Creation of LTS branch "lts_2019_08_08"20190808

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GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d
Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced

1 files changed, 416 insertions, 0 deletions

diff --git a/absl/random/beta_distribution.h b/absl/random/beta_distribution.h
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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_BETA_DISTRIBUTION_H_
+#define ABSL_RANDOM_BETA_DISTRIBUTION_H_
+
+#include <cassert>
+#include <cmath>
+#include <istream>
+#include <limits>
+#include <ostream>
+#include <type_traits>
+
+#include "absl/random/internal/distribution_impl.h"
+#include "absl/random/internal/fast_uniform_bits.h"
+#include "absl/random/internal/fastmath.h"
+#include "absl/random/internal/iostream_state_saver.h"
+
+namespace absl {
+inline namespace lts_2019_08_08 {
+
+// absl::beta_distribution:
+// Generate a floating-point variate conforming to a Beta distribution:
+//   pdf(x) \propto x^(alpha-1) * (1-x)^(beta-1),
+// where the params alpha and beta are both strictly positive real values.
+//
+// The support is the open interval (0, 1), but the return value might be equal
+// to 0 or 1, due to numerical errors when alpha and beta are very different.
+//
+// Usage note: One usage is that alpha and beta are counts of number of
+// successes and failures. When the total number of trials are large, consider
+// approximating a beta distribution with a Gaussian distribution with the same
+// mean and variance. One could use the skewness, which depends only on the
+// smaller of alpha and beta when the number of trials are sufficiently large,
+// to quantify how far a beta distribution is from the normal distribution.
+template <typename RealType = double>
+class beta_distribution {
+ public:
+  using result_type = RealType;
+
+  class param_type {
+   public:
+    using distribution_type = beta_distribution;
+
+    explicit param_type(result_type alpha, result_type beta)
+        : alpha_(alpha), beta_(beta) {
+      assert(alpha >= 0);
+      assert(beta >= 0);
+      assert(alpha <= (std::numeric_limits<result_type>::max)());
+      assert(beta <= (std::numeric_limits<result_type>::max)());
+      if (alpha == 0 || beta == 0) {
+        method_ = DEGENERATE_SMALL;
+        x_ = (alpha >= beta) ? 1 : 0;
+        return;
+      }
+      // a_ = min(beta, alpha), b_ = max(beta, alpha).
+      if (beta < alpha) {
+        inverted_ = true;
+        a_ = beta;
+        b_ = alpha;
+      } else {
+        inverted_ = false;
+        a_ = alpha;
+        b_ = beta;
+      }
+      if (a_ <= 1 && b_ >= ThresholdForLargeA()) {
+        method_ = DEGENERATE_SMALL;
+        x_ = inverted_ ? result_type(1) : result_type(0);
+        return;
+      }
+      // For threshold values, see also:
+      // Evaluation of Beta Generation Algorithms, Ying-Chao Hung, et. al.
+      // February, 2009.
+      if ((b_ < 1.0 && a_ + b_ <= 1.2) || a_ <= ThresholdForSmallA()) {
+        // Choose Joehnk over Cheng when it's faster or when Cheng encounters
+        // numerical issues.
+        method_ = JOEHNK;
+        a_ = result_type(1) / alpha_;
+        b_ = result_type(1) / beta_;
+        if (std::isinf(a_) || std::isinf(b_)) {
+          method_ = DEGENERATE_SMALL;
+          x_ = inverted_ ? result_type(1) : result_type(0);
+        }
+        return;
+      }
+      if (a_ >= ThresholdForLargeA()) {
+        method_ = DEGENERATE_LARGE;
+        // Note: on PPC for long double, evaluating
+        // `std::numeric_limits::max() / ThresholdForLargeA` results in NaN.
