expm1rel

Compute the relative error exponential.

The relative error exponential is defined as

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 );
    }
}