201 lines
7.4 KiB
C++
201 lines
7.4 KiB
C++
// Copyright 2017 The Abseil Authors.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// https://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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#ifndef ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_
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#define ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_
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#include <cstdint>
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#include <istream>
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#include <limits>
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#include "absl/base/optimization.h"
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#include "absl/random/internal/fast_uniform_bits.h"
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#include "absl/random/internal/iostream_state_saver.h"
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namespace absl {
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ABSL_NAMESPACE_BEGIN
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// absl::bernoulli_distribution is a drop in replacement for
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// std::bernoulli_distribution. It guarantees that (given a perfect
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// UniformRandomBitGenerator) the acceptance probability is *exactly* equal to
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// the given double.
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//
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// The implementation assumes that double is IEEE754
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class bernoulli_distribution {
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public:
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using result_type = bool;
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class param_type {
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public:
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using distribution_type = bernoulli_distribution;
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explicit param_type(double p = 0.5) : prob_(p) {
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assert(p >= 0.0 && p <= 1.0);
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}
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double p() const { return prob_; }
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friend bool operator==(const param_type& p1, const param_type& p2) {
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return p1.p() == p2.p();
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}
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friend bool operator!=(const param_type& p1, const param_type& p2) {
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return p1.p() != p2.p();
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}
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private:
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double prob_;
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};
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bernoulli_distribution() : bernoulli_distribution(0.5) {}
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explicit bernoulli_distribution(double p) : param_(p) {}
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explicit bernoulli_distribution(param_type p) : param_(p) {}
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// no-op
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void reset() {}
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template <typename URBG>
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bool operator()(URBG& g) { // NOLINT(runtime/references)
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return Generate(param_.p(), g);
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}
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template <typename URBG>
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bool operator()(URBG& g, // NOLINT(runtime/references)
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const param_type& param) {
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return Generate(param.p(), g);
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}
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param_type param() const { return param_; }
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void param(const param_type& param) { param_ = param; }
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double p() const { return param_.p(); }
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result_type(min)() const { return false; }
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result_type(max)() const { return true; }
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friend bool operator==(const bernoulli_distribution& d1,
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const bernoulli_distribution& d2) {
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return d1.param_ == d2.param_;
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}
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friend bool operator!=(const bernoulli_distribution& d1,
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const bernoulli_distribution& d2) {
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return d1.param_ != d2.param_;
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}
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private:
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static constexpr uint64_t kP32 = static_cast<uint64_t>(1) << 32;
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template <typename URBG>
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static bool Generate(double p, URBG& g); // NOLINT(runtime/references)
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param_type param_;
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};
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template <typename CharT, typename Traits>
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std::basic_ostream<CharT, Traits>& operator<<(
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std::basic_ostream<CharT, Traits>& os, // NOLINT(runtime/references)
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const bernoulli_distribution& x) {
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auto saver = random_internal::make_ostream_state_saver(os);
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os.precision(random_internal::stream_precision_helper<double>::kPrecision);
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os << x.p();
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return os;
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}
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template <typename CharT, typename Traits>
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std::basic_istream<CharT, Traits>& operator>>(
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std::basic_istream<CharT, Traits>& is, // NOLINT(runtime/references)
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bernoulli_distribution& x) { // NOLINT(runtime/references)
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auto saver = random_internal::make_istream_state_saver(is);
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auto p = random_internal::read_floating_point<double>(is);
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if (!is.fail()) {
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x.param(bernoulli_distribution::param_type(p));
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}
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return is;
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}
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template <typename URBG>
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bool bernoulli_distribution::Generate(double p,
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URBG& g) { // NOLINT(runtime/references)
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random_internal::FastUniformBits<uint32_t> fast_u32;
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while (true) {
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// There are two aspects of the definition of `c` below that are worth
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// commenting on. First, because `p` is in the range [0, 1], `c` is in the
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// range [0, 2^32] which does not fit in a uint32_t and therefore requires
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// 64 bits.
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//
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// Second, `c` is constructed by first casting explicitly to a signed
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// integer and then casting explicitly to an unsigned integer of the same
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// size. This is done because the hardware conversion instructions produce
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// signed integers from double; if taken as a uint64_t the conversion would
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// be wrong for doubles greater than 2^63 (not relevant in this use-case).
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// If converted directly to an unsigned integer, the compiler would end up
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// emitting code to handle such large values that are not relevant due to
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// the known bounds on `c`. To avoid these extra instructions this
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// implementation converts first to the signed type and then convert to
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// unsigned (which is a no-op).
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const uint64_t c = static_cast<uint64_t>(static_cast<int64_t>(p * kP32));
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const uint32_t v = fast_u32(g);
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// FAST PATH: this path fails with probability 1/2^32. Note that simply
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// returning v <= c would approximate P very well (up to an absolute error
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// of 1/2^32); the slow path (taken in that range of possible error, in the
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// case of equality) eliminates the remaining error.
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if (ABSL_PREDICT_TRUE(v != c)) return v < c;
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// It is guaranteed that `q` is strictly less than 1, because if `q` were
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// greater than or equal to 1, the same would be true for `p`. Certainly `p`
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// cannot be greater than 1, and if `p == 1`, then the fast path would
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// necessary have been taken already.
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const double q = static_cast<double>(c) / kP32;
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// The probability of acceptance on the fast path is `q` and so the
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// probability of acceptance here should be `p - q`.
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//
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// Note that `q` is obtained from `p` via some shifts and conversions, the
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// upshot of which is that `q` is simply `p` with some of the
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// least-significant bits of its mantissa set to zero. This means that the
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// difference `p - q` will not have any rounding errors. To see why, pretend
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// that double has 10 bits of resolution and q is obtained from `p` in such
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// a way that the 4 least-significant bits of its mantissa are set to zero.
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// For example:
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// p = 1.1100111011 * 2^-1
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// q = 1.1100110000 * 2^-1
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// p - q = 1.011 * 2^-8
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// The difference `p - q` has exactly the nonzero mantissa bits that were
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// "lost" in `q` producing a number which is certainly representable in a
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// double.
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const double left = p - q;
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// By construction, the probability of being on this slow path is 1/2^32, so
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// P(accept in slow path) = P(accept| in slow path) * P(slow path),
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// which means the probability of acceptance here is `1 / (left * kP32)`:
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const double here = left * kP32;
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// The simplest way to compute the result of this trial is to repeat the
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// whole algorithm with the new probability. This terminates because even
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// given arbitrarily unfriendly "random" bits, each iteration either
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// multiplies a tiny probability by 2^32 (if c == 0) or strips off some
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// number of nonzero mantissa bits. That process is bounded.
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if (here == 0) return false;
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p = here;
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}
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}
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ABSL_NAMESPACE_END
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} // namespace absl
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#endif // ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_
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