hypot

Compute the hypotenuse avoiding overflow and underflow.

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 ~1.4142e308
    
    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 );
}