THUAI6/CAPI/cpp/grpc/include/absl/profiling/internal/exponential_biased.h

// 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_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_
#define ABSL_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_

#include <stdint.h>

#include "absl/base/config.h"
#include "absl/base/macros.h"

namespace absl
{
    ABSL_NAMESPACE_BEGIN
    namespace profiling_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 profiling_internal
    ABSL_NAMESPACE_END
}  // namespace absl

#endif  // ABSL_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_