math.js

/**
MIT License

Copyright (c) 2022 Jérôme Lécuyer https://github.com/Jiogo18

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
 */
/**
 * Math equation v1
 * by @Jiogo18
 * for @Jig0ll & @Robotek
 */

const MinMax = (min, x, max) => Math.max(min, Math.min(x, max));
const distance = (a, b) => Math.sqrt(a * a + b * b);
const distancePointOrigine = p => Math.sqrt(p.re * p.re + p.im * p.im);
const distancePoints = (p1, p2) => Math.sqrt(Math.pow(p1.re - p2.re, 2) + Math.pow(p1.im - p2.im, 2));
const pointCart = (re, im) => new Object({ re, im });
const pointExpo = (r, angle) => new Object({ r, angle });
const expToCart = (angle, r) => pointCart(r * Math.cos(angle), r * Math.sin(angle));
const cartToExp = p => pointExpo(distancePointOrigine(p), Math.atan(p.im / p.re) + (p.re < 0 && Math.PI));
const valideOctet = v => MinMax(0, Math.round(v), 255);
const modulo = (a, b) => a - Math.floor(a / b) * b;

class Color {
	decValue;
	get r() {
		return (this.decValue & 0xff0000) >> 16;
	}
	get g() {
		return (this.decValue & 0x00ff00) >> 8;
	}
	get b() {
		return this.decValue & 0x0000ff;
	}
	/**
	 * @param {number} value
	 */
	constructor(value) {
		this.decValue = value;
	}
	static fromRGB(r, g, b) {
		return new Color((valideOctet(r) << 16) | (valideOctet(g) << 8) | valideOctet(b));
	}
	hue_rotation(angle) {
		var cosA = Math.cos(angle);
		var sinA = Math.sin(angle);
		var ratio_partage = (1 / 3) * (1 - cosA);
		var sqrt1_3 = Math.sqrt(1 / 3);
		var m0 = ratio_partage + cosA;
		var m1 = ratio_partage - sqrt1_3 * sinA;
		var m2 = ratio_partage + sqrt1_3 * sinA;
		var rx = this.r * m0 + this.g * m1 + this.b * m2;
		var gx = this.r * m2 + this.g * m0 + this.b * m1;
		var bx = this.r * m1 + this.g * m2 + this.b * m0;
		return Color.fromRGB(rx, gx, bx);
	}
	lumiere(lumiere) {
		return Color.fromRGB(this.r * lumiere, this.g * lumiere, this.b * lumiere);
	}
}

const n = '[\\d\\.]';
const reel = `[\\+\\-]?\\.?\\d+\\.?\\d*(?:e-\\d+)?`;
const op = '\\+\\-\\*\\/';
const prefix_nochar = '(?<=^|[^\\w\\d])';
const suffix_nochar = '(?=[^\\w\\d]|$)';
const MATH = {};
function listCompare(strOperator, funcOperator) {
	// 10d6 >= 3 = (n: 5 6 4 ~~1~~ ~~1~~ 3 6 3 4 6) = 8
	return [
		`(\\d[\\d \\.${op}]*) *${strOperator} *(${reel})`,
		match => {
			return (
				'(n: ' +
				match[1]
					.replace(/ +/, ' ')
					.replace(/^ /, '')
					.replace(/ $/, '')
					.split(' ')
					.map(v => parseFloat(v) || 0)
					.map(v => (funcOperator(v, match[2]) ? v : `~~${v}~~`))
					.join(' ') +
				')'
			);
		},
	];
}
function funcOperation(strFunction, nbArgs, funcOperator) {
	var param = new Array(nbArgs).fill(`(${reel})`);
	return [
		`${prefix_nochar}${strFunction}\\\( *${param.join(' *, *')} *\\\)`,
		match => {
			const args = new Array(nbArgs).fill(0).map((v, i) => parseFloat(match[1 + i]) ?? undefined);
			return funcOperator(...args);
		},
	];
}
function pairOperation(strOperator, funcOperator) {
	strOperator = strOperator.replace(/(.)/g, '\\$1');
	return [
		`(${reel}) *${strOperator} *(${reel})`,
		match => '+' + funcOperator(parseFloat(match[1]) || undefined, parseFloat(match[2]) || undefined),
	];
}

