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.h

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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.
+
+#ifndef ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_
+#define ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_
+
+#include <stdint.h>
+
+#include "absl/base/config.h"
+#include "absl/base/macros.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace base_internal {
+
+// ExponentialBiased provides a small and fast random number generator for a
+// rounded exponential distribution. This generator manages very little state,
+// and imposes no synchronization overhead. This makes it useful in specialized
+// scenarios requiring minimum overhead, such as stride based periodic sampling.
+//
+// ExponentialBiased provides two closely related functions, GetSkipCount() and
+// GetStride(), both returning a rounded integer defining a number of events
+// required before some event with a given mean probability occurs.
+//
+// The distribution is useful to generate a random wait time or some periodic
+// event with a given mean probability. For example, if an action is supposed to
+// happen on average once every 'N' events, then we can get a random 'stride'
+// counting down how long before the event to happen. For example, if we'd want
+// to sample one in every 1000 'Frobber' calls, our code could look like this:
+//
+//   Frobber::Frobber() {
+//     stride_ = exponential_biased_.GetStride(1000);
+//   }
+//
+//   void Frobber::Frob(int arg) {
+//     if (--stride == 0) {
+//       SampleFrob(arg);
+//       stride_ = exponential_biased_.GetStride(1000);
+//     }
+//     ...
+//   }
+//
+// The rounding of the return value creates a bias, especially for smaller means
+// where the distribution of the fraction is not evenly distributed. We correct
+// this bias by tracking the fraction we rounded up or down on each iteration,
+// effectively tracking the distance between the cumulative value, and the
+// rounded cumulative value. For example, given a mean of 2:
+//
+//   raw = 1.63076, cumulative = 1.63076, rounded = 2, bias = -0.36923
+//   raw = 0.14624, cumulative = 1.77701, rounded = 2, bias =  0.14624
+//   raw = 4.93194, cumulative = 6.70895, rounded = 7, bias = -0.06805
+//   raw = 0.24206, cumulative = 6.95101, rounded = 7, bias =  0.24206
+//   etc...
+//
+// Adjusting with rounding bias is relatively trivial:
+//
+//    double value = bias_ + exponential_distribution(mean)();
+//    double rounded_value = std::round(value);
+//    bias_ = value - rounded_value;
+//    return rounded_value;
+//
+// This class is thread-compatible.
+class ExponentialBiased {
+ public:
+  // The number of bits set by NextRandom.
+  static constexpr int kPrngNumBits = 48;
+
+  // `GetSkipCount()` returns the number of events to skip before some chosen
+  // event happens. For example, randomly tossing a coin, we will on average
+  // throw heads once before we get tails. We can simulate random coin tosses
+  // using GetSkipCount() as:
+  //
+  //   ExponentialBiased eb;
+  //   for (...) {
+  //     int number_of_heads_before_tail = eb.GetSkipCount(1);
+  //     for (int flips = 0; flips < number_of_heads_before_tail; ++flips) {
+  //       printf("head...");
+  //     }
+  //     printf("tail\n");
+  //   }
+  //
+  int64_t GetSkipCount(int64_t mean);
+
+  // GetStride() returns the number of events required for a specific event to
+  // happen. See the class comments for a usage example. `GetStride()` is
+  // equivalent to `GetSkipCount(mean - 1) + 1`. When to use `GetStride()` or
+  // `GetSkipCount()` depends mostly on what best fits the use case.
+  int64_t GetStride(int64_t mean);
+
+  // Computes a random number in the range [0, 1<<(kPrngNumBits+1) - 1]
+  //
+  // This is public to enable testing.
+  static uint64_t NextRandom(uint64_t rnd);
+
+ private:
+  void Initialize();
+
+  uint64_t rng_{0};
+  double bias_{0};
+  bool initialized_{false};
+};
+
+// Returns the next prng value.
+// pRNG is: aX+b mod c with a = 0x5DEECE66D, b =  0xB, c = 1<<48
+// This is the lrand64 generator.
+inline uint64_t ExponentialBiased::NextRandom(uint64_t rnd) {
+  const uint64_t prng_mult = uint64_t{0x5DEECE66D};
+  const uint64_t prng_add = 0xB;
+  const uint64_t prng_mod_power = 48;
+  const uint64_t prng_mod_mask =
+      ~((~static_cast<uint64_t>(0)) << prng_mod_power);
+  return (prng_mult * rnd + prng_add) & prng_mod_mask;
+}
+
+}  // namespace base_internal
+ABSL_NAMESPACE_END
+}  // namespace absl
+
+#endif  // ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_