kernelLog1p

Compute log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)].

Usage

var kernelLog1p = require( '@stdlib/math/base/special/kernel-log1p' );

kernelLog1p( f )

Computes log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)].

var v = kernelLog1p( 1.0 );
// returns ~0.1931

v = kernelLog1p( 1.4142135623730951 );
// returns ~0.4672

v = kernelLog1p( NaN );
// returns NaN

Notes

This function is a helper function for computing logarithms in base e. Argument reduction and adding the final term of the polynomial must be done by the caller for increased accuracy when different bases are used. For reference, see @stdlib/math/base/special/log2 and @stdlib/math/base/special/log10.

Examples

var linspace = require( '@stdlib/array/base/linspace' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var kernelLog1p = require( '@stdlib/math/base/special/kernel-log1p' );

var x = linspace( sqrt( 2.0 ) / 2.0, sqrt( 2.0 ), 100 );

var i;
for ( i = 0; i < x.length; i++ ) {
    console.log( 'kernelLog1p(%d) = %d', x[ i ], kernelLog1p( x[ i ] ) );
}

C APIs

Usage

#include "stdlib/math/base/special/kernel_log1p.h"

stdlib_base_kernel_log1p( f )

Computes log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)].

double out = stdlib_base_kernel_log1p( 1.0 );
// returns ~0.1931

out = stdlib_base_kernel_log1p( 1.4142135623730951 );
// returns ~0.4672

The function accepts the following arguments:

f: [in] double input value.

double stdlib_base_kernel_log1p( const double f );

Examples

#include "stdlib/math/base/special/kernel_log1p.h"
#include <stdio.h>

int main( void ) {
    const double x[] = { 0.7071, 0.7856, 0.8642, 0.9428, 1.0213, 1.0999, 1.1785, 1.2570, 1.3356, 1.4142 };

    double out;
    int i;
    for ( i = 0; i < 10; i++ ) {
        out = stdlib_base_kernel_log1p( x[ i ] );
        printf ( "x[ i ]: %lf, out: %lf\n", x[ i ], out );
    }
}