https://github.com/stdlib-js/math-base-special-expm1rel
Relative error exponential.
https://github.com/stdlib-js/math-base-special-expm1rel
err error euler exp expm1 exponential function javascript math mathematics natural node node-js nodejs number power relative stdlib
Last synced: 27 days ago
JSON representation
Relative error exponential.
- Host: GitHub
- URL: https://github.com/stdlib-js/math-base-special-expm1rel
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T17:04:13.000Z (about 5 years ago)
- Default Branch: main
- Last Pushed: 2026-04-30T03:58:29.000Z (about 2 months ago)
- Last Synced: 2026-04-30T05:13:59.913Z (about 2 months ago)
- Topics: err, error, euler, exp, expm1, exponential, function, javascript, math, mathematics, natural, node, node-js, nodejs, number, power, relative, stdlib
- Language: Python
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 740 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
- Notice: NOTICE
Awesome Lists containing this project
README
About stdlib...
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# expm1rel
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Compute the relative error exponential.
The relative error exponential is defined as
```math
f(x) = \frac{e^x - 1}{x}
```
## Installation
```bash
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][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] 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
```javascript
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );
```
#### expm1rel( x )
Computes the relative error exponential.
```javascript
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
```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 100, -50.0, 50.0, opts );
logEachMap( '(e^%0.3f - 1)/%0.3f = %0.3f', x, x, expm1rel );
```
* * *
## C APIs
### Usage
```c
#include "stdlib/math/base/special/expm1rel.h"
```
#### stdlib_base_expm1rel( x )
Computes the relative error exponential.
```c
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.
```c
double stdlib_base_expm1rel( const double x );
```
### Examples
```c
#include "stdlib/math/base/special/expm1rel.h"
#include
#include
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 );
}
}
```
* * *
## See Also
- [`@stdlib/math-base/special/exp`][@stdlib/math/base/special/exp]: natural exponential function.
- [`@stdlib/math-base/special/expm1`][@stdlib/math/base/special/expm1]: compute exp(x) - 1.
* * *
## Notice
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].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-expm1rel.svg
[npm-url]: https://npmjs.org/package/@stdlib/math-base-special-expm1rel
[test-image]: https://github.com/stdlib-js/math-base-special-expm1rel/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/math-base-special-expm1rel/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-expm1rel/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-expm1rel?branch=main
[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/math-base-special-expm1rel/tree/deno
[deno-readme]: https://github.com/stdlib-js/math-base-special-expm1rel/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/math-base-special-expm1rel/tree/umd
[umd-readme]: https://github.com/stdlib-js/math-base-special-expm1rel/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/math-base-special-expm1rel/tree/esm
[esm-readme]: https://github.com/stdlib-js/math-base-special-expm1rel/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/math-base-special-expm1rel/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-expm1rel/main/LICENSE
[@stdlib/math/base/special/exp]: https://github.com/stdlib-js/math-base-special-exp
[@stdlib/math/base/special/expm1]: https://github.com/stdlib-js/math-base-special-expm1