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 );
}