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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
Exponential function
where `b` is the **base** and `x` is the **exponent**.
## Installation ```bash npm install @stdlib/math-base-special-fast-pow-int ```
## 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] int32_t` 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 #include #include 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 ); } } ```
* * * ## See Also - [`@stdlib/math-base/special/pow`][@stdlib/math/base/special/pow]: exponential function.
* * * ## 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 © 2016-2026. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-fast-pow-int.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-fast-pow-int [test-image]: https://github.com/stdlib-js/math-base-special-fast-pow-int/actions/workflows/test.yml/badge.svg?branch=v0.3.1 [test-url]: https://github.com/stdlib-js/math-base-special-fast-pow-int/actions/workflows/test.yml?query=branch:v0.3.1 [coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-fast-pow-int/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-fast-pow-int?branch=main [chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com [stdlib]: https://github.com/stdlib-js/stdlib [stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors [umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules [deno-url]: https://github.com/stdlib-js/math-base-special-fast-pow-int/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-special-fast-pow-int/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-special-fast-pow-int/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-special-fast-pow-int/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-special-fast-pow-int/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-special-fast-pow-int/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-special-fast-pow-int/blob/main/branches.md [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 [@stdlib/math/base/special/pow]: https://www.npmjs.com/package/@stdlib/math-base-special-pow