frexp

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

Installation

npm install @stdlib/math-base-special-frexp

Usage

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

frexp( x )

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

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.

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

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( 0.0 );
// 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 of the normalized fraction resides on the interval [0.5,1).

frexp.assign( x, out, stride, offset )

Splits a double-precision floating-point number into a normalized fraction and an integer power of two and assigns results to a provided output array.

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

var out = new Float64Array( 2 );

var y = frexp.assign( 4.0, out, 1, 0 );
// returns <Float64Array>[ 0.5, 3 ]

var bool = ( y === out );
// returns true

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( '@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

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 );
}

C APIs

Usage

#include "stdlib/math/base/special/frexp.h"

stdlib_base_frexp( x, frac, exp )

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

#include <stdint.h>

double frac;
int32_t exp;
stdlib_base_frexp( 4.0, &frac, &exp );

The function accepts the following arguments:

• x: [in] double input value.
• frac: [out] double* destination for the normalized fraction.
• exp: [out] int32_t* destination for the integer power of two.

void stdlib_base_frexp( const double x, double *frac, int32_t *exp );

Examples

#include "stdlib/math/base/special/frexp.h"
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>

int main( void ) {
    const double x[] = { 4.0, 0.0, -0.0, 1.0, -1.0, 3.14, -3.14, 1.0e308, -1.0e308, 1.0/0.0, -1.0/0.0, 0.0/0.0 };

    double frac;
    int32_t exp;
    int i;
    for ( i = 0; i < 12; i++ ) {
        stdlib_base_frexp( x[i], &frac, &exp );
        printf( "x: %f => frac: %f, exp: %" PRId32 "\n", x[i], frac, exp );
    }
}

See Also

• @stdlib/math-base/special/ldexp: multiply a double-precision floating-point number by an integer power of two.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.