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| 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 | + |
| 20 | +'use strict'; |
| 21 | + |
| 22 | +// MODULES // |
| 23 | + |
| 24 | +var log = require( '@stdlib/console/log' ); |
| 25 | +var abs = require( '@stdlib/math/base/special/abs' ); |
| 26 | +var sqrt = require( './../lib' ); |
| 27 | + |
| 28 | + |
| 29 | +// FUNCTIONS // |
| 30 | + |
| 31 | +/** |
| 32 | +* Computes a rough square root approximation using a small fixed number of Newton iterations. |
| 33 | +* |
| 34 | +* @private |
| 35 | +* @param {number} x - input value |
| 36 | +* @returns {number} approximate square root |
| 37 | +*/ |
| 38 | +function approxSqrt( x ) { |
| 39 | + var guess; |
| 40 | + var i; |
| 41 | + |
| 42 | + if ( x < 0.0 ) { |
| 43 | + return NaN; |
| 44 | + } |
| 45 | + if ( x === 0.0 ) { |
| 46 | + return 0.0; |
| 47 | + } |
| 48 | + guess = ( x > 1.0 ) ? x / 2.0 : 1.0; |
| 49 | + for ( i = 0; i < 5; i++ ) { |
| 50 | + guess = 0.5 * ( guess + ( x / guess ) ); |
| 51 | + } |
| 52 | + return guess; |
| 53 | +} |
| 54 | + |
| 55 | +/** |
| 56 | +* Computes the arithmetic mean. |
| 57 | +* |
| 58 | +* @private |
| 59 | +* @param {Array<number>} values - input array |
| 60 | +* @returns {number} mean value |
| 61 | +*/ |
| 62 | +function mean( values ) { |
| 63 | + var sum; |
| 64 | + var i; |
| 65 | + |
| 66 | + if ( values.length === 0 ) { |
| 67 | + return NaN; |
| 68 | + } |
| 69 | + sum = 0.0; |
| 70 | + for ( i = 0; i < values.length; i++ ) { |
| 71 | + sum += values[ i ]; |
| 72 | + } |
| 73 | + return sum / values.length; |
| 74 | +} |
| 75 | + |
| 76 | +/** |
| 77 | +* Computes the relative error between two numbers. |
| 78 | +* |
| 79 | +* @private |
| 80 | +* @param {number} value - computed value |
| 81 | +* @param {number} expected - reference value |
| 82 | +* @returns {number} relative error |
| 83 | +*/ |
| 84 | +function relativeError( value, expected ) { |
| 85 | + var denom = ( expected === 0.0 ) ? 1e-16 : expected; |
| 86 | + return abs( ( value - expected ) / denom ); |
| 87 | +} |
| 88 | + |
| 89 | + |
| 90 | +// MAIN // |
| 91 | + |
| 92 | +/** |
| 93 | +* Evaluate the mean relative error between a simple Newton approximation and `@stdlib`'s sqrt implementation. |
| 94 | +* |
| 95 | +* @private |
| 96 | +*/ |
| 97 | +function main() { |
| 98 | + var approx; |
| 99 | + var errors; |
| 100 | + var expected; |
| 101 | + var values; |
| 102 | + var i; |
| 103 | + |
| 104 | + values = [ |
| 105 | + 0.5, |
| 106 | + 1.5, |
| 107 | + 2.5, |
| 108 | + 10.0, |
| 109 | + 25.0, |
| 110 | + 100.0 |
| 111 | + ]; |
| 112 | + errors = []; |
| 113 | + for ( i = 0; i < values.length; i++ ) { |
| 114 | + expected = sqrt( values[ i ] ); |
| 115 | + approx = approxSqrt( values[ i ] ); |
| 116 | + errors.push( relativeError( approx, expected ) ); |
| 117 | + } |
| 118 | + log( 'Mean relative error (approx vs @stdlib sqrt): %d', mean( errors ) ); |
| 119 | +} |
| 120 | + |
| 121 | +main(); |
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