diff --git a/base/tools/normhermitepolyf/README.md b/base/tools/normhermitepolyf/README.md
new file mode 100644
index 000000000..ccf1218b9
--- /dev/null
+++ b/base/tools/normhermitepolyf/README.md
@@ -0,0 +1,181 @@
+
+
+# Normalized Hermite Polynomial
+
+> Evaluate a normalized [Hermite polynomial][hermite-polynomial] using single-precision floating-point arithmetic.
+
+
+
+
+
+The normalized (aka "probabilist") [Hermite polynomials][hermite-polynomial] are given by
+
+
+
+```math
+He_{n}(x)=(-1)^{n} e^{\frac{x^2}{2}} \frac{\mathrm d^{n}}{\mathrm d x^{n}} e^{-\frac{x^2}{2}}
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var normhermitepolyf = require( '@stdlib/math/base/tools/normhermitepolyf' );
+```
+
+#### normhermitepolyf( n, x )
+
+Evaluates a normalized [Hermite polynomial][hermite-polynomial] of degree `n` using single-precision floating-point arithmetic.
+
+```javascript
+var v = normhermitepolyf( 1, 1.0 );
+// returns 1.0
+
+v = normhermitepolyf( 1, 0.5 );
+// returns 0.5
+
+v = normhermitepolyf( 0, 0.5 );
+// returns 1.0
+
+v = normhermitepolyf( 2, 0.5 );
+// returns -0.75
+
+v = normhermitepolyf( -1, 0.5 );
+// returns NaN
+```
+
+#### normhermitepolyf.factory( n )
+
+Returns a function for evaluating a normalized [Hermite polynomial][hermite-polynomial] of degree `n` using single-precision floating-point arithmetic.
+
+```javascript
+var polyval = normhermitepolyf.factory( 2 );
+
+var v = polyval( 0.5 );
+// returns -0.75
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var smap = require( '@stdlib/strided/base/smap' );
+var logEach = require( '@stdlib/console/log-each' );
+var normhermitepolyf = require( '@stdlib/math/base/tools/normhermitepolyf' );
+
+// Generate random values at which to evaluate a polynomial:
+var x = uniform( 10, -50.0, 50.0, {
+ 'dtype': 'float32'
+});
+
+// Create a polynomial function of degree 1:
+var f = normhermitepolyf.factory( 1 );
+
+// Allocate an output array:
+var y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 1, x, y );
+
+// Create a polynomial function of degree 2:
+f = normhermitepolyf.factory( 2 );
+
+// Allocate an output array:
+y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 2, x, y );
+
+// Create a polynomial function of degree 3:
+f = normhermitepolyf.factory( 3 );
+
+// Allocate an output array:
+y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 3, x, y );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[hermite-polynomial]: https://en.wikipedia.org/wiki/Hermite_polynomials
+
+
+
+
diff --git a/base/tools/normhermitepolyf/benchmark/benchmark.factory.js b/base/tools/normhermitepolyf/benchmark/benchmark.factory.js
new file mode 100644
index 000000000..c29828680
--- /dev/null
+++ b/base/tools/normhermitepolyf/benchmark/benchmark.factory.js
@@ -0,0 +1,81 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var factory = require( './../lib/factory.js' );
+
+
+// MAIN //
+
+bench( pkg+'::create:factory', function benchmark( b ) {
+ var n;
+ var f;
+ var i;
+
+ n = discreteUniform( 10, 1, 10, {
+ 'dtype': 'float32'
+ });
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ f = factory( n[ i%n.length ] );
+ if ( typeof f !== 'function' ) {
+ b.fail( 'should return a function' );
+ }
+ }
+ b.toc();
+ if ( typeof f !== 'function' ) {
+ b.fail( 'should return a function' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
+
+bench( pkg+'::evaluate:factory', function benchmark( b ) {
+ var x;
+ var v;
+ var f;
+ var i;
+
+ f = factory( 2 );
+ x = uniform( 10, -5.0, 5.0, {
+ 'dtype': 'float32'
+ });
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ v = f( x[ i%x.length ] );
+ if ( isnanf( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnanf( v ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/base/tools/normhermitepolyf/benchmark/benchmark.js b/base/tools/normhermitepolyf/benchmark/benchmark.js
new file mode 100644
index 000000000..14aed4cc6
--- /dev/null
+++ b/base/tools/normhermitepolyf/benchmark/benchmark.js
@@ -0,0 +1,56 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var pkg = require( './../package.json' ).name;
+var normhermitepolyf = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+ var opts;
+ var x;
+ var y;
+ var i;
+
+ opts = {
+ 'dtype': 'float32'
+ };
+ x = uniform( 10, -5.0, 5.0, opts );
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ y = normhermitepolyf( 2, x[ i%x.length ] );
+ if ( isnanf( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ }
+ b.toc();
+ if ( isnanf( y ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+});
diff --git a/base/tools/normhermitepolyf/benchmark/python/scipy/benchmark.py b/base/tools/normhermitepolyf/benchmark/python/scipy/benchmark.py
new file mode 100644
index 000000000..772e3405a
--- /dev/null
+++ b/base/tools/normhermitepolyf/benchmark/python/scipy/benchmark.py
@@ -0,0 +1,116 @@
+#!/usr/bin/env python
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Benchmark scipy.special.eval_hermitenorm."""
+
+from __future__ import print_function
+import timeit
+
+NAME = "normhermitepolyf"
+REPEATS = 3
+ITERATIONS = 1000000
+COUNT = [0] # use a list to allow modification within nested scopes
+
+
+def print_version():
+ """Print the TAP version."""
+ print("TAP version 13")
+
+
+def print_summary(total, passing):
+ """Print the benchmark summary.
+
+ # Arguments
+
+ * `total`: total number of tests
+ * `passing`: number of passing tests
+
+ """
+ print("#")
+ print("1.." + str(total)) # TAP plan
+ print("# total " + str(total))
+ print("# pass " + str(passing))
+ print("#")
+ print("# ok")
+
+
+def print_results(iterations, elapsed):
+ """Print benchmark results.
+
+ # Arguments
+
+ * `iterations`: number of iterations
+ * `elapsed`: elapsed time (in seconds)
+
+ # Examples
+
+ ``` python
+ python> print_results(100000, 0.131009101868)
+ ```
+ """
+ rate = iterations / elapsed
+
+ print(" ---")
+ print(" iterations: " + str(iterations))
+ print(" elapsed: " + str(elapsed))
+ print(" rate: " + str(rate))
+ print(" ...")
+
+
+def benchmark(name, setup, stmt, iterations):
+ """Run the benchmark and print benchmark results.
+
+ # Arguments
+
+ * `name`: benchmark name (suffix)
+ * `setup`: benchmark setup
+ * `stmt`: statement to benchmark
+ * `iterations`: number of iterations
+
+ # Examples
+
+ ``` python
+ python> benchmark("::random", "from random import random;", "y = random()", 1000000)
+ ```
+ """
+ t = timeit.Timer(stmt, setup=setup)
+
+ i = 0
+ while i < REPEATS:
+ print("# python::scipy::" + NAME + name)
+ COUNT[0] += 1
+ elapsed = t.timeit(number=iterations)
+ print_results(iterations, elapsed)
+ print("ok " + str(COUNT[0]) + " benchmark finished")
+ i += 1
+
+
+def main():
+ """Run the benchmarks."""
