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Diffstat (limited to 'absl/random/uniform_int_distribution.h')
| -rw-r--r-- | absl/random/uniform_int_distribution.h | 273 |
1 files changed, 273 insertions, 0 deletions
diff --git a/absl/random/uniform_int_distribution.h b/absl/random/uniform_int_distribution.h new file mode 100644 index 00000000..4970486a --- /dev/null +++ b/absl/random/uniform_int_distribution.h @@ -0,0 +1,273 @@ +// 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: uniform_int_distribution.h +// ----------------------------------------------------------------------------- +// +// This header defines a class for representing a uniform integer distribution +// over the closed (inclusive) interval [a,b]. You use this distribution in +// combination with an Abseil random bit generator to produce random values +// according to the rules of the distribution. +// +// `absl::uniform_int_distribution` is a drop-in replacement for the C++11 +// `std::uniform_int_distribution` [rand.dist.uni.int] but is considerably +// faster than the libstdc++ implementation. + +#ifndef ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_ +#define ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_ + +#include <cassert> +#include <istream> +#include <limits> +#include <type_traits> + +#include "absl/base/optimization.h" +#include "absl/random/internal/distribution_impl.h" +#include "absl/random/internal/fast_uniform_bits.h" +#include "absl/random/internal/iostream_state_saver.h" +#include "absl/random/internal/traits.h" + +namespace absl { + +// absl::uniform_int_distribution<T> +// +// This distribution produces random integer values uniformly distributed in the +// closed (inclusive) interval [a, b]. +// +// Example: +// +// absl::BitGen gen; +// +// // Use the distribution to produce a value between 1 and 6, inclusive. +// int die_roll = absl::uniform_int_distribution<int>(1, 6)(gen); +// +template <typename IntType = int> +class uniform_int_distribution { + private: + using unsigned_type = + typename random_internal::make_unsigned_bits<IntType>::type; + + public: + using result_type = IntType; + + class param_type { + public: + using distribution_type = uniform_int_distribution; + + explicit param_type( + result_type lo = 0, + result_type hi = (std::numeric_limits<result_type>::max)()) + : lo_(lo), + range_(static_cast<unsigned_type>(hi) - + static_cast<unsigned_type>(lo)) { + // [rand.dist.uni.int] precondition 2 + assert(lo <= hi); + } + + result_type a() const { return lo_; } + result_type b() const { + return static_cast<result_type>(static_cast<unsigned_type>(lo_) + range_); + } + + friend bool operator==(const param_type& a, const param_type& b) { + return a.lo_ == b.lo_ && a.range_ == b.range_; + } + + friend bool operator!=(const param_type& a, const param_type& b) { + return !(a == b); + } + + private: + friend class uniform_int_distribution; + unsigned_type range() const { return range_; } + + result_type lo_; + unsigned_type range_; + + static_assert(std::is_integral<result_type>::value, + "Class-template absl::uniform_int_distribution<> must be " + "parameterized using an integral type."); + }; // param_type + + uniform_int_distribution() : uniform_int_distribution(0) {} + + explicit uniform_int_distribution( + result_type lo, + result_type hi = (std::numeric_limits<result_type>::max)()) + : param_(lo, hi) {} + + explicit uniform_int_distribution(const param_type& param) : param_(param) {} + + // uniform_int_distribution<T>::reset() + // + // Resets the uniform int distribution. Note that this function has no effect + // because the distribution already produces independent values. + void reset() {} + + template <typename URBG> + result_type operator()(URBG& gen) { // NOLINT(runtime/references) + return (*this)(gen, param()); + } + + template <typename URBG> + result_type operator()( + URBG& gen, const param_type& param) { // NOLINT(runtime/references) + return param.a() + Generate(gen, param.range()); + } + + result_type a() const { return param_.a(); } + result_type b() const { return param_.b(); } + + param_type param() const { return param_; } + void param(const param_type& params) { param_ = params; } + + result_type(min)() const { return a(); } + result_type(max)() const { return b(); } + + friend bool operator==(const uniform_int_distribution& a, + const uniform_int_distribution& b) { + return a.param_ == b.param_; + } + friend bool operator!=(const uniform_int_distribution& a, + const uniform_int_distribution& b) { + return !