94 lines
3.4 KiB
C++
94 lines
3.4 KiB
C++
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// 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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#include "absl/base/internal/exponential_biased.h"
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#include <stdint.h>
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#include <algorithm>
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#include <atomic>
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#include <cmath>
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#include <limits>
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#include "absl/base/attributes.h"
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#include "absl/base/optimization.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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// The algorithm generates a random number between 0 and 1 and applies the
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// inverse cumulative distribution function for an exponential. Specifically:
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// Let m be the inverse of the sample period, then the probability
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// distribution function is m*exp(-mx) so the CDF is
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// p = 1 - exp(-mx), so
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// q = 1 - p = exp(-mx)
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// log_e(q) = -mx
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// -log_e(q)/m = x
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// log_2(q) * (-log_e(2) * 1/m) = x
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// In the code, q is actually in the range 1 to 2**26, hence the -26 below
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int64_t ExponentialBiased::GetSkipCount(int64_t mean) {
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if (ABSL_PREDICT_FALSE(!initialized_)) {
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Initialize();
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}
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uint64_t rng = NextRandom(rng_);
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rng_ = rng;
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// Take the top 26 bits as the random number
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// (This plus the 1<<58 sampling bound give a max possible step of
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// 5194297183973780480 bytes.)
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// The uint32_t cast is to prevent a (hard-to-reproduce) NAN
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// under piii debug for some binaries.
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double q = static_cast<uint32_t>(rng >> (kPrngNumBits - 26)) + 1.0;
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// Put the computed p-value through the CDF of a geometric.
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double interval = bias_ + (std::log2(q) - 26) * (-std::log(2.0) * mean);
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// Very large values of interval overflow int64_t. To avoid that, we will
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// cheat and clamp any huge values to (int64_t max)/2. This is a potential
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// source of bias, but the mean would need to be such a large value that it's
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// not likely to come up. For example, with a mean of 1e18, the probability of
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// hitting this condition is about 1/1000. For a mean of 1e17, standard
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// calculators claim that this event won't happen.
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if (interval > static_cast<double>(std::numeric_limits<int64_t>::max() / 2)) {
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// Assume huge values are bias neutral, retain bias for next call.
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return std::numeric_limits<int64_t>::max() / 2;
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}
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double value = std::rint(interval);
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bias_ = interval - value;
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return value;
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}
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int64_t ExponentialBiased::GetStride(int64_t mean) {
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return GetSkipCount(mean - 1) + 1;
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}
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void ExponentialBiased::Initialize() {
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// We don't get well distributed numbers from `this` so we call NextRandom() a
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// bunch to mush the bits around. We use a global_rand to handle the case
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// where the same thread (by memory address) gets created and destroyed
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// repeatedly.
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ABSL_CONST_INIT static std::atomic<uint32_t> global_rand(0);
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uint64_t r = reinterpret_cast<uint64_t>(this) +
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global_rand.fetch_add(1, std::memory_order_relaxed);
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for (int i = 0; i < 20; ++i) {
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r = NextRandom(r);
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}
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rng_ = r;
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initialized_ = true;
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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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