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Exponential Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

[Exponential function][exponential-function].

The [exponential function][exponential-function] is defined as

math
y = b^x

where b is the base and x is the exponent.

## Installation

bash
npm install @stdlib/math-base-special-fast-pow-int

Alternatively,

- To load the package in a website via a script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [deno][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [umd][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage

javascript
var pow = require( '@stdlib/math-base-special-fast-pow-int' );

#### pow( base, exponent )

Evaluates the [exponential function][exponential-function] given a signed 32-bit integer exponent.

javascript
var v = pow( 2.0, 3 );
// returns 8.0

v = pow( 100.0, 0 );
// returns 1.0

v = pow( 3.14, 1 );
// returns 3.14

v = pow( -3.14, 1 );
// returns -3.14

v = pow( 2.0, -2 );
// returns 0.25

v = pow( NaN, 3 );
// returns NaN

## Notes

- This implementation is not recommended for high-precision applications due to error accumulation. As a trivial example, consider

javascript
    var v = pow( 10.0, 308 );
    // returns 1.0000000000000006e+308

where the expected result is 1.0e+308.

- If provided a negative exponent, the implementation first computes the reciprocal of the base and then evaluates the exponential function. This can introduce significant error. For example,

javascript
    var v = pow( -459, -98 );
    // returns 1.3878956588399783e-261

where the expected result is 1.3878956588399598e-261. From the bit sequences,

text
    0000100111000101110110100000000111001011001011010001000101010110
    0000100111000101110110100000000111001011001011010001000100000100

one observes that the returned value differs in the last 7 bits of the significand.

## Examples

javascript
var pow = require( '@stdlib/math-base-special-fast-pow-int' );

var x;
var y;
var v;

x = 10.0;
for ( y = 0; y < 309; y++ ) {
    v = pow( x, y );
    console.log( '%d^%d = %d', x, y, v );
}

## C APIs

### Usage

c
#include "stdlib/math/base/special/fast/pow.h"

#### stdlib_base_fast_pow( x, y )

Evaluates the [exponential function][exponential-function] given a signed 32-bit integer exponent.

c
double out = stdlib_base_fast_pow( 2.0, 3 );
// returns 8.0

out = stdlib_base_fast_pow( 3.14, 0 );
// returns 1.0

The function accepts the following arguments:

- x: [in] double base.
- y: [in] double exponent.

c
double stdlib_base_fast_pow( const double x, const int32_t y );

### Examples

c
#include "stdlib/math/base/special/fast/pow.h"
#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>

int main( void ) {
    const double x[] = { 3.14, 2.0, 2.0, 0.0 };
    const int32_t y[] = { 0, 3, -2, 0 };

    double z;
    int i;
    for ( i = 0; i < 4; i++ ) {
        z = stdlib_base_fast_pow( x[ i ], y[ i ] );
        printf( "pow( %lf, %d ) = %lf\n", x[ i ], y[ i ], z );
    }
}

*

## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].