time-to-botec

Benchmark sampling in different programming languages
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trigamma.js (2874B)

      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_65_0/boost/math/special_functions/trigamma.hpp}. The implementation follows the original but has been reformatted and 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 floor = require( './../../../../base/special/floor' );
     37 var sinpi = require( './../../../../base/special/sinpi' );
     38 var PI_SQUARED = require( '@stdlib/constants/float64/pi-squared' );
     39 var rateval12 = require( './rational_p12q12.js' );
     40 var rateval24 = require( './rational_p24q24.js' );
     41 var rateval48 = require( './rational_p48q48.js' );
     42 var rateval816 = require( './rational_p816q816.js' );
     43 var rateval16INF = require( './rational_p16infq16inf.js' );
     44 
     45 
     46 // VARIABLES //
     47 
     48 var YOFFSET24 = 3.558437347412109375;
     49 
     50 
     51 // MAIN //
     52 
     53 /**
     54 * Evaluates the trigamma function.
     55 *
     56 * @param {number} x - input value
     57 * @returns {number} function value
     58 *
     59 * @example
     60 * var v = trigamma( -2.5 );
     61 * // returns ~9.539
     62 *
     63 * @example
     64 * var v = trigamma( 1.0 );
     65 * // returns ~1.645
     66 *
     67 * @example
     68 * var v = trigamma( 10.0 );
     69 * // returns ~0.105
     70 *
     71 * @example
     72 * var v = trigamma( NaN );
     73 * // returns NaN
     74 *
     75 * @example
     76 * var v = trigamma( -1.0 );
     77 * // returns NaN
     78 */
     79 function trigamma( x ) {
     80 	var result;
     81 	var s;
     82 	var y;
     83 	var z;
     84 
     85 	result = 0.0;
     86 
     87 	// Check for negative arguments and use reflection:
     88 	if ( x <= 0 ) {
     89 		if ( floor( x ) === x ) {
     90 			return NaN;
     91 		}
     92 		s = sinpi( x );
     93 		z = 1.0 - x;
     94 		return -trigamma( z ) + ( PI_SQUARED / ( s*s ) );
     95 	}
     96 	if ( x < 1.0 ) {
     97 		result = 1.0 / ( x*x );
     98 		x += 1.0;
     99 	}
    100 	if ( x <= 2.0 ) {
    101 		result += ( 2.0+rateval12( x ) ) / ( x*x );
    102 	}
    103 	else if ( x <= 4.0 ) {
    104 		result += ( YOFFSET24+rateval24( x ) ) / ( x*x );
    105 	}
    106 	else if ( x <= 8.0 ) {
    107 		y = 1.0 / x;
    108 		result += ( 1.0+rateval48( y ) ) / x;
    109 	}
    110 	else if ( x <= 16.0 ) {
    111 		y = 1.0 / x;
    112 		result += ( 1.0+rateval816( y ) ) / x;
    113 	}
    114 	else {
    115 		y = 1.0 / x;
    116 		result += ( 1.0+rateval16INF( y ) ) / x;
    117 	}
    118 	return result;
    119 }
    120 
    121 
    122 // EXPORTS //
    123 
    124 module.exports = trigamma;