21 * The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_53_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html}. The implementation follows the original but has been modified for JavaScript.
     22 *
     23 * ```text
     24 * (C) Copyright John Maddock 2006.
     25 *
     26 * Use, modification and distribution are subject to the
     27 * Boost Software License, Version 1.0. (See accompanying file
     28 * LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
     29 * ```
     30 */
     31 
     32 'use strict';
     33 
     34 // MODULES //
     35 
     36 var ln = require( './../../../../base/special/ln' );
     37 var polyval = require( './polyval_p.js' );
     38 
     39 
     40 // MAIN //
     41 
     42 /**
     43 * Evaluates the digamma function via asymptotic expansion.
     44 *
     45 * @private
     46 * @param {number} x - input value
     47 * @returns {number} function value
     48 */
     49 function digamma( x ) {
     50 	var y;
     51 	var z;
     52 	x -= 1.0;
     53 	y = ln(x) + ( 1.0 / (2.0*x) );
     54 	z = 1.0 / (x*x);
     55 	return y - ( z*polyval( z ) );
     56 }
     57 
     58 
     59 // EXPORTS //
     60 
     61 module.exports = digamma;