Compute the hypotenuse avoiding overflow and underflow.
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> Compute the [hypotenuse][hypotenuse] avoiding overflow and underflow.
``bash`
npm install @stdlib/math-base-special-hypot
`javascript`
var hypot = require( '@stdlib/math-base-special-hypot' );
#### hypot( x, y )
Computes the [hypotenuse][hypotenuse] avoiding overflow and underflow.
`javascript
var h = hypot( -5.0, 12.0 );
// returns 13.0
h = hypot( -0.0, -0.0 );
// returns +0.0
`
If either argument is NaN and the other argument is not +-Infinity, the function returns NaN.
`javascript
var h = hypot( NaN, 12.0 );
// returns NaN
h = hypot( 5.0, NaN );
// returns NaN
`
- 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.
`javascript
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.
`javascript
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.
`javascript
var h = hypot( 1.0e154, 1.0e154 );
// returns ~1.4142e+154
h = hypot( 1.0e-200, 1.0e-200 );
// returns ~1.4142e-200
`
`javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var hypot = require( '@stdlib/math-base-special-hypot' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 100, -50, 50, opts );
var y = discreteUniform( 100, -50, 50, opts );
logEachMap( 'h(%d,%d) = %0.4f', x, y, hypot );
`
*
`c`
#include "stdlib/math/base/special/hypot.h"
#### stdlib_base_hypot( x, y )
Computes the hypotenuse avoiding overflow and underflow.
`c`
double h = stdlib_base_hypot( 5.0, 12.0 );
// returns 13.0
The function accepts the following arguments:
- x: [in] double input value.[in] double
- y: input value.
`c`
double stdlib_base_hypot( const double x, const double y );
`c
#include "stdlib/math/base/special/hypot.h"
#include
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 );
}
}
`
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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---
See [LICENSE][stdlib-license].
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd-url]: https://github.com/stdlib-js/math-base-special-hypot/tree/umd
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[esm-readme]: https://github.com/stdlib-js/math-base-special-hypot/blob/esm/README.md
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[hypotenuse]: https://en.wikipedia.org/wiki/Pythagorean_theorem