// Formula parser and solver - Created by Jurgen Westerhof 2024
// MIT license
// https://turtletoy.net/turtle/187a81ec7d

const formulaText = 'Math.abs(a*x**2 + b*x + c)'; //type=string
const a = 3; //min=-30 max=30 step=.5
const b = -16; //min=-30 max=30 step=.5
const c = 5; //min=-30 max=30 step=.5

const fn = new Formula(formulaText);
console.info(formulaText);
console.info('Parsed', fn.getParsed());
console.info('Variabes', fn.getVariables());

const results = Array.from({length: 26},
    (e, x) => `f(${x}) = ${fn.solve({x: x, a: a, b: (vars) => b, c: c})}` // 'b: (vars) => b' could be 'b: b', but I added it this way as an example that you can feed custom functions as values. The 'vars' variable is a handle to an object containing all values passed to solve()
);

new 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"}).print(
    new Turtle(-97, -93),
    `f(x) = ${formulaText}
a=${a}, b=${b}, c=${c}
${results.join("\n")}`,
    .5
);

/* Usage:

// You can use 'normal' javascript notation
let e = new Formula('2 * (3 + 4) - 1/2**2');
let o = e.solve());

// including the Math namespace
let f = new Formula('Math.sin(2 * Math.PI * Math.random())');
o = f.solve();

// You can also use custom variables
let g = new Formula('2 * Math.PI * i / max');
o = g.solve({i: 2, max: 5});

// Which might be usefull in a loop:
array.map((e,i,a) => g.solve({i: i, max: a.length - 1}));

// You can also solve using a function as value for a custom variable.
// On solving the function will get an hashmap as the first (and only)
//  parameter with a key in it for every custom variable in the solve() call:
g.solve({i: (varMap) => varMap.max - 1, max: 5}); // i = 5 - 1 = 4, max = 5

*/

/////////////////////////////////////////////////////////////////
// Formula parser and solver - Created by Jurgen Westerhof 2024
// https://turtletoy.net/turtle/187a81ec7d
/////////////////////////////////////////////////////////////////
function Formula(string) {
    const types = {
        'Function': 'Function',
        'Literal': 'Literal',
        'Variable': 'Variable',
        'Arithmetic': 'Arithmetic',
        'Unary': 'Unary',
    };
    const operators = [ //ordered by operator precedence (PEMDAS)
        ['**', (a, b) => a**b],
        ['*', (a, b) => a*b],
        ['/', (a, b) => a/b],
        ['%', (a, b) => a%b],
        ['+', (a, b) => a+b],
        ['-', (a, b) => a-b],
        ['<<', (a, b) => a<<b],
        ['>>', (a, b) => a>>b],
        ['|', (a, b) => a|b],
        ['^', (a, b) => a^b],
        ['&', (a, b) => a&b],
    ];
    class Formula {
        #variables;
        #parsed;
        #raw;
        constructor(string) {
            this.#raw = string;
            this.#variables = [];
            this.#parsed = this.tokenize(string);
        }
        getVariables() {
            return this.#variables.map(e => e);
        }
        getParsed() {
            const clone = (v) => (typeof v == 'object')? v.map(vv => clone(vv)): v;
            return this.#parsed.map(v => clone(v));
        }
        tokenize(str) {
            const tokens = [];
            let m;

