large scale refactoring

lib/prng/PRNG/Mt19937.js

@@ -0,0 +1,67 @@
+/**
+ * @module prng
+ */
+const N = 624
+const M = 397
+
+const twist = (u, v) => ((((u & 0x80000000) | (v & 0x7fffffff)) >>> 1) ^ ((v & 1) ? 0x9908b0df : 0))
+
+const nextState = (state) => {
+  let p = 0
+  let j
+  for (j = N - M + 1; --j; p++) {
+    state[p] = state[p + M] ^ twist(state[p], state[p + 1])
+  }
+  for (j = M; --j; p++) {
+    state[p] = state[p + M - N] ^ twist(state[p], state[p + 1])
+  }
+  state[p] = state[p + M - N] ^ twist(state[p], state[0])
+}
+
+/**
+ * This is a port of Shawn Cokus's implementation of the original Mersenne Twister algorithm (http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/MTARCOK/mt19937ar-cok.c).
+ * MT has a very high period of 2^19937. Though the authors of xorshift describe that a high period is not
+ * very relevant (http://vigna.di.unimi.it/xorshift/). It is four times slower than xoroshiro128plus and
+ * needs to recompute its state after generating 624 numbers.
+ *
+ * @example
+ * const gen = new Mt19937(new Date().getTime())
+ * console.log(gen.next())
+ *
+ * @public
+ */
+export class Mt19937 {
+  /**
+   * @param {Number} seed The starting point for the random number generation. If you use the same seed, the generator will return the same sequence of random numbers.
+   */
+  constructor (seed) {
+    this.seed = seed
+    const state = new Uint32Array(N)
+    state[0] = seed
+    for (let i = 1; i < N; i++) {
+      state[i] = (Math.imul(1812433253, (state[i - 1] ^ (state[i - 1] >>> 30))) + i) & 0xFFFFFFFF
+    }
+    this._state = state
+    this._i = 0
+    nextState(this._state)
+  }
+
+  /**
+   * Generate a random signed integer.
+   *
+   * @return {Number} A 32 bit signed integer.
+   */
+  next () {
+    if (this._i === N) {
+      // need to compute a new state
+      nextState(this._state)
+      this._i = 0
+    }
+    let y = this._state[this._i++]
+    y ^= (y >>> 11)
+    y ^= (y << 7) & 0x9d2c5680
+    y ^= (y << 15) & 0xefc60000
+    y ^= (y >>> 18)
+    return y
+  }
+}

lib/prng/PRNG/PRNG.tests.js

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+/**
+ * @module prng
+ */
+
+import { Mt19937 } from './Mt19937.js'
+import { Xoroshiro128plus } from './Xoroshiro128plus.js'
+import { Xorshift32 } from './Xorshift32.js'
+import * as time from '../../time.js'
+
+const DIAMETER = 300
+const NUMBERS = 10000
+
+const runPRNG = (name, Gen) => {
+  console.log('== ' + name + ' ==')
+  const gen = new Gen(1234)
+  let head = 0
+  let tails = 0
+  const date = time.getUnixTime()
+  const canvas = document.createElement('canvas')
+  canvas.height = DIAMETER
+  canvas.width = DIAMETER
+  const ctx = canvas.getContext('2d')
+  const vals = new Set()
+  ctx.fillStyle = 'blue'
+  for (let i = 0; i < NUMBERS; i++) {
+    const n = gen.next() & 0xFFFFFF
+    const x = (gen.next() >>> 0) % DIAMETER
+    const y = (gen.next() >>> 0) % DIAMETER
+    ctx.fillRect(x, y, 1, 2)
+    if ((n & 1) === 1) {
+      head++
+    } else {
+      tails++
+    }
+    if (vals.has(n)) {
+      console.warn(`The generator generated a duplicate`)
+    }
+    vals.add(n)
+  }
+  console.log('time: ', time.getUnixTime() - date)
+  console.log('head:', head, 'tails:', tails)
+  console.log('%c       ', `font-size: 200px; background: url(${canvas.toDataURL()}) no-repeat;`)
+  const h1 = document.createElement('h1')
+  h1.insertBefore(document.createTextNode(name), null)
+  document.body.insertBefore(h1, null)
+  document.body.appendChild(canvas)
+}
+
+runPRNG('mt19937', Mt19937)
+runPRNG('xoroshiro128plus', Xoroshiro128plus)
+runPRNG('xorshift32', Xorshift32)

lib/prng/PRNG/README.md

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+# Pseudo Random Number Generators (PRNG)
+
+Given a seed a PRNG generates a sequence of numbers that cannot be reasonably predicted. Two PRNGs must generate the same random sequence of numbers if  given the same seed.
+
+TODO: explain what POINT is

