README.md

powm1

Evaluate bˣ - 1.

$$y = b^x - 1$$

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

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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var powm1 = require( '@stdlib/math/base/special/powm1' );

var opts = {
    'dtype': 'float64'
};
var b = discreteUniform( 100, 0, 10, opts );
var x = discreteUniform( 100, -5, 5, opts );

logEachMap( '%d^%d - 1 = %0.4f', b, x, powm1 );

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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 );
    }
}

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See Also

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