Split a double-precision floating-point number into a normalized fraction and an integer power of two.
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> Split a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.
``bash`
npm install @stdlib/math-base-special-frexp
`javascript`
var frexp = require( '@stdlib/math-base-special-frexp' );
#### frexp( 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
`
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).
#### frexp.assign( x, out, stride, offset )
Splits a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two and assigns results to a provided output array.
`javascript
var Float64Array = require( '@stdlib/array-float64' );
var out = new Float64Array( 2 );
var y = frexp.assign( 4.0, out, 1, 0 );
// returns
var bool = ( y === out );
// returns true
`
- 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
`
`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 );
}
`
*
`c`
#include "stdlib/math/base/special/frexp.h"
#### stdlib_base_frexp( x, frac, exp )
Splits a [double-precision floating-point number][ieee754] into a normalized fraction and an integer power of two.
`c
#include
double frac;
int32_t exp;
stdlib_base_frexp( 4.0, &frac, &exp );
`
The function accepts the following arguments:
- x: [in] double input value.[out] double*
- frac: destination for the normalized fraction.[out] int32_t*
- exp: destination for the integer power of two.
`c`
void stdlib_base_frexp( const double x, double frac, int32_t exp );
`c
#include "stdlib/math/base/special/frexp.h"
#include
#include
#include
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 );
}
}
`
*
- [@stdlib/math-base/special/ldexp][@stdlib/math/base/special/ldexp]: multiply a double-precision floating-point number by an integer power of two.
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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[@stdlib/math/base/special/abs]: https://www.npmjs.com/package/@stdlib/math-base-special-abs
[@stdlib/math/base/special/ldexp]: https://www.npmjs.com/package/@stdlib/math-base-special-ldexp