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0001 // Copyright 2019 The Abseil Authors. 0002 // 0003 // Licensed under the Apache License, Version 2.0 (the "License"); 0004 // you may not use this file except in compliance with the License. 0005 // You may obtain a copy of the License at 0006 // 0007 // https://www.apache.org/licenses/LICENSE-2.0 0008 // 0009 // Unless required by applicable law or agreed to in writing, software 0010 // distributed under the License is distributed on an "AS IS" BASIS, 0011 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 0012 // See the License for the specific language governing permissions and 0013 // limitations under the License. 0014 0015 #ifndef ABSL_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_ 0016 #define ABSL_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_ 0017 0018 #include <stdint.h> 0019 0020 #include "absl/base/config.h" 0021 #include "absl/base/macros.h" 0022 0023 namespace absl { 0024 ABSL_NAMESPACE_BEGIN 0025 namespace profiling_internal { 0026 0027 // ExponentialBiased provides a small and fast random number generator for a 0028 // rounded exponential distribution. This generator manages very little state, 0029 // and imposes no synchronization overhead. This makes it useful in specialized 0030 // scenarios requiring minimum overhead, such as stride based periodic sampling. 0031 // 0032 // ExponentialBiased provides two closely related functions, GetSkipCount() and 0033 // GetStride(), both returning a rounded integer defining a number of events 0034 // required before some event with a given mean probability occurs. 0035 // 0036 // The distribution is useful to generate a random wait time or some periodic 0037 // event with a given mean probability. For example, if an action is supposed to 0038 // happen on average once every 'N' events, then we can get a random 'stride' 0039 // counting down how long before the event to happen. For example, if we'd want 0040 // to sample one in every 1000 'Frobber' calls, our code could look like this: 0041 // 0042 // Frobber::Frobber() { 0043 // stride_ = exponential_biased_.GetStride(1000); 0044 // } 0045 // 0046 // void Frobber::Frob(int arg) { 0047 // if (--stride == 0) { 0048 // SampleFrob(arg); 0049 // stride_ = exponential_biased_.GetStride(1000); 0050 // } 0051 // ... 0052 // } 0053 // 0054 // The rounding of the return value creates a bias, especially for smaller means 0055 // where the distribution of the fraction is not evenly distributed. We correct 0056 // this bias by tracking the fraction we rounded up or down on each iteration, 0057 // effectively tracking the distance between the cumulative value, and the 0058 // rounded cumulative value. For example, given a mean of 2: 0059 // 0060 // raw = 1.63076, cumulative = 1.63076, rounded = 2, bias = -0.36923 0061 // raw = 0.14624, cumulative = 1.77701, rounded = 2, bias = 0.14624 0062 // raw = 4.93194, cumulative = 6.70895, rounded = 7, bias = -0.06805 0063 // raw = 0.24206, cumulative = 6.95101, rounded = 7, bias = 0.24206 0064 // etc... 0065 // 0066 // Adjusting with rounding bias is relatively trivial: 0067 // 0068 // double value = bias_ + exponential_distribution(mean)(); 0069 // double rounded_value = std::rint(value); 0070 // bias_ = value - rounded_value; 0071 // return rounded_value; 0072 // 0073 // This class is thread-compatible. 0074 class ExponentialBiased { 0075 public: 0076 // The number of bits set by NextRandom. 0077 static constexpr int kPrngNumBits = 48; 0078 0079 // `GetSkipCount()` returns the number of events to skip before some chosen 0080 // event happens. For example, randomly tossing a coin, we will on average 0081 // throw heads once before we get tails. We can simulate random coin tosses 0082 // using GetSkipCount() as: 0083 // 0084 // ExponentialBiased eb; 0085 // for (...) { 0086 // int number_of_heads_before_tail = eb.GetSkipCount(1); 0087 // for (int flips = 0; flips < number_of_heads_before_tail; ++flips) { 0088 // printf("head..."); 0089 // } 0090 // printf("tail\n"); 0091 // } 0092 // 0093 int64_t GetSkipCount(int64_t mean); 0094 0095 // GetStride() returns the number of events required for a specific event to 0096 // happen. See the class comments for a usage example. `GetStride()` is 0097 // equivalent to `GetSkipCount(mean - 1) + 1`. When to use `GetStride()` or 0098 // `GetSkipCount()` depends mostly on what best fits the use case. 0099 int64_t GetStride(int64_t mean); 0100 0101 // Computes a random number in the range [0, 1<<(kPrngNumBits+1) - 1] 0102 // 0103 // This is public to enable testing. 0104 static uint64_t NextRandom(uint64_t rnd); 0105 0106 private: 0107 void Initialize(); 0108 0109 uint64_t rng_{0}; 0110 double bias_{0}; 0111 bool initialized_{false}; 0112 }; 0113 0114 // Returns the next prng value. 0115 // pRNG is: aX+b mod c with a = 0x5DEECE66D, b = 0xB, c = 1<<48 0116 // This is the lrand64 generator. 0117 inline uint64_t ExponentialBiased::NextRandom(uint64_t rnd) { 0118 const uint64_t prng_mult = uint64_t{0x5DEECE66D}; 0119 const uint64_t prng_add = 0xB; 0120 const uint64_t prng_mod_power = 48; 0121 const uint64_t prng_mod_mask = 0122 ~((~static_cast<uint64_t>(0)) << prng_mod_power); 0123 return (prng_mult * rnd + prng_add) & prng_mod_mask; 0124 } 0125 0126 } // namespace profiling_internal 0127 ABSL_NAMESPACE_END 0128 } // namespace absl 0129 0130 #endif // ABSL_PROFILING_INTERNAL_EXPONENTIAL_BIASED_H_
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