diff options
Diffstat (limited to 'absl/random/bernoulli_distribution.h')
| -rw-r--r-- | absl/random/bernoulli_distribution.h | 200 |
1 files changed, 200 insertions, 0 deletions
diff --git a/absl/random/bernoulli_distribution.h b/absl/random/bernoulli_distribution.h new file mode 100644 index 00000000..0afc2c14 --- /dev/null +++ b/absl/random/bernoulli_distribution.h @@ -0,0 +1,200 @@ +// 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_BERNOULLI_DISTRIBUTION_H_ +#define ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_ + +#include <cstdint> +#include <istream> +#include <limits> + +#include "absl/base/optimization.h" +#include "absl/random/internal/fast_uniform_bits.h" +#include "absl/random/internal/iostream_state_saver.h" + +namespace absl { +inline namespace lts_2019_08_08 { + +// absl::bernoulli_distribution is a drop in replacement for +// std::bernoulli_distribution. It guarantees that (given a perfect +// UniformRandomBitGenerator) the acceptance probability is *exactly* equal to +// the given double. +// +// The implementation assumes that double is IEEE754 +class bernoulli_distribution { + public: + using result_type = bool; + + class param_type { + public: + using distribution_type = bernoulli_distribution; + + explicit param_type(double p = 0.5) : prob_(p) { + assert(p >= 0.0 && p <= 1.0); + } + + double p() const { return prob_; } + + friend bool operator==(const param_type& p1, const param_type& p2) { + return p1.p() == p2.p(); + } + friend bool operator!=(const param_type& p1, const param_type& p2) { + return p1.p() != p2.p(); + } + + private: + double prob_; + }; + + bernoulli_distribution() : bernoulli_distribution(0.5) {} + + explicit bernoulli_distribution(double p) : param_(p) {} + + explicit bernoulli_distribution(param_type p) : param_(p) {} + + // no-op + void reset() {} + + template <typename URBG> + bool operator()(URBG& g) { // NOLINT(runtime/references) + return Generate(param_.p(), g); + } + + template <typename URBG> + bool operator()(URBG& g, // NOLINT(runtime/references) + const param_type& param) { + return Generate(param.p(), g); + } + + param_type param() const { return param_; } + void param(const param_type& param) { param_ = param; } + + double p() const { return param_.p(); } + + result_type(min)() const { return false; } + result_type(max)() const { return true; } + + friend bool operator==(const bernoulli_distribution& d1, + const bernoulli_distribution& d2) { + return d1.param_ == d2.param_; + } + + friend bool operator!=(const bernoulli_distribution& d1, + const bernoulli_distribution& d2) { + return d1.param_ != d2.param_; + } + + private: + static constexpr uint64_t kP32 = static_cast<uint64_t>(1) << 32; + + template <typename URBG> + static bool Generate(double p, URBG& g); // NOLINT(runtime/references) + + param_type param_; +}; + +template <typename CharT, typename Traits> +std::basic_ostream<CharT, Traits>& operator<<( + std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references) + const bernoulli_distribution& x) { + auto saver = random_internal::make_ostream_state_saver(os); + os.precision(random_internal::stream_precision_helper<double>::kPrecision); + os << x.p(); + return os; +} + +template <typename CharT, typename Traits> +std::basic_istream<CharT, Traits>& operator>>( + std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references) + bernoulli_distribution& x) { // NOLINT(runtime/references) + auto saver = random_internal::make_istream_state_saver(is); + auto p = random_internal::read_floating_point<double>(is); + if (!is.fail()) { + x.param(bernoulli_distribution::param_type(p)); + } + return is; +} + +template <typename URBG> +bool bernoulli_distribution::Generate(double p, + URBG& g) { // NOLINT(runtime/references) + random_internal::FastUniformBits<uint32_t> fast_u32; + + while (true) { + // There are two aspects of the definition of `c` below that are worth + // commenting on. First, because `p` is in the range [0, 1], `c` is in the + // range [0, 2^32] which does not fit in a uint32_t and therefore requires + // 64 bits. + // + // Second, `c` is constructed by first casting explicitly to a signed + // integer and then converting implicitly to an unsigned integer of the same + // size. This is done because the hardware conversion instructions produce + // signed integers from double; if taken as a uint64_t the conversion would + // be wrong for doubles greater than 2^63 (not relevant in this use-case). + // If converted directly to an unsigned integer, the compiler would end up + // emitting code to handle such large values that are not relevant due to + // the known bounds on `c`. To avoid these extra instructions this + // implementation converts first to the signed type and then use the + // implicit conversion to unsigned (which is a no-op). + const uint64_t c = static_cast<int64_t>(p * kP32); + const uint32_t v = fast_u32(g); + // FAST PATH: this path fails with probability 1/2^32. Note that simply + // returning v <= c would approximate P very well (up to an absolute error + // of 1/2^32); the slow path (taken in that range of possible error, in the + // case of equality) eliminates the remaining error. + if (ABSL_PREDICT_TRUE(v != c)) return v < c; + + // It is guaranteed that `q` is strictly less than 1, because if `q` were + // greater than or equal to 1, the same would be true for `p`. Certainly `p` + // cannot be greater than 1, and if `p == 1`, then the fast path would + // necessary have been taken already. + const double q = static_cast<double>(c) / kP32; + + // The probability of acceptance on the fast path is `q` and so the + // probability of acceptance here should be `p - q`. + // + // Note that `q` is obtained from `p` via some shifts and conversions, the + // upshot of which is that `q` is simply `p` with some of the + // least-significant bits of its mantissa set to zero. This means that the + // difference `p - q` will not have any rounding errors. To see why, pretend + // that double has 10 bits of resolution and q is obtained from `p` in such + // a way that the 4 least-significant bits of its mantissa are set to zero. + // For example: + // p = 1.1100111011 * 2^-1 + // q = 1.1100110000 * 2^-1 + // p - q = 1.011 * 2^-8 + // The difference `p - q` has exactly the nonzero mantissa bits that were + // "lost" in `q` producing a number which is certainly representable in a + // double. + const double left = p - q; + + // By construction, the probability of being on this slow path is 1/2^32, so + // P(accept in slow path) = P(accept| in slow path) * P(slow path), + // which means the probability of acceptance here is `1 / (left * kP32)`: + const double here = left * kP32; + + // The simplest way to compute the result of this trial is to repeat the + // whole algorithm with the new probability. This terminates because even + // given arbitrarily unfriendly "random" bits, each iteration either + // multiplies a tiny probability by 2^32 (if c == 0) or strips off some + // number of nonzero mantissa bits. That process is bounded. + if (here == 0) return false; + p = here; + } +} + +} // inline namespace lts_2019_08_08 +} // namespace absl + +#endif // ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_ |