@stdlib/math-base-special-expm1rel

0.2.2 • Public • Published

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expm1rel

Compute the relative error exponential.

The relative error exponential is defined as

Installation

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

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 );
}```

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 );
}
}```

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.

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Install

`npm i @stdlib/math-base-special-expm1rel`

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