# frexp
> Split a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.
## 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 [ 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)`.
## 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
```
## Examples
```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 );
}
```
[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