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feat: add math/base/tools/evalpolyf 
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‎lib/node_modules/@stdlib/math/base/tools/evalpolyf/README.md

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<!--
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@license Apache-2.0
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Copyright (c) 2024 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# evalpolyf
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> Evaluate a [polynomial][polynomial] using single-precision floating-point arithmetic.
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<section class="intro">
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A [polynomial][polynomial] in a variable `x` can be expressed as
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<!-- <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."> -->
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```math
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c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `c_n, c_{n-1}, ..., c_0` are constants.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var evalpolyf = require( '@stdlib/math/base/tools/evalpolyf' );
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```
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#### evalpolyf( c, x )
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Evaluates a [polynomial][polynomial] having coefficients `c` and degree `n` at a value `x`, where `n = c.length-1`.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var v = evalpolyf( new Float32Array( [ 3.0, 2.0, 1.0 ] ), 10 ); // => 3*10^0 + 2*10^1 + 1*10^2
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// returns 123.0
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```
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The coefficients should be ordered in **ascending** degree, thus matching summation notation.
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#### evalpolyf.factory( c )
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Uses code generation to in-line coefficients and return a function for evaluating a [polynomial][polynomial] using single-precision floating-point arithmetic.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var polyval = evalpolyf.factory( new Float32Array( [ 3.0, 2.0, 1.0 ] ) );
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var v = polyval( 10.0 ); // => 3*10^0 + 2*10^1 + 1*10^2
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// returns 123.0
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v = polyval( 5.0 ); // => 3*5^0 + 2*5^1 + 1*5^2
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// returns 38.0
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- For hot code paths in which coefficients are invariant, a compiled function will be more performant than `evalpolyf()`.
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- 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.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var uniform = require( '@stdlib/random/base/uniform' );
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var evalpolyf = require( '@stdlib/math/base/tools/evalpolyf' );
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// Create an array of random coefficients:
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var coef = discreteUniform( 10, -100, 100, {
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'dtype': 'float32'
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});
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// Evaluate the polynomial at random values:
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var v;
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var i;
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for ( i = 0; i < 100; i++ ) {
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v = uniform( 0.0, 100.0 );
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console.log( 'f(%d) = %d', v, evalpolyf( coef, v ) );
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}
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// Generate an `evalpolyf` function:
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var polyval = evalpolyf.factory( coef );
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for ( i = 0; i < 100; i++ ) {
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v = uniform( -50.0, 50.0 );
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console.log( 'f(%d) = %d', v, polyval( v ) );
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}
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[polynomial]: https://en.wikipedia.org/wiki/Polynomial
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[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/math/base/tools/evalpolyf/benchmark/benchmark.factory.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var factory = require( './../lib/factory.js' );
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// MAIN //
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bench( pkg+'::create:factory', function benchmark( b ) {
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var values;
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var opts;
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var f;
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var i;
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opts = {
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'dtype': 'float32'
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};
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values = [
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uniform( 10, 0.0, 100.0, opts ),
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uniform( 10, 0.0, 100.0, opts ),
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uniform( 10, 0.0, 100.0, opts )
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];
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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f = factory( values[ i%values.length ] );
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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}
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b.toc();
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if ( typeof f !== 'function' ) {
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b.fail( 'should return a function' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+'::evaluate:factory', function benchmark( b ) {
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var values;
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var opts;
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var v;
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var f;
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var i;
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opts = {
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'dtype': 'float32'
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};
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f = factory( uniform( 10, 0.0, 100.0, opts ) );
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values = uniform( 10, 0.0, 100.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = f( values[ i%values.length ] );
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/math/base/tools/evalpolyf/benchmark/benchmark.factory.length.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pkg = require( './../package.json' ).name;
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var factory = require( './../lib/factory.js' );
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var polyval;
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var opts;
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opts = {
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'dtype': 'float32'
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};
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polyval = factory( uniform( len, 0.0, 100.0, opts ) );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var x;
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var v;
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var i;
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x = uniform( 10, 0.0, 100.0, opts );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = polyval( x[ i%x.length ] );
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( pkg+':factory:len='+len, f );
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}
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}
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main();

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