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kernelLog1p

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

Installation

npm install @stdlib/math-base-special-kernel-log1p

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 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 ] ) );
}

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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 );
    }
}

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See Also

• @stdlib/math-base/special/log1p: evaluate the natural logarithm of 1+x.

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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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Copyright

Copyright © 2016-2024. The Stdlib Authors.