impractical B-M test
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176
rng_trainer.html
176
rng_trainer.html
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@ -29,8 +29,163 @@
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</div>
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<div id="seq"></div>
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<script>
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const error = e => { throw new Error(e) }
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const floatField = {
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mul: (a, b) => a * b,
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add: (a, b) => a + b,
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neg: a => -a,
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inv: a => 1 / a,
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zero: 0,
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unity: 1
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}
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const gf2 = {
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mul: (a, b) => a * b,
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add: (a, b) => (a + b) % 2,
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neg: a => a,
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inv: a => a == 1 ? 1 : error("not invertible"),
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zero: 0,
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unity: 1
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}
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const evalPoly = (poly, x, field) => {
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let a = field.zero
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let b = field.unity
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for (const coef of poly) {
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a = field.add(field.mul(b, coef))
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b = field.mul(b, x)
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}
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return a
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}
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const arrayOf = (n, x) => new Array(n).fill(x)
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const xPowN = (n, field) => arrayOf(n, field.zero).concat([field.unity])
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const polyField = field => {
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const unity = [field.unity]
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const zero = []
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const add = (a, b) => {
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const [ap, bp] = a.length > b.length ? [a, b] : [b, a]
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return ap.map((aix, ix) => field.add(aix, bp[ix] ?? field.zero))
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}
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const mul = (a, b) => {
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const out = arrayOf(a.length + b.length - 1, field.zero)
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for (let i = 0; i < a.length; i++) {
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for (let j = 0; j < b.length; j++) {
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out[i + j] = field.add(out[i + j], field.mul(a[i], b[j]))
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}
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}
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return out
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}
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const neg = a => a.map(field.neg)
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return {
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add,
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mul,
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neg,
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unity,
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zero,
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inv: () => error("unimplemented")
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}
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}
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// blatantly copied from Wikipedia https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm#Pseudocode
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const berlekampMassey = (sequence, field) => {
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const polys = polyField(field)
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const N = sequence.length
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let C = polys.unity
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let B = polys.unity
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let L = 0;
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let m = 1;
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let b = field.unity;
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for (let n = 0; n < N; n++) {
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let d = sequence[n]
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for (let i = 1; i <= L; i++) {
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d = field.add(d, field.mul(C[i], sequence[n - i]))
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}
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if (d == field.zero) {
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m += 1
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} else if (2 * L <= n) {
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const T = C
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C = polys.add(C, polys.neg(polys.mul(polys.mul([field.mul(d, field.inv(b))], xPowN(m, field)), B)))
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L = n + 1 - L
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B = T
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b = d
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m = 1
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} else {
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C = polys.add(C, polys.neg(polys.mul(polys.mul([field.mul(d, field.inv(b))], xPowN(m, field)), B)))
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m += 1
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}
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}
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return C
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}
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const polyToKey = p => p.join("")
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const polyRecurrence = (polynomial, sequence) => gf2.mul(gf2.neg(gf2.inv(polynomial[0])), polynomial.slice(1).map((coef, ix) => gf2.mul(coef, sequence[sequence.length - 1 - ix])).reduce(gf2.add, gf2.zero))
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const bmEnsemble = sequence => {
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const seqlen = 10
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const polys = new Map()
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for (let i = 0; i < sequence.length; i++) {
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const result = berlekampMassey(sequence.slice(i, i + seqlen), gf2)
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polys.set(polyToKey(result), [1, 2, result])
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}
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for (let i = 0; i < sequence.length - 1; i++) {
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const chunk = sequence.slice(0, i)
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for (const [polystr, score] of polys.entries()) {
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const poly = score[2]
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if (chunk.length >= poly.length - 1) {
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const prediction = polyRecurrence(poly, chunk)
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if (prediction == sequence[i]) {
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score[0] += 1
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}
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score[1] += 1
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}
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}
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}
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let max = 0
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let pred = 0
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for (const [polystr, score] of polys.entries()) {
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const bits = score[0] - score[1] - polystr.length
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//console.log(polystr, bits)
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const weight = 2**bits
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max += weight
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pred += weight * polyRecurrence(score[2], sequence)
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}
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console.log("BM", pred / max)
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return max > 0 ? pred / max > 0.5 : 0
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}
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const aaronsonPredictor = sequence => {
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let k = 4
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const m = new Map()
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for (let i = 0; i < sequence.length - 1; i++) {
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const slic = polyToKey(sequence.slice(Math.max(i - k + 1, 0), i + 1))
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if (!m.get(slic)) m.set(slic, [0, 0])
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const score = m.get(slic)
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score[1] += 1
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score[0] += sequence[i + 1]
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}
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var res
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while (k) {
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const slic = polyToKey(sequence.slice(-k))
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if (res = m.get(slic)) {
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const prob = res[0] / res[1]
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console.log("AO", prob, slic)
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return prob > 0.5
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}
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k -= 1
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}
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return 0
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}
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let correct = {
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"aaronson": 0,
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"bm": 0
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}
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var working = true
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const FINALSEQLEN = 100
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const FINALSEQLEN = 300
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const tests = {
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"RNG1": []
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}
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@ -39,9 +194,18 @@
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if (working) {
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seq.push(val)
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qty.innerText = `${seq.length}/${FINALSEQLEN}`
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if (seq.length > 0) {
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correct.bm += bmEnsemble(seq.slice(0, seq.length - 1)) == seq[seq.length - 1] ? 1 : 0
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correct.aaronson += aaronsonPredictor(seq.slice(0, seq.length - 1)) == seq[seq.length - 1] ? 1 : 0
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}
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if (seq.length === FINALSEQLEN) {
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working = false
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qty.innerText = "Done"
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let accuracy = ""
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for (const [name, count] of Object.entries(correct)) {
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accuracy += `; ${name} ${count / FINALSEQLEN * 100}%`
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}
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qty.innerText = `Done${accuracy}`
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console.log(correct)
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}
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}
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}
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@ -49,13 +213,13 @@
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working = true
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seq = []
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}
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l.onclick = () => push("L")
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r.onclick = () => push("R")
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l.onclick = () => push(0)
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r.onclick = () => push(1)
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window.onkeypress = ev => {
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if (ev.key.toLowerCase() == "l" || ev.key == "1") {
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push("L")
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push(0)
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} else if (ev.key.toLowerCase() == "r" || ev.key == "2") {
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push("R")
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push(1)
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}
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}
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</script>
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