--- /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_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 {
+
+// 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;
+}
+
+} // namespace absl
+
+#endif // ABSL_RANDOM_BETA_DISTRIBUTION_H_
git://repos.xcallymotion.com / motion2.git / blobdiff