const transfoCalc = [
	[
		// transfo sign
		[/\+ *\+/, () => '+'],
		[/\- *\-/, () => '+'],
		[/\+ *\-/, () => '-'],
		[/\- *\+/, () => '-'],
		[/\* *\+/, () => '*'],
		[/\/ *\+/, () => '/'],
		[/ {2}/, () => ' '],
	],
	[
		[`[${op}]*~~[\\d\\. ${op}]*~~`, () => '', 'before'], //deleted number
		[`#([\\dA-Fa-f]+)`, match => parseInt(match[1], 16)], //hexadecimal
		[`0x([\\dA-Fa-f]+)`, match => parseInt(match[1], 16)], //hexadecimal
		[`0[bB]([01]+)`, match => parseInt(match[1], 2)], //binaire
		[`${prefix_nochar}true${suffix_nochar}`, () => 1],
		[`${prefix_nochar}false${suffix_nochar}`, () => 0],
	],
	[
		[`\\(n: [\\d \\.${op}]*\\)`, match => match[0].match(new RegExp(`${n}+`, 'g'))?.length || 0], //deleted number
	],
	[
		// specialCalc
		[...listCompare('>', (a = 0, b = 0) => a > b), 'after'],
		listCompare('>=', (a = 0, b = 0) => a >= b),
		listCompare('==?', (a = 0, b = 0) => a == b),
		listCompare('!=', (a = 0, b = 0) => a == b),
		listCompare('<=', (a = 0, b = 0) => a <= b),
		listCompare('<', (a = 0, b = 0) => a < b),
	],
	[
		// transfoMult
		pairOperation('^^', (a = 0, b = 0) => Math.pow(a, b)),
		pairOperation('/', (a = 0, b = 0) => a / b), // 1 / 2 * 3
		pairOperation('*', (a = 0, b = 0) => a * b),
		pairOperation('%', (a = 0, b = 0) => modulo(a, b)),
	],
	[
		// transfoAddition
		pairOperation('+', (a = 0, b = 0) => a + b),
		pairOperation('-', (a = 0, b = 0) => a - b),
		pairOperation(' ', (a = 0, b = 0) => a + b),
	],
	[
		// transfo fonctions
		funcOperation('max', 2, (a, b) => Math.max(a, b)),
		funcOperation('min', 2, (a, b) => Math.min(a, b)),
		funcOperation('minmax', 3, (min, x, max) => MinMax(min, x, max)),
		funcOperation('range', 3, (min, x, max) => (min <= x && x <= max ? 1 : 0)),
		funcOperation('abs', 1, a => Math.abs(a)),
		funcOperation('sqrt', 1, a => Math.sqrt(a)),
		funcOperation('pow', 2, (a, b) => Math.pow(a, b)),
		funcOperation('exp', 1, x => Math.exp(x)),
		funcOperation('round', 1, a => Math.round(a)),
		funcOperation('floor', 1, a => Math.floor(a)),
		funcOperation('ceil', 1, a => Math.ceil(a)),
		funcOperation('random', 0, () => Math.random()),
		funcOperation('pi', 0, () => 3.141593),
		funcOperation('cos', 1, a => Math.cos(a)),
		funcOperation('sin', 1, a => Math.sin(a)),
		funcOperation('tan', 1, a => Math.tan(a)),
		funcOperation('acos', 1, a => Math.acos(a)),
		funcOperation('asin', 1, a => Math.asin(a)),
		funcOperation('atan', 1, a => Math.atan(a)),
		funcOperation('modulo', 2, (a, b = 1) => modulo(a, b)),
		funcOperation('angle_complexe', 2, (a, b) => modulo(Math.atan(b / a) + (a < 0 ? Math.PI : 0), 2 * Math.PI)),
		funcOperation('triangle', 4, (x, x0, y0, pente) => y0 - pente * Math.abs(x - x0)),
		funcOperation('distance', 2, (x1, y1) => distance(x1, y1)),
		funcOperation('heaviside', 1, t => 0 <= t),
		funcOperation('porte', 3, (t, t1, t2) => t1 <= t && t <= t2),
		funcOperation('pente_cosale', 1, t => (0 <= t ? t : 0)),
		funcOperation('rgb', 3, (r, g, b) => (MinMax(0, r, 255) << 16) | (MinMax(0, g, 255) << 8) | MinMax(0, b, 255)),
		funcOperation('red', 1, c => (c & 0xff0000) >> 16),
		funcOperation('green', 1, c => (c & 0x00ff00) >> 8),
		funcOperation('blue', 1, c => c & 0x0000ff),
		funcOperation('huerotate', 2, (c, angle) => new Color(c).hue_rotation(angle).decValue),
		funcOperation('lumiere', 2, (c, lumiere) => new Color(c).lumiere(lumiere).decValue),
	],
	[
		// transfoAddition
		[`\\( *\\+? *(${reel}) *\\)`, match => match[1]],
		[`\\( *\\- *(${reel}) *\\)`, match => -match[1]],
		//[/\([ \+\-\*\/]*\)/, () => 0],
	],
	[
		// binary manipulation
		pairOperation('<<', (a = 0, b = 0) => a << b),
		pairOperation('>>', (a = 0, b = 0) => a >> b),
		pairOperation('&', (a = 0, b = 0) => a & b),
		pairOperation('|', (a = 0, b = 0) => a | b),
		pairOperation('^', (a = 0, b = 0) => a ^ b),
	],
	[
		// transfoOperator
		pairOperation('||', (a = 0, b = 0) => a || b),
		pairOperation('&&', (a = 0, b = 0) => a && b),
	],
];

