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 /*
  * PCG Random Number Generation for C++
  *
  * Copyright 2014-2019 Melissa O'Neill <oneill@pcg-random.org>,
  *                     and the PCG Project contributors.
  *
  * SPDX-License-Identifier: (Apache-2.0 OR MIT)
  *
  * Licensed under the Apache License, Version 2.0 (provided in
  * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0)
  * or under the MIT license (provided in LICENSE-MIT.txt and at
  * http://opensource.org/licenses/MIT), at your option. This file may not
  * be copied, modified, or distributed except according to those terms.
  *
  * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either
  * express or implied.  See your chosen license for details.
  *
  * For additional information about the PCG random number generation scheme,
  * visit http://www.pcg-random.org/.
  */
 
 /*
  * This code provides the reference implementation of the PCG family of
  * random number generators.  The code is complex because it implements
  *
  *      - several members of the PCG family, specifically members corresponding
  *        to the output functions:
  *             - XSH RR         (good for 64-bit state, 32-bit output)
  *             - XSH RS         (good for 64-bit state, 32-bit output)
  *             - XSL RR         (good for 128-bit state, 64-bit output)
  *             - RXS M XS       (statistically most powerful generator)
  *             - XSL RR RR      (good for 128-bit state, 128-bit output)
  *             - and RXS, RXS M, XSH, XSL       (mostly for testing)
  *      - at potentially *arbitrary* bit sizes
  *      - with four different techniques for random streams (MCG, one-stream
  *        LCG, settable-stream LCG, unique-stream LCG)
  *      - and the extended generation schemes allowing arbitrary periods
  *      - with all features of C++11 random number generation (and more),
  *        some of which are somewhat painful, including
  *            - initializing with a SeedSequence which writes 32-bit values
  *              to memory, even though the state of the generator may not
  *              use 32-bit values (it might use smaller or larger integers)
  *            - I/O for RNGs and a prescribed format, which needs to handle
  *              the issue that 8-bit and 128-bit integers don't have working
  *              I/O routines (e.g., normally 8-bit = char, not integer)
  *            - equality and inequality for RNGs
  *      - and a number of convenience typedefs to mask all the complexity
  *
  * The code employes a fairly heavy level of abstraction, and has to deal
  * with various C++ minutia.  If you're looking to learn about how the PCG
  * scheme works, you're probably best of starting with one of the other
  * codebases (see www.pcg-random.org).  But if you're curious about the
  * constants for the various output functions used in those other, simpler,
  * codebases, this code shows how they are calculated.
  *
  * On the positive side, at least there are convenience typedefs so that you
  * can say
  *
  *      pcg32 myRNG;
  *
  * rather than:
  *
  *      pcg_detail::engine<
  *          uint32_t,                                           // Output Type
  *          uint64_t,                                           // State Type
  *          pcg_detail::xsh_rr_mixin<uint32_t, uint64_t>, true, // Output Func
  *          pcg_detail::specific_stream<uint64_t>,              // Stream Kind
  *          pcg_detail::default_multiplier<uint64_t>            // LCG Mult
  *      > myRNG;
  *
  */
 
 #ifndef PCG_RAND_HPP_INCLUDED
 #define PCG_RAND_HPP_INCLUDED 1
 
 #include <algorithm>
 #include <cinttypes>
 #include <cstddef>
 #include <cstdlib>
 #include <cstring>
 #include <cassert>
 #include <limits>
 #include <iostream>
 #include <iterator>
 #include <type_traits>
 #include <utility>
 #include <locale>
 #include <new>
 #include <stdexcept>
 
 #ifdef _MSC_VER
     #pragma warning(disable:4146)
 #endif
 
 #ifdef _MSC_VER
     #define PCG_ALWAYS_INLINE __forceinline
 #elif __GNUC__
     #define PCG_ALWAYS_INLINE __attribute__((always_inline))
 #else
     #define PCG_ALWAYS_INLINE inline
 #endif
 
