@stdlib/math-base-special-expm1rel
v0.2.4TypeScript
Relative error exponential.
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Published by The Stdlib Authors
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expm1rel
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> Compute the relative error exponential.
The relative error exponential is defined as
Installation
``bash`
npm install @stdlib/math-base-special-expm1rel
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
$3
`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 );
$3
`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].
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[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
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[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
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[@stdlib/math/base/special/exp]: https://www.npmjs.com/package/@stdlib/math-base-special-exp
[@stdlib/math/base/special/expm1]: https://www.npmjs.com/package/@stdlib/math-base-special-expm1