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Diffstat (limited to 'absl/random/beta_distribution.h')
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diff --git a/absl/random/beta_distribution.h b/absl/random/beta_distribution.h new file mode 100644 index 00000000..d7afd61c --- /dev/null +++ b/absl/random/beta_distribution.h @@ -0,0 +1,414 @@ +// 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_ |