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968a34ffdaadd7db062a9621dfbdf8b2d16e05af Export of internal Abseil changes. by Abseil Team - 3e2e9b5557e76d098de4b8a2a659125b98ca519b Merge pull request #231 from uilianries/feature/conan by Mark Barolak - 111ca7060a6ff50115ca85b59f6b5d8c8c5e9105 Export of internal Abseil changes. by Abseil Team - 389ec3f906f018661a5308458d623d01f96d7b23 Export of internal Abseil changes. by Abseil Team - 8fbcdb90952c57828c4a9c2f6d79fcd7cae9088f Export of internal Abseil changes. by Abseil Team - 455dc17ba1af9635f0b60155bc565bc572a1e722 Export of internal Abseil changes. by Abseil Team - f197d7c72a54064cfde5a2058f1513a4a0ee36fb Export of internal Abseil changes. by Abseil Team - 284378a71b32dfb3af4e3661f585e671d1b603a3 Export of internal Abseil changes. by Abseil Team GitOrigin-RevId: 9ee91d3e430fb33a4590486573792eb0fa146c2d Change-Id: Ia06e548bc106cc9d136f6c65714be6645317aced --- absl/random/zipf_distribution.h | 271 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 271 insertions(+) create mode 100644 absl/random/zipf_distribution.h (limited to 'absl/random/zipf_distribution.h') diff --git a/absl/random/zipf_distribution.h b/absl/random/zipf_distribution.h new file mode 100644 index 00000000..bba98e88 --- /dev/null +++ b/absl/random/zipf_distribution.h @@ -0,0 +1,271 @@ +// 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_ZIPF_DISTRIBUTION_H_ +#define ABSL_RANDOM_ZIPF_DISTRIBUTION_H_ + +#include +#include +#include +#include +#include +#include + +#include "absl/random/internal/iostream_state_saver.h" +#include "absl/random/uniform_real_distribution.h" + +namespace absl { +inline namespace lts_2019_08_08 { + +// absl::zipf_distribution produces random integer-values in the range [0, k], +// distributed according to the discrete probability function: +// +// P(x) = (v + x) ^ -q +// +// The parameter `v` must be greater than 0 and the parameter `q` must be +// greater than 1. If either of these parameters take invalid values then the +// behavior is undefined. +// +// IntType is the result_type generated by the generator. It must be of integral +// type; a static_assert ensures this is the case. +// +// The implementation is based on W.Hormann, G.Derflinger: +// +// "Rejection-Inversion to Generate Variates from Monotone Discrete +// Distributions" +// +// http://eeyore.wu-wien.ac.at/papers/96-04-04.wh-der.ps.gz +// +template +class zipf_distribution { + public: + using result_type = IntType; + + class param_type { + public: + using distribution_type = zipf_distribution; + + // Preconditions: k > 0, v > 0, q > 1 + // The precondidtions are validated when NDEBUG is not defined via + // a pair of assert() directives. + // If NDEBUG is defined and either or both of these parameters take invalid + // values, the behavior of the class is undefined. + explicit param_type(result_type k = (std::numeric_limits::max)(), + double q = 2.0, double v = 1.0); + + result_type k() const { return k_; } + double q() const { return q_; } + double v() const { return v_; } + + friend bool operator==(const param_type& a, const param_type& b) { + return a.k_ == b.k_ && a.q_ == b.q_ && a.v_ == b.v_; + } + friend bool operator!=(const param_type& a, const param_type& b) { + return !(a == b); + } + + private: + friend class zipf_distribution; + inline double h(double x) const; + inline double hinv(double x) const; + inline double compute_s() const; + inline double pow_negative_q(double x) const; + + // Parameters here are exactly the same as the parameters of Algorithm ZRI + // in the paper. + IntType k_; + double q_; + double v_; + + double one_minus_q_; // 1-q + double s_; + double one_minus_q_inv_; // 1 / 1-q + double hxm_; // h(k + 0.5) + double hx0_minus_hxm_; // h(x0) - h(k + 0.5) + + static_assert(std::is_integral::value, + "Class-template absl::zipf_distribution<> must be " + "parameterized using an integral type."); + }; + + zipf_distribution() + : zipf_distribution((std::numeric_limits::max)()) {} + + explicit zipf_distribution(result_type k, double q = 2.0, double v = 1.0) + : param_(k, q, v) {} + + explicit zipf_distribution(const param_type& p) : param_(p) {} + + void reset() {} + + template + result_type operator()(URBG& g) { // NOLINT(runtime/references) + return (*this)(g, param_); + } + + template + result_type operator()(URBG& g, // NOLINT(runtime/references) + const param_type& p); + + result_type k() const { return param_.k(); } + double q() const { return param_.q(); } + double v() const { return param_.v(); } + + 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 k(); } + + friend bool operator==(const zipf_distribution& a, + const zipf_distribution& b) { + return a.param_ == b.param_; + } + friend bool operator!