// 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_