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# ldexp

> Multiply a [double-precision floating-point number][ieee754] by an integer power of two.

<section class="usage">

## Usage

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

#### ldexp( frac, exp )

Multiplies a [double-precision floating-point number][ieee754] by an `integer` power of two (i.e., `x = frac * 2^exp`).

```javascript
var x = ldexp( 0.5, 3 ); // => 0.5 * 2^3 = 0.5 * 8
// returns 4.0

x = ldexp( 4.0, -2 ); // => 4 * 2^(-2) = 4 * (1/4)
// returns 1.0
```

If `frac` equals positive or negative zero, `NaN`, or positive or negative `infinity`, the function returns a value equal to `frac`.

```javascript
var x = ldexp( 0.0, 20 );
// returns 0.0

x = ldexp( -0.0, 39 );
// returns -0.0

x = ldexp( NaN, -101 );
// returns NaN

x = ldexp( Infinity, 11 );
// returns Infinity

x = ldexp( -Infinity, -118 );
// returns -Infinity
```

<section class="usage">

<section class="notes">

## Notes

-   This function is the inverse of [`frexp`][@stdlib/math/base/special/frexp].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var pow = require( '@stdlib/math/base/special/pow' );
var frexp = require( '@stdlib/math/base/special/frexp' );
var ldexp = require( '@stdlib/math/base/special/ldexp' );

var sign;
var frac;
var exp;
var x;
var f;
var v;
var i;

for ( i = 0; i < 100; i++ ) {
    if ( randu() < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    // Generate a random number:
    frac = randu() * 10.0;
    exp = round( randu()*616.0 ) - 308;
    x = sign * frac * pow( 10.0, exp );

    // Break the number into a normalized fraction and an integer power of two:
    f = frexp( x );

    // Reconstitute the original number:
    v = ldexp( f[ 0 ], f[ 1 ] );
    console.log( '%d = %d * 2^%d = %d', x, f[ 0 ], f[ 1 ], 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/ldexp.h"
```

#### stdlib_base_ldexp( frac, exp )

Multiplies a [double-precision floating-point number][ieee754] by an integer power of two (i.e., `x = frac * 2^exp`).

```c
double x = stdlib_base_ldexp( 0.5, 3 ); // => 0.5 * 2^3 = 0.5 * 8
// returns 4.0
```

The function accepts the following arguments:

-   **frac**: `[in] double` input value.
-   **exp**: `[in] int32_t` integer power of two.

```c
double stdlib_base_ldexp( const double frac, const int32_t exp );
```

</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/ldexp.h"
#include "stdlib/math/base/special/frexp.h"
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>
#include <inttypes.h>
#include <math.h>

static double rand_double() {
    int r = rand();
    return (double)r / ( (double)RAND_MAX + 1.0 );
}

int main( void ) {
    double sign;
    double frac;
    int32_t exp;
    double x;
    double v;
    int i;

    for ( i = 0; i < 100; i++ ) {
        if ( rand_double() < 0.5 ) {
            sign = -1.0;
        } else {
            sign = 1.0;
        }
        // Generate a random number:
        frac = rand_double() * 10.0;
        exp = (int32_t)( rand_double()*616.0 ) - 308;
        x = sign * frac * pow( 10.0, exp );

        // Break the number into a normalized fraction and an integer power of two:
        stdlib_base_frexp( x, &frac, &exp );

        // Reconstitute the original number:
        v = stdlib_base_ldexp( frac, exp );

        printf( "%e = %lf * 2^%" PRId32 " = %e\n", x, frac, exp, v );
    }
}
```

</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/frexp`][@stdlib/math/base/special/frexp]</span><span class="delimiter">: </span><span class="description">split a double-precision floating-point number into a normalized fraction and an integer power of two.</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">

[ieee754]: https://en.wikipedia.org/wiki/IEEE_754-1985

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

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

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

</section>

<!-- /.links -->
