frexp

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

Installation

$ npm install math-float64-frexp

Usage

var frexp = require( 'math-float64-frexp' );

frexp( x )

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

var out = frexp( 4 );
// returns [ 0.5, 3 ]

The first element of the returned array is the normalized fraction and the second is the exponent. The normalized fraction and exponent satisfy the relation x = frac * 2**exp.

var pow = require( 'math-power' );

var x = 4;
var out = frexp( x );
// returns [ 0.5, 3 ]

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

var bool = ( x === frac * pow(2,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.

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

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

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

out = frexp( Number.POSITIVE_INFINITY );
// returns [ +infinity, 0 ]

out = frexp( Number.NEGATIVE_INFINITY );
// returns [ -infinity, 0 ]

For all other numeric input values, the absolute value of the normalized fraction resides on the interval [1/2,1).

Notes

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

  var pow = require( 'math-power' );
  
  // x ~ 2**1023
  var x = 8.988939926493918e+307;
  
  var out = frexp( x );
  // returns [ 0.5000263811533315, 1024 ]
  
  // Naive reconstitution:
  var y = out[ 0 ] * pow( 2, out[ 1 ] );
  // returns +infinity
  
  // Account for 2**1024 evaluating as infinity by recognizing 2**1024 = 2**1 * 2**1023:
  y = out[ 0 ] * pow( 2, out[1]-1023 ) * pow( 2, 1023 );
  // returns 8.988939926493918e+307

Examples

var round = require( 'math-round' );
var pow = require( 'math-power' );
var frexp = require( 'math-float64-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 ( Math.random() < 0.5 ) {
		sign = -1;
	} else {
		sign = 1;
	}
	frac = Math.random() * 10;
	exp = round( Math.random()*616 ) - 308;
	x = sign * frac * pow( 10, exp );
	f = frexp( x );
	if ( f[ 1 ] > 1023 ) {
		v = f[ 0 ] * pow( 2, f[1]-1023 ) * pow( 2, 1023 );
	} else {
		v = f[ 0 ] * pow( 2, f[ 1 ] );
	}
	console.log( '%d = %d * 2^%d = %d', x, f[ 0 ], f[ 1 ], v );
}

To run the example code from the top-level application directory,

$ node ./examples/index.js

Tests

Unit

This repository uses tape for unit tests. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

Browser Support

This repository uses Testling for browser testing. To run the tests in a (headless) local web browser, execute the following command in the top-level application directory:

$ make test-browsers

To view the tests in a local web browser,

$ make view-browser-tests

License

MIT license.

Copyright

Copyright © 2016. The Compute.io Authors.