first commit

test.js

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+const elems =  {
+    '[]': 'Nothing',
+    '["Nothing","Nothing"]': 'Null',
+    '["Null","Nothing"]': 'Void',
+    '["Null","Null"]': 'Set',
+    '["Set","Set"]': 'Count',
+    '["Count","Set"]': 'Number',
+    '["Null","Number"]': 'Negative',
+    '["Negative","Negative"]': 'Positive',
+    '["Negative","Positive"]': 'Inverse',
+    '["Inverse","Number"]': 'Fraction',
+    '["Fraction","Expand"]': 'Part',
+    '["Number","Part"]': 'Digit',
+    '["Digit","Expand"]': 'Letter',
+    '["Letter","Set"]': 'Word',
+    '["Inverse","Word"]': 'Not',
+    '["Not","Null"]': 'True',
+    '["Not","True"]': 'False',
+    '["True","False"]': 'Boolean',
+    '["Set","Boolean"]': 'Binary',
+    '["Binary","Operator"]': 'Function',
+    '["Function","Zero"]': 'Algebra',
+    '["Algebra","Calculus"]': 'Mathematics',
+    '["Mathematics","Deabstraction"]': 'Science',
+    '["Science","Combination"]': 'Chemistry',
+    '["Chemistry","Object"]': 'Chemical',
+    '["Chemical","Pattern"]': 'Crystal',
+    '["Crystal","Cold"]': 'Rock',
+    '["Rock","Wind"]': 'Stone',
+    '["Stone","Wind"]': 'Cobblestone',
+    '["Cobblestone","Sand"]': 'Gravel',
+    '["Gravel","Life"]': 'Dirt',
+}
+
+const compCache = {};
+const deCompCache = {};
+
+function indexr(n) {
+    let j;
+    try {
+        j = JSON.parse(Object.keys(elems)[Object.values(elems).findIndex(x => x == n)]);
+    } catch (err) {
+        return 0n;
+    }
+    return comp(j);
+}
+
+function comp(e, ignore = false) {
+    if (!e || typeof e != 'object' || e.length == 0) return 0n;
+    let a, b;
+    if (ignore) {
+        a = e[0];
+        b = e[1];
+    } else {
+        let [j, k] = e;
+
+        a = compCache[j] || indexr(j);
+        compCache[j] = a;
+
+        b = compCache[k] || indexr(k);
+        compCache[k] = b;
+    }
+    if (b > a) {
+        return (b * b + b) / 2n + a + 1n;
+    } else {
+        return (a * a + a) / 2n + b + 1n;
+    }
+}
+
+function decomp(e) {
+    // if (e == 0) return 0;
+
+    if (typeof e != 'bigint') {
+        e = BigInt(isNaN(Number(e)) ? 0 : e);
+    }
+
+    if (e == 0n) return elems['[]'];
+
+    let s = 0n;
+    if (e > 0n) s = (bsqrt(4n * e + 1n) - 1n) / 2n;
+
+    let h = e - (s * s + s) / 2n - 1n;
+
+    let h2 = compCache[h] || decomp(h);
+    compCache[h] = h2;
+
+    let s2 = compCache[s] || decomp(s);
+    compCache[s] = s2;
+
+    let out = JSON.stringify([h2,s2]);
+
+    if (elems[out]) return elems[out];
+
+    out = JSON.stringify([s2,h2]);
+
+    if (elems[out]) return elems[out];
+
+    return [h2,s2]
+}
+
+function bsqrt(value) {
+    if (value < 0n) {
+        throw 'square root of negative numbers is not supported'
+    }
+
+    if (value < 2n) {
+        return value;
+    }
+
+    function newtonIteration(n, x0) {
+        const x1 = ((n / x0) + x0) >> 1n;
+        if (x0 === x1 || x0 === (x1 - 1n)) {
+            return x0;
+        }
+        return newtonIteration(n, x1);
+    }
+
+    return newtonIteration(value, 1n);
+}
+
+for (let i in elems) {
+    let compd = indexr(elems[i]);
+
+    compd += '';
+
+    let l = compd.length;
+    compd = compd.slice(0,Math.min(l,10));
+
+    console.log(`${elems[i]}: ${compd}... (${l} digits)`)
+}