118 lines
3.2 KiB
Markdown
118 lines
3.2 KiB
Markdown
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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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# Kernel Sine
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> Compute the [sine][sine] of a number on `[-π/4, π/4]`.
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<section class="usage">
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## Usage
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```javascript
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var kernelSin = require( '@stdlib/math/base/special/kernel-sin' );
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```
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#### kernelSin( x, y )
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Computes the [sine][sine] of a `number` on `[-π/4, π/4]`. For increased accuracy, the number for which the [sine][sine] should be evaluated can be supplied as a [double-double number][double-double-arithmetic] (i.e., a non-evaluated sum of two [double-precision floating-point numbers][ieee754] `x` and `y`).
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```javascript
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var v = kernelSin( 0.0, 0.0 );
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// returns ~0.0
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v = kernelSin( 3.141592653589793/6.0, 0.0 );
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// returns ~0.5
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v = kernelSin( 0.619, 9.279e-18 );
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// returns ~0.58
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v = kernelSin( NaN, 0.0 );
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// returns NaN
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v = kernelSin( 3.0, NaN );
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// returns NaN
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v = kernelSin( NaN, NaN );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- As components of a [double-double number][double-double-arithmetic], the two [double-precision floating-point numbers][ieee754] `x` and `y` must satisfy
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<!-- <equation class="equation" label="eq:double_double_inequality" align="center" raw="|y| \leq \frac{1}{2} \operatorname{ulp}(x)" alt="Inequality for the two components of a double-double number."> -->
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<div class="equation" align="center" data-raw-text="|y| \leq \frac{1}{2} \operatorname{ulp}(x)" data-equation="eq:double_double_inequality">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/kernel-sin/docs/img/equation_double_double_inequality.svg" alt="Inequality for the two components of a double-double number.">
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<br>
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</div>
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<!-- </equation> -->
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where `ulp` stands for [units in the last place][ulp].
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</section>
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<!-- /.notes -->
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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 linspace = require( '@stdlib/array/linspace' );
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var PI = require( '@stdlib/constants/float64/pi' );
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var kernelSin = require( '@stdlib/math/base/special/kernel-sin' );
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var x = linspace( -PI/4.0, PI/4.0, 100 );
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var i;
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for ( i = 0; i < x.length; i++ ) {
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console.log( 'kernelSin(%d) = %d', x[ i ], kernelSin( x[ i ], 0.0 ) );
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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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[sine]: https://en.wikipedia.org/wiki/Sine
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[double-double-arithmetic]: https://en.wikipedia.org/wiki/Quadruple-precision_floating-point_format#Double-double_arithmetic
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[ieee754]: https://en.wikipedia.org/wiki/IEEE_floating_point
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[ulp]: https://en.wikipedia.org/wiki/Unit_in_the_last_place
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</section>
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<!-- /.links -->
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