Add test to check PRNG quality.

test/cctest/test-random-number-generator.cc

 // Copyright 2013 the V8 project authors. All rights reserved.
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are
 // met:
 //
 //     * Redistributions of source code must retain the above copyright
 //       notice, this list of conditions and the following disclaimer.
 //     * Redistributions in binary form must reproduce the above
 //       copyright notice, this list of conditions and the following
 //       disclaimer in the documentation and/or other materials provided
@@ skipping 33 matching lines @@
     FLAG_random_seed = static_cast<int>(kRandomSeeds[n]);
     v8::Isolate::CreateParams create_params;
     create_params.array_buffer_allocator = CcTest::array_buffer_allocator();
     v8::Isolate* i = v8::Isolate::New(create_params);
     v8::base::RandomNumberGenerator& rng =
         *reinterpret_cast<Isolate*>(i)->random_number_generator();
     CHECK_EQ(kRandomSeeds[n], rng.initial_seed());
     i->Dispose();
   }
 }
+
+
+// Chi squared for getting m 0s out of n bits.
+double ChiSquared(int m, int n) {
+  double ys_minus_np1 = (m - n / 2.0);
+  double chi_squared_1 = ys_minus_np1 * ys_minus_np1 * 2.0 / n;
+  double ys_minus_np2 = ((n - m) - n / 2.0);
+  double chi_squared_2 = ys_minus_np2 * ys_minus_np2 * 2.0 / n;
+  return chi_squared_1 + chi_squared_2;
+}
+
+
+// Test for correlations between recent bits from the PRNG, or bits that are
+// biased.
+void RandomBitCorrelation(int random_bit) {
+  FLAG_random_seed = 31415926;
+  v8::Isolate::CreateParams create_params;
+  create_params.array_buffer_allocator = CcTest::array_buffer_allocator();
+  v8::Isolate* isolate = v8::Isolate::New(create_params);
+  Isolate* i_isolate = reinterpret_cast<Isolate*>(isolate);
+  v8::base::RandomNumberGenerator* rng = i_isolate->random_number_generator();
+#ifdef DEBUG
+  const int kHistory = 2;
+  const int kRepeats = 1000;
+#else
+  const int kHistory = 8;
+  const int kRepeats = 10000;
+#endif
+  uint32_t history[kHistory];
+  // The predictor bit is either constant 0 or 1, or one of the bits from the
+  // history.
+  for (int predictor_bit = -2; predictor_bit < 32; predictor_bit++) {
+    // The predicted bit is one of the bits from the PRNG.
+    for (int 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 (int i = ago; i >= 0; i--) {
+        history[i] = bit_cast<uint32_t>(rng->NextInt());
+      }
+
+      // Find out how many of the bits are the same as the prediction bit.
+      int m = 0;
+      for (int i = 0; i < kRepeats; i++) {
+        v8::HandleScope scope(isolate);
+        uint32_t random = bit_cast<uint32_t>(rng->NextInt());
+        for (int j = ago - 1; j >= 0; j--) history[j + 1] = history[j];
+        history[0] = random;
+
+        int predicted;
+        if (predictor_bit >= 0) {
+          predicted = (history[ago] >> predictor_bit) & 1;
+        } else {
+          predicted = predictor_bit == -2 ? 0 : 1;
+        }
+        int bit = (random >> 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).
+      double chi_squared = ChiSquared(m, kRepeats);
+      if (chi_squared > 24) {
+        int percent = static_cast<int>(m * 100.0 / kRepeats);
+        if (predictor_bit < 0) {
+          PrintF("Bit %d is %d %d%% of the time\n", random_bit,
+                 predictor_bit == -2 ? 0 : 1, percent);
+        } else {
+          PrintF("Bit %d is the same as bit %d %d ago %d%% of the time\n",
+                 random_bit, predictor_bit, ago, percent);
+        }
+      }
+
+      // For 1 degree of freedom this corresponds to 1 in a million.  We are
+      // running ~8000 tests, so that would be surprising.
+      CHECK(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;
+    }
+  }
+  isolate->Dispose();
+}
+
+
+#define TEST_RANDOM_BIT(BIT) \
+  TEST(RandomBitCorrelations##BIT) { RandomBitCorrelation(BIT); }
+
+TEST_RANDOM_BIT(0)
+TEST_RANDOM_BIT(1)
+TEST_RANDOM_BIT(2)
+TEST_RANDOM_BIT(3)
+TEST_RANDOM_BIT(4)
+TEST_RANDOM_BIT(5)
+TEST_RANDOM_BIT(6)
+TEST_RANDOM_BIT(7)
+TEST_RANDOM_BIT(8)
+TEST_RANDOM_BIT(9)
+TEST_RANDOM_BIT(10)
+TEST_RANDOM_BIT(11)
+TEST_RANDOM_BIT(12)
+TEST_RANDOM_BIT(13)
+TEST_RANDOM_BIT(14)
+TEST_RANDOM_BIT(15)
+TEST_RANDOM_BIT(16)
+TEST_RANDOM_BIT(17)
+TEST_RANDOM_BIT(18)
+TEST_RANDOM_BIT(19)
+TEST_RANDOM_BIT(20)
+TEST_RANDOM_BIT(21)
+TEST_RANDOM_BIT(22)
+TEST_RANDOM_BIT(23)
+TEST_RANDOM_BIT(24)
+TEST_RANDOM_BIT(25)
+TEST_RANDOM_BIT(26)
+TEST_RANDOM_BIT(27)
+TEST_RANDOM_BIT(28)
+TEST_RANDOM_BIT(29)
+TEST_RANDOM_BIT(30)
+TEST_RANDOM_BIT(31)
+
+#undef TEST_RANDOM_BIT