131 lines
4.8 KiB
C++
131 lines
4.8 KiB
C++
// Copyright 2019 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_
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#define ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_
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#include <stdint.h>
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#include "absl/base/config.h"
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#include "absl/base/macros.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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namespace base_internal {
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// ExponentialBiased provides a small and fast random number generator for a
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// rounded exponential distribution. This generator manages very little state,
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// and imposes no synchronization overhead. This makes it useful in specialized
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// scenarios requiring minimum overhead, such as stride based periodic sampling.
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//
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// ExponentialBiased provides two closely related functions, GetSkipCount() and
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// GetStride(), both returning a rounded integer defining a number of events
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// required before some event with a given mean probability occurs.
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//
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// The distribution is useful to generate a random wait time or some periodic
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// event with a given mean probability. For example, if an action is supposed to
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// happen on average once every 'N' events, then we can get a random 'stride'
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// counting down how long before the event to happen. For example, if we'd want
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// to sample one in every 1000 'Frobber' calls, our code could look like this:
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//
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// Frobber::Frobber() {
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// stride_ = exponential_biased_.GetStride(1000);
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// }
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//
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// void Frobber::Frob(int arg) {
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// if (--stride == 0) {
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// SampleFrob(arg);
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// stride_ = exponential_biased_.GetStride(1000);
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// }
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// ...
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// }
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//
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// The rounding of the return value creates a bias, especially for smaller means
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// where the distribution of the fraction is not evenly distributed. We correct
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// this bias by tracking the fraction we rounded up or down on each iteration,
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// effectively tracking the distance between the cumulative value, and the
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// rounded cumulative value. For example, given a mean of 2:
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//
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// raw = 1.63076, cumulative = 1.63076, rounded = 2, bias = -0.36923
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// raw = 0.14624, cumulative = 1.77701, rounded = 2, bias = 0.14624
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// raw = 4.93194, cumulative = 6.70895, rounded = 7, bias = -0.06805
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// raw = 0.24206, cumulative = 6.95101, rounded = 7, bias = 0.24206
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// etc...
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//
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// Adjusting with rounding bias is relatively trivial:
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//
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// double value = bias_ + exponential_distribution(mean)();
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// double rounded_value = std::rint(value);
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// bias_ = value - rounded_value;
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// return rounded_value;
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//
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// This class is thread-compatible.
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class ExponentialBiased {
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public:
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// The number of bits set by NextRandom.
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static constexpr int kPrngNumBits = 48;
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// `GetSkipCount()` returns the number of events to skip before some chosen
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// event happens. For example, randomly tossing a coin, we will on average
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// throw heads once before we get tails. We can simulate random coin tosses
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// using GetSkipCount() as:
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//
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// ExponentialBiased eb;
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// for (...) {
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// int number_of_heads_before_tail = eb.GetSkipCount(1);
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// for (int flips = 0; flips < number_of_heads_before_tail; ++flips) {
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// printf("head...");
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// }
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// printf("tail\n");
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// }
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//
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int64_t GetSkipCount(int64_t mean);
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// GetStride() returns the number of events required for a specific event to
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// happen. See the class comments for a usage example. `GetStride()` is
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// equivalent to `GetSkipCount(mean - 1) + 1`. When to use `GetStride()` or
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// `GetSkipCount()` depends mostly on what best fits the use case.
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int64_t GetStride(int64_t mean);
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// Computes a random number in the range [0, 1<<(kPrngNumBits+1) - 1]
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//
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// This is public to enable testing.
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static uint64_t NextRandom(uint64_t rnd);
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private:
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void Initialize();
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uint64_t rng_{0};
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double bias_{0};
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bool initialized_{false};
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};
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// Returns the next prng value.
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// pRNG is: aX+b mod c with a = 0x5DEECE66D, b = 0xB, c = 1<<48
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// This is the lrand64 generator.
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inline uint64_t ExponentialBiased::NextRandom(uint64_t rnd) {
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const uint64_t prng_mult = uint64_t{0x5DEECE66D};
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const uint64_t prng_add = 0xB;
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const uint64_t prng_mod_power = 48;
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const uint64_t prng_mod_mask =
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~((~static_cast<uint64_t>(0)) << prng_mod_power);
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return (prng_mult * rnd + prng_add) & prng_mod_mask;
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}
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} // namespace base_internal
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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_BASE_INTERNAL_EXPONENTIAL_BIASED_H_
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