+ print_version()
+
+ name = ""
+ setup = "from scipy.special import eval_hermitenorm; from random import random;"
+ stmt = "y = eval_hermitenorm(2, random()*10.0 - 5.0)"
+ benchmark(name, setup, stmt, ITERATIONS)
+
+ print_summary(COUNT[0], COUNT[0])
+
+
+if __name__ == "__main__":
+ main()
diff --git a/base/tools/normhermitepolyf/docs/img/equation_normalized_hermite_polynomials.svg b/base/tools/normhermitepolyf/docs/img/equation_normalized_hermite_polynomials.svg
new file mode 100644
index 000000000..d3c5dd49e
--- /dev/null
+++ b/base/tools/normhermitepolyf/docs/img/equation_normalized_hermite_polynomials.svg
@@ -0,0 +1,79 @@
+
\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/docs/repl.txt b/base/tools/normhermitepolyf/docs/repl.txt
new file mode 100644
index 000000000..01841879e
--- /dev/null
+++ b/base/tools/normhermitepolyf/docs/repl.txt
@@ -0,0 +1,53 @@
+
+{{alias}}( n, x )
+ Evaluates a normalized Hermite polynomial using single-precision floating-
+ point arithmetic.
+
+ Parameters
+ ----------
+ n: integer
+ Nonnegative polynomial degree.
+
+ x: number
+ Value at which to evaluate the polynomial.
+
+ Returns
+ -------
+ y: number
+ Function value.
+
+ Examples
+ --------
+ > var y = {{alias}}( 1, 0.5 )
+ 0.5
+ > y = {{alias}}( -1, 0.5 )
+ NaN
+ > y = {{alias}}( 0, 0.5 )
+ 1.0
+ > y = {{alias}}( 2, 0.5 )
+ -0.75
+
+
+{{alias}}.factory( n )
+ Returns a function for evaluating a normalized Hermite polynomial using
+ single-precision floating-point arithmetic.
+
+ Parameters
+ ----------
+ n: integer
+ Nonnegative polynomial degree.
+
+ Returns
+ -------
+ fcn: Function
+ Function for evaluating a normalized Hermite polynomial.
+
+ Examples
+ --------
+ > var f = {{alias}}.factory( 2 );
+ > var v = f( 0.5 )
+ -0.75
+
+ See Also
+ --------
+
diff --git a/base/tools/normhermitepolyf/docs/types/index.d.ts b/base/tools/normhermitepolyf/docs/types/index.d.ts
new file mode 100644
index 000000000..92a0da999
--- /dev/null
+++ b/base/tools/normhermitepolyf/docs/types/index.d.ts
@@ -0,0 +1,97 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// TypeScript Version: 4.1
+
+///
+
+/**
+* Evaluates a normalized Hermite polynomial using single-precision floating-point arithmetic.
+*
+* @param x - value at which to evaluate a normalized Hermite polynomial
+* @returns result
+*/
+type PolynomialFunction = ( x: number ) => number;
+
+/**
+* Interface for evaluating normalized Hermite polynomials.
+*/
+interface NormHermitePoly {
+ /**
+ * Evaluates a normalized Hermite polynomial using single-precision floating-point arithmetic.
+ *
+ * @param n - nonnegative polynomial degree
+ * @param x - evaluation point
+ * @returns function value
+ *
+ * @example
+ * var v = normhermitepolyf( 1, 0.5 );
+ * // returns 0.5
+ *
+ * @example
+ * var v = normhermitepolyf( 0, 0.5 );
+ * // returns 1.0
+ *
+ * @example
+ * var v = normhermitepolyf( 2, 0.5 );
+ * // returns -0.75
+ *
+ * @example
+ * var v = normhermitepolyf( -1, 0.5 );
+ * // returns NaN
+ */
+ ( n: number, x: number ): number;
+
+ /**
+ * Returns a function for evaluating a normalized Hermite polynomial using single-precision floating-point arithmetic.
+ *
+ * @param n - polynomial degree
+ * @returns function for evaluating a normalized Hermite polynomial
+ *
+ * @example
+ * var polyval = normhermitepolyf.factory( 2 );
+ *
+ * var v = polyval( 0.5 );
+ * // returns -0.75
+ */
+ factory( n: number ): PolynomialFunction;
+}
+
+/**
+* Evaluates a normalized Hermite polynomial using single-precision floating-point arithmetic.
+*
+* @param n - nonnegative polynomial degree
+* @param x - evaluation point
+* @returns function value
+*
+* @example
+* var v = normhermitepolyf( 1, 0.5 );
+* // returns 0.5
+*
+* @example
+* var polyval = normhermitepolyf.factory( 2 );
+*
+* var v = polyval( 0.5 );
+* // returns -0.75
+*/
+declare var normhermitepolyf: NormHermitePoly;
+
+
+// EXPORTS //
+
+export = normhermitepolyf;
diff --git a/base/tools/normhermitepolyf/docs/types/test.ts b/base/tools/normhermitepolyf/docs/types/test.ts
new file mode 100644
index 000000000..b50537b2c
--- /dev/null
+++ b/base/tools/normhermitepolyf/docs/types/test.ts
@@ -0,0 +1,91 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+import normhermitepolyf = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+ normhermitepolyf( 6, 1.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a number...
+{
+ normhermitepolyf( true, 1.0 ); // $ExpectError
+ normhermitepolyf( false, 1.0 ); // $ExpectError
+ normhermitepolyf( 'abc', 1.0 ); // $ExpectError
+ normhermitepolyf( [], 1.0 ); // $ExpectError
+ normhermitepolyf( {}, 1.0 ); // $ExpectError
+ normhermitepolyf( ( x: number ): number => x, 1.0 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a number...
+{
+ normhermitepolyf( 6, true ); // $ExpectError
+ normhermitepolyf( 6, false ); // $ExpectError
+ normhermitepolyf( 6, 'abc' ); // $ExpectError
+ normhermitepolyf( 6, [] ); // $ExpectError
+ normhermitepolyf( 6, {} ); // $ExpectError
+ normhermitepolyf( 6, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an insufficient number of arguments...
+{
+ normhermitepolyf(); // $ExpectError
+ normhermitepolyf( 4 ); // $ExpectError
+}
+
+// Attached to main export is a `factory` method which returns a function...
+{
+ normhermitepolyf.factory( 3 ); // $ExpectType PolynomialFunction
+}
+
+// The compiler throws an error if the `factory` method is provided a first argument which is not a number...
+{
+ normhermitepolyf.factory( true ); // $ExpectError
+ normhermitepolyf.factory( false ); // $ExpectError
+ normhermitepolyf.factory( 'abc' ); // $ExpectError
+ normhermitepolyf.factory( [] ); // $ExpectError
+ normhermitepolyf.factory( {} ); // $ExpectError
+ normhermitepolyf.factory( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the `factory` method is provided an unsupported number of arguments...
