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# powm1

> Evaluate `bˣ - 1`.

<section class="intro">

<!-- <equation class="equation" label="eq:exponential_function_minus_one" align="center" raw="y = b^x - 1" alt="Exponential function minus one"> -->

<div class="equation" align="center" data-raw-text="y = b^x - 1" data-equation="eq:exponential_function_minus_one">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@bb29798906e119fcb2af99e94b60407a270c9b32/lib/node_modules/@stdlib/math/base/special/powm1/docs/img/equation_exponential_function_minus_one.svg" alt="Exponential function minus one">
    <br>
</div>

<!-- </equation> -->

When `b` is close to `1` and/or `x` is small, this implementation is more accurate than naively computing `bˣ` minus `1`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var powm1 = require( '@stdlib/math/base/special/powm1' );
```

#### powm1( b, x )

Evaluates `bˣ - 1`.

```javascript
var y = powm1( 2.0, 3.0 );
// returns 7.0

y = powm1( 4.0, 0.5 );
// returns 1.0

y = powm1( 0.0, 100.0 );
// returns -1.0

y = powm1( 100.0, 0.0 );
// returns 0.0

y = powm1( 0.0, 0.0 );
// returns 0.0

y = powm1( 3.141592653589793, 5.0 );
// returns ~305.0197

y = powm1( NaN, 3.0 );
// returns NaN

y = powm1( 5.0, NaN );
// returns NaN
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var logEachMap = require( '@stdlib/console/log-each-map' );
var powm1 = require( '@stdlib/math/base/special/powm1' );

var opts = {
    'dtype': 'float64'
};
var b = discreteUniform( 100, 0, 10, opts );
var x = discreteUniform( 100, -5, 5, opts );

logEachMap( '%d^%d - 1 = %0.4f', b, x, powm1 );
```

</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/powm1.h"
```

#### stdlib_base_powm1( b, x )

Evaluates `bˣ - 1`.

```c
double out = stdlib_base_powm1( 3.141592653589793, 5.0 );
// returns ~305.0197

out = stdlib_base_powm1( 4.0, 0.5 );
// returns 1.0
```

The function accepts the following arguments:

-   **b**: `[in] double` base.
-   **x**: `[in] double` exponent.

```c
double stdlib_base_powm1( const double b, const double x );
```

</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/powm1.h"
#include <stdlib.h>
#include <stdio.h>

int main( void ) {
    double out;
    double b;
    double x;
    int i;

    for ( i = 0; i < 100; i++ ) {
        b = ( ( (double)rand() / (double)RAND_MAX ) * 10.0 );
        x = ( ( (double)rand() / (double)RAND_MAX ) * 10.0 ) - 5.0;
        out = stdlib_base_powm1( b, x );
        printf( "powm1(%lf, %lf) = %lf\n", b, x, out );
    }
}
```

</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 -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

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

[@stdlib/math/base/special/pow]: https://github.com/stdlib-js/math/tree/main/base/special/pow

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

</section>

<!-- /.links -->
