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/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );

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

out = normalize( NINF );
// returns [ -Infinity, 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]) );
}