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    @stdlib/math-base-special-hypot
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    0.0.7 • Public • Published

    hypot

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    Compute the hypotenuse avoiding overflow and underflow.

    Installation

    npm install @stdlib/math-base-special-hypot

    Usage

    var hypot = require( '@stdlib/math-base-special-hypot' );

    hypot( x, y )

    Computes the hypotenuse avoiding overflow and underflow.

    var h = hypot( -5.0, 12.0 );
    // returns 13.0
    
    h = hypot( -0.0, -0.0 );
    // returns +0.0

    If either argument is NaN, the function returns NaN.

    var h = hypot( NaN, 12.0 );
    // returns NaN
    
    h = hypot( 5.0, NaN );
    // returns NaN

    Notes

    • 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.

      var sqrt = require( '@stdlib/math-base-special-sqrt' );
      
      var x2 = 1.0e154 * 1.0e154;
      // returns 1.0e308
      
      var h = sqrt( x2 + x2 );
      // returns Infinity

      Similarly, for sufficiently small x and/or y, computing the hypotenuse will underflow.

      var sqrt = require( '@stdlib/math-base-special-sqrt' );
      
      var x2 = 1.0e-200 * 1.0e-200;
      // returns 0.0
      
      var h = sqrt( x2 + x2 );
      // returns 0.0

      This implementation uses a numerically stable algorithm which avoids overflow and underflow.

      var h = hypot( 1.0e154, 1.0e154 );
      // returns ~1.4142e+154
      
      h = hypot( 1.0e-200, 1.0e-200 );
      // returns ~1.4142e-200

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var round = require( '@stdlib/math-base-special-round' );
    var hypot = require( '@stdlib/math-base-special-hypot' );
    
    var x;
    var y;
    var h;
    var i;
    
    for ( i = 0; i < 100; i++ ) {
        x = round( randu()*100.0 ) - 50.0;
        y = round( randu()*100.0 ) - 50.0;
        h = hypot( x, y );
        console.log( 'h(%d,%d) = %d', x, y, h );
    }

    C APIs

    Usage

    #include "stdlib/math/base/special/hypot.h

    stdlib_base_hypot( x, y )

    Computes the hypotenuse avoiding overflow and underflow.

    double h = stdlib_base_hypot( 5.0, 12.0 );
    // returns 13.0

    The function accepts the following arguments:

    • x: [in] double input value.
    • y: [in] double input value.
    double stdlib_base_hypot( const double x, const double y );

    Examples

    #include "stdlib/math/base/special/hypot.h"
    #include <stdio.h>
    
    int main() {
        double x[] = { 3.0, 4.0, 5.0, 12.0 };
    
        double y;
        int i;
        for ( i = 0; i < 4; i += 2 ) {
            y = stdlib_base_hypot( x[ i ], x[ i+1 ] );
            printf( "hypot(%lf, %lf) = %lf\n", x[ i ], x[ i+1 ], y );
        }
    }

    Notice

    This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

    For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-special-hypot

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    124

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    48.3 kB

    Total Files

    15

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser