Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 2408x 2408x 2408x 2408x 2408x 2408x 2408x 2408x 100x 100x 2408x 200x 200x 2408x 101x 101x 2007x 2408x 2x 2x 2x 1001x 1001x 1001x 1001x 1001x 2408x 2005x 2005x 2005x 2005x 10010x 10010x 10010x 10010x 10010x 2005x 2007x 2408x 3x 3x 3x 3x 3x | /**
* @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.
*
*
* ## Notice
*
* The original C++ code and copyright notice are from the [Boost library]{@link http://www.boost.org/doc/libs/1_60_0/boost/math/tools/rational.hpp}. The implementation has been modified for JavaScript.
*
* ```text
* (C) Copyright John Maddock 2006.
*
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
* ```
*/
'use strict';
// MODULES //
var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
var absf = require( '@stdlib/math/base/special/absf' );
// MAIN //
/**
* Evaluates a rational function (i.e., the ratio of two polynomials described by the coefficients stored in \\(P\\) and \\(Q\\)) using single-precision floating-point arithmetic.
*
* ## Notes
*
* - Coefficients should be sorted in ascending degree.
* - The implementation 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
* @param {number} x - value at which to evaluate the rational function
* @returns {number} evaluated rational function
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* var P = new Float32Array( [ -6.0, -5.0 ] );
* var Q = new Float32Array( [ 3.0, 0.5 ] );
*
* var v = evalrationalf( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 ) / ( 3*6^0 + 0.5*6^1 ) = (-6-30)/(3+3)
* // returns -6.0
*
* @example
* var Float32Array = require( '@stdlib/array/float32' );
*
* // 2x^3 + 4x^2 - 5x^1 - 6x^0 => degree 4
* var P = new Float32Array( [ -6.0, -5.0, 4.0, 2.0 ] );
*
* // 0.5x^1 + 3x^0 => degree 2
* var Q = new Float32Array( [ 3.0, 0.5, 0.0, 0.0 ] ); // zero-padded
*
* var v = evalrationalf( P, Q, 6.0 ); // => ( -6*6^0 - 5*6^1 + 4*6^2 + 2*6^3 ) / ( 3*6^0 + 0.5*6^1 + 0*6^2 + 0*6^3 ) = (-6-30+144+432)/(3+3)
* // returns ~90.0
*/
function evalrationalf( P, Q, x ) {
var len;
var s1;
var s2;
var i;
len = P.length;
if ( len === 0 ) {
return NaN;
}
if ( len !== Q.length ) {
return NaN;
}
if ( x === 0.0 || len === 1 ) {
return float64ToFloat32( P[ 0 ] / Q[ 0 ] );
}
// Use Horner's method...
if ( absf( x ) <= 1.0 ) {
s1 = P[ len-1 ];
s2 = Q[ len-1 ];
for ( i = len-2; i >= 0; --i ) {
s1 = float64ToFloat32( s1 * x );
s2 = float64ToFloat32( s2 * x );
s1 = float64ToFloat32( s1 + P[ i ] );
s2 = float64ToFloat32( s2 + Q[ i ] );
}
} else {
x = float64ToFloat32( 1.0 / x ); // use inverse to avoid overflow
s1 = P[ 0 ];
s2 = Q[ 0 ];
for ( i = 1; i < len; ++i ) {
s1 = float64ToFloat32( s1 * x );
s2 = float64ToFloat32( s2 * x );
s1 = float64ToFloat32( s1 + P[ i ] );
s2 = float64ToFloat32( s2 + Q[ i ] );
}
}
return float64ToFloat32( s1 / s2 );
}
// EXPORTS //
module.exports = evalrationalf;
|