+{
+ normhermitepolyf.factory(); // $ExpectError
+ normhermitepolyf.factory( 4, 21 ); // $ExpectError
+}
+
+// The `factory` method returns a function which returns a number...
+{
+ const polyval = normhermitepolyf.factory( 3 );
+ polyval( 1.0 ); // $ExpectType number
+}
+
+// The compiler throws an error if the function returned by the `factory` method is provided a first argument which is not a number...
+{
+ const polyval = normhermitepolyf.factory( 3 );
+ polyval( true ); // $ExpectError
+ polyval( false ); // $ExpectError
+ polyval( 'abc' ); // $ExpectError
+ polyval( [] ); // $ExpectError
+ polyval( {} ); // $ExpectError
+ polyval( ( x: number ): number => x ); // $ExpectError
+}
diff --git a/base/tools/normhermitepolyf/examples/index.js b/base/tools/normhermitepolyf/examples/index.js
new file mode 100644
index 000000000..a1a279a0b
--- /dev/null
+++ b/base/tools/normhermitepolyf/examples/index.js
@@ -0,0 +1,60 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var smap = require( '@stdlib/strided/base/smap' );
+var logEach = require( '@stdlib/console/log-each' );
+var normhermitepolyf = require( './../lib' );
+
+// Generate random values at which to evaluate a polynomial:
+var x = uniform( 10, -50.0, 50.0, {
+ 'dtype': 'float32'
+});
+
+// Create a polynomial function of degree 1:
+var f = normhermitepolyf.factory( 1 );
+
+// Allocate an output array:
+var y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 1, x, y );
+
+// Create a polynomial function of degree 2:
+f = normhermitepolyf.factory( 2 );
+
+// Allocate an output array:
+y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 2, x, y );
+
+// Create a polynomial function of degree 3:
+f = normhermitepolyf.factory( 3 );
+
+// Allocate an output array:
+y = zeros( x.length, 'float32' );
+
+// Evaluate the polynomial:
+smap( x.length, x, 1, y, 1, f );
+logEach( 'He_%d(%.3f) = %.3f', 3, x, y );
diff --git a/base/tools/normhermitepolyf/lib/factory.js b/base/tools/normhermitepolyf/lib/factory.js
new file mode 100644
index 000000000..0a0c7cda1
--- /dev/null
+++ b/base/tools/normhermitepolyf/lib/factory.js
@@ -0,0 +1,83 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
+var constantFunction = require( '@stdlib/utils/constant-function' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var isint = require( './../../../../base/assert/is-integer' );
+
+
+// MAIN //
+
+/**
+* Returns a function for evaluating a normalized Hermite polynomial using single-precision floating-point arithmetic.
+*
+* @param {NonNegativeInteger} n - polynomial degree
+* @returns {Function} function for evaluating a normalized Hermite polynomial
+*
+* @example
+* var polyval = factory( 2 );
+*
+* var v = polyval( 0.5 );
+* // returns -0.75
+*/
+function factory( n ) {
+ if ( n < 0 || isnanf( n ) || !isint( n ) ) {
+ return constantFunction( NaN );
+ }
+ if ( n === 0 ) {
+ return constantFunction( 1.0 );
+ }
+ return polyval;
+
+ /**
+ * Evaluates a normalized Hermite polynomial using single-precision floating-point arithmetic.
+ *
+ * @private
+ * @param {number} x - value at which to evaluate a normalized Hermite polynomial
+ * @returns {number} result
+ */
+ function polyval( x ) {
+ var y1;
+ var y2;
+ var y3;
+ var i;
+
+ if ( isnanf( x ) ) {
+ return NaN;
+ }
+ x = float64ToFloat32( x );
+ y2 = 1.0;
+ y3 = 0.0;
+ for ( i = n; i > 1; i-- ) {
+ y1 = float64ToFloat32( float64ToFloat32( x*y2 ) - float64ToFloat32( i*y3 ) ); // eslint-disable-line max-len
+ y3 = y2;
+ y2 = y1;
+ }
+ return float64ToFloat32( float64ToFloat32( x*y2 ) - y3);
+ }
+}
+
+
+// EXPORTS //
+
+module.exports = factory;
diff --git a/base/tools/normhermitepolyf/lib/index.js b/base/tools/normhermitepolyf/lib/index.js
new file mode 100644
index 000000000..47b63ed7d
--- /dev/null
+++ b/base/tools/normhermitepolyf/lib/index.js
@@ -0,0 +1,64 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+/**
+* Evaluate a normalized Hermite polynomial using single-precision floating-point arithmetic.
+*
+* @module @stdlib/math/base/tools/normhermitepolyf
+*
+* @example
+* var normhermitepolyf = require( '@stdlib/math/base/tools/normhermitepolyf' );
+*
+* var v = normhermitepolyf( 1, 0.5 );
+* // returns 0.5
+*
+* v = normhermitepolyf( 0, 0.5 );
+* // returns 1.0
+*
+* v = normhermitepolyf( 2, 0.5 );
+* // returns -0.75
+*
+* v = normhermitepolyf( -1, 0.5 );
+* // returns NaN
+*
+* @example
+* var factory = require( '@stdlib/math/base/tools/normhermitepolyf' ).factory;
+*
+* var polyval = factory( 2 );
+*
+* var v = polyval( 0.5 );
+* // returns -0.75
+*/
+
+// MODULES //
+
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var main = require( './main.js' );
+var factory = require( './factory.js' );
+
+
+// MAIN //
+
+setReadOnly( main, 'factory', factory );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/base/tools/normhermitepolyf/lib/main.js b/base/tools/normhermitepolyf/lib/main.js
new file mode 100644
index 000000000..e4931d1c2
--- /dev/null
+++ b/base/tools/normhermitepolyf/lib/main.js
@@ -0,0 +1,83 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var isint = require( './../../../../base/assert/is-integer' );
+
+
+// MAIN //
+
+/**
+* Evaluates a normalized Hermite polynomial using single-precision floating-point arithmetic.
