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normalize

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

Installation

npm install @stdlib/number-float64-base-normalize

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

normalize( x )

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

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

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 ]

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

Returns a normal number y and exponent exp satisfying x = y * 2^exp and assigns results to a provided output array.

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

var out = new Float64Array( 2 );

var v = normalize.assign( 3.14e-319, out, 1, 0);
// returns <Float64Array>[ 1.4141234400356668e-303, -52 ]

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

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var randu = require( '@stdlib/random-base-uniform' );
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( 0.0, 10.0 );

    // Generate an exponent on the interval (-308,-324):
    exp = discreteUniform( -323, -309 );

    // 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]) );
}

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C APIs

Usage

#include "stdlib/number/float64/base/normalize.h"

stdlib_base_float64_normalize( x, *y, *exp )

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

#include <stdint.h>

double y;
int32_t exp;

stdlib_base_float64_normalize( 3.14, &y, &exp );

The function accepts the following arguments:

• x: [in] double input value.
• y: [out] double* destination for normal number.
• exp: [out] int32_t* destination for exponent.

void stdlib_base_float64_normalize( const double x, double *y, int32_t *exp );

Examples

#include "stdlib/number/float64/base/normalize.h"
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>

int main( void ) {
    double x[] = { 1.0, 3.14, 0.0, -0.0, 3.14e-308, 3.14e308, 1.0/0.0, 0.0/0.0 };
    int32_t exp;
    double y;
    int i;

    for ( i = 0; i < 8; i++ ) {
        stdlib_base_float64_normalize( x[ i ], &y, &exp );
        printf( "%lf => y: %lf, exp: %" PRId32 "\n", x[ i ], y, exp );
    }
}

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See Also

• @stdlib/number-float32/base/normalize: return a normal number y and exponent exp satisfying x = y * 2^exp.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.