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bernoulli_distribution.h (7632B)

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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
//
//      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 <cassert>
#include <cstdint>
#include <istream>
#include <ostream>

#include "absl/base/config.h"
#include "absl/base/optimization.h"
#include "absl/random/internal/fast_uniform_bits.h"
#include "absl/random/internal/iostream_state_saver.h"

namespace absl {
ABSL_NAMESPACE_BEGIN

// 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 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;
 }
}

ABSL_NAMESPACE_END
}  // namespace absl

#endif  // ABSL_RANDOM_BERNOULLI_DISTRIBUTION_H_