powm1

Evaluate bˣ - 1.

When b is close to 1 and/or x is small, this implementation is more accurate than naively computing bˣ minus 1.

Installation

npm install @stdlib/math-base-special-powm1

Usage

var powm1 = require( '@stdlib/math-base-special-powm1' );

powm1( b, x )

Evaluates bˣ - 1.

var y = powm1( 2.0, 3.0 );
// returns 7.0

y = powm1( 4.0, 0.5 );
// returns 1.0

y = powm1( 0.0, 100.0 );
// returns -1.0

y = powm1( 100.0, 0.0 );
// returns 0.0

y = powm1( 0.0, 0.0 );
// returns 0.0

y = powm1( 3.141592653589793, 5.0 );
// returns ~305.0197

y = powm1( NaN, 3.0 );
// returns NaN

y = powm1( 5.0, NaN );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var powm1 = require( '@stdlib/math-base-special-powm1' );

var b;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    b = round( randu()*10.0 );
    x = round( randu()*10.0 ) - 5.0;
    y = powm1( b, x );
    console.log( '%d^%d - 1 = %d', b, x, y );
}

C APIs

Usage

#include "stdlib/math/base/special/powm1.h"

stdlib_base_powm1( base, exponent )

Evaluates bˣ - 1.

double out = stdlib_base_powm1( 3.141592653589793, 5.0 );
// returns ~305.0197

out = stdlib_base_powm1( 4.0, 0.5 );
// returns 1.0

The function accepts the following arguments:

• base: [in] double base.
• exponent: [in] double exponent.

double stdlib_base_powm1( const double base, const double exponent );

Examples

#include "stdlib/math/base/special/powm1.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double out;
    double b;
    double x;
    int i;

    for ( i = 0; i < 100; i++ ) {
        b = ( ( (double)rand() / (double)RAND_MAX ) * 10.0 );
        x = ( ( (double)rand() / (double)RAND_MAX ) * 10.0 ) - 5.0;
        out = stdlib_base_powm1( b, x );
        printf( "powm1(%lf, %lf) = %lf\n", b, x, out );
    }
}

See Also

• @stdlib/math-base/special/pow: exponential function.

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.

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Copyright

Copyright © 2016-2024. The Stdlib Authors.