(a == b); + } + + private: + // Generates a value in the *closed* interval [0, R] + template <typename URBG> + unsigned_type Generate(URBG& g, // NOLINT(runtime/references) + unsigned_type R); + param_type param_; +}; + +// ----------------------------------------------------------------------------- +// Implementation details follow +// ----------------------------------------------------------------------------- +template <typename CharT, typename Traits, typename IntType> +std::basic_ostream<CharT, Traits>& operator<<( + std::basic_ostream<CharT, Traits>& os, + const uniform_int_distribution<IntType>& x) { + using stream_type = + typename random_internal::stream_format_type<IntType>::type; + auto saver = random_internal::make_ostream_state_saver(os); + os << static_cast<stream_type>(x.a()) << os.fill() + << static_cast<stream_type>(x.b()); + return os; +} + +template <typename CharT, typename Traits, typename IntType> +std::basic_istream<CharT, Traits>& operator>>( + std::basic_istream<CharT, Traits>& is, + uniform_int_distribution<IntType>& x) { + using param_type = typename uniform_int_distribution<IntType>::param_type; + using result_type = typename uniform_int_distribution<IntType>::result_type; + using stream_type = + typename random_internal::stream_format_type<IntType>::type; + + stream_type a; + stream_type b; + + auto saver = random_internal::make_istream_state_saver(is); + is >> a >> b; + if (!is.fail()) { + x.param( + param_type(static_cast<result_type>(a), static_cast<result_type>(b))); + } + return is; +} + +template <typename IntType> +template <typename URBG> +typename random_internal::make_unsigned_bits<IntType>::type +uniform_int_distribution<IntType>::Generate( + URBG& g, // NOLINT(runtime/references) + typename random_internal::make_unsigned_bits<IntType>::type R) { + random_internal::FastUniformBits<unsigned_type> fast_bits; + unsigned_type bits = fast_bits(g); + const unsigned_type Lim = R + 1; + if ((R & Lim) == 0) { + // If the interval's length is a power of two range, just take the low bits. + return bits & R; + } + + // Generates a uniform variate on [0, Lim) using fixed-point multiplication. + // The above fast-path guarantees that Lim is representable in unsigned_type. + // + // Algorithm adapted from + // http://lemire.me/blog/2016/06/30/fast-random-shuffling/, with added + // explanation. + // + // The algorithm creates a uniform variate `bits` in the interval [0, 2^N), + // and treats it as the fractional part of a fixed-point real value in [0, 1), + // multiplied by 2^N. For example, 0.25 would be represented as 2^(N - 2), + // because 2^N * 0.25 == 2^(N - 2). + // + // Next, `bits` and `Lim` are multiplied with a wide-multiply to bring the + // value into the range [0, Lim). The integral part (the high word of the + // multiplication result) is then very nearly the desired result. However, + // this is not quite accurate; viewing the multiplication result as one + // double-width integer, the resulting values for the sample are mapped as + // follows: + // + // If the result lies in this interval: Return this value: + // [0, 2^N) 0 + // [2^N, 2 * 2^N) 1 + // ... ... + // [K * 2^N, (K + 1) * 2^N) K + // ... ... + // [(Lim - 1) * 2^N, Lim * 2^N) Lim - 1 + // + // While all of these intervals have the same size, the result of `bits * Lim` + // must be a multiple of `Lim`, and not all of these intervals contain the + // same number of multiples of `Lim`. In particular, some contain + // `F = floor(2^N / Lim)` and some contain `F + 1 = ceil(2^N / Lim)`. This + // difference produces a small nonuniformity, which is corrected by applying + // rejection sampling to one of the values in the "larger intervals" (i.e., + // the intervals containing `F + 1` multiples of `Lim`. + // + // An interval contains `F + 1` multiples of `Lim` if and only if its smallest + // value modulo 2^N is less than `2^N % Lim`. The unique value satisfying + // this property is used as the one for rejection. That is, a value of + // `bits * Lim` is rejected if `(bit * Lim) % 2^N < (2^N % Lim)`. + + using helper = random_internal::wide_multiply<unsigned_type>; + auto product = helper::multiply(bits, Lim); + + // Two optimizations here: + // * Rejection occurs with some probability less than 1/2, and for reasonable + // ranges considerably less (in particular, less than 1/(F+1)), so + // ABSL_PREDICT_FALSE is apt. + // * `Lim` is an overestimate of `threshold`, and doesn't require a divide. + if (ABSL_PREDICT_FALSE(helper::lo(product) < Lim)) { + // This quantity is exactly equal to `2^N % Lim`, but does not require high + // precision calculations: `2^N % Lim` is congruent to `(2^N - Lim) % Lim`. + // Ideally this could be expressed simply as `-X` rather than `2^N - X`, but + // for types smaller than int, this calculation is incorrect due to integer + // promotion rules. + const unsigned_type threshold = + ((std::numeric_limits<unsigned_type>::max)() - Lim + 1) % Lim; + while (helper::lo(product) < threshold) { + bits = fast_bits(g); + product = helper::multiply(bits, Lim); + } + } + + return helper::hi(product); +} + +} // namespace absl + +#endif // ABSL_RANDOM_UNIFORM_INT_DISTRIBUTION_H_ |