@stdlib/math-base-special-frexp/README.md

Split a double-precision floating-point number into a normalized fraction and an integer power of two.

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# frexp

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Split a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-frexp
```

</section>

<section class="usage">

## Usage

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

#### frexp( x )

Splits a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.

```javascript
var out = frexp( 4.0 );
// returns [ 0.5, 3 ]
```

By default, the function returns the normalized fraction and the exponent as a two-element `array`. The normalized fraction and exponent satisfy the relation `x = frac * 2^exp`.

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

var x = 4.0;
var out = frexp( x );
// returns [ 0.5, 3 ]

var frac = out[ 0 ];
var exp = out[ 1 ];

var bool = ( x === frac * pow(2.0, exp) );
// returns true
```

If provided positive or negative zero, `NaN`, or positive or negative `infinity`, the function returns a two-element `array` containing the input value and an exponent equal to `0`.

```javascript
var out = frexp( 0.0 );
// returns [ 0.0, 0 ]

out = frexp( -0.0 );
// returns [ -0.0, 0 ]

out = frexp( NaN );
// returns [ NaN, 0 ]

out = frexp( Infinity );
// returns [ Infinity, 0 ]

out = frexp( -Infinity );
// returns [ -Infinity, 0 ]
```

For all other numeric input values, the [absolute value][@stdlib/math/base/special/abs] of the normalized fraction resides on the interval `[0.5,1)`.

#### frexp.assign( x, out, stride, offset )

Splits a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two and assigns results to a provided output array.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var out = new Float64Array( 2 );

var y = frexp.assign( 4.0, out, 1, 0 );
// returns <Float64Array>[ 0.5, 3 ]

var bool = ( y === out );
// returns true
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Care should be taken when reconstituting a [double-precision floating-point number][ieee754] from a normalized fraction and an exponent. For example,

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

    var x = 8.988939926493918e+307; // x ~ 2^1023

    var out = frexp( x );
    // returns [ 0.5000263811533315, 1024 ]

    // Naive reconstitution:
    var y = out[ 0 ] * pow( 2.0, out[ 1 ] );
    // returns Infinity

    // Account for 2^1024 evaluating as infinity by recognizing 2^1024 = 2^1 * 2^1023:
    y = out[ 0 ] * pow( 2.0, out[1]-1023 ) * pow( 2.0, 1023 );
    // returns 8.988939926493918e+307
    ```

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var pow = require( '@stdlib/math-base-special-pow' );
var BIAS = require( '@stdlib/constants-float64-exponent-bias' );
var frexp = require( '@stdlib/math-base-special-frexp' );

var sign;
var frac;
var exp;
var x;
var f;
var v;
var i;

// Generate random numbers and break each into a normalized fraction and an integer power of two...
for ( i = 0; i < 100; i++ ) {
    if ( randu() < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    frac = randu() * 10.0;
    exp = round( randu()*616.0 ) - 308;
    x = sign * frac * pow( 10.0, exp );
    f = frexp( x );
    if ( f[ 1 ] > BIAS ) {
        v = f[ 0 ] * pow( 2.0, f[1]-BIAS ) * pow( 2.0, BIAS );
    } else {
        v = f[ 0 ] * pow( 2.0, f[ 1 ] );
    }
    console.log( '%d = %d * 2^%d = %d', x, f[ 0 ], f[ 1 ], v );
}
```

</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/frexp.h"
```

#### stdlib_base_frexp( x, frac, exp )

Splits a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.

```c
#include <stdint.h>

double frac;
int32_t exp;
stdlib_base_frexp( 4.0, &frac, &exp );
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **frac**: `[out] double*` destination for the normalized fraction.
-   **exp**: `[out] int32_t*` destination for the integer power of two.

```c
void stdlib_base_frexp( const double x, double *frac, int32_t *exp );
```

</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/frexp.h"
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>

int main( void ) {
    const double x[] = { 4.0, 0.0, -0.0, 1.0, -1.0, 3.14, -3.14, 1.0e308, -1.0e308, 1.0/0.0, -1.0/0.0, 0.0/0.0 };

    double frac;
    int32_t exp;
    int i;
    for ( i = 0; i < 12; i++ ) {
        stdlib_base_frexp( x[i], &frac, &exp );
        printf( "x: %f => frac: %f, exp: %" PRId32 "\n", x[i], frac, exp );
    }
}
```

</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/ldexp`][@stdlib/math/base/special/ldexp]</span><span class="delimiter">: </span><span class="description">multiply a double-precision floating-point number by an integer power of two.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].

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[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

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