Evaluate a correction term for double-precision base-2 and base-10 logarithms when 1+f is in [√2/2, √2].
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> Evaluate a correction term for double-precision base-2 and base-10 logarithms when 1+f is in [√2/2, √2].
``bash`
npm install @stdlib/math-base-special-kernel-log1p
`javascript`
var kernelLog1p = require( '@stdlib/math-base-special-kernel-log1p' );
#### kernelLog1p( f )
Evaluates a correction term for double-precision base-2 and base-10 logarithms when 1+f is in [√2/2, √2].
`javascript
var v = kernelLog1p( 1.0 );
// returns ~0.1931
v = kernelLog1p( 1.4142135623730951 );
// returns ~0.4672
v = kernelLog1p( NaN );
// returns NaN
`
- 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][@stdlib/math/base/special/log2] and [@stdlib/math/base/special/log10][@stdlib/math/base/special/log10].
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var sqrt = require( '@stdlib/math-base-special-sqrt' );
var kernelLog1p = require( '@stdlib/math-base-special-kernel-log1p' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, sqrt( 2.0 ) / 2.0, sqrt( 2.0 ), opts );
logEachMap( 'kernelLog1p(%0.4f) = %0.4f', x, kernelLog1p );
`
*
`c`
#include "stdlib/math/base/special/kernel_log1p.h"
#### stdlib_base_kernel_log1p( f )
Evaluates a correction term for double-precision base-2 and base-10 logarithms when 1+f is in [√2/2, √2].
`c
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.
`c`
double stdlib_base_kernel_log1p( const double f );
`c
#include "stdlib/math/base/special/kernel_log1p.h"
#include
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 );
}
}
`
*
- [@stdlib/math-base/special/log1p][@stdlib/math/base/special/log1p]: evaluate the natural logarithm of 1+x.
*
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
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[@stdlib/math/base/special/log2]: https://www.npmjs.com/package/@stdlib/math-base-special-log2
[@stdlib/math/base/special/log10]: https://www.npmjs.com/package/@stdlib/math-base-special-log10
[@stdlib/math/base/special/log1p]: https://www.npmjs.com/package/@stdlib/math-base-special-log1p