Relative error exponential.
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Compute the relative error exponential.
math
f(x) = \frac{e^x - 1}{x}bash
npm install @stdlib/math-base-special-expm1relscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var expm1rel = require( '@stdlib/math-base-special-expm1rel' );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 NaNx is near zero, exp(x)-1 can suffer catastrophic cancellation (i.e., a significant loss in precision). expm1rel avoids such a loss in precision.javascript
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
#include "stdlib/math/base/special/expm1rel.h"c
double out = stdlib_base_expm1rel( 0.0 );
// returns 1.0
out = stdlib_base_expm1rel( 1.0 );
// returns ~1.718[in] double input value.c
double stdlib_base_expm1rel( const double x );c
#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 );
}
}
