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# hypot

> Compute the [hypotenuse][hypotenuse] avoiding overflow and underflow.

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## 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
```

</section>

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## 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
    ```

</section>

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## Examples

<!-- eslint no-undef: "error" -->

```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 );
}
```

</section>

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* * *

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## C APIs

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### 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 );
```

</section>

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</section>

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### Examples

```c
#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 );
    }
}
```

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[hypotenuse]: http://en.wikipedia.org/wiki/Pythagorean_theorem

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