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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/ory
, 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/ory
, 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.