test/mjsunit/random-bit-correlations.js

// Copyright 2015 the V8 project authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

// Flags: --random-seed=20 --nostress-opt --noalways-opt --predictable

(function() {
  var kHistory = 2;
  var kRepeats = 100;
  var history = new Uint32Array(kHistory);

  function random() {
    return (Math.random() * Math.pow(2, 32)) >>> 0;
  }

  function ChiSquared(m, n) {
    var ys_minus_np1 = (m - n / 2.0);
    var chi_squared_1 = ys_minus_np1 * ys_minus_np1 * 2.0 / n;
    var ys_minus_np2 = ((n - m) - n / 2.0);
    var chi_squared_2 = ys_minus_np2 * ys_minus_np2 * 2.0 / n;
    return chi_squared_1 + chi_squared_2;
  }
  for (var predictor_bit = -2; predictor_bit < 32; predictor_bit++) {
    // The predicted bit is one of the bits from the PRNG.
    for (var random_bit = 0; random_bit < 32; random_bit++) {
      for (var ago = 0; ago < kHistory; ago++) {
        // We don't want to check whether each bit predicts itself.
        if (ago == 0 && predictor_bit == random_bit) continue;
        // Enter the new random value into the history
        for (var i = ago; i >= 0; i--) {
          history[i] = random();
        }
        // Find out how many of the bits are the same as the prediction bit.
        var m = 0;
        for (var i = 0; i < kRepeats; i++) {
          for (var j = ago - 1; j >= 0; j--) history[j + 1] = history[j];
          history[0] = random();
          var predicted;
          if (predictor_bit >= 0) {
            predicted = (history[ago] >> predictor_bit) & 1;
          } else {
            predicted = predictor_bit == -2 ? 0 : 1;
          }
          var bit = (history[0] >> random_bit) & 1;
          if (bit == predicted) m++;
        }
        // Chi squared analysis for k = 2 (2, states: same/not-same) and one
        // degree of freedom (k - 1).
        var chi_squared = ChiSquared(m, kRepeats);
        if (chi_squared > 24) {
          var percent = Math.floor(m * 100.0 / kRepeats);
          if (predictor_bit < 0) {
            var bit_value = predictor_bit == -2 ? 0 : 1;
            print(`Bit ${random_bit} is ${bit_value} ${percent}% of the time`);
          } else {
            print(`Bit ${random_bit} is the same as bit ${predictor_bit} ` +
              `${ago} ago ${percent}% of the time`);
          }
        }
        // For 1 degree of freedom this corresponds to 1 in a million.  We are
        // running ~8000 tests, so that would be surprising.
        assertTrue(chi_squared <= 24);
        // If the predictor bit is a fixed 0 or 1 then it makes no sense to
        // repeat the test with a different age.
        if (predictor_bit < 0) break;
      }
    }
  }
})();