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+// 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_