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# frexp

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

<section class="usage">

## Usage

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

#### frexp( \[out,] 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
```

To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

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

var out = new Float64Array( 2 );

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

var bool = ( y === out );
// 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)`.

</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 -->

<section class="links">

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

[@stdlib/math/base/special/abs]: https://www.npmjs.com/package/@stdlib/math/tree/main/base/special/abs

</section>

<!-- /.links -->