lib/prng/PRNG/Xoroshiro128plus.js

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+/**
+ * @module prng
+ */
+
+import { Xorshift32 } from './Xorshift32.js'
+
+/**
+ * This is a variant of xoroshiro128plus - the fastest full-period generator passing BigCrush without systematic failures.
+ *
+ * This implementation follows the idea of the original xoroshiro128plus implementation,
+ * but is optimized for the JavaScript runtime. I.e.
+ * * The operations are performed on 32bit integers (the original implementation works with 64bit values).
+ * * The initial 128bit state is computed based on a 32bit seed and Xorshift32.
+ * * This implementation returns two 32bit values based on the 64bit value that is computed by xoroshiro128plus.
+ *   Caution: The last addition step works slightly different than in the original implementation - the add carry of the
+ *   first 32bit addition is not carried over to the last 32bit.
+ *
+ * [Reference implementation](http://vigna.di.unimi.it/xorshift/xoroshiro128plus.c)
+ */
+export class Xoroshiro128plus {
+  constructor (seed) {
+    this.seed = seed
+    // This is a variant of Xoroshiro128plus to fill the initial state
+    const xorshift32 = new Xorshift32(seed)
+    this.state = new Uint32Array(4)
+    for (let i = 0; i < 4; i++) {
+      this.state[i] = xorshift32.next()
+    }
+    this._fresh = true
+  }
+  next () {
+    const state = this.state
+    if (this._fresh) {
+      this._fresh = false
+      return (state[0] + state[2]) & 0xFFFFFFFF
+    } else {
+      this._fresh = true
+      const s0 = state[0]
+      const s1 = state[1]
+      const s2 = state[2] ^ s0
+      const s3 = state[3] ^ s1
+      // function js_rotl (x, k) {
+      //   k = k - 32
+      //   const x1 = x[0]
+      //   const x2 = x[1]
+      //   x[0] = x2 << k | x1 >>> (32 - k)
+      //   x[1] = x1 << k | x2 >>> (32 - k)
+      // }
+      // rotl(s0, 55) // k = 23 = 55 - 32; j = 9 =  32 - 23
+      state[0] = (s1 << 23 | s0 >>> 9) ^ s2 ^ (s2 << 14 | s3 >>> 18)
+      state[1] = (s0 << 23 | s1 >>> 9) ^ s3 ^ (s3 << 14)
+      // rol(s1, 36) // k = 4 = 36 - 32; j = 23 = 32 - 9
+      state[2] = s3 << 4 | s2 >>> 28
+      state[3] = s2 << 4 | s3 >>> 28
+      return (state[1] + state[3]) & 0xFFFFFFFF
+    }
+  }
+}
+
+/*
+
+// reference implementation
+#include <stdint.h>
+#include <stdio.h>
+
+uint64_t s[2];
+
+static inline uint64_t rotl(const uint64_t x, int k) {
+    return (x << k) | (x >> (64 - k));
+}
+
+uint64_t next(void) {
+    const uint64_t s0 = s[0];
+    uint64_t s1 = s[1];
+    s1 ^= s0;
+    s[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14); // a, b
+    s[1] = rotl(s1, 36); // c
+    return (s[0] + s[1]) & 0xFFFFFFFF;
+}
+
+int main(void)
+{
+    int i;
+    s[0] = 1111 | (1337ul << 32);
+    s[1] = 1234 | (9999ul << 32);
+
+    printf("1000 outputs of genrand_int31()\n");
+    for (i=0; i<100; i++) {
+        printf("%10lu ", i);
+        printf("%10lu ", next());
+        printf("- %10lu ", s[0] >> 32);
+        printf("%10lu ", (s[0] << 32) >> 32);
+        printf("%10lu ", s[1] >> 32);
+        printf("%10lu ", (s[1] << 32) >> 32);
+        printf("\n");
+        // if (i%5==4) printf("\n");
+    }
+    return 0;
+}
+
+*/

lib/prng/PRNG/Xorshift32.js

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+/**
+ * @module prng
+ */
+
+/**
+ * Xorshift32 is a very simple but elegang PRNG with a period of `2^32-1`.
+ */
+export class Xorshift32 {
+  /**
+   * @param {number} seed The starting point for the random number generation. If you use the same seed, the generator will return the same sequence of random numbers.
+   */
+  constructor (seed) {
+    this.seed = seed
+    this._state = seed
+  }
+  /**
+   * Generate a random signed integer.
+   *
+   * @return {Number} A 32 bit signed integer.
+   */
+  next () {
+    let x = this._state
+    x ^= x << 13
+    x ^= x >> 17
+    x ^= x << 5
+    this._state = x
+    return x
+  }
+}