+        result_type r = a_ / b_;
+        x_ = (inverted_ ? result_type(1) : r) / (1 + r);
+        return;
+      }
+      x_ = a_ + b_;
+      log_x_ = std::log(x_);
+      if (a_ <= 1) {
+        method_ = CHENG_BA;
+        y_ = result_type(1) / a_;
+        gamma_ = a_ + a_;
+        return;
+      }
+      method_ = CHENG_BB;
+      result_type r = (a_ - 1) / (b_ - 1);
+      y_ = std::sqrt((1 + r) / (b_ * r * 2 - r + 1));
+      gamma_ = a_ + result_type(1) / y_;
+    }
+
+    result_type alpha() const { return alpha_; }
+    result_type beta() const { return beta_; }
+
+    friend bool operator==(const param_type& a, const param_type& b) {
+      return a.alpha_ == b.alpha_ && a.beta_ == b.beta_;
+    }
+
+    friend bool operator!=(const param_type& a, const param_type& b) {
+      return !(a == b);
+    }
+
+   private:
+    friend class beta_distribution;
+
+#ifdef COMPILER_MSVC
+    // MSVC does not have constexpr implementations for std::log and std::exp
+    // so they are computed at runtime.
+#define ABSL_RANDOM_INTERNAL_LOG_EXP_CONSTEXPR
+#else
+#define ABSL_RANDOM_INTERNAL_LOG_EXP_CONSTEXPR constexpr
+#endif
+
+    // The threshold for whether std::exp(1/a) is finite.
+    // Note that this value is quite large, and a smaller a_ is NOT abnormal.
+    static ABSL_RANDOM_INTERNAL_LOG_EXP_CONSTEXPR result_type
+    ThresholdForSmallA() {
+      return result_type(1) /
+             std::log((std::numeric_limits<result_type>::max)());
+    }
+
+    // The threshold for whether a * std::log(a) is finite.
+    static ABSL_RANDOM_INTERNAL_LOG_EXP_CONSTEXPR result_type
+    ThresholdForLargeA() {
+      return std::exp(
+          std::log((std::numeric_limits<result_type>::max)()) -
+          std::log(std::log((std::numeric_limits<result_type>::max)())) -
+          ThresholdPadding());
+    }
+
+#undef ABSL_RANDOM_INTERNAL_LOG_EXP_CONSTEXPR
+
+    // Pad the threshold for large A for long double on PPC. This is done via a
+    // template specialization below.
+    static constexpr result_type ThresholdPadding() { return 0; }
+
+    enum Method {
+      JOEHNK,    // Uses algorithm Joehnk
+      CHENG_BA,  // Uses algorithm BA in Cheng
+      CHENG_BB,  // Uses algorithm BB in Cheng
+
+      // Note: See also:
+      //   Hung et al. Evaluation of beta generation algorithms. Communications
+      //   in Statistics-Simulation and Computation 38.4 (2009): 750-770.
+      // especially:
+      //   Zechner, Heinz, and Ernst Stadlober. Generating beta variates via
+      //   patchwork rejection. Computing 50.1 (1993): 1-18.
+
+      DEGENERATE_SMALL,  // a_ is abnormally small.
+      DEGENERATE_LARGE,  // a_ is abnormally large.
+    };
+
+    result_type alpha_;
+    result_type beta_;
+
+    result_type a_;  // the smaller of {alpha, beta}, or 1.0/alpha_ in JOEHNK
+    result_type b_;  // the larger of {alpha, beta}, or 1.0/beta_ in JOEHNK
+    result_type x_;  // alpha + beta, or the result in degenerate cases
+    result_type log_x_;  // log(x_)
+    result_type y_;      // "beta" in Cheng
+    result_type gamma_;  // "gamma" in Cheng
+
+    Method method_;
+
+    // Placing this last for optimal alignment.
+    // Whether alpha_ != a_, i.e. true iff alpha_ > beta_.
