Abseil Common Libraries (C++) (grcp 依赖)
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260 lines
8.8 KiB
260 lines
8.8 KiB
// Copyright 2017 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_RANDOM_GAUSSIAN_DISTRIBUTION_H_ |
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#define ABSL_RANDOM_GAUSSIAN_DISTRIBUTION_H_ |
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// absl::gaussian_distribution implements the Ziggurat algorithm |
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// for generating random gaussian numbers. |
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// |
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// Implementation based on "The Ziggurat Method for Generating Random Variables" |
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// by George Marsaglia and Wai Wan Tsang: http://www.jstatsoft.org/v05/i08/ |
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// |
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#include <cmath> |
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#include <cstdint> |
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#include <istream> |
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#include <limits> |
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#include <type_traits> |
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#include "absl/random/internal/distribution_impl.h" |
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#include "absl/random/internal/fast_uniform_bits.h" |
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#include "absl/random/internal/iostream_state_saver.h" |
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namespace absl { |
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namespace random_internal { |
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// absl::gaussian_distribution_base implements the underlying ziggurat algorithm |
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// using the ziggurat tables generated by the gaussian_distribution_gentables |
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// binary. |
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// |
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// The specific algorithm has some of the improvements suggested by the |
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// 2005 paper, "An Improved Ziggurat Method to Generate Normal Random Samples", |
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// Jurgen A Doornik. (https://www.doornik.com/research/ziggurat.pdf) |
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class gaussian_distribution_base { |
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public: |
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template <typename URBG> |
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inline double zignor(URBG& g); // NOLINT(runtime/references) |
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private: |
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friend class TableGenerator; |
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template <typename URBG> |
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inline double zignor_fallback(URBG& g, // NOLINT(runtime/references) |
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bool neg); |
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// Constants used for the gaussian distribution. |
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static constexpr double kR = 3.442619855899; // Start of the tail. |
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static constexpr double kRInv = 0.29047645161474317; // ~= (1.0 / kR) . |
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static constexpr double kV = 9.91256303526217e-3; |
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static constexpr uint64_t kMask = 0x07f; |
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// The ziggurat tables store the pdf(f) and inverse-pdf(x) for equal-area |
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// points on one-half of the normal distribution, where the pdf function, |
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// pdf = e ^ (-1/2 *x^2), assumes that the mean = 0 & stddev = 1. |
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// |
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// These tables are just over 2kb in size; larger tables might improve the |
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// distributions, but also lead to more cache pollution. |
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// |
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// x = {3.71308, 3.44261, 3.22308, ..., 0} |
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// f = {0.00101, 0.00266, 0.00554, ..., 1} |
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struct Tables { |
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double x[kMask + 2]; |
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double f[kMask + 2]; |
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}; |
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static const Tables zg_; |
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random_internal::FastUniformBits<uint64_t> fast_u64_; |
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}; |
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} // namespace random_internal |
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// absl::gaussian_distribution: |
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// Generates a number conforming to a Gaussian distribution. |
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template <typename RealType = double> |
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class gaussian_distribution : random_internal::gaussian_distribution_base { |
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public: |
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using result_type = RealType; |
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class param_type { |
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public: |
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using distribution_type = gaussian_distribution; |
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explicit param_type(result_type mean = 0, result_type stddev = 1) |
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: mean_(mean), stddev_(stddev) {} |
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// Returns the mean distribution parameter. The mean specifies the location |
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// of the peak. The default value is 0.0. |
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result_type mean() const { return mean_; } |
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// Returns the deviation distribution parameter. The default value is 1.0. |
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result_type stddev() const { return stddev_; } |
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friend bool operator==(const param_type& a, const param_type& b) { |
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return a.mean_ == b.mean_ && a.stddev_ == b.stddev_; |
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} |
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friend bool operator!=(const param_type& a, const param_type& b) { |
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return !(a == b); |
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} |
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private: |
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result_type mean_; |
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result_type stddev_; |
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static_assert( |
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std::is_floating_point<RealType>::value, |
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"Class-template absl::gaussian_distribution<> must be parameterized " |
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"using a floating-point type."); |
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}; |
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gaussian_distribution() : gaussian_distribution(0) {} |
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explicit gaussian_distribution(result_type mean, result_type stddev = 1) |
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: param_(mean, stddev) {} |
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explicit gaussian_distribution(const param_type& p) : param_(p) {} |
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void reset() {} |
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// Generating functions |
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template <typename URBG> |
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result_type operator()(URBG& g) { // NOLINT(runtime/references) |
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return (*this)(g, param_); |
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} |
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template <typename URBG> |
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result_type operator()(URBG& g, // NOLINT(runtime/references) |
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const param_type& p); |
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param_type param() const { return param_; } |
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void param(const param_type& p) { param_ = p; } |
