THUAI6/CAPI/cpp/grpc/include/absl/random/bernoulli_distribution.h

// 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_