+*
+* @param {NonNegativeInteger} n - nonnegative polynomial degree
+* @param {number} x - evaluation point
+* @returns {number} function value
+*
+* @example
+* var v = normhermitepolyf( 1, 0.5 );
+* // returns 0.5
+*
+* @example
+* var v = normhermitepolyf( 0, 0.5 );
+* // returns 1.0
+*
+* @example
+* var v = normhermitepolyf( 2, 0.5 );
+* // returns -0.75
+*
+* @example
+* var v = normhermitepolyf( -1, 0.5 );
+* // returns NaN
+*/
+function normhermitepolyf( n, x ) {
+ var y1;
+ var y2;
+ var y3;
+ var i;
+
+ if ( isnanf( n ) || isnanf( x ) || n < 0 || !isint( n ) ) {
+ return NaN;
+ }
+ if ( n === 0 ) {
+ // `x` is completely canceled from the expression:
+ return 1.0;
+ }
+ x = float64ToFloat32( x );
+ if ( n === 1 ) {
+ return x;
+ }
+ y2 = 1.0;
+ y3 = 0.0;
+ for ( i = n; i > 1; i-- ) {
+ y1 = float64ToFloat32( float64ToFloat32( x*y2 ) - float64ToFloat32( i*y3 ) ); // eslint-disable-line max-len
+ y3 = y2;
+ y2 = y1;
+ }
+ return float64ToFloat32( float64ToFloat32( x*y2 ) - y3 );
+}
+
+
+// EXPORTS //
+
+module.exports = normhermitepolyf;
diff --git a/base/tools/normhermitepolyf/package.json b/base/tools/normhermitepolyf/package.json
new file mode 100644
index 000000000..31bb53a56
--- /dev/null
+++ b/base/tools/normhermitepolyf/package.json
@@ -0,0 +1,67 @@
+{
+ "name": "@stdlib/math/base/tools/normhermitepolyf",
+ "version": "0.0.0",
+ "description": "Evaluate a normalized Hermite polynomial using single-precision floating-point arithmetic.",
+ "license": "Apache-2.0",
+ "author": {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ },
+ "contributors": [
+ {
+ "name": "The Stdlib Authors",
+ "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+ }
+ ],
+ "main": "./lib",
+ "directories": {
+ "benchmark": "./benchmark",
+ "doc": "./docs",
+ "example": "./examples",
+ "lib": "./lib",
+ "test": "./test"
+ },
+ "types": "./docs/types",
+ "scripts": {},
+ "homepage": "https://github.com/stdlib-js/stdlib",
+ "repository": {
+ "type": "git",
+ "url": "git://github.com/stdlib-js/stdlib.git"
+ },
+ "bugs": {
+ "url": "https://github.com/stdlib-js/stdlib/issues"
+ },
+ "dependencies": {},
+ "devDependencies": {},
+ "engines": {
+ "node": ">=0.10.0",
+ "npm": ">2.7.0"
+ },
+ "os": [
+ "aix",
+ "darwin",
+ "freebsd",
+ "linux",
+ "macos",
+ "openbsd",
+ "sunos",
+ "win32",
+ "windows"
+ ],
+ "keywords": [
+ "stdlib",
+ "stdmath",
+ "mathematics",
+ "math",
+ "hermite",
+ "eval",
+ "evaluate",
+ "poly",
+ "polyval",
+ "evalpoly",
+ "polynomial",
+ "normalized",
+ "probabilist",
+ "special"
+ ]
+}
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_1.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_1.json
new file mode 100644
index 000000000..5c7c25c8f
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_1.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_2.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_2.json
new file mode 100644
index 000000000..78c1fe442
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_2.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_5.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_5.json
new file mode 100644
index 000000000..2510ec862
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_negative_5.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_1.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_1.json
new file mode 100644
index 000000000..1cb85c047
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_1.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_2.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_2.json
new file mode 100644
index 000000000..9f297071e
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_2.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_5.json b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_5.json
new file mode 100644
index 000000000..f0c443a85
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/medium_positive_5.json
@@ -0,0 +1 @@
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32299636844628.957, 32527929308226.035, 32757520698133.363, 32988396714913.6, 33220582687447.14, 33454064123812.074, 33688866607790.03, 33924975453174.375, 34162416500626.008, 34401174867842.83, 34641276654353.625, 34882717193795.957, 35125491604996.336, 35369626379540.2, 35615106136892.81, 35861946985446.14, 36110175989380.914, 36359756110861.14, 36610714327519.836, 36863078106896.875, 37116809746809.82, 37371936626911.39, 37628464493481.14, 37886421359068.28, 38145768622224.336, 38406534205806.53, 38668723919247.805, 38932366328416.06, 39197421917035.3, 39463919159454.83, 39731887042040.125, 40001285352072.4, 40272142983014.234, 40544465855647.81, 40818283524408.82, 41093554834098.21, 41370309244383.95, 41648552740150.7, 41928315452454.82, 42209555267573.734, 42492302219909.055, 42776586878650.164, 43062366400541.84, 43349671256688.96, 43638507544986.46, 43928906426420.86, 44220824070711.41, 44514291538834.234, 44809340441393.72, 45105926196995.14, 45404080314773.44, 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63619712852476.98, 64012222901613.86, 64406667872049.586, 64803054908767.484, 65201425526809.54, 65601718369950.84, 66003974820436.2, 66408236953868.74, 66814442453331.81, 67222633259900.8, 67632816641988.33, 68045035431638.72, 68459226013886.125, 68875431083918.43, 69293694047942.13, 69713950304488.695, 70136243121145.63, 70560579890811.88, 70987004794419.25, 71415451897736.52, 71845965240705.06, 72278552287833.22, 72713258005361.44, 73150015106189.39, 73588868413170.98, 74029863488537.12, 74472932017214.69, 74918119416234.62, 75365433276252.55, 75814919963566.84, 76266509774573.03, 76720248927930.03, 77176145086851.94, 77634245432560.9, 78094478852269.02, 78556892377094.4, 79021533806641.14, 79488330957552.69, 79957331477464.25, 80428543157398.23, 80902014631122.27, 81377672269472.75, 81855564551740.02, 82335740744619.25, 82818126120679.03, 83302769790239.27, 83789679673187.69, 84278905889932.27, 84770372229992.61, 85264128654848.5, 85760183158499.34, 86258586726376.61, 86759261643390.34, 87262258733465.53, 87767629638290.16, 88275295500036.77, 88785307796936.36, 89297674653514.55, 89812448596523.38, 90329549225301.97, 90849028900521.88, 91370895821769.62, 91895203412454.4, 92421869706956.67, 92950947959956.08, 93482492275029.98, 94016419498187.05, 94552783562271.22, 95091592799056.39, 95632902229315.05, 96176627094878.8, 96722822243092.23, 97271543390419.25, 97822704560666.44, 98376361294831.69, 98932522057933.19, 99491243504487.88, 100052438014267.52, 100616162063582.53, 101182424194065.11, 101751282010348.36, 102322646225104.6, 102896574261993.66, 103473124446221.28, 104052206224862.53, 104633877740057.39, 105218147668343.27, 105805075306407.78, 106394568393353.67, 106986686039989.62, 107581437000416.1, 108178881555157.94, 108778925711697.12, 109381629561839.52, 109987054132165.73, 110595104115784.72, 111205840348410.64, 111819271720710.39, 