// 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. // // ----------------------------------------------------------------------------- // File: distributions.h // ----------------------------------------------------------------------------- // // This header defines functions representing distributions, which you use in // combination with an Abseil random bit generator to produce random values // according to the rules of that distribution. // // The Abseil random library defines the following distributions within this // file: // // * `absl::Uniform` for uniform (constant) distributions having constant // probability // * `absl::Bernoulli` for discrete distributions having exactly two outcomes // * `absl::Beta` for continuous distributions parameterized through two // free parameters // * `absl::Exponential` for discrete distributions of events occurring // continuously and independently at a constant average rate // * `absl::Gaussian` (also known as "normal distributions") for continuous // distributions using an associated quadratic function // * `absl::LogUniform` for continuous uniform distributions where the log // to the given base of all values is uniform // * `absl::Poisson` for discrete probability distributions that express the // probability of a given number of events occurring within a fixed interval // * `absl::Zipf` for discrete probability distributions commonly used for // modelling of rare events // // Prefer use of these distribution function classes over manual construction of // your own distribution classes, as it allows library maintainers greater // flexibility to change the underlying implementation in the future. #ifndef ABSL_RANDOM_DISTRIBUTIONS_H_ #define ABSL_RANDOM_DISTRIBUTIONS_H_ #include <algorithm> #include <cmath> #include <limits> #include <random> #include <type_traits> #include "absl/base/internal/inline_variable.h" #include "absl/random/bernoulli_distribution.h" #include "absl/random/beta_distribution.h" #include "absl/random/exponential_distribution.h" #include "absl/random/gaussian_distribution.h" #include "absl/random/internal/distribution_caller.h" // IWYU pragma: export #include "absl/random/internal/uniform_helper.h" // IWYU pragma: export #include "absl/random/log_uniform_int_distribution.h" #include "absl/random/poisson_distribution.h" #include "absl/random/uniform_int_distribution.h" #include "absl/random/uniform_real_distribution.h" #include "absl/random/zipf_distribution.h" namespace absl { ABSL_NAMESPACE_BEGIN ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalClosedClosedTag, IntervalClosedClosed, {}); ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalClosedClosedTag, IntervalClosed, {}); ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalClosedOpenTag, IntervalClosedOpen, {}); ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalOpenOpenTag, IntervalOpenOpen, {}); ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalOpenOpenTag, IntervalOpen, {}); ABSL_INTERNAL_INLINE_CONSTEXPR(IntervalOpenClosedTag, IntervalOpenClosed, {}); // ----------------------------------------------------------------------------- // absl::Uniform<T>(tag, bitgen, lo, hi) // ----------------------------------------------------------------------------- // // `absl::Uniform()` produces random values of type `T` uniformly distributed in // a defined interval {lo, hi}. The interval `tag` defines the type of interval // which should be one of the following possible values: // // * `absl::IntervalOpenOpen` // * `absl::IntervalOpenClosed` // * `absl::IntervalClosedOpen` // * `absl::IntervalClosedClosed` // // where "open" refers to an exclusive value (excluded) from the output, while // "closed" refers to an inclusive value (included) from the output. // // In the absence of an explicit return type `T`, `absl::Uniform()` will deduce // the return type based on the provided endpoint arguments {A lo, B hi}. // Given these endpoints, one of {A, B} will be chosen as the return type, if // a type can be implicitly converted into the other in a lossless way. The // lack of any such implicit conversion between {A, B} will produce a // compile-time error // // See https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) // // Example: // // absl::BitGen bitgen; // // // Produce a random float value between 0.0 and 1.0, inclusive // auto x = absl::Uniform(absl::IntervalClosedClosed, bitgen, 0.0f, 1.0f); // // // The most common interval of `absl::IntervalClosedOpen` is available by // // default: // // auto x = absl::Uniform(bitgen, 0.0f, 1.0f); // // // Return-types are typically inferred from the arguments, however callers // // can optionally provide an explicit return-type to the template. // // auto x = absl::Uniform<float>(bitgen, 0, 1); // template <typename R = void, typename TagType, typename URBG> typename absl::enable_if_t<!std::is_same<R, void>::value, R> // Uniform(TagType tag, URBG&& urbg, // NOLINT(runtime/references) R lo, R hi) { using gen_t = absl::decay_t<URBG>; using distribution_t = random_internal::UniformDistributionWrapper<R>; auto a = random_internal::uniform_lower_bound(tag, lo, hi); auto b = random_internal::uniform_upper_bound(tag, lo, hi); if (!random_internal::is_uniform_range_valid(a, b)) return lo; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, tag, lo, hi); } // absl::Uniform<T>(bitgen, lo, hi) // // Overload of `Uniform()` using the default closed-open interval of [lo, hi), // and returning values of type `T` template <typename R = void, typename URBG> typename