 /*
  * The pcg_extras namespace contains some support code that is likley to
  * be useful for a variety of RNGs, including:
  *      - 128-bit int support for platforms where it isn't available natively
  *      - bit twiddling operations
  *      - I/O of 128-bit and 8-bit integers
  *      - Handling the evilness of SeedSeq
  *      - Support for efficiently producing random numbers less than a given
  *        bound
  */
 
 #include "pcg_extras.hpp"
 
 namespace arrow_vendored {
 namespace pcg_detail {
 
 using namespace pcg_extras;
 
 /*
  * The LCG generators need some constants to function.  This code lets you
  * look up the constant by *type*.  For example
  *
  *      default_multiplier<uint32_t>::multiplier()
  *
  * gives you the default multipler for 32-bit integers.  We use the name
  * of the constant and not a generic word like value to allow these classes
  * to be used as mixins.
  */
 
 template <typename T>
 struct default_multiplier {
     // Not defined for an arbitrary type
 };
 
 template <typename T>
 struct default_increment {
     // Not defined for an arbitrary type
 };
 
 #define PCG_DEFINE_CONSTANT(type, what, kind, constant) \
         template <>                                     \
         struct what ## _ ## kind<type> {                \
             static constexpr type kind() {              \
                 return constant;                        \
             }                                           \
         };
 
 PCG_DEFINE_CONSTANT(uint8_t,  default, multiplier, 141U)
 PCG_DEFINE_CONSTANT(uint8_t,  default, increment,  77U)
 
 PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U)
 PCG_DEFINE_CONSTANT(uint16_t, default, increment,  47989U)
 
 PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U)
 PCG_DEFINE_CONSTANT(uint32_t, default, increment,  2891336453U)
 
 PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL)
 PCG_DEFINE_CONSTANT(uint64_t, default, increment,  1442695040888963407ULL)
 
 PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier,
         PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL))
 PCG_DEFINE_CONSTANT(pcg128_t, default, increment,
         PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL))
 
 /* Alternative (cheaper) multipliers for 128-bit */
 
 template <typename T>
 struct cheap_multiplier : public default_multiplier<T> {
     // For most types just use the default.
 };
 
 template <>
 struct cheap_multiplier<pcg128_t> {
     static constexpr uint64_t multiplier() {
         return 0xda942042e4dd58b5ULL;
     }
 };
 
 
 /*
  * Each PCG generator is available in four variants, based on how it applies
  * the additive constant for its underlying LCG; the variations are:
  *
  *     single stream   - all instances use the same fixed constant, thus
  *                       the RNG always somewhere in same sequence
  *     mcg             - adds zero, resulting in a single stream and reduced
  *                       period
  *     specific stream - the constant can be changed at any time, selecting
  *                       a different random sequence
  *     unique stream   - the constant is based on the memory address of the
  *                       object, thus every RNG has its own unique sequence
  *
  * This variation is provided though mixin classes which define a function
  * value called increment() that returns the nesessary additive constant.
  */
 
 
 
 /*
  * unique stream
  */
 
 
 template <typename itype>
 class unique_stream {
 protected:
     static constexpr bool is_mcg = false;
 
     // Is never called, but is provided for symmetry with specific_stream
     void set_stream(...)
     {
         abort();
     }
 
 public:
     typedef itype state_type;
 
     constexpr itype increment() const {
         return itype(reinterpret_cast<uintptr_t>(this) | 1);
     }
 
     constexpr itype stream() const
     {
          return increment() >> 1;
     }
 
     static constexpr bool can_specify_stream = false;
 
     static constexpr size_t streams_pow2()
     {
         return (sizeof(itype) < sizeof(size_t) ? sizeof(itype)
                                                : sizeof(size_t))*8 - 1u;
     }
 
 protected:
     constexpr unique_stream() = default;
 };
 
 
 /*
  * no stream (mcg)
  */
 
 template <typename itype>
 class no_stream {
 protected:
     static constexpr bool is_mcg = true;
 