+    bool inverted_;
+
+    static_assert(std::is_floating_point<RealType>::value,
+                  "Class-template absl::beta_distribution<> must be "
+                  "parameterized using a floating-point type.");
+  };
+
+  beta_distribution() : beta_distribution(1) {}
+
+  explicit beta_distribution(result_type alpha, result_type beta = 1)
+      : param_(alpha, beta) {}
+
+  explicit beta_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 0; }
+  result_type(max)() const { return 1; }
+
+  result_type alpha() const { return param_.alpha(); }
+  result_type beta() const { return param_.beta(); }
+
+  friend bool operator==(const beta_distribution& a,
+                         const beta_distribution& b) {
+    return a.param_ == b.param_;
+  }
+  friend bool operator!=(const beta_distribution& a,
+                         const beta_distribution& b) {
+    return a.param_ != b.param_;
+  }
+
+ private:
+  template <typename URBG>
+  result_type AlgorithmJoehnk(URBG& g,  // NOLINT(runtime/references)
+                              const param_type& p);
+
+  template <typename URBG>
+  result_type AlgorithmCheng(URBG& g,  // NOLINT(runtime/references)
+                             const param_type& p);
+
+  template <typename URBG>
+  result_type DegenerateCase(URBG& g,  // NOLINT(runtime/references)
+                             const param_type& p) {
+    if (p.method_ == param_type::DEGENERATE_SMALL && p.alpha_ == p.beta_) {
+      // Returns 0 or 1 with equal probability.
+      random_internal::FastUniformBits<uint8_t> fast_u8;
+      return static_cast<result_type>((fast_u8(g) & 0x10) !=
+                                      0);  // pick any single bit.
+    }
+    return p.x_;
+  }
+
+  param_type param_;
+  random_internal::FastUniformBits<uint64_t> fast_u64_;
+};
+
+#if defined(__powerpc64__) || defined(__PPC64__) || defined(__powerpc__) || \
+    defined(__ppc__) || defined(__PPC__)
+// PPC needs a more stringent boundary for long double.
+template <>
+constexpr long double
+beta_distribution<long double>::param_type::ThresholdPadding() {
+  return 10;
+}
+#endif
+
+template <typename RealType>
+template <typename URBG>
+typename beta_distribution<RealType>::result_type
+beta_distribution<RealType>::AlgorithmJoehnk(
+    URBG& g,  // NOLINT(runtime/references)
+    const param_type& p) {
+  // Based on Joehnk, M. D. Erzeugung von betaverteilten und gammaverteilten
+  // Zufallszahlen. Metrika 8.1 (1964): 5-15.
+  // This method is described in Knuth, Vol 2 (Third Edition), pp 134.
+  using RandU64ToReal = typename random_internal::RandU64ToReal<result_type>;
+  using random_internal::PositiveValueT;
+  result_type u, v, x, y, z;
+  for (;;) {
+    u = RandU64ToReal::template Value<PositiveValueT, false>(fast_u64_(g));
+    v = RandU64ToReal::template Value<PositiveValueT, false>(fast_u64_(g));
+
+    // Direct method. std::pow is slow for float, so rely on the optimizer to
+    // remove the std::pow() path for that case.
+    if (!std::is_same<float, result_type>::value) {
+      x = std::pow(u, p.a_);
+      y = std::pow(v, p.b_);
+      z = x + y;
+      if (z > 1) {
+        // Reject if and only if `x + y > 1.0`
+        continue;
+      }
+      if (z > 0) {
+        // When both alpha and beta are small, x and y are both close to 0, so
+        // divide by (x+y) directly may result in nan.
+        return x / z;
+      }
+    }
+
+    // Log transform.
+    // x = log( pow(u, p.a_) ), y = log( pow(v, p.b_) )
+    // since u, v <= 1.0,  x, y < 0.
+    x = std::log(u) * p.a_;
+    y = std::log(v) * p.b_;
+    if (!std::isfinite(x) || !std::isfinite(y)) {
+      continue;
+    }
+    // z = log( pow(u, a) + pow(v, b) )
+    z = x > y ? (x + std::log(1 + std::exp(y - x)))
+              : (y + std::log(1 + std::exp(x - y)));
+    // Reject iff log(x+y) > 0.
