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