hypot

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( void ) {
    const 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.