     // Is never called, but is provided for symmetry with specific_stream
     void set_stream(...)
     {
         abort();
     }
 
 public:
     typedef itype state_type;
 
     static constexpr itype increment() {
         return 0;
     }
 
     static constexpr bool can_specify_stream = false;
 
     static constexpr size_t streams_pow2()
     {
         return 0u;
     }
 
 protected:
     constexpr no_stream() = default;
 };
 
 
 /*
  * single stream/sequence (oneseq)
  */
 
 template <typename itype>
 class oneseq_stream : public default_increment<itype> {
 protected:
     static constexpr bool is_mcg = false;
 
     // Is never called, but is provided for symmetry with specific_stream
     void set_stream(...)
     {
         abort();
     }
 
 public:
     typedef itype state_type;
 
     static constexpr itype stream()
     {
          return default_increment<itype>::increment() >> 1;
     }
 
     static constexpr bool can_specify_stream = false;
 
     static constexpr size_t streams_pow2()
     {
         return 0u;
     }
 
 protected:
     constexpr oneseq_stream() = default;
 };
 
 
 /*
  * specific stream
  */
 
 template <typename itype>
 class specific_stream {
 protected:
     static constexpr bool is_mcg = false;
 
     itype inc_ = default_increment<itype>::increment();
 
 public:
     typedef itype state_type;
     typedef itype stream_state;
 
     constexpr itype increment() const {
         return inc_;
     }
 
     itype stream()
     {
          return inc_ >> 1;
     }
 
     void set_stream(itype specific_seq)
     {
          inc_ = (specific_seq << 1) | 1;
     }
 
     static constexpr bool can_specify_stream = true;
 
     static constexpr size_t streams_pow2()
     {
         return (sizeof(itype)*8) - 1u;
     }
 
 protected:
     specific_stream() = default;
 
     specific_stream(itype specific_seq)
         : inc_(itype(specific_seq << 1) | itype(1U))
     {
         // Nothing (else) to do.
     }
 };
 
 
 /*
  * This is where it all comes together.  This function joins together three
  * mixin classes which define
  *    - the LCG additive constant (the stream)
  *    - the LCG multiplier
  *    - the output function
  * in addition, we specify the type of the LCG state, and the result type,
  * and whether to use the pre-advance version of the state for the output
  * (increasing instruction-level parallelism) or the post-advance version
  * (reducing register pressure).
  *
  * Given the high level of parameterization, the code has to use some
  * template-metaprogramming tricks to handle some of the suble variations
  * involved.
  */
 
 template <typename xtype, typename itype,
           typename output_mixin,
           bool output_previous = true,
           typename stream_mixin = oneseq_stream<itype>,
           typename multiplier_mixin = default_multiplier<itype> >
 class engine : protected output_mixin,
                public stream_mixin,
                protected multiplier_mixin {
 protected:
     itype state_;
 
     struct can_specify_stream_tag {};
     struct no_specifiable_stream_tag {};
 
     using stream_mixin::increment;
     using multiplier_mixin::multiplier;
 
 public:
     typedef xtype result_type;
     typedef itype state_type;
 
     static constexpr size_t period_pow2()
     {
         return sizeof(state_type)*8 - 2*stream_mixin::is_mcg;
     }
 
     // It would be nice to use std::numeric_limits for these, but
     // we can't be sure that it'd be defined for the 128-bit types.
 
