# Normalize

Return a normal number `y` and exponent `exp` satisfying `x = y * 2^exp`.

## Usage

``````var normalize = require( '@stdlib/number/float64/base/normalize' );
``````

#### normalize( [out,] x )

Returns a normal number `y` and exponent `exp` satisfying `x = y * 2^exp`.

``````var out = normalize( 3.14e-319 );
// returns [ 1.4141234400356668e-303, -52 ]
``````

By default, the function returns `y` and `exp` as a two-element `array`.

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

var out = normalize( 3.14e-319 );
// returns [ 1.4141234400356668e-303, -52 ]

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

var bool = ( y*pow(2.0, exp) === 3.14e-319 );
// returns true
``````

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

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

var out = new Float64Array( 2 );

var v = normalize( out, 3.14e-319 );
// returns <Float64Array>[ 1.4141234400356668e-303, -52 ]

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

The function expects a finite, non-zero `numeric` value `x`. If `x == 0`,

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

If `x` is either positive or negative `infinity` or `NaN`,

``````var PINF = require( '@stdlib/constants/math/float64-pinf' );
var NINF = require( '@stdlib/constants/math/float64-ninf' );

var out = normalize( PINF );
// returns [ PINF, 0 ]

out = normalize( NINF );
// returns [ NINF, 0 ]

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

## Examples

``````var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var pow = require( '@stdlib/math/base/special/pow' );
var normalize = require( '@stdlib/number/float64/base/normalize' );

var frac;
var exp;
var x;
var v;
var i;

// Generate denormalized numbers and then normalize them...
for ( i = 0; i < 100; i++ ) {
// Generate a random fraction:
frac = randu() * 10.0;

// Generate an exponent on the interval (-308,-324):
exp = -309 - round( randu()*14.0 );

// Create a subnormal number (~2.23e-308, ~4.94e-324):
x = frac * pow( 10.0, exp );

// Determine a `y` and an `exp` to "normalize" the subnormal:
v = normalize( x );

console.log( '%d = %d * 2^%d = %d', x, v[0], v[1], v[0]*pow(2.0, v[1]) );
}
``````