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# evalpoly

> Evaluate a [polynomial][polynomial] using double-precision floating-point arithmetic.

<section class="intro">

A [polynomial][polynomial] in a variable `x` can be expressed as

<!-- <equation class="equation" label="eq:polynomial" align="center" raw="c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i" alt="Polynomial expression."> -->

<div class="equation" align="center" data-raw-text="c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i" data-equation="eq:polynomial">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/tools/evalpoly/docs/img/equation_polynomial.svg" alt="Polynomial expression.">
    <br>
</div>

<!-- </equation> -->

where `c_n, c_{n-1}, ..., c_0` are constants.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var evalpoly = require( '@stdlib/math/base/tools/evalpoly' );
```

#### evalpoly( c, x )

Evaluates a [polynomial][polynomial] having coefficients `c` and degree `n` at a value `x`, where `n = c.length-1`.

```javascript
var v = evalpoly( [ 3.0, 2.0, 1.0 ], 10 ); // => 3*10^0 + 2*10^1 + 1*10^2
// returns 123.0
```

The coefficients should be ordered in **ascending** degree, thus matching summation notation.

#### evalpoly.factory( c )

Uses code generation to in-line coefficients and return a function for evaluating a [polynomial][polynomial] using double-precision floating-point arithmetic.

```javascript
var polyval = evalpoly.factory( [ 3.0, 2.0, 1.0 ] );

var v = polyval( 10.0 ); // => 3*10^0 + 2*10^1 + 1*10^2
// returns 123.0

v = polyval( 5.0 ); // => 3*5^0 + 2*5^1 + 1*5^2
// returns 38.0
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   For hot code paths in which coefficients are invariant, a compiled function will be more performant than `evalpoly()`.
-   While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict [content security policy][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var uniform = require( '@stdlib/random/base/uniform' );
var evalpoly = require( '@stdlib/math/base/tools/evalpoly' );

// Create an array of random coefficients:
var coef = discreteUniform( 10, -100, 100 );

// Evaluate the polynomial at random values:
var v;
var i;
for ( i = 0; i < 100; i++ ) {
    v = uniform( 0.0, 100.0 );
    console.log( 'f(%d) = %d', v, evalpoly( coef, v ) );
}

// Generate an `evalpoly` function:
var polyval = evalpoly.factory( coef );
for ( i = 0; i < 100; i++ ) {
    v = uniform( -50.0, 50.0 );
    console.log( 'f(%d) = %d', v, polyval( v ) );
}
```

</section>

<!-- /.examples -->

<!-- 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/tools/evalrational`][@stdlib/math/base/tools/evalrational]</span><span class="delimiter">: </span><span class="description">evaluate a rational function using double-precision floating-point arithmetic.</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">

[polynomial]: https://en.wikipedia.org/wiki/Polynomial

[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP

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

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

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

</section>

<!-- /.links -->