/**
 * @param {string} equation Line
 * @param {string[]|undefined} equaStep Empty array
 */
MATH.parseMath = (equation, equaStep) => {
	equation = equation.replace(/^ */, '').replace('&gt;', '>').replace('&lt;', '<');
	//`!r 1++2 * 5` donne `1+2*5`
	equaStep ??= [];
	equaStep.push(equation);
	var previousLine;
	do {
		previousLine = equation;
		for (const transfoGrp of transfoCalc) {
			const equationTransformed = applyTransfo(equation, transfoGrp);
			if (equationTransformed != equation) {
				if (transfoGrp.some(t => t[2] === 'after')) {
					// l'une des transfos demande l'update avec la nouvelle version
					equaStep.push(equationTransformed);
				} else if (transfoGrp.some(t => t[2] === 'before')) {
					// l'une des transfos demande l'update avec la version précédente
					if (equaStep[equaStep.length - 1] !== equation) equaStep.push(equation);
				} else {
					equaStep.push(equationTransformed);
				}
				equation = equationTransformed;
				break;
			}
		}
	} while (equation != previousLine && equation.length < 100000);

	if (equation == '') equation = 0;
	equaStep.push(equation);
	return equation;
};

/**
 * @param {string} equation
 * @param {[string,Function][]} rules
 */
function getFirstMatch(equation, rules) {
	return rules
		.map(rule => {
			return { rule, match: equation.match(new RegExp(rule[0], 'ig')) };
		})
		.filter(result => result.match)
		.sort((a, b) => Math.sign(a.match.index, b.match.index))?.[0];
}

/**
 * @param {string} equation
 * @param {[string,Function][]} rules
 */
function applyTransfo(equation, rules) {
	var i = 0;
	var result;
	while ((result = getFirstMatch(equation, rules))) {
		const rule = result.rule;
		const regex = new RegExp(rule[0], 'i');
		const replacement = rule[1](equation.match(regex));
		equation = equation.replace(result.match[0], replacement);

		if (i++ > 100) throw new Error('équation trop grande ou impossible à résoudre');
	}
	return equation;
}