time-to-botec

Benchmark sampling in different programming languages
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README.md (2981B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
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     11    http://www.apache.org/licenses/LICENSE-2.0
     12 
     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
     18 
     19 -->
     20 
     21 # Epsilon
     22 
     23 > Difference between one and the smallest value greater than one that can be represented as a [double-precision floating-point number][ieee754].
     24 
     25 <section class="intro">
     26 
     27 [Epsilon][machine-epsilon] is defined as
     28 
     29 <!-- <equation class="equation" label="eq:epsilon_float64" align="center" raw="\epsilon = b^{-(p-1)}" alt="Epsilon for a double-precision floating-point number."> -->
     30 
     31 <div class="equation" align="center" data-raw-text="\epsilon = b^{-(p-1)}" data-equation="eq:epsilon_float64">
     32     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float64/eps/docs/img/equation_epsilon_float64.svg" alt="Epsilon for a double-precision floating-point number.">
     33     <br>
     34 </div>
     35 
     36 <!-- </equation> -->
     37 
     38 where `b` is the radix (base) and `p` is the precision (number of radix bits in the significand). For [double-precision floating-point numbers][ieee754], `b` is `2` and `p` is `53`.
     39 
     40 </section>
     41 
     42 <!-- /.intro -->
     43 
     44 <section class="usage">
     45 
     46 ## Usage
     47 
     48 ```javascript
     49 var FLOAT64_EPSILON = require( '@stdlib/constants/float64/eps' );
     50 ```
     51 
     52 #### FLOAT64_EPSILON
     53 
     54 Difference between one and the smallest value greater than one that can be represented as a [double-precision floating-point number][ieee754].
     55 
     56 ```javascript
     57 var bool = ( FLOAT64_EPSILON === 2.220446049250313e-16 );
     58 // returns true
     59 ```
     60 
     61 </section>
     62 
     63 <!-- /.usage -->
     64 
     65 <section class="examples">
     66 
     67 ## Examples
     68 
     69 <!-- eslint no-undef: "error" -->
     70 
     71 ```javascript
     72 var abs = require( '@stdlib/math/base/special/abs' );
     73 var max = require( '@stdlib/math/base/special/max' );
     74 var randu = require( '@stdlib/random/base/randu' );
     75 var FLOAT64_EPSILON = require( '@stdlib/constants/float64/eps' );
     76 
     77 var bool;
     78 var a;
     79 var b;
     80 var i;
     81 
     82 function isApprox( a, b ) {
     83     var delta;
     84     var tol;
     85 
     86     delta = abs( a - b );
     87     tol = FLOAT64_EPSILON * max( abs( a ), abs( b ) );
     88 
     89     return ( delta <= tol );
     90 }
     91 
     92 for ( i = 0; i < 100; i++ ) {
     93     a = randu() * 10.0;
     94     b = a + (randu()*5.0e-15) - 2.5e-15;
     95     bool = isApprox( a, b );
     96     console.log( '%d %s approximately equal to %d. Delta: %d.', a, ( bool ) ? 'is' : 'is not', b, abs( a - b ) );
     97 }
     98 ```
     99 
    100 </section>
    101 
    102 <!-- /.examples -->
    103 
    104 <section class="links">
    105 
    106 [ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985
    107 
    108 [machine-epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
    109 
    110 </section>
    111 
    112 <!-- /.links -->