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+// 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/base/config.h"
+#include "absl/random/internal/fast_uniform_bits.h"
+#include "absl/random/internal/generate_real.h"
+#include "absl/random/internal/iostream_state_saver.h"
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+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 ABSL_DLL 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) {
+  using random_internal::GeneratePositiveTag;
+  using random_internal::GenerateRealFromBits;
+
+  // This fallback path happens approximately 0.05% of the time.
+  double x, y;
+  do {
+    // kRInv = 1/r, U(0, 1)
+    x = kRInv *
+        std::log(GenerateRealFromBits<double, GeneratePositiveTag, false>(
+            fast_u64_(g)));
+    y = -std::log(
+        GenerateRealFromBits<double, GeneratePositiveTag, 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)
+  using random_internal::GeneratePositiveTag;
+  using random_internal::GenerateRealFromBits;
+  using random_internal::GenerateSignedTag;
+
+  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 = GenerateRealFromBits<double, GenerateSignedTag, 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 = GenerateRealFromBits<double, GeneratePositiveTag, 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
+ABSL_NAMESPACE_END
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_GAUSSIAN_DISTRIBUTION_H_