npm package: @stdlib/math-base-special-fast-pow-int
Description: Exponential function.
Author: The Stdlib Authors
Latest version: 0.3.1

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</details>

# Exponential Function

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

> [Exponential function][exponential-function].

<section class="intro">

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

<!-- <equation class="equation" label="eq:exponential_function" align="center" raw="y = b^x" alt="Exponential function"> -->

<div class="equation" align="center" data-raw-text="y = b^x" data-equation="eq:exponential_function">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@c1bdd27898df04d752ddb2dca37ca049e4c94d9b/lib/node_modules/@stdlib/math/base/special/fast/pow-int/docs/img/equation_exponential_function.svg" alt="Exponential function">
    <br>
</div>

<!-- </equation> -->

where `b` is the **base** and `x` is the **exponent**.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<section class="notes">

## 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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```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 );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### 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] int32_t` exponent.

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

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### 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 );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/pow`][@stdlib/math/base/special/pow]</span><span class="delimiter">: </span><span class="description">exponential function.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-fast-pow-int/main/LICENSE

[exponential-function]: https://en.wikipedia.org/wiki/Exponential_function

<!-- <related-links> -->

[@stdlib/math/base/special/pow]: https://www.npmjs.com/package/@stdlib/math-base-special-pow

<!-- </related-links> -->

</section>

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