     static constexpr result_type min()
     {
         return result_type(0UL);
     }
 
     static constexpr result_type max()
     {
         return result_type(~result_type(0UL));
     }
 
 protected:
     itype bump(itype state)
     {
         return state * multiplier() + increment();
     }
 
     itype base_generate()
     {
         return state_ = bump(state_);
     }
 
     itype base_generate0()
     {
         itype old_state = state_;
         state_ = bump(state_);
         return old_state;
     }
 
 public:
     result_type operator()()
     {
         if (output_previous)
             return this->output(base_generate0());
         else
             return this->output(base_generate());
     }
 
     result_type operator()(result_type upper_bound)
     {
         return bounded_rand(*this, upper_bound);
     }
 
 protected:
     static itype advance(itype state, itype delta,
                          itype cur_mult, itype cur_plus);
 
     static itype distance(itype cur_state, itype newstate, itype cur_mult,
                           itype cur_plus, itype mask = ~itype(0U));
 
     itype distance(itype newstate, itype mask = itype(~itype(0U))) const
     {
         return distance(state_, newstate, multiplier(), increment(), mask);
     }
 
 public:
     void advance(itype delta)
     {
         state_ = advance(state_, delta, this->multiplier(), this->increment());
     }
 
     void backstep(itype delta)
     {
         advance(-delta);
     }
 
     void discard(itype delta)
     {
         advance(delta);
     }
 
     bool wrapped()
     {
         if (stream_mixin::is_mcg) {
             // For MCGs, the low order two bits never change. In this
             // implementation, we keep them fixed at 3 to make this test
             // easier.
             return state_ == 3;
         } else {
             return state_ == 0;
         }
     }
 
     engine(itype state = itype(0xcafef00dd15ea5e5ULL))
         : state_(this->is_mcg ? state|state_type(3U)
                               : bump(state + this->increment()))
     {
         // Nothing else to do.
     }
 
     // This function may or may not exist.  It thus has to be a template
     // to use SFINAE; users don't have to worry about its template-ness.
 
     template <typename sm = stream_mixin>
     engine(itype state, typename sm::stream_state stream_seed)
         : stream_mixin(stream_seed),
           state_(this->is_mcg ? state|state_type(3U)
                               : bump(state + this->increment()))
     {
         // Nothing else to do.
     }
 
     template<typename SeedSeq>
     engine(SeedSeq&& seedSeq, typename std::enable_if<
                   !stream_mixin::can_specify_stream
                && !std::is_convertible<SeedSeq, itype>::value
                && !std::is_convertible<SeedSeq, engine>::value,
                no_specifiable_stream_tag>::type = {})
         : engine(generate_one<itype>(std::forward<SeedSeq>(seedSeq)))
     {
         // Nothing else to do.
     }
 
     template<typename SeedSeq>
     engine(SeedSeq&& seedSeq, typename std::enable_if<
                    stream_mixin::can_specify_stream
                && !std::is_convertible<SeedSeq, itype>::value
                && !std::is_convertible<SeedSeq, engine>::value,
         can_specify_stream_tag>::type = {})
     {
         itype seeddata[2];
         generate_to<2>(std::forward<SeedSeq>(seedSeq), seeddata);
         seed(seeddata[1], seeddata[0]);
     }
 
 
     template<typename... Args>
     void seed(Args&&... args)
     {
         new (this) engine(std::forward<Args>(args)...);
     }
 
     template <typename xtype1, typename itype1,
               typename output_mixin1, bool output_previous1,
               typename stream_mixin_lhs, typename multiplier_mixin_lhs,
               typename stream_mixin_rhs, typename multiplier_mixin_rhs>
     friend bool operator==(const engine<xtype1,itype1,
                                      output_mixin1,output_previous1,
                                      stream_mixin_lhs, multiplier_mixin_lhs>&,
                            const engine<xtype1,itype1,
                                      output_mixin1,output_previous1,
                                      stream_mixin_rhs, multiplier_mixin_rhs>&);
 
     template <typename xtype1, typename itype1,
               typename output_mixin1, bool output_previous1,
               typename stream_mixin_lhs, typename multiplier_mixin_lhs,
               typename stream_mixin_rhs, typename multiplier_mixin_rhs>
     friend itype1 operator-(const engine<xtype1,itype1,
                                      output_mixin1,output_previous1,
                                      stream_mixin_lhs, multiplier_mixin_lhs>&,
                             const engine<xtype1,itype1,
                                      output_mixin1,output_previous1,
                                      stream_mixin_rhs, multiplier_mixin_rhs>&);
 
