time-to-botec

README.md (5052B)

---

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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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 ### 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 );
     }
 }
 ```
 
 </section>
 
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 [hypotenuse]: http://en.wikipedia.org/wiki/Pythagorean_theorem
 
 </section>
 
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