=(const zipf_distribution& a, + const zipf_distribution& b) { + return a.param_ != b.param_; + } + + private: + param_type param_; +}; + +// -------------------------------------------------------------------------- +// Implementation details follow +// -------------------------------------------------------------------------- + +template +zipf_distribution::param_type::param_type( + typename zipf_distribution::result_type k, double q, double v) + : k_(k), q_(q), v_(v), one_minus_q_(1 - q) { + assert(q > 1); + assert(v > 0); + assert(k > 0); + one_minus_q_inv_ = 1 / one_minus_q_; + + // Setup for the ZRI algorithm (pg 17 of the paper). + // Compute: h(i max) => h(k + 0.5) + constexpr double kMax = 18446744073709549568.0; + double kd = static_cast(k); + // TODO(absl-team): Determine if this check is needed, and if so, add a test + // that fails for k > kMax + if (kd > kMax) { + // Ensure that our maximum value is capped to a value which will + // round-trip back through double. + kd = kMax; + } + hxm_ = h(kd + 0.5); + + // Compute: h(0) + const bool use_precomputed = (v == 1.0 && q == 2.0); + const double h0x5 = use_precomputed ? (-1.0 / 1.5) // exp(-log(1.5)) + : h(0.5); + const double elogv_q = (v_ == 1.0) ? 1 : pow_negative_q(v_); + + // h(0) = h(0.5) - exp(log(v) * -q) + hx0_minus_hxm_ = (h0x5 - elogv_q) - hxm_; + + // And s + s_ = use_precomputed ? 0.46153846153846123 : compute_s(); +} + +template +double zipf_distribution::param_type::h(double x) const { + // std::exp(one_minus_q_ * std::log(v_ + x)) * one_minus_q_inv_; + x += v_; + return (one_minus_q_ == -1.0) + ? (-1.0 / x) // -exp(-log(x)) + : (std::exp(std::log(x) * one_minus_q_) * one_minus_q_inv_); +} + +template +double zipf_distribution::param_type::hinv(double x) const { + // std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x)) - v_; + return -v_ + ((one_minus_q_ == -1.0) + ? (-1.0 / x) // exp(-log(-x)) + : std::exp(one_minus_q_inv_ * std::log(one_minus_q_ * x))); +} + +template +double zipf_distribution::param_type::compute_s() const { + // 1 - hinv(h(1.5) - std::exp(std::log(v_ + 1) * -q_)); + return 1.0 - hinv(h(1.5) - pow_negative_q(v_ + 1.0)); +} + +template +double zipf_distribution::param_type::pow_negative_q(double x) const { + // std::exp(std::log(x) * -q_); + return q_ == 2.0 ? (1.0 / (x * x)) : std::exp(std::log(x) * -q_); +} + +template +template +typename zipf_distribution::result_type +zipf_distribution::operator()( + URBG& g, const param_type& p) { // NOLINT(runtime/references) + absl::uniform_real_distribution uniform_double; + double k; + for (;;) { + const double v = uniform_double(g); + const double u = p.hxm_ + v * p.hx0_minus_hxm_; + const double x = p.hinv(u); + k = rint(x); // std::floor(x + 0.5); + if (k > p.k()) continue; // reject k > max_k + if (k - x <= p.s_) break; + const double h = p.h(k + 0.5); + const double r = p.pow_negative_q(p.v_ + k); + if (u >= h - r) break; + } + IntType ki = static_cast(k); + assert(ki <= p.k_); + return ki; +} + +template +std::basic_ostream& operator<<( + std::basic_ostream& os, // NOLINT(runtime/references) + const zipf_distribution& x) { + using stream_type = + typename random_internal::stream_format_type::type; + auto saver = random_internal::make_ostream_state_saver(os); + os.precision(random_internal::stream_precision_helper::kPrecision); + os << static_cast(x.k()) << os.fill() << x.q() << os.fill() + << x.v(); + return os; +} + +template +std::basic_istream& operator>>( + std::basic_istream& is, // NOLINT(runtime/references) + zipf_distribution& x) { // NOLINT(runtime/references) + using result_type = typename zipf_distribution::result_type; + using param_type = typename zipf_distribution::param_type; + using stream_type = + typename random_internal::stream_format_type::type; + stream_type k; + double q; + double v; + + auto saver = random_internal::make_istream_state_saver(is); + is >> k >> q >> v; + if (!is.fail()) { + x.param(param_type(static_cast(k), q, v)); + } + return is; +} + +} // inline namespace lts_2019_08_08 +} // namespace absl + +#endif // ABSL_RANDOM_ZIPF_DISTRIBUTION_H_ -- cgit v1.2.3