absl::enable_if_t<!std::is_same<R, void>::value, R> // Uniform(URBG&& urbg, // NOLINT(runtime/references) R lo, R hi) { using gen_t = absl::decay_t<URBG>; using distribution_t = random_internal::UniformDistributionWrapper<R>; constexpr auto tag = absl::IntervalClosedOpen; auto a = random_internal::uniform_lower_bound(tag, lo, hi); auto b = random_internal::uniform_upper_bound(tag, lo, hi); if (!random_internal::is_uniform_range_valid(a, b)) return lo; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, lo, hi); } // absl::Uniform(tag, bitgen, lo, hi) // // Overload of `Uniform()` using different (but compatible) lo, hi types. Note // that a compile-error will result if the return type cannot be deduced // correctly from the passed types. template <typename R = void, typename TagType, typename URBG, typename A, typename B> typename absl::enable_if_t<std::is_same<R, void>::value, random_internal::uniform_inferred_return_t<A, B>> Uniform(TagType tag, URBG&& urbg, // NOLINT(runtime/references) A lo, B hi) { using gen_t = absl::decay_t<URBG>; using return_t = typename random_internal::uniform_inferred_return_t<A, B>; using distribution_t = random_internal::UniformDistributionWrapper<return_t>; auto a = random_internal::uniform_lower_bound<return_t>(tag, lo, hi); auto b = random_internal::uniform_upper_bound<return_t>(tag, lo, hi); if (!random_internal::is_uniform_range_valid(a, b)) return lo; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, tag, static_cast<return_t>(lo), static_cast<return_t>(hi)); } // absl::Uniform(bitgen, lo, hi) // // Overload of `Uniform()` using different (but compatible) lo, hi types and the // default closed-open interval of [lo, hi). Note that a compile-error will // result if the return type cannot be deduced correctly from the passed types. template <typename R = void, typename URBG, typename A, typename B> typename absl::enable_if_t<std::is_same<R, void>::value, random_internal::uniform_inferred_return_t<A, B>> Uniform(URBG&& urbg, // NOLINT(runtime/references) A lo, B hi) { using gen_t = absl::decay_t<URBG>; using return_t = typename random_internal::uniform_inferred_return_t<A, B>; using distribution_t = random_internal::UniformDistributionWrapper<return_t>; constexpr auto tag = absl::IntervalClosedOpen; auto a = random_internal::uniform_lower_bound<return_t>(tag, lo, hi); auto b = random_internal::uniform_upper_bound<return_t>(tag, lo, hi); if (!random_internal::is_uniform_range_valid(a, b)) return lo; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, static_cast<return_t>(lo), static_cast<return_t>(hi)); } // absl::Uniform<unsigned T>(bitgen) // // Overload of Uniform() using the minimum and maximum values of a given type // `T` (which must be unsigned), returning a value of type `unsigned T` template <typename R, typename URBG> typename absl::enable_if_t<!std::is_signed<R>::value, R> // Uniform(URBG&& urbg) { // NOLINT(runtime/references) using gen_t = absl::decay_t<URBG>; using distribution_t = random_internal::UniformDistributionWrapper<R>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg); } // ----------------------------------------------------------------------------- // absl::Bernoulli(bitgen, p) // ----------------------------------------------------------------------------- // // `absl::Bernoulli` produces a random boolean value, with probability `p` // (where 0.0 <= p <= 1.0) equaling `true`. // // Prefer `absl::Bernoulli` to produce boolean values over other alternatives // such as comparing an `absl::Uniform()` value to a specific output. // // See https://en.wikipedia.org/wiki/Bernoulli_distribution // // Example: // // absl::BitGen bitgen; // ... // if (absl::Bernoulli(bitgen, 1.0/3721.0)) { // std::cout << "Asteroid field navigation successful."; // } // template <typename URBG> bool Bernoulli(URBG&& urbg, // NOLINT(runtime/references) double p) { using gen_t = absl::decay_t<URBG>; using distribution_t = absl::bernoulli_distribution; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, p); } // ----------------------------------------------------------------------------- // absl::Beta<T>(bitgen, alpha, beta) // ----------------------------------------------------------------------------- // // `absl::Beta` produces a floating point number distributed in the closed // interval [0,1] and parameterized by two values `alpha` and `beta` as per a // Beta distribution. `T` must be a floating point type, but may be inferred // from the types of `alpha` and `beta`. // // See https://en.wikipedia.org/wiki/Beta_distribution. // // Example: // // absl::BitGen bitgen; // ... // double sample = absl::Beta(bitgen, 3.0, 2.0); // template <typename RealType, typename URBG> RealType Beta(URBG&& urbg, // NOLINT(runtime/references) RealType alpha, RealType beta) { static_assert( std::is_floating_point<RealType>::value, "Template-argument 'RealType' must be a floating-point type, in " "absl::Beta<RealType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::beta_distribution<RealType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, alpha, beta); } // ----------------------------------------------------------------------------- // absl::Exponential<T>(bitgen, lambda = 1) // ----------------------------------------------------------------------------- // // `absl::Exponential` produces a floating point number representing the // distance (time) between two consecutive events in a point process of events // occurring continuously and independently at a constant average rate. `T` must // be a floating point type, but may be inferred from the type of `lambda`. // // See https://en.wikipedia.org/wiki/Exponential_distribution. // // Example: // // absl::BitGen bitgen; // ... // double call_length = absl::Exponential(bitgen, 7.0); // template <typename RealType, typename URBG> RealType Exponential(URBG&& urbg, // NOLINT(runtime/references) RealType lambda = 1) { static_assert( std::is_floating_point<RealType>::value, "Template-argument 'RealType' must be a floating-point type, in " "absl::Exponential<RealType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::exponential_distribution<RealType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, lambda); } // ----------------------------------------------------------------------------- // absl::Gaussian<T>(bitgen, mean = 0, stddev = 1) // ----------------------------------------------------------------------------- // // `absl::Gaussian` produces a floating point number selected from the Gaussian // (ie. "Normal") distribution. `T` must be a floating point type, but may be // inferred from the types of `mean` and `stddev`. // // See https://en.wikipedia.org/wiki/Normal_distribution // // Example: // // absl::BitGen bitgen; // ... // double giraffe_height = absl::Gaussian(bitgen, 16.3, 3.3); // template <typename RealType, typename URBG> RealType Gaussian(URBG&& urbg, // NOLINT(runtime/references) RealType mean = 0, RealType stddev = 1) { static_assert( std::is_floating_point<RealType>::value, "Template-argument 'RealType' must be a floating-point type, in " "absl::Gaussian<RealType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::gaussian_distribution<RealType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, mean, stddev); } // ----------------------------------------------------------------------------- // absl::LogUniform<T>(bitgen, lo, hi, base = 2) // ----------------------------------------------------------------------------- // // `absl::LogUniform` produces random values distributed where the log to a // given base of all values is uniform in a closed interval [lo, hi]. `T` must // be an integral type, but may be inferred from the types of `lo` and `hi`. // // I.e., `LogUniform(0, n, b)` is uniformly distributed across buckets // [0], [1, b-1], [b, b^2-1] .. [b^(k-1), (b^k)-1] .. [b^floor(log(n, b)), n] // and is uniformly distributed within each bucket. // // The resulting probability density is inversely related to bucket size, though // values in the final bucket may be more likely than previous values. (In the // extreme case where n = b^i the final value will be tied with zero as the most // probable result. // // If `lo` is nonzero then this distribution is shifted to the desired interval, // so LogUniform(lo, hi, b) is equivalent to LogUniform(0, hi-lo, b)+lo. // // See http://ecolego.facilia.se/ecolego/show/Log-Uniform%20Distribution // // Example: // // absl::BitGen bitgen; // ... // int v = absl::LogUniform(bitgen, 0, 1000); // template <typename IntType, typename URBG> IntType LogUniform(URBG&& urbg, // NOLINT(runtime/references) IntType lo, IntType hi, IntType base = 2) { static_assert(std::is_integral<IntType>::value, "Template-argument 'IntType' must be an integral type, in " "absl::LogUniform<IntType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::log_uniform_int_distribution<IntType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, lo, hi, base); } // ----------------------------------------------------------------------------- // absl::Poisson<T>(bitgen, mean = 1) // ----------------------------------------------------------------------------- // // `absl::Poisson` produces discrete probabilities for a given number of events // occurring within a fixed interval within the closed interval [0, max]. `T` // must be an integral type. // // See https://en.wikipedia.org/wiki/Poisson_distribution // // Example: // // absl::BitGen bitgen; // ... // int requests_per_minute = absl::Poisson<int>(bitgen, 3.2); // template <typename IntType, typename URBG> IntType Poisson(URBG&& urbg, // NOLINT(runtime/references) double mean = 1.0) { static_assert(std::is_integral<IntType>::value, "Template-argument 'IntType' must be an integral type, in " "absl::Poisson<IntType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::poisson_distribution<IntType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, mean); } // ----------------------------------------------------------------------------- // absl::Zipf<T>(bitgen, hi = max, q = 2, v = 1) // ----------------------------------------------------------------------------- // // `absl::Zipf` produces discrete probabilities commonly used for modelling of // rare events over the closed interval [0, hi]. The parameters `v` and `q` // determine the skew of the distribution. `T` must be an integral type, but // may be inferred from the type of `hi`. // // See http://mathworld.wolfram.com/ZipfDistribution.html // // Example: // // absl::BitGen bitgen; // ... // int term_rank = absl::Zipf<int>(bitgen); // template <typename IntType, typename URBG> IntType Zipf(URBG&& urbg, // NOLINT(runtime/references) IntType hi = (std::numeric_limits<IntType>::max)(), double q = 2.0, double v = 1.0) { static_assert(std::is_integral<IntType>::value, "Template-argument 'IntType' must be an integral type, in " "absl::Zipf<IntType, URBG>(...)"); using gen_t = absl::decay_t<URBG>; using distribution_t = typename absl::zipf_distribution<IntType>; return random_internal::DistributionCaller<gen_t>::template Call< distribution_t>(&urbg, hi, q, v); } ABSL_NAMESPACE_END } // namespace absl #endif // ABSL_RANDOM_DISTRIBUTIONS_H_