112435460264981.5, 113054308900811.69, 113675879466745.16, 114300234757668.86, 114927276347124.72, 115557066834063.42, 116189615246775.19, 116824985408074.06, 117463077075419.9, 118103953872756.16, 118747624907489.38, 119394155043201.44, 120043442196651.12, 120695551029588.33, 121350547194669.2, 122008327211828.95, 122668956529652.64, 123332444394831.06, 123998857523522.77, 124668090551352.89, 125340209987399.4, 126015225158418.56, 126693203857213.73, 127374038809878.17, 128057797599097.64, 128744548833856.12, 129434183791403.08, 130126770868309.0, 130822319532275.38, 131520899492196.19, 132222400071119.19, 132926890762439.4, 133634442108807.9, 134344941950670.9, 135058460612848.19, 135775007705043.77, 136494654893424.9, 137217288018884.62, 137942978526624.56, 138671736107967.23, 139403633566239.53, 140138554716558.1, 140876572138121.7, 141617759496154.34, 142361999069084.94, 143109364295618.97, 143859865010742.38, 144613576040985.8, 145370377592569.03, 146130344262292.4, 146893485967709.4, 147659878710611.75, 148429400598165.38, 149202127399191.3, 149978136006159.47, 150757302934180.1, 151539704840303.4, 152325351787407.4, 153114321867917.34, 153906489450362.75, 154701932388459.16, 155500729683962.5, 156302754077438.38, 157108084329446.34, 157916730649245.6, 158728773263593.72, 159544082718245.8, 160362738995422.4, 161184752388503.44, 162010204363718.66, 162838963244135.94, 163671110248078.2, 164506727780952.25, 165345682480364.5, 166188056501268.56, 167033860285087.06, 167883177502302.5, 168735872518489.78, 169592028750257.78, 170451656724099.06, 171314841390363.0, 172181444814075.47, 173051551688262.38, 173925247932957.88, 174802393868907.47, 175683075156215.03, 176567302471076.38, 177455163039559.75, 178346514831390.5, 179241444809205.47, 180140041188518.5]}
\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/random2.json b/base/tools/normhermitepolyf/test/fixtures/python/random2.json
new file mode 100644
index 000000000..5057b868a
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/random2.json
@@ -0,0 +1 @@
+{"n": [4, 17, 7, 18, 19, 3, 7, 15, 10, 18, 6, 1, 4, 7, 1, 18, 13, 12, 11, 7, 12, 7, 8, 14, 14, 5, 13, 5, 8, 9, 13, 14, 2, 16, 8, 1, 4, 13, 12, 8, 17, 14, 9, 3, 8, 15, 14, 6, 5, 18, 6, 3, 14, 11, 1, 18, 5, 3, 4, 15, 11, 10, 3, 11, 7, 10, 16, 19, 4, 8, 11, 1, 18, 6, 15, 17, 1, 7, 1, 2, 1, 2, 3, 17, 13, 4, 17, 1, 4, 14, 11, 15, 14, 14, 9, 9, 10, 19, 1, 18], "x": [45.895835876464844, 22.09214210510254, 7.745064735412598, 22.47156524658203, 45.152687072753906, 47.310970306396484, 34.60221862792969, 35.9521598815918, 9.38438606262207, 17.3791446685791, 12.630452156066895, 47.619911193847656, 5.791712284088135, 38.13872528076172, 40.03205871582031, 33.48503875732422, 28.251218795776367, 35.52806091308594, 10.560770034790039, 17.956308364868164, 41.48725128173828, 25.07436752319336, 48.00590896606445, 39.321048736572266, 32.668182373046875, 31.060686111450195, 49.7415657043457, 36.6003532409668, 3.720856189727783, 42.97201919555664, 31.957660675048828, 36.505714416503906, 41.4112548828125, 40.075809478759766, 40.2384033203125, 42.36631774902344, 20.32078742980957, 0.09362303465604782, 45.95627212524414, 23.38872528076172, 19.11545181274414, 10.277792930603027, 3.793100357055664, 23.107934951782227, 35.03868865966797, 38.848331451416016, 39.57504653930664, 44.46074676513672, 36.02516555786133, 37.25418472290039, 28.700199127197266, 16.686716079711914, 49.9504508972168, 19.502548217773438, 42.54890441894531, 33.929378509521484, 27.86937713623047, 9.865081787109375, 21.359281539916992, 38.322303771972656, 48.215248107910156, 21.511051177978516, 18.990497589111328, 0.8217055201530457, 28.51963233947754, 13.280563354492188, 42.597110748291016, 42.72492218017578, 14.236122131347656, 32.40830993652344, 17.084213256835938, 33.92168426513672, 33.995269775390625, 29.91448211669922, 10.172126770019531, 49.93890380859375, 46.18699645996094, 21.37078094482422, 4.1539788246154785, 4.084967136383057, 35.50692367553711, 30.286880493164062, 5.186511516571045, 31.272645950317383, 47.702816009521484, 28.588171005249023, 7.15334939956665, 28.0970458984375, 41.76885986328125, 15.987401962280273, 16.25307846069336, 35.524993896484375, 29.13581085205078, 40.622283935546875, 14.979894638061523, 21.361791610717773, 1.2187235355377197, 43.416927337646484, 17.561908721923828, 21.171302795410156], "expected": [4424402.302833011, 5.332987418865195e+22, 1134480.6146514374, 1.5605210079616623e+24, 2.5249056128618598e+31, 105755.53243812206, 58354610157.19601, 1.9962749679263704e+23, 2996818419.367526, 1.2226226128900613e+22, 3685306.2829471244, 47.619911193847656, 926.9317320298231, 115682938486.59465, 40.03205871582031, 2.4387046295314494e+27, 6.613242523666777e+18, 3.836703697639622e+18, 105986037325.0757, 563297483.9306823, 2.501612831090321e+19, 6025254510.7880945, 27865448916687.625, 1.990586428202784e+22, 1.4463572385609212e+21, 28611277.68818566, 1.1055989017570078e+22, 65189233.59150782, -3021.697550157684, 489971159118343.7, 3.3568010356012642e+19, 6.968094976355347e+21, 1713.8920309692621, 4.1055425180110164e+25, 6754375659566.351, 42.36631774902344, 168040.21375248354, 12430.927146004655, 8.599984189689589e+19, 85026395371.0608, 4.1164419471615077e+21, 54578570448961.51, -12532.20757138024, 12269.77406787357, 2220368466517.3745, 6.457967475094343e+23, 2.1800288249277936e+22, 7665799978.509284, 60210815.306172565, 1.7088101566904427e+28, 548728069.5030031, 4596.297432602482, 5.8027262034117325e+23, 133835042697389.94, 42.54890441894531, 3.103126260927665e+27, 16596611.436284516, 930.4729225905741, 205401.37847937288, 5.253318729222982e+23, 3.1967692262696556e+18, 19212411332946.49, 6791.74254224353, -1284.3764556563763, 14952643747.606644, 130486807183.00232, 1.0993307387371492e+26, 8.747110849994978e+30, 39860.98010904512, 1184679347938.9746, 29777936516701.855, 33.92168426513672, 3.215112533249976e+27, 704648214.4552526, 394761729712825.2, 7.07344402141347e+28, 46.18699645996094, 1943248604.638679, 4.1539788246154785, 15.68695650532959, 35.50692367553711, 916.2951300072018, 123.95711547173568, 2.2720715751591654e+25, 6.398967917395753e+21, 663051.6532648862, 2331941448322.1724, 28.0970458984375, 3033295.718800463, 4.898296331742611e+16, 16842887793404.826, 1.665266293481378e+23, 2.849191560559194e+20, 3.151864374654459e+22, 32169533456.41238, 854867743596.8541, 976.3551997055056, 1.1905682729201329e+31, 17.561908721923828, 5.12154354721826e+23]}
\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/runner.py b/base/tools/normhermitepolyf/test/fixtures/python/runner.py
new file mode 100644
index 000000000..1ad83f1f3
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/runner.py
@@ -0,0 +1,111 @@
+#!/usr/bin/env python
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2024 The Stdlib Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+"""Generate fixtures."""
