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Exponential Function

Exponential function.

The exponential function is defined as

$$y = b^x$$

where b is the base and x is the exponent.

Installation

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 available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

pow( base, exponent )

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

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

  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,

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

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

  0000100111000101110110100000000111001011001011010001000101010110
  0000100111000101110110100000000111001011001011010001000100000100
  

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

Examples

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 );
}

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C APIs

Usage

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

stdlib_base_fast_pow( x, y )

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

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.

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

Examples

#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 );
    }
}

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See Also

• @stdlib/math-base/special/pow: exponential function.

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Notice

This package is part of 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.