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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 <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_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_

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