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# Binary Logarithm

> Evaluate the [binary logarithm][binary-logarithm].

<section class="intro">

The [binary logarithm][binary-logarithm] (logarithm with base 2) is defined for any positive real number as

<!-- <equation class="equation" label="eq:binary_logarithm" align="center" raw="\quad \log_{2} \left( x \right) = y \quad \text{such that} \quad 2^y = x" alt="Equation for the binary logarithm."> -->

<div class="equation" align="center" data-raw-text="\quad \log_{2} \left( x \right) = y \quad \text{such that} \quad 2^y = x" data-equation="eq:binary_logarithm">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8cb4d022f6163be6523964802725ed2a74f2497b/lib/node_modules/@stdlib/math/base/special/log2/docs/img/equation_binary_logarithm.svg" alt="Equation for the binary logarithm.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var log2 = require( '@stdlib/math/base/special/log2' );
```

#### log2( x )

Evaluates the [binary logarithm][binary-logarithm].

```javascript
var v = log2( 4.0 );
// returns 2.0

v = log2( 0.0 );
// returns -Infinity

v = log2( Infinity );
// returns Infinity

v = log2( NaN );
// returns NaN
```

For negative numbers, the [binary logarithm][binary-logarithm] is **not** defined.

```javascript
var v = log2( -4.0 );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var log2 = require( '@stdlib/math/base/special/log2' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 100, 0, 100, opts );

logEachMap( 'log2(%d) = %0.4f', x, log2 );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/log2.h"
```

#### stdlib_base_log2( x )

Evaluates the binary logarithm.

```c
double out = stdlib_base_log2( 4.0 );
// returns 2.0
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.

```c
double stdlib_base_log2( const double x );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/log2.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;
    for ( i = 0; i < 100; i++ ) {
        x = ( ( (double)rand() / (double)RAND_MAX ) * 100.0 );
        v = stdlib_base_log2( x );
        printf( "log2(%lf) = %lf\n", x, v );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math/base/special/exp2`][@stdlib/math/base/special/exp2]</span><span class="delimiter">: </span><span class="description">base 2 exponential function.</span>
-   <span class="package-name">[`@stdlib/math/base/special/ln`][@stdlib/math/base/special/ln]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of a double-precision floating-point number.</span>
-   <span class="package-name">[`@stdlib/math/base/special/log`][@stdlib/math/base/special/log]</span><span class="delimiter">: </span><span class="description">compute the base `b` logarithm of a double-precision floating-point number.</span>

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[binary-logarithm]: https://en.wikipedia.org/wiki/Binary_logarithm

<!-- <related-links> -->

[@stdlib/math/base/special/exp2]: https://github.com/stdlib-js/math/tree/main/base/special/exp2

[@stdlib/math/base/special/ln]: https://github.com/stdlib-js/math/tree/main/base/special/ln

[@stdlib/math/base/special/log]: https://github.com/stdlib-js/math/tree/main/base/special/log

<!-- </related-links> -->

</section>

<!-- /.links -->
