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// 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
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// See the License for the specific language governing permissions and
// limitations under the License.
#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 {
// 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 {
using result_type = bool;
class param_type {
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();
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_;
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 << 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 (! {
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 casting explicitly 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 convert to
// unsigned (which is a no-op).
const uint64_t c = static_cast<uint64_t>(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;
} // namespace absl