+
+import os
+import json
+import numpy as np
+from scipy.special import eval_hermitenorm
+
+# Get the file path:
+FILE = os.path.realpath(__file__)
+
+# Extract the directory in which this file resides:
+DIR = os.path.dirname(FILE)
+
+
+def gen(n, x, name):
+ """Generate fixture data and write to file.
+
+ # Arguments
+
+ * `n`: degree(s)
+ * `x`: domain
+ * `name::str`: output filename
+
+ # Examples
+
+ ``` python
+ python> n = 1
+ python> x = linspace(-1000, 1000, 2001)
+ python> gen(n, x, './data.json')
+ ```
+ """
+ y = eval_hermitenorm(n, x)
+ if isinstance(n, np.ndarray):
+ data = {
+ "n": n.tolist(),
+ "x": x.tolist(),
+ "expected": y.tolist()
+ }
+ else:
+ data = {
+ "n": n,
+ "x": x.tolist(),
+ "expected": y.tolist()
+ }
+
+ # Based on the script directory, create an output filepath:
+ filepath = os.path.join(DIR, name)
+
+ # Write the data to the output filepath as JSON:
+ with open(filepath, "w", encoding="utf-8") as outfile:
+ json.dump(data, outfile)
+
+
+def main():
+ """Generate fixture data."""
+ # Random values across `n` and `x`:
+ n = np.random.randint(1, 20, 100)
+ x = np.float32(np.random.random(100)*50.0)
+ gen(n, x, "random2.json")
+
+ # Medium negative:
+ x = np.linspace(-709.78, -1.0, 1000, dtype=np.float32)
+ gen(1, x, "medium_negative_1.json")
+ gen(2, x, "medium_negative_2.json")
+ gen(5, x, "medium_negative_5.json")
+
+ # Medium positive:
+ x = np.linspace(1.0, 709.78, 1000, dtype=np.float32)
+ gen(1, x, "medium_positive_1.json")
+ gen(2, x, "medium_positive_2.json")
+ gen(5, x, "medium_positive_5.json")
+
+ # Small positive:
+ x = np.linspace(2.0**-30, 0.1, 1000, dtype=np.float32)
+ gen(1, x, "small_positive_1.json")
+ gen(2, x, "small_positive_2.json")
+ gen(5, x, "small_positive_5.json")
+
+ # Small negative:
+ x = np.linspace(-0.1, -2.0**-30, 1000, dtype=np.float32)
+ gen(1, x, "small_negative_1.json")
+ gen(2, x, "small_negative_2.json")
+ gen(5, x, "small_negative_5.json")
+
+ # Tiny values:
+ x = np.linspace(-2.0**-30, 2.0**-30, 1000, dtype=np.float32)
+ gen(1, x, "tiny_1.json")
+ gen(2, x, "tiny_2.json")
+ gen(5, x, "tiny_5.json")
+
+
+if __name__ == "__main__":
+ main()
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_negative_1.json b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_1.json
new file mode 100644
index 000000000..78e894a73
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_1.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_negative_2.json b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_2.json
new file mode 100644
index 000000000..6fc347dc9
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_2.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_negative_5.json b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_5.json
new file mode 100644
index 000000000..5b70535cc
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_negative_5.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_positive_1.json b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_1.json
new file mode 100644
index 000000000..5d14c6f92
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_1.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_positive_2.json b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_2.json
new file mode 100644
index 000000000..edde658f1
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_2.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/small_positive_5.json b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_5.json
new file mode 100644
index 000000000..021fe2823
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/small_positive_5.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/tiny_1.json b/base/tools/normhermitepolyf/test/fixtures/python/tiny_1.json
new file mode 100644
index 000000000..68deb488b
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/tiny_1.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/fixtures/python/tiny_2.json b/base/tools/normhermitepolyf/test/fixtures/python/tiny_2.json
new file mode 100644
index 000000000..4b5cde74a
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/tiny_2.json
@@ -0,0 +1 @@
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diff --git a/base/tools/normhermitepolyf/test/fixtures/python/tiny_5.json b/base/tools/normhermitepolyf/test/fixtures/python/tiny_5.json
new file mode 100644
index 000000000..4bbabd970
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/fixtures/python/tiny_5.json
@@ -0,0 +1 @@
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7.984762850909988e-09, 8.01273047912332e-09, 8.040698107336652e-09, 8.068665735549985e-09, 8.096633363763317e-09, 8.12460099197665e-09, 8.152568620189982e-09, 8.180536248403314e-09, 8.208503876616646e-09, 8.236471504829979e-09, 8.264439133043311e-09, 8.292406761256643e-09, 8.320374389469976e-09, 8.348342017683308e-09, 8.37630964589664e-09, 8.404277274109972e-09, 8.432244902323305e-09, 8.460212530536637e-09, 8.48818015874997e-09, 8.516147786963302e-09, 8.544115415176634e-09, 8.572083043389966e-09, 8.600050671603299e-09, 8.628018299816631e-09, 8.655985928029963e-09, 8.683953556243296e-09, 8.711921184456628e-09, 8.73988881266996e-09, 8.767856440883293e-09, 8.795824069096625e-09, 8.823791697309957e-09, 8.85175932552329e-09, 8.879726953736622e-09, 8.907694581949954e-09, 8.935662210163287e-09, 8.963629838376619e-09, 8.991597466589951e-09, 9.019565094803284e-09, 9.047532723016616e-09, 9.075500351229948e-09, 9.103468812110549e-09, 9.131436440323881e-09, 9.159404068537214e-09, 9.187371696750546e-09, 9.215339324963878e-09, 9.24330695317721e-09, 9.271274581390543e-09, 9.299242209603875e-09, 9.327209837817207e-09, 9.35517746603054e-09, 9.383145094243872e-09, 9.411112722457204e-09, 9.439080350670537e-09, 9.467047978883869e-09, 9.495015607097201e-09, 9.522983235310534e-09, 9.550950863523866e-09, 9.578918491737198e-09, 9.60688611995053e-09, 9.634853748163863e-09, 9.662821376377195e-09, 9.690789004590528e-09, 9.71875663280386e-09, 9.746724261017192e-09, 9.774691889230525e-09, 9.802659517443857e-09, 9.83062714565719e-09, 9.858594773870522e-09, 9.886562402083854e-09, 9.914530030297186e-09, 9.942497658510518e-09, 9.97046528672385e-09, 9.998432914937183e-09, 1.0026400543150515e-08, 1.0054368171363848e-08, 1.008233579957718e-08, 1.0110303427790512e-08, 1.0138271056003845e-08, 1.0166238684217177e-08, 1.019420631243051e-08, 1.0222173940643842e-08, 1.0250141568857174e-08, 1.0278109197070506e-08, 1.0306076825283839e-08, 1.0334044453497171e-08, 1.0362012081710503e-08, 1.0389979709923836e-08, 1.0417947338137168e-08, 1.04459149663505e-08, 1.0473882594563833e-08, 1.0501851055444433e-08, 1.0529818683657766e-08, 1.0557786311871098e-08, 1.058575394008443e-08, 1.0613721568297763e-08, 1.0641689196511095e-08, 1.0669656824724427e-08, 1.069762445293776e-08, 1.0725592081151092e-08, 1.0753559709364424e-08, 1.0781527337577756e-08, 1.0809494965791089e-08, 1.0837462594004421e-08, 1.0865430222217753e-08, 1.0893397850431086e-08, 1.0921365478644418e-08, 1.094933310685775e-08, 1.0977300735071083e-08, 1.1005268363284415e-08, 1.1033235991497747e-08, 1.106120361971108e-08, 1.1089171247924412e-08, 1.1117138876137744e-08, 1.1145106504351077e-08, 1.1173074132564409e-08, 1.1201041760777741e-08, 1.1229009388991074e-08, 1.1256977017204406e-08, 1.1284944645417738e-08, 1.131291227363107e-08, 1.1340879901844403e-08, 1.1368847530057735e-08, 1.1396815158271068e-08, 1.14247827864844e-08, 