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Benchmark sampling in different programming languages
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evalrational.js (3029B)

      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_60_0/boost/math/tools/rational.hpp}. The implementation 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 abs = require( './../../../../base/special/abs' );
     37 
     38 
     39 // MAIN //
     40 
     41 /**
     42 * Evaluates a rational function, i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\).
     43 *
     44 * ## Notes
     45 *
     46 * -   Coefficients should be sorted in ascending degree.
     47 * -   The implementation uses [Horner's rule][horners-method] for efficient computation.
     48 *
     49 * [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
     50 *
     51 *
     52 * @param {NumericArray} P - numerator polynomial coefficients sorted in ascending degree
     53 * @param {NumericArray} Q - denominator polynomial coefficients sorted in ascending degree
     54 * @param {number} x - value at which to evaluate the rational function
     55 * @returns {number} evaluated rational function
     56 *
     57 * @example
     58 * var P = [ -6.0, -5.0 ];
     59 * var Q = [ 3.0, 0.5 ];
     60 *
     61 * var v = evalrational( P, Q, 6.0 ); //  => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
     62 * // returns -6.0
     63 *
     64 * @example
     65 * // 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
     66 * var P = [ -6.0, -5.0, 4.0, 2.0 ];
     67 *
     68 * // 0.5x^1 + 3x^0 => degree 2
     69 * var Q = [ 3.0, 0.5, 0.0, 0.0 ]; // zero-padded
     70 *
     71 * var v = evalrational( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 + 4*6^2 + 2*6^3 ) / ( 3*6^0 + 0.5*6^1 + 0*6^2 + 0*6^3 ) = (-6-30+144+432)/(3+3)
     72 * // returns 90.0
     73 */
     74 function evalrational( P, Q, x ) {
     75 	var len;
     76 	var s1;
     77 	var s2;
     78 	var i;
     79 
     80 	len = P.length;
     81 	if ( len === 0 ) {
     82 		return NaN;
     83 	}
     84 	if ( len !== Q.length ) {
     85 		return NaN;
     86 	}
     87 	if ( x === 0.0 || len === 1 ) {
     88 		return P[ 0 ] / Q[ 0 ];
     89 	}
     90 	// Use Horner's method...
     91 	if ( abs( x ) <= 1.0 ) {
     92 		s1 = P[ len-1 ];
     93 		s2 = Q[ len-1 ];
     94 		for ( i = len-2; i >= 0; --i ) {
     95 			s1 *= x;
     96 			s2 *= x;
     97 			s1 += P[ i ];
     98 			s2 += Q[ i ];
     99 		}
    100 	} else {
    101 		x = 1.0 / x; // use inverse to avoid overflow
    102 		s1 = P[ 0 ];
    103 		s2 = Q[ 0 ];
    104 		for ( i = 1; i < len; ++i ) {
    105 			s1 *= x;
    106 			s2 *= x;
    107 			s1 += P[ i ];
    108 			s2 += Q[ i ];
    109 		}
    110 	}
    111 	return s1 / s2;
    112 }
    113 
    114 
    115 // EXPORTS //
    116 
    117 module.exports = evalrational;