113 lines
3.0 KiB
Markdown
113 lines
3.0 KiB
Markdown
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<!--
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Epsilon
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> Difference between one and the smallest value greater than one that can be represented as a [half-precision floating-point number][half-precision-floating-point-format].
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<section class="intro">
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[Epsilon][machine-epsilon] is defined as
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<!-- <equation class="equation" label="eq:epsilon_float16" align="center" raw="\epsilon = b^{-(p-1)}" alt="Epsilon for a half-precision floating-point number."> -->
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<div class="equation" align="center" data-raw-text="\epsilon = b^{-(p-1)}" data-equation="eq:epsilon_float16">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@5d87cc7cb2c58aeb732872f89562d2c89571cc8a/lib/node_modules/@stdlib/constants/float16/eps/docs/img/equation_epsilon_float16.svg" alt="Epsilon for a half-precision floating-point number.">
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<br>
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</div>
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<!-- </equation> -->
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where `b` is the radix (base) and `p` is the precision (number of radix bits in the significand). For [half-precision floating-point numbers][half-precision-floating-point-format], `b` is `2` and `p` is `11`.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var FLOAT16_EPSILON = require( '@stdlib/constants/float16/eps' );
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```
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#### FLOAT16_EPSILON
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Difference between one and the smallest value greater than one that can be represented as a [half-precision floating-point number][half-precision-floating-point-format].
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```javascript
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var bool = ( FLOAT16_EPSILON === 0.0009765625 );
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// returns true
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```
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var abs = require( '@stdlib/math/base/special/abs' );
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var maxabs = require( '@stdlib/math/base/special/maxabs' );
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var randu = require( '@stdlib/random/base/randu' );
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var FLOAT16_EPSILON = require( '@stdlib/constants/float16/eps' );
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var bool;
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var a;
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var b;
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var i;
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function isApprox( a, b ) {
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var delta;
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var tol;
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delta = abs( a - b );
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tol = FLOAT16_EPSILON * maxabs( a, b );
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return ( delta <= tol );
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}
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for ( i = 0; i < 100; i++ ) {
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a = randu() * 10.0;
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b = a + (randu()*2.0e-3) - 1.0e-3;
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bool = isApprox( a, b );
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console.log( '%d %s approximately equal to %d', a, ( bool ) ? 'is' : 'is not', b );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[half-precision-floating-point-format]: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
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[machine-epsilon]: https://en.wikipedia.org/wiki/Machine_epsilon
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</section>
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<!-- /.links -->
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