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276 lines
9.3 KiB
276 lines
9.3 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/base/config.h"
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#include "absl/random/internal/fast_uniform_bits.h"
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#include "absl/random/internal/generate_real.h"
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#include "absl/random/internal/iostream_state_saver.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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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 ABSL_DLL 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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using random_internal::GeneratePositiveTag;
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using random_internal::GenerateRealFromBits;
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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 *
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std::log(GenerateRealFromBits<double, GeneratePositiveTag, false>(
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fast_u64_(g)));
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y = -std::log(
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GenerateRealFromBits<double, GeneratePositiveTag, 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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using random_internal::GeneratePositiveTag;
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using random_internal::GenerateRealFromBits;
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using random_internal::GenerateSignedTag;
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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 = GenerateRealFromBits<double, GenerateSignedTag, false>(
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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 = GenerateRealFromBits<double, GeneratePositiveTag, false>(
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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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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_RANDOM_GAUSSIAN_DISTRIBUTION_H_
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