     template <typename CharT, typename Traits,
               typename xtype1, typename itype1,
               typename output_mixin1, bool output_previous1,
               typename stream_mixin1, typename multiplier_mixin1>
     friend std::basic_ostream<CharT,Traits>&
     operator<<(std::basic_ostream<CharT,Traits>& out,
                const engine<xtype1,itype1,
                               output_mixin1,output_previous1,
                               stream_mixin1, multiplier_mixin1>&);
 
     template <typename CharT, typename Traits,
               typename xtype1, typename itype1,
               typename output_mixin1, bool output_previous1,
               typename stream_mixin1, typename multiplier_mixin1>
     friend std::basic_istream<CharT,Traits>&
     operator>>(std::basic_istream<CharT,Traits>& in,
                engine<xtype1, itype1,
                         output_mixin1, output_previous1,
                         stream_mixin1, multiplier_mixin1>& rng);
 };
 
 template <typename CharT, typename Traits,
           typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin, typename multiplier_mixin>
 std::basic_ostream<CharT,Traits>&
 operator<<(std::basic_ostream<CharT,Traits>& out,
            const engine<xtype,itype,
                           output_mixin,output_previous,
                           stream_mixin, multiplier_mixin>& rng)
 {
     using pcg_extras::operator<<;
 
     auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left);
     auto space = out.widen(' ');
     auto orig_fill = out.fill();
 
     out << rng.multiplier() << space
         << rng.increment() << space
         << rng.state_;
 
     out.flags(orig_flags);
     out.fill(orig_fill);
     return out;
 }
 
 
 template <typename CharT, typename Traits,
           typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin, typename multiplier_mixin>
 std::basic_istream<CharT,Traits>&
 operator>>(std::basic_istream<CharT,Traits>& in,
            engine<xtype,itype,
                     output_mixin,output_previous,
                     stream_mixin, multiplier_mixin>& rng)
 {
     using pcg_extras::operator>>;
 
     auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws);
 
     itype multiplier, increment, state;
     in >> multiplier >> increment >> state;
 
     if (!in.fail()) {
         bool good = true;
         if (multiplier != rng.multiplier()) {
            good = false;
         } else if (rng.can_specify_stream) {
            rng.set_stream(increment >> 1);
         } else if (increment != rng.increment()) {
            good = false;
         }
         if (good) {
             rng.state_ = state;
         } else {
             in.clear(std::ios::failbit);
         }
     }
 
     in.flags(orig_flags);
     return in;
 }
 
 
 template <typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin, typename multiplier_mixin>
 itype engine<xtype,itype,output_mixin,output_previous,stream_mixin,
              multiplier_mixin>::advance(
     itype state, itype delta, itype cur_mult, itype cur_plus)
 {
     // The method used here is based on Brown, "Random Number Generation
     // with Arbitrary Stride,", Transactions of the American Nuclear
     // Society (Nov. 1994).  The algorithm is very similar to fast
     // exponentiation.
     //
     // Even though delta is an unsigned integer, we can pass a
     // signed integer to go backwards, it just goes "the long way round".
 
     constexpr itype ZERO = 0u;  // itype may be a non-trivial types, so
     constexpr itype ONE  = 1u;  // we define some ugly constants.
     itype acc_mult = 1;
     itype acc_plus = 0;
     while (delta > ZERO) {
        if (delta & ONE) {
           acc_mult *= cur_mult;
           acc_plus = acc_plus*cur_mult + cur_plus;
        }
        cur_plus = (cur_mult+ONE)*cur_plus;
        cur_mult *= cur_mult;
        delta >>= 1;
     }
     return acc_mult * state + acc_plus;
 }
 
