text: // 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::rint(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_
  