1.1452750414697732e-08, 1.1480718042911064e-08, 1.1508685671124397e-08, 1.1536653299337729e-08, 1.1564620927551061e-08, 1.1592588555764394e-08, 1.1620556183977726e-08, 1.1648523812191058e-08, 1.167649144040439e-08, 1.1704459068617723e-08, 1.1732426696831055e-08, 1.1760394325044388e-08, 1.178836195325772e-08, 1.1816329581471052e-08, 1.1844297209684385e-08, 1.1872264837897717e-08, 1.1900233298778318e-08, 1.192820092699165e-08, 1.1956168555204982e-08, 1.1984136183418315e-08, 1.2012103811631647e-08, 1.204007143984498e-08, 1.2068039068058312e-08, 1.2096006696271644e-08, 1.2123974324484976e-08, 1.2151941952698309e-08, 1.2179909580911641e-08, 1.2207877209124973e-08, 1.2235844837338306e-08, 1.2263812465551638e-08, 1.229178009376497e-08, 1.2319747721978302e-08, 1.2347715350191635e-08, 1.2375682978404967e-08, 1.24036506066183e-08, 1.2431618234831632e-08, 1.2459585863044964e-08, 1.2487553491258296e-08, 1.2515521119471629e-08, 1.2543488747684961e-08, 1.2571456375898293e-08, 1.2599424004111626e-08, 1.2627391632324958e-08, 1.265535926053829e-08, 1.2683326888751623e-08, 1.2711294516964955e-08, 1.2739262145178287e-08, 1.276722977339162e-08, 1.2795197401604952e-08, 1.2823165029818284e-08, 1.2851132658031617e-08, 1.2879100286244949e-08, 1.2907067914458281e-08, 1.2935035542671613e-08, 1.2963003170884946e-08, 1.2990970799098278e-08, 1.301893842731161e-08, 1.3046906055524943e-08, 1.3074873683738275e-08, 1.3102841311951607e-08, 1.313080894016494e-08, 1.3158776568378272e-08, 1.3186744196591604e-08, 1.3214711824804937e-08, 1.3242679453018269e-08, 1.3270647081231601e-08, 1.3298615542112202e-08, 1.3326583170325534e-08, 1.3354550798538867e-08, 1.3382518426752199e-08, 1.3410486054965531e-08, 1.3438453683178864e-08, 1.3466421311392196e-08, 1.3494388939605528e-08, 1.352235656781886e-08, 1.3550324196032193e-08, 1.3578291824245525e-08, 1.3606259452458858e-08, 1.363422708067219e-08, 1.3662194708885522e-08, 1.3690162337098855e-08, 1.3718129965312187e-08, 1.374609759352552e-08, 1.3774065221738852e-08, 1.3802032849952184e-08, 1.3830000478165516e-08, 1.3857968106378848e-08, 1.388593573459218e-08, 1.3913903362805513e-08, 1.3941870991018845e-08, 1.3969838619232178e-08]}
\ No newline at end of file
diff --git a/base/tools/normhermitepolyf/test/test.factory.js b/base/tools/normhermitepolyf/test/test.factory.js
new file mode 100644
index 000000000..5860b62f1
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/test.factory.js
@@ -0,0 +1,564 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var abs = require( './../../../../base/special/abs' );
+var EPS = require( '@stdlib/constants/float32/eps' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
+var factory = require( './../lib' ).factory;
+
+
+// FIXTURES //
+
+var random2 = require( './fixtures/python/random2.json' );
+
+var mediumNegative1 = require( './fixtures/python/medium_negative_1.json' );
+var mediumNegative2 = require( './fixtures/python/medium_negative_2.json' );
+var mediumNegative5 = require( './fixtures/python/medium_negative_5.json' );
+
+var mediumPositive1 = require( './fixtures/python/medium_positive_1.json' );
+var mediumPositive2 = require( './fixtures/python/medium_positive_2.json' );
+var mediumPositive5 = require( './fixtures/python/medium_positive_5.json' );
+
+var smallPositive1 = require( './fixtures/python/small_positive_1.json' );
+var smallPositive2 = require( './fixtures/python/small_positive_2.json' );
+var smallPositive5 = require( './fixtures/python/small_positive_5.json' );
+
+var smallNegative1 = require( './fixtures/python/small_negative_1.json' );
+var smallNegative2 = require( './fixtures/python/small_negative_2.json' );
+var smallNegative5 = require( './fixtures/python/small_negative_5.json' );
+
+var tiny1 = require( './fixtures/python/tiny_1.json' );
+var tiny2 = require( './fixtures/python/tiny_2.json' );
+var tiny5 = require( './fixtures/python/tiny_5.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof factory, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function returns a function', function test( t ) {
+ t.strictEqual( typeof factory( 2 ), 'function', 'returns a function' );
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `Hen(x)` for random `n` and `x`', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = random2.n;
+ x = random2.x;
+ expected = random2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ f = factory( n[ i ] );
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He1(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive1.n;
+ x = smallPositive1.x;
+ expected = smallPositive1.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive2.n;
+ x = smallPositive2.x;
+ expected = smallPositive2.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He5(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive5.n;
+ x = smallPositive5.x;
+ expected = smallPositive5.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He1(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative1.n;
+ x = smallNegative1.x;
+ expected = smallNegative1.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He2(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative2.n;
+ x = smallNegative2.x;
+ expected = smallNegative2.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He5(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative5.n;
+ x = smallNegative5.x;
+ expected = smallNegative5.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He1(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny1.n;
+ x = tiny1.x;
+ expected = tiny1.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He2(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny2.n;
+ x = tiny2.x;
+ expected = tiny2.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He5(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny5.n;
+ x = tiny5.x;
+ expected = tiny5.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He1(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive1.n;
+ x = mediumPositive1.x;
+ expected = mediumPositive1.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He2(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive2.n;
+ x = mediumPositive2.x;
+ expected = mediumPositive2.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He5(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive5.n;
+ x = mediumPositive5.x;
+ expected = mediumPositive5.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He1(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative1.n;
+ x = mediumNegative1.x;
+ expected = mediumNegative1.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He2(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative2.n;
+ x = mediumNegative2.x;
+ expected = mediumNegative2.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which accurately computes `He5(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var f;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative5.n;
+ x = mediumNegative5.x;
+ expected = mediumNegative5.expected;
+
+ f = factory( n );
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = f( x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns a function which returns `1.0` whenever `n` is `0`', function test( t ) {
+ var f;
+ var y;
+
+ f = factory( 0 );
+
+ y = f( -1.0 );
+ t.strictEqual( y, 1.0, 'returns expected value' );
+
+ y = f( 0.0 );
+ t.strictEqual( y, 1.0, 'returns expected value' );
+
+ y = f( 1.0 );