            nextToken: for(let i = 0; i < str.length; i++) {
                //Skip whitespace
                if(/\s/.test(str[i])) continue;
                //Parse Math namespace
                if(str.substr(i, 5) == 'Math.') {
                    i += 5;
                    m = new RegExp(`^.{${i}}(?<payload>(?<const>[A-Z][A-Z0-9]*)|(?<fn>[a-z][a-z0-9]*)).*?`).exec(str);
                    if(Math[m.groups.payload] === undefined) {
                        console.error(`Math.${m.groups.payload} is undefined`);
                    }
                    if(m.groups.const) {
                        tokens.push([types.Literal, Math[m.groups.payload]]);
                    } else {
                        tokens.push([types.Function, m.groups.payload]);
                    }
                    i+=m.groups.payload.length-1;
                    continue nextToken;
                }
                //Parse variable
                // taking a shortcut here: unicode in variable names not accepted: https://stackoverflow.com/questions/1661197/what-characters-are-valid-for-javascript-variable-names
                m = new RegExp('^' + '\.'.repeat(i) + '(?<payload>[a-zA-Z_$][0-9a-zA-Z_$]*).*').exec(str);
                if(m !== null) {
                    tokens.push([types.Variable, m.groups.payload]);
                    if(!this.#variables.includes(m.groups.payload)) {
                        this.#variables.push(m.groups.payload);
                    }
                    i+= m.groups.payload.length - 1;
                    continue nextToken;
                }
                //Parse unary
                if((tokens.length == 0 || tokens[tokens.length - 1][0] == types.Arithmetic) && (str[i] == '-' || str[i] == '+' || str[i] == '~')) {
                    tokens.push([types.Unary, str[i]]);
                    continue nextToken;
                }
                //Parse (group) (including function parameters)
                if(str[i] == '(') {
                    const isFunction = (tokens.length > 0 && tokens[tokens.length - 1][0] == types.Function);
                    let cnt = 1;
                    let k = i + 1;
                    let j = 0;
                    let fnArgs = [];
                    for(; 0 < cnt && k+j < str.length; j++) {
                        if(str[k+j] == '(') cnt++;
                        if(str[k+j] == ')') cnt--;
                        if(str[k+j] == ',' && cnt == 1) {
                            fnArgs.push(this.tokenize(str.substr(i+1, j)));
                            i += j+1;
                            k += j+1;
                            j=0;
                        }
                    }
                    if(cnt == 0) {
                        if(isFunction) {
                            fnArgs.push(this.tokenize(str.substr(i+1, j-1)));
                            tokens[tokens.length - 1].push(fnArgs)
                        } else {
                            tokens.push(this.tokenize(str.substr(i+1, j-1)));
                        }
                        i += j;
                        continue nextToken;
                    }
                    console.error(`Opened bracket at character ${i} not closed: ${str.substr(i)}`);
                    throw new Error(`Opened bracket at character ${i} not closed: ${str.substr(i)}`);
                }
                //Parse literal
                m = new RegExp(`^.{${i}}(?<payload>\\d+(\\.\\d+)?|\\.\\d+).*?`).exec(str);
                if(m !== null) {
                    tokens.push([types.Literal, +m.groups.payload]);
                    i+=m.groups.payload.length-1;
                    continue nextToken;
                }
                //Parse operator
                m = new RegExp(`^.{${i}}(?<payload>\\${operators.map(o => o[0].split('').join('\\')).join('|\\')})`).exec(str);
                if(m !== null) {
                    tokens.push([types.Arithmetic, m.groups.payload]);
                    i+=m.groups.payload.length-1;
                    continue nextToken;
                }
                //Something I didn't think of occured
                console.error(`Unable to parse '${str}' because a character at ${i}: ${str[i]}`);
                throw new Error(`Unable to parse '${str}' because a character at ${i}: ${str[i]}`);
            }
            return tokens;
        }
        solve(variableMap = {}) {
            return this.solveInt(
                this.#parsed,
                //Map required variables to values assuming 0 if not set
                this.#variables.reduce((a, c) => {
                    let val = 0;
                    if(variableMap[c] === undefined) {
                        console.warn(`Variable ${c} not set in argument to solve() of ${this.#raw}.`);
                        throw new Error(`Variable ${c} not set in argument to solve() of ${this.#raw}.`);
                    } else {
                        val = variableMap[c];
                    }
                    return {...a, [c]: val};
                }, {})
            );
        }
        solveInt(tokenss, variableMap) {
            if(tokenss.length == 0) return 0;
            
            const clone = (v) => (typeof v == 'object')? v.map(vv => clone(vv)): v;
            const tokens = tokenss.map(v => clone(v));
            
