// 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_