+ t.strictEqual( y, 1.0, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function returns a function which returns `NaN` whenever `n` is `NaN`', function test( t ) {
+ var f;
+ var y;
+
+ f = factory( NaN );
+
+ y = f( 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function returns a function which returns `NaN` when `x` is `NaN`', function test( t ) {
+ var f;
+ var y;
+
+ f = factory( 1 );
+
+ y = f( NaN );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});
+
+tape( 'the function returns a function which returns `NaN` when `n` is a negative integer`', function test( t ) {
+ var f;
+ var y;
+
+ f = factory( -1 );
+
+ y = f( 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});
+
+tape( 'the function returns a function which returns `NaN` when `n` is not an integer`', function test( t ) {
+ var f;
+ var y;
+
+ f = factory( 1.01 );
+
+ y = f( 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});
diff --git a/base/tools/normhermitepolyf/test/test.js b/base/tools/normhermitepolyf/test/test.js
new file mode 100644
index 000000000..85e665e9d
--- /dev/null
+++ b/base/tools/normhermitepolyf/test/test.js
@@ -0,0 +1,502 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+* http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var tape = require( 'tape' );
+var abs = require( './../../../../base/special/abs' );
+var EPS = require( '@stdlib/constants/float32/eps' );
+var isnanf = require( './../../../../base/assert/is-nanf' );
+var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
+var normhermitepolyf = require( './../lib' );
+
+
+// FIXTURES //
+
+var random2 = require( './fixtures/python/random2.json' );
+
+var mediumNegative1 = require( './fixtures/python/medium_negative_1.json' );
+var mediumNegative2 = require( './fixtures/python/medium_negative_2.json' );
+var mediumNegative5 = require( './fixtures/python/medium_negative_5.json' );
+
+var mediumPositive1 = require( './fixtures/python/medium_positive_1.json' );
+var mediumPositive2 = require( './fixtures/python/medium_positive_2.json' );
+var mediumPositive5 = require( './fixtures/python/medium_positive_5.json' );
+
+var smallPositive1 = require( './fixtures/python/small_positive_1.json' );
+var smallPositive2 = require( './fixtures/python/small_positive_2.json' );
+var smallPositive5 = require( './fixtures/python/small_positive_5.json' );
+
+var smallNegative1 = require( './fixtures/python/small_negative_1.json' );
+var smallNegative2 = require( './fixtures/python/small_negative_2.json' );
+var smallNegative5 = require( './fixtures/python/small_negative_5.json' );
+
+var tiny1 = require( './fixtures/python/tiny_1.json' );
+var tiny2 = require( './fixtures/python/tiny_2.json' );
+var tiny5 = require( './fixtures/python/tiny_5.json' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof normhermitepolyf, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is a `factory` method', function test( t ) {
+ t.strictEqual( typeof normhermitepolyf.factory, 'function', 'has method' );
+ t.end();
+});
+
+tape( 'the function accurately computes `Hen(x)` for random `n` and `x`', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = random2.n;
+ x = random2.x;
+ expected = random2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n[ i ], x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n[ i ] + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He1(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive1.n;
+ x = smallPositive1.x;
+ expected = smallPositive1.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive2.n;
+ x = smallPositive2.x;
+ expected = smallPositive2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He5(x)` for small positive numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallPositive5.n;
+ x = smallPositive5.x;
+ expected = smallPositive5.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He1(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative1.n;
+ x = smallNegative1.x;
+ expected = smallNegative1.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative2.n;
+ x = smallNegative2.x;
+ expected = smallNegative2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He5(x)` for small negative numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = smallNegative5.n;
+ x = smallNegative5.x;
+ expected = smallNegative5.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He1(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny1.n;
+ x = tiny1.x;
+ expected = tiny1.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny2.n;
+ x = tiny2.x;
+ expected = tiny2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He5(x)` for tiny numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = tiny5.n;
+ x = tiny5.x;
+ expected = tiny5.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He1(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive1.n;
+ x = mediumPositive1.x;
+ expected = mediumPositive1.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive2.n;
+ x = mediumPositive2.x;
+ expected = mediumPositive2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He5(x)` for positive medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumPositive5.n;
+ x = mediumPositive5.x;
+ expected = mediumPositive5.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He1(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative1.n;
+ x = mediumNegative1.x;
+ expected = mediumNegative1.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He2(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative2.n;
+ x = mediumNegative2.x;
+ expected = mediumNegative2.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 1.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function accurately computes `He5(x)` for negative medium numbers', function test( t ) {
+ var expected;
+ var delta;
+ var tol;
+ var x;
+ var v;
+ var i;
+ var n;
+ var e;
+
+ n = mediumNegative5.n;
+ x = mediumNegative5.x;
+ expected = mediumNegative5.expected;
+
+ for ( i = 0; i < x.length; i++ ) {
+ v = normhermitepolyf( n, x[ i ] );
+ e = float64ToFloat32( expected[ i ] );
+ delta = abs( v - e );
+ tol = 5.0 * EPS * abs( e );
+ t.ok( delta <= tol, 'within tolerance. n: ' + n + '. x: ' + x[ i ] + '. Value: ' + v + '. Expected: ' + e + '. Delta: ' + delta + '. Tolerance: ' + tol + '.' );
+ }
+ t.end();
+});
+
+tape( 'the function returns `1.0` whenever `n` is `0`', function test( t ) {
+ var y;
+
+ y = normhermitepolyf( 0, -1.0 );
+ t.strictEqual( y, 1.0, 'returns expected value.0' );
+
+ y = normhermitepolyf( 0, 0.0 );
+ t.strictEqual( y, 1.0, 'returns expected value.0' );
+
+ y = normhermitepolyf( 0, 1.0 );
+ t.strictEqual( y, 1.0, 'returns expected value.0' );
+
+ t.end();
+});
+
+tape( 'the function returns `NaN` whenever `n` is `NaN`', function test( t ) {
+ var y;
+
+ y = normhermitepolyf( NaN, 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function returns `NaN` when `x` is `NaN`', function test( t ) {
+ var y;
+
+ y = normhermitepolyf( 0, NaN );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});
+
+tape( 'the function returns `NaN` when `n` is a negative integer`', function test( t ) {
+ var y;
+
+ y = normhermitepolyf( -1, 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});
+
+tape( 'the function returns `NaN` when `n` is not an integer`', function test( t ) {
+ var y;
+
+ y = normhermitepolyf( 1.01, 0.0 );
+ t.strictEqual( isnanf( y ), true, 'returns expected value');
+
+ t.end();
+});