+    if (z > 0) {
+      continue;
+    }
+    return std::exp(x - z);
+  }
+}
+
+template <typename RealType>
+template <typename URBG>
+typename beta_distribution<RealType>::result_type
+beta_distribution<RealType>::AlgorithmCheng(
+    URBG& g,  // NOLINT(runtime/references)
+    const param_type& p) {
+  // Based on Cheng, Russell CH. Generating beta variates with nonintegral
+  // shape parameters. Communications of the ACM 21.4 (1978): 317-322.
+  // (https://dl.acm.org/citation.cfm?id=359482).
+  using RandU64ToReal = typename random_internal::RandU64ToReal<result_type>;
+  using random_internal::PositiveValueT;
+
+  static constexpr result_type kLogFour =
+      result_type(1.3862943611198906188344642429163531361);  // log(4)
+  static constexpr result_type kS =
+      result_type(2.6094379124341003746007593332261876);  // 1+log(5)
+
+  const bool use_algorithm_ba = (p.method_ == param_type::CHENG_BA);
+  result_type u1, u2, v, w, z, r, s, t, bw_inv, lhs;
+  for (;;) {
+    u1 = RandU64ToReal::template Value<PositiveValueT, false>(fast_u64_(g));
+    u2 = RandU64ToReal::template Value<PositiveValueT, false>(fast_u64_(g));
+    v = p.y_ * std::log(u1 / (1 - u1));
+    w = p.a_ * std::exp(v);
+    bw_inv = result_type(1) / (p.b_ + w);
+    r = p.gamma_ * v - kLogFour;
+    s = p.a_ + r - w;
+    z = u1 * u1 * u2;
+    if (!use_algorithm_ba && s + kS >= 5 * z) {
+      break;
+    }
+    t = std::log(z);
+    if (!use_algorithm_ba && s >= t) {
+      break;
+    }
+    lhs = p.x_ * (p.log_x_ + std::log(bw_inv)) + r;
+    if (lhs >= t) {
+      break;
+    }
+  }
+  return p.inverted_ ? (1 - w * bw_inv) : w * bw_inv;
+}
+
+template <typename RealType>
+template <typename URBG>
+typename beta_distribution<RealType>::result_type
+beta_distribution<RealType>::operator()(URBG& g,  // NOLINT(runtime/references)
+                                        const param_type& p) {
+  switch (p.method_) {
+    case param_type::JOEHNK:
+      return AlgorithmJoehnk(g, p);
+    case param_type::CHENG_BA:
+      ABSL_FALLTHROUGH_INTENDED;
+    case param_type::CHENG_BB:
+      return AlgorithmCheng(g, p);
+    default:
+      return DegenerateCase(g, p);
+  }
+}
+
+template <typename CharT, typename Traits, typename RealType>
+std::basic_ostream<CharT, Traits>& operator<<(
+    std::basic_ostream<CharT, Traits>& os,  // NOLINT(runtime/references)
+    const beta_distribution<RealType>& x) {
+  auto saver = random_internal::make_ostream_state_saver(os);
+  os.precision(random_internal::stream_precision_helper<RealType>::kPrecision);
+  os << x.alpha() << os.fill() << x.beta();
+  return os;
+}
+
+template <typename CharT, typename Traits, typename RealType>
+std::basic_istream<CharT, Traits>& operator>>(
+    std::basic_istream<CharT, Traits>& is,  // NOLINT(runtime/references)
+    beta_distribution<RealType>& x) {       // NOLINT(runtime/references)
+  using result_type = typename beta_distribution<RealType>::result_type;
+  using param_type = typename beta_distribution<RealType>::param_type;
+  result_type alpha, beta;
+
+  auto saver = random_internal::make_istream_state_saver(is);
+  alpha = random_internal::read_floating_point<result_type>(is);
+  if (is.fail()) return is;
+  beta = random_internal::read_floating_point<result_type>(is);
+  if (!is.fail()) {
+    x.param(param_type(alpha, beta));
+  }
+  return is;
+}
+
+}  // inline namespace lts_2019_08_08
+}  // namespace absl
+
+#endif  // ABSL_RANDOM_BETA_DISTRIBUTION_H_