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* @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( '@stdlib/math/base/assert/is-nanf' );
var isint = require( '@stdlib/math/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;
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