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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 Fcn = require( '@stdlib/function/ctor' );
var evalrationalf = require( './main.js' );
// MAIN //
/**
* Generates a function for evaluating a rational function using single-precision floating-point arithmetic.
*
* ## Notes
*
* - The compiled function uses [Horner's rule][horners-method] for efficient computation.
*
* [horners-method]: https://en.wikipedia.org/wiki/Horner%27s_method
*
* @param {NumericArray} P - numerator polynomial coefficients sorted in ascending degree
* @param {NumericArray} Q - denominator polynomial coefficients sorted in ascending degree
* @returns {Function} function for evaluating a rational function
*
* @example
* var P = [ 20.0, 8.0, 3.0 ];
* var Q = [ 10.0, 9.0, 1.0 ];
*
* var rational = factory( P, Q );
*
* var v = rational( 10.0 ); // => (20*10^0 + 8*10^1 + 3*10^2) / (10*10^0 + 9*10^1 + 1*10^2) = (20+80+300)/(10+90+100)
* // returns 2.0
*
* v = rational( 2.0 ); // => (20*2^0 + 8*2^1 + 3*2^2) / (10*2^0 + 9*2^1 + 1*2^2) = (20+16+12)/(10+18+4)
* // returns 1.5
*/
function factory( P, Q ) {
var f;
var r;
var n;
var m;
var i;
// Avoid exceeding maximum stack size on V8 :(. Note that the value of `500` was empirically determined...
if ( P.length > 500 ) {
return rational;
}
// Code generation. Start with the function definition...
f = 'return function evalrationalf(x){';
// Create the function body...
n = P.length;
// Declare variables...
f += 'var ax,s1,s2;';
// If no coefficients, the function always returns NaN...
if ( n === 0 ) {
f += 'return NaN;';
}
// If P and Q have different lengths, the function always returns NaN...
else if ( n !== Q.length ) {
f += 'return NaN;';
}
// If P and Q have only one coefficient, the function always returns the ratio of the first coefficients...
else if ( n === 1 ) {
r = float64ToFloat32( P[ 0 ] / Q[ 0 ] );
f += 'return ' + r + ';';
}
// If more than one coefficient, apply Horner's method to both the numerator and denominator...
else {
// If `x == 0`, return the ratio of the first coefficients...
r = float64ToFloat32( P[ 0 ] / Q[ 0 ] );
f += 'if(x===0.0){return ' + r + ';}';
// Compute the absolute value of `x`...
f += 'if(x<0.0){ax=-x;}else{ax=x;}';
// If `abs(x) <= 1`, evaluate the numerator and denominator of the rational function using Horner's method...
f += 'if(ax<=1.0){';
f += 's1 = f64_to_f32(' + P[ 0 ];
m = n - 1;
for ( i = 1; i < n; i++ ) {
f += '+f64_to_f32(x*';
if ( i < m ) {
f += '(';
}
f += P[ i ];
}
// Close all the parentheses...
for ( i = 0; i < 2*m; i++ ) {
f += ')';
}
f += ';';
f += 's2 = f64_to_f32(' + Q[ 0 ];
m = n - 1;
for ( i = 1; i < n; i++ ) {
f += '+f64_to_f32(x*';
if ( i < m ) {
f += '(';
}
f += Q[ i ];
}
// Close all the parentheses...
for ( i = 0; i < 2*m; i++ ) {
f += ')';
}
f += ';';
// Close the if statement...
f += '}else{';
// If `abs(x) > 1`, evaluate the numerator and denominator via the inverse to avoid overflow...
f += 'x = f64_to_f32(1.0/x);';
m = n - 1;
f += 's1 = f64_to_f32(' + P[ m ];
for ( i = m - 1; i >= 0; i-- ) {
f += '+f64_to_f32(x*';
if ( i > 0 ) {
f += '(';
}
f += P[ i ];
}
// Close all the parentheses...
for ( i = 0; i < 2*m; i++ ) {
f += ')';
}
f += ';';
m = n - 1;
f += 's2 = f64_to_f32(' + Q[ m ];
for ( i = m - 1; i >= 0; i-- ) {
f += '+f64_to_f32(x*';
if ( i > 0 ) {
f += '(';
}
f += Q[ i ];
}
// Close all the parentheses...
for ( i = 0; i < 2*m; i++ ) {
f += ')';
}
f += ';';
// Close the else statement...
f += '}';
// Return the ratio of the two sums...
f += 'return f64_to_f32(s1/s2);';
}
// Close the function:
f += '}';
// Add a source directive for debugging:
f += '//# sourceURL=evalrationalf.factory.js';
// Create the function in the global scope:
return ( new Fcn( 'f64_to_f32', f ) )( float64ToFloat32 );
/*
* function evalrationalf( x ) {
* var ax, s1, s2;
* if ( x === 0.0 ) {
* return f64_to_f32( P[0] / Q[0] );
* }
* if ( x < 0.0 ) {
* ax = -x;
* } else {
* ax = x;
* }
* if ( ax <= 1.0 ) {
* s1 = f64_to_f32(P[0]+f64_to_f32(x*f64_to_f32(P[1]+f64_to_f32(x*f64_to_f32(P[2]+f64_to_f32(x*f64_to_f32(P[3]+...+f64_to_f32(x*f64_to_f32(P[n-2]+f64_to_f32(x*P[n-1]))))))))));
* s2 = f64_to_f32(Q[0]+f64_to_f32(x*(Q[1]+f64_to_f32(x*(Q[2]+f64_to_f32(x*(Q[3]+...+f64_to_f32(x*(Q[n-2]+f64_to_f32(x*Q[n-1]))))))))));
* } else {
* x = 1.0/x;
* s1 = f64_to_f32(P[n-1]+f64_to_f32(x*(P[n-2]+f64_to_f32(x*(P[n-3]+f64_to_f32(x*(P[n-4]+...+f64_to_f32(x*(P[1]+f64_to_f32(x*P[0]))))))))));
* s2 = f64_to_f32(Q[n-1]+f64_to_f32(x*(Q[n-2]+f64_to_f32(x*(Q[n-3]+f64_to_f32(x*(Q[n-4]+...+f64_to_f32(x*(Q[1]+f64_to_f32(x*Q[0]))))))))));
* }
* return f64_to_f32( s1 / s2 );
* }
*/
/**
* Evaluates a rational function.
*
* @private
* @param {number} x - value at which to evaluate a rational function
* @returns {number} evaluated rational function
*/
function rational( x ) {
return evalrationalf( P, Q, x );
}
}
// EXPORTS //
module.exports = factory;
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