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expm1rel

Compute the relative error exponential.

The relative error exponential is defined as

$$f(x) = \frac{e^x - 1}{x}$$

Installation

npm install @stdlib/math-base-special-expm1rel

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 expm1rel = require( '@stdlib/math-base-special-expm1rel' );

expm1rel( x )

Computes the relative error exponential.

var v = expm1rel( 0.0 );
// returns 1.0

v = expm1rel( 1.0 );
// returns ~1.718

v = expm1rel( -1.0 );
// returns ~0.632

v = expm1rel( NaN );
// returns NaN

Notes

• When x is near zero, exp(x)-1 can suffer catastrophic cancellation (i.e., a significant loss in precision). expm1rel avoids such a loss in precision.

Examples

var randu = require( '@stdlib/random-base-randu' );
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );

var x;
var y;
var a;
var i;

for ( i = 0; i < 100; i++ ) {
    x = (randu()*100.0) - 50.0;
    a = x.toFixed( 3 );
    y = expm1rel( x );
    console.log( '(e^%d - 1)/%d = %d', a, a, y );
}

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C APIs

Usage

#include "stdlib/math/base/special/expm1rel.h"

stdlib_base_exmp1rel( x )

Computes the relative error exponential.

double out = stdlib_base_expm1rel( 0.0 );
// returns 1.0

out = stdlib_base_expm1rel( 1.0 );
// returns ~1.718

The function accepts the following arguments:

• x: [in] double input value.

double stdlib_base_expm1rel( const double x );

Examples

#include "stdlib/math/base/special/expm1rel.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double x;
    double v;
    int i;

    for ( i = 0; i < 100; i++ ) {
        x = ( ( (double)rand() / (double)RAND_MAX ) * 100.0 ) - 50.0;
        v = stdlib_base_expm1rel( x );
        printf( "(e^%lf - 1)/%lf = %lf\n", x, x, v );
    }
}

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See Also

• @stdlib/math-base/special/exp: natural exponential function.
• @stdlib/math-base/special/expm1: compute exp(x) - 1.

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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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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.