# 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 ~1.4142e+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 );
}
}
``````