Add 'third_party/abseil_cpp/' from commit '768eb2ca28'

git-subtree-dir: third_party/abseil_cpp
git-subtree-mainline: ffb2ae54be
git-subtree-split: 768eb2ca28

third_party/abseil_cpp/absl/base/internal/exponential_biased.cc

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+// Copyright 2019 The Abseil Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "absl/base/internal/exponential_biased.h"
+
+#include <stdint.h>
+
+#include <algorithm>
+#include <atomic>
+#include <cmath>
+#include <limits>
+
+#include "absl/base/attributes.h"
+#include "absl/base/optimization.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace base_internal {
+
+// The algorithm generates a random number between 0 and 1 and applies the
+// inverse cumulative distribution function for an exponential. Specifically:
+// Let m be the inverse of the sample period, then the probability
+// distribution function is m*exp(-mx) so the CDF is
+// p = 1 - exp(-mx), so
+// q = 1 - p = exp(-mx)
+// log_e(q) = -mx
+// -log_e(q)/m = x
+// log_2(q) * (-log_e(2) * 1/m) = x
+// In the code, q is actually in the range 1 to 2**26, hence the -26 below
+int64_t ExponentialBiased::GetSkipCount(int64_t mean) {
+  if (ABSL_PREDICT_FALSE(!initialized_)) {
+    Initialize();
+  }
+
+  uint64_t rng = NextRandom(rng_);
+  rng_ = rng;
+
+  // Take the top 26 bits as the random number
+  // (This plus the 1<<58 sampling bound give a max possible step of
+  // 5194297183973780480 bytes.)
+  // The uint32_t cast is to prevent a (hard-to-reproduce) NAN
+  // under piii debug for some binaries.
+  double q = static_cast<uint32_t>(rng >> (kPrngNumBits - 26)) + 1.0;
+  // Put the computed p-value through the CDF of a geometric.
+  double interval = bias_ + (std::log2(q) - 26) * (-std::log(2.0) * mean);
+  // Very large values of interval overflow int64_t. To avoid that, we will
+  // cheat and clamp any huge values to (int64_t max)/2. This is a potential
+  // source of bias, but the mean would need to be such a large value that it's
+  // not likely to come up. For example, with a mean of 1e18, the probability of
+  // hitting this condition is about 1/1000. For a mean of 1e17, standard
+  // calculators claim that this event won't happen.
+  if (interval > static_cast<double>(std::numeric_limits<int64_t>::max() / 2)) {
+    // Assume huge values are bias neutral, retain bias for next call.
+    return std::numeric_limits<int64_t>::max() / 2;
+  }
+  double value = std::round(interval);
+  bias_ = interval - value;
+  return value;
+}
+
+int64_t ExponentialBiased::GetStride(int64_t mean) {
+  return GetSkipCount(mean - 1) + 1;
+}
+
+void ExponentialBiased::Initialize() {
+  // We don't get well distributed numbers from `this` so we call NextRandom() a
+  // bunch to mush the bits around. We use a global_rand to handle the case
+  // where the same thread (by memory address) gets created and destroyed
+  // repeatedly.
+  ABSL_CONST_INIT static std::atomic<uint32_t> global_rand(0);
+  uint64_t r = reinterpret_cast<uint64_t>(this) +
+               global_rand.fetch_add(1, std::memory_order_relaxed);
+  for (int i = 0; i < 20; ++i) {
+    r = NextRandom(r);
+  }
+  rng_ = r;
+  initialized_ = true;
+}
+
+}  // namespace base_internal
+ABSL_NAMESPACE_END
+}  // namespace absl