 template <typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin, typename multiplier_mixin>
 itype engine<xtype,itype,output_mixin,output_previous,stream_mixin,
                multiplier_mixin>::distance(
     itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask)
 {
     constexpr itype ONE  = 1u;  // itype could be weird, so use constant
     bool is_mcg = cur_plus == itype(0);
     itype the_bit = is_mcg ? itype(4u) : itype(1u);
     itype distance = 0u;
     while ((cur_state & mask) != (newstate & mask)) {
        if ((cur_state & the_bit) != (newstate & the_bit)) {
            cur_state = cur_state * cur_mult + cur_plus;
            distance |= the_bit;
        }
        assert((cur_state & the_bit) == (newstate & the_bit));
        the_bit <<= 1;
        cur_plus = (cur_mult+ONE)*cur_plus;
        cur_mult *= cur_mult;
     }
     return is_mcg ? distance >> 2 : distance;
 }
 
 template <typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin_lhs, typename multiplier_mixin_lhs,
           typename stream_mixin_rhs, typename multiplier_mixin_rhs>
 itype operator-(const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
                const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
 {
     static_assert(
         std::is_same<stream_mixin_lhs, stream_mixin_rhs>::value &&
             std::is_same<multiplier_mixin_lhs, multiplier_mixin_rhs>::value,
         "Incomparable generators");
     if (lhs.increment() == rhs.increment()) {
        return rhs.distance(lhs.state_);
     } else  {
        constexpr itype ONE = 1u;
        itype lhs_diff = lhs.increment() + (lhs.multiplier()-ONE) * lhs.state_;
        itype rhs_diff = rhs.increment() + (rhs.multiplier()-ONE) * rhs.state_;
        if ((lhs_diff & itype(3u)) != (rhs_diff & itype(3u))) {
            rhs_diff = -rhs_diff;
        }
        return rhs.distance(rhs_diff, lhs_diff, rhs.multiplier(), itype(0u));
     }
 }
 
 
 template <typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin_lhs, typename multiplier_mixin_lhs,
           typename stream_mixin_rhs, typename multiplier_mixin_rhs>
 bool operator==(const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
                 const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
 {
     return    (lhs.multiplier() == rhs.multiplier())
            && (lhs.increment()  == rhs.increment())
            && (lhs.state_       == rhs.state_);
 }
 
 template <typename xtype, typename itype,
           typename output_mixin, bool output_previous,
           typename stream_mixin_lhs, typename multiplier_mixin_lhs,
           typename stream_mixin_rhs, typename multiplier_mixin_rhs>
 inline bool operator!=(const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
                        const engine<xtype,itype,
                                output_mixin,output_previous,
                                stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
 {
     return !operator==(lhs,rhs);
 }
 
 
 template <typename xtype, typename itype,
          template<typename XT,typename IT> class output_mixin,
          bool output_previous = (sizeof(itype) <= 8),
          template<typename IT> class multiplier_mixin = default_multiplier>
 using oneseq_base  = engine<xtype, itype,
                         output_mixin<xtype, itype>, output_previous,
                         oneseq_stream<itype>,
                         multiplier_mixin<itype> >;
 
 template <typename xtype, typename itype,
          template<typename XT,typename IT> class output_mixin,
          bool output_previous = (sizeof(itype) <= 8),
          template<typename IT> class multiplier_mixin = default_multiplier>
 using unique_base = engine<xtype, itype,
                          output_mixin<xtype, itype>, output_previous,
                          unique_stream<itype>,
                          multiplier_mixin<itype> >;
 
 template <typename xtype, typename itype,
          template<typename XT,typename IT> class output_mixin,
          bool output_previous = (sizeof(itype) <= 8),
          template<typename IT> class multiplier_mixin = default_multiplier>
 using setseq_base = engine<xtype, itype,
                          output_mixin<xtype, itype>, output_previous,
                          specific_stream<itype>,
                          multiplier_mixin<itype> >;
 
 template <typename xtype, typename itype,
          template<typename XT,typename IT> class output_mixin,
          bool output_previous = (sizeof(itype) <= 8),
          template<typename IT> class multiplier_mixin = default_multiplier>
 using mcg_