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result_type(min)() const { |
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return -std::numeric_limits<result_type>::infinity(); |
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} |
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result_type(max)() const { |
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return std::numeric_limits<result_type>::infinity(); |
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} |
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result_type mean() const { return param_.mean(); } |
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result_type stddev() const { return param_.stddev(); } |
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friend bool operator==(const gaussian_distribution& a, |
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const gaussian_distribution& b) { |
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return a.param_ == b.param_; |
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} |
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friend bool operator!=(const gaussian_distribution& a, |
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const gaussian_distribution& b) { |
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return a.param_ != b.param_; |
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} |
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private: |
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param_type param_; |
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}; |
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// -------------------------------------------------------------------------- |
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// Implementation details only below |
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// -------------------------------------------------------------------------- |
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template <typename RealType> |
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template <typename URBG> |
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typename gaussian_distribution<RealType>::result_type |
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gaussian_distribution<RealType>::operator()( |
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URBG& g, // NOLINT(runtime/references) |
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const param_type& p) { |
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return p.mean() + p.stddev() * static_cast<result_type>(zignor(g)); |
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} |
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template <typename CharT, typename Traits, typename RealType> |
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std::basic_ostream<CharT, Traits>& operator<<( |
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std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references) |
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const gaussian_distribution<RealType>& x) { |
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auto saver = random_internal::make_ostream_state_saver(os); |
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os.precision(random_internal::stream_precision_helper<RealType>::kPrecision); |
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os << x.mean() << os.fill() << x.stddev(); |
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return os; |
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} |
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template <typename CharT, typename Traits, typename RealType> |
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std::basic_istream<CharT, Traits>& operator>>( |
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std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references) |
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gaussian_distribution<RealType>& x) { // NOLINT(runtime/references) |
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using result_type = typename gaussian_distribution<RealType>::result_type; |
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using param_type = typename gaussian_distribution<RealType>::param_type; |
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auto saver = random_internal::make_istream_state_saver(is); |
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auto mean = random_internal::read_floating_point<result_type>(is); |
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if (is.fail()) return is; |
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auto stddev = random_internal::read_floating_point<result_type>(is); |
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if (!is.fail()) { |
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x.param(param_type(mean, stddev)); |
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} |
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return is; |
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} |
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namespace random_internal { |
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template <typename URBG> |
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inline double gaussian_distribution_base::zignor_fallback(URBG& g, bool neg) { |
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// This fallback path happens approximately 0.05% of the time. |
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double x, y; |
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do { |
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// kRInv = 1/r, U(0, 1) |
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x = kRInv * std::log(RandU64ToDouble<PositiveValueT, false>(fast_u64_(g))); |
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y = -std::log(RandU64ToDouble<PositiveValueT, false>(fast_u64_(g))); |
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} while ((y + y) < (x * x)); |
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return neg ? (x - kR) : (kR - x); |
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} |
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template <typename URBG> |
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inline double gaussian_distribution_base::zignor( |
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URBG& g) { // NOLINT(runtime/references) |
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while (true) { |
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// We use a single uint64_t to generate both a double and a strip. |
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// These bits are unused when the generated double is > 1/2^5. |
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// This may introduce some bias from the duplicated low bits of small |
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// values (those smaller than 1/2^5, which all end up on the left tail). |
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uint64_t bits = fast_u64_(g); |
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int i = static_cast<int>(bits & kMask); // pick a random strip |
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double j = RandU64ToDouble<SignedValueT, false>(bits); // U(-1, 1) |
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const double x = j * zg_.x[i]; |
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// Retangular box. Handles >97% of all cases. |
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// For any given box, this handles between 75% and 99% of values. |
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// Equivalent to U(01) < (x[i+1] / x[i]), and when i == 0, ~93.5% |
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if (std::abs(x) < zg_.x[i + 1]) { |
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return x; |
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} |
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// i == 0: Base box. Sample using a ratio of uniforms. |
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if (i == 0) { |
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// This path happens about 0.05% of the time. |
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return zignor_fallback(g, j < 0); |
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} |
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// i > 0: Wedge samples using precomputed values. |
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double v = RandU64ToDouble<PositiveValueT, false>(fast_u64_(g)); // U(0, 1) |
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if ((zg_.f[i + 1] + v * (zg_.f[i] - zg_.f[i + 1])) < |
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std::exp(-0.5 * x * x)) { |
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return x; |
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} |
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// The wedge was missed; reject the value and try again. |
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} |
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} |
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} // namespace random_internal |
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} // namespace absl |
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#endif // ABSL_RANDOM_GAUSSIAN_DISTRIBUTION_H_
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