137 lines
4.5 KiB
JavaScript
137 lines
4.5 KiB
JavaScript
/**
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* LogarithmPlotter - 2D plotter software to make BODE plots, sequences and distribution functions.
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* Copyright (C) 2021-2024 Ad5001
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*
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* This program is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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// Contains polyfill math functions used for reference.
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.pragma library
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function factorial(x) {
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if (x < 0) // Integrating by less than 0
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if(isFinite(n))
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return Infinity
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else
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throw new EvalError("Cannot calculate the factorial of -∞.")
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return gamma(x+1)
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}
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let GAMMA_G = 4.7421875
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let GAMMA_P = [
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0.99999999999999709182,
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57.156235665862923517, -59.597960355475491248,
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14.136097974741747174, -0.49191381609762019978,
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0.33994649984811888699e-4,
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0.46523628927048575665e-4, -0.98374475304879564677e-4,
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0.15808870322491248884e-3, -0.21026444172410488319e-3,
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0.21743961811521264320e-3, -0.16431810653676389022e-3,
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0.84418223983852743293e-4, -0.26190838401581408670e-4,
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0.36899182659531622704e-5
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]
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function gamma(n) {
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if(n <= 0) // Integrating by less than 0
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if(isFinite(n))
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return Infinity
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else
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throw new EvalError("Cannot calculate Γ(-∞).")
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if(n >= 171.35)
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return Infinity // Would return more than 2^1024 - 1 (aka Number.INT_MAX)
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if(n === Math.round(n) && isFinite(n)) {
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// Calculating (n-1)!
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let res = n - 1
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for(let i = n - 2; i > 1; i++)
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res *= i
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if(res === 0)
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res = 1 // 0! is per definition 1
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return res
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}
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// Section below adapted function adapted from math.js
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if(n < 0.5)
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return Math.PI / (Math.sin(Math.PI * n) * gamma(1 - n))
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if(n > 85.0) { // Extended Stirling Approx
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let twoN = n * n
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let threeN = twoN * n
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let fourN = threeN * n
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let fiveN = fourN * n
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return Math.sqrt(2 * Math.PI / n) * Math.pow((n / Math.E), n) *
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(1 + (1 / (12 * n)) + (1 / (288 * twoN)) - (139 / (51840 * threeN)) -
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(571 / (2488320 * fourN)) + (163879 / (209018880 * fiveN)) +
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(5246819 / (75246796800 * fiveN * n)))
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}
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--n
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let x = GAMMA_P[0]
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for (let i = 1; i < GAMMA_P.length; ++i) {
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x += GAMMA_P[i] / (n + i)
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}
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let t = n + GAMMA_G + 0.5
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return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x
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}
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function arrayMap(f, arr) {
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if (typeof f != 'function')
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throw new EvalError(qsTranslate('error', 'First argument to map is not a function.'))
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if (!Array.isArray(arr))
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throw new EvalError(qsTranslate('error', 'Second argument to map is not an array.'))
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return arr.map(f)
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}
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function arrayFold(f, init, arr) {
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if (typeof f != 'function')
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throw new EvalError(qsTranslate('error', 'First argument to fold is not a function.'))
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if (!Array.isArray(arr))
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throw new EvalError(qsTranslate('error', 'Second argument to fold is not an array.'))
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return arr.reduce(f, init)
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}
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function arrayFilter(f, arr) {
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if (typeof f != 'function')
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throw new EvalError(qsTranslate('error', 'First argument to filter is not a function.'))
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if (!Array.isArray(arr))
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throw new EvalError(qsTranslate('error', 'Second argument to filter is not an array.'))
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return arr.filter(f)
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}
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function arrayFilter(f, arr) {
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if (typeof f != 'function')
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throw new EvalError(qsTranslate('error', 'First argument to filter is not a function.'))
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if (!Array.isArray(arr))
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throw new EvalError(qsTranslate('error', 'Second argument to filter is not an array.'))
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return arr.filter(f)
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}
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function arrayJoin(sep, arr) {
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if (!Array.isArray(arr))
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throw new Error(qsTranslate('error', 'Second argument to join is not an array.'))
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return arr.join(sep)
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}
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function indexOf(target, s) {
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if (!(Array.isArray(s) || typeof s === 'string'))
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throw new Error(qsTranslate('error', 'Second argument to indexOf is not a string or array.'))
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return s.indexOf(target)
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}
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