# hypot
> Compute the [hypotenuse][hypotenuse] avoiding overflow and underflow.
## Usage
```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`, the function returns `NaN`.
```javascript
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.
```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
```
## Examples
```javascript
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
```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.
- **y**: `[in] double` input value.
```c
double stdlib_base_hypot( const double x, const double y );
```
### Examples
```c
#include "stdlib/math/base/special/hypot.h"
#include
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 );
}
}
```
[hypotenuse]: http://en.wikipedia.org/wiki/Pythagorean_theorem