            //Resolve functions
            for(let i = 0; i < tokens.length; i++) {
                if(tokens[i][0] == types.Function) {
                    const literals = tokens[i][2].map(v => this.solveInt(v, variableMap));
                    tokens[i] = [types.Literal, Math[tokens[i][1]].apply(null, literals)];
                }
            }
            //Resolve (group)s
            for(let i = 0; i < tokens.length; i++) {
                if(typeof tokens[i][0] == 'object') {
                    tokens[i] = [types.Literal, this.solveInt(tokens[i], variableMap)];
                }
                if(tokens[i][0] == types.Variable) {
                    tokens[i] = [types.Literal, typeof variableMap[tokens[i][1]] == 'function'? variableMap[tokens[i][1]](variableMap): variableMap[tokens[i][1]]];
                }
            }
            //Resolve unary
            for(let i = 0; i < tokens.length; i++) {
                if(tokens[i][0] == types.Unary) {
                    switch(tokens[i][1]) {
                        case '-':
                        case '+':
                            tokens[i+1][1] = tokens[i+1][1]*(tokens[i][1]=='-'?-1:1);
                            break;
                        case '~':
                            tokens[i+1][1] = ~tokens[i+1][1];
                    }
                    tokens.splice(i, 1);
                    i--;
                }
            }
            //Resolve operators
            operators.forEach(op => {
                for(let i = 0; i < tokens.length; i++) {
                    if(tokens[i][0] == types.Arithmetic && tokens[i][1] == op[0]) {
                        tokens[i-1][1] = op[1](tokens[i-1][1], tokens[i+1][1]);
                        tokens.splice(i, 2);
                        i-=2;
                    }
                }
            });
            //Get solution
            if(tokens.length == 1 && tokens[0][0] == types.Literal) {
                return tokens[0][1];
            }
            //Something I didn't think of occured
            console.error('Something went wrong solving token ' + i, tokens);
            throw new Error('Something went wrong solving token ' + i);
        }
    }
    return new Formula(string);
}

////////////////////////////////////////////////////////////////
// Text utility code. Created by Reinder Nijhoff 2024
// https://turtletoy.net/turtle/0f84fd3ae4
////////////////////////////////////////////////////////////////

function Text(fontData) {
    const decode = (data) => {
        const b = atob(data), a = new Int16Array(b.length / 2), g = {};
        for (let i = 0; i < b.length; i+=2) {
            a[i / 2 | 0] = b.charCodeAt(i) | (b.charCodeAt(i + 1) << 8);
        }
        for (let i = 0;i < a.length; i++) {
            let u = String.fromCharCode(a[i++]), x = a[i++], d = [], p = [];
            for (;a[i] !== -16384; i++) a[i] === 16384 ? (d.push(p), p = []) : p.push(a[i]);
            g[u] = { x, d };
        }
        return g;
    }
    const rotAdd = (a, b, h) => [Math.cos(h)*a[0] - Math.sin(h)*a[1] + b[0],
                                 Math.cos(h)*a[1] + Math.sin(h)*a[0] + b[1]];

    const data = Object.fromEntries(Object.entries(fontData).map(([key, value]) =>
        [key, key === 'glyphs' ? decode(value) : value]));

    class Text {
        print (t, str, scale = 1) {
            let pos = t ? [t.x(), t.y()] : [0,0], h = t ? t.h() * Math.PI * 2 / t.fullCircle() : 0, 
                      o = pos, s = scale / data.unitsPerEm;
            str.split('').map(c => {
                if (c == '\n') {
                    pos = o = rotAdd([0, 14 * scale], o, h);
                    return;
                }
                const glyph = (data.glyphs[c] || data.glyphs[' ']), d = glyph.d;
                d.forEach( (p, k) => {
                    t && t.up();
                    for (let i=0; i<p.length; i+=2) {
                        t && t.goto(rotAdd([p[i]*s, p[i+1]*s], pos, h));
                        t && t.down();
                    }
                });
                pos = rotAdd([glyph.x*s, 0], pos, h);
            });
            return rotAdd([0, 10*scale], pos, h);
        }
    }

    return new Text();
}