246 lines
4.9 KiB
Markdown
246 lines
4.9 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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# hypot
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> Compute the [hypotenuse][hypotenuse] avoiding overflow and underflow.
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var hypot = require( '@stdlib/math/base/special/hypot' );
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```
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#### hypot( x, y )
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Computes the [hypotenuse][hypotenuse] avoiding overflow and underflow.
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```javascript
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var h = hypot( -5.0, 12.0 );
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// returns 13.0
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h = hypot( -0.0, -0.0 );
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// returns +0.0
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```
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If either argument is `NaN`, the function returns `NaN`.
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```javascript
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var h = hypot( NaN, 12.0 );
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// returns NaN
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h = hypot( 5.0, 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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<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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## Notes
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- The textbook approach to calculating the hypotenuse is subject to overflow and underflow. For example, for a sufficiently large `x` and/or `y`, computing the hypotenuse will overflow.
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```javascript
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var sqrt = require( '@stdlib/math/base/special/sqrt' );
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var x2 = 1.0e154 * 1.0e154;
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// returns 1.0e308
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var h = sqrt( x2 + x2 );
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// returns Infinity
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```
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Similarly, for sufficiently small `x` and/or `y`, computing the hypotenuse will underflow.
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```javascript
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var sqrt = require( '@stdlib/math/base/special/sqrt' );
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var x2 = 1.0e-200 * 1.0e-200;
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// returns 0.0
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var h = sqrt( x2 + x2 );
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// returns 0.0
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```
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This implementation uses a numerically stable algorithm which avoids overflow and underflow.
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```javascript
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var h = hypot( 1.0e154, 1.0e154 );
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// returns ~1.4142e+154
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h = hypot( 1.0e-200, 1.0e-200 );
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// returns ~1.4142e-200
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```
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</section>
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<!-- /.notes -->
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<!-- Package usage examples. -->
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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 randu = require( '@stdlib/random/base/randu' );
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var round = require( '@stdlib/math/base/special/round' );
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var hypot = require( '@stdlib/math/base/special/hypot' );
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var x;
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var y;
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var h;
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var i;
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for ( i = 0; i < 100; i++ ) {
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x = round( randu()*100.0 ) - 50.0;
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y = round( randu()*100.0 ) - 50.0;
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h = hypot( x, y );
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console.log( 'h(%d,%d) = %d', x, y, h );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/math/base/special/hypot.h
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```
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#### stdlib_base_hypot( x, y )
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Computes the hypotenuse avoiding overflow and underflow.
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```c
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double h = stdlib_base_hypot( 5.0, 12.0 );
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// returns 13.0
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```
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The function accepts the following arguments:
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- **x**: `[in] double` input value.
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- **y**: `[in] double` input value.
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```c
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double stdlib_base_hypot( const double x, const double y );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/math/base/special/hypot.h"
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#include <stdio.h>
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int main() {
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double x[] = { 3.0, 4.0, 5.0, 12.0 };
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double y;
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int i;
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for ( i = 0; i < 4; i += 2 ) {
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y = stdlib_base_hypot( x[ i ], x[ i+1 ] );
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printf( "hypot(%lf, %lf) = %lf\n", x[ i ], x[ i+1 ], y );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="references">
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</section>
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<!-- /.references -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[hypotenuse]: http://en.wikipedia.org/wiki/Pythagorean_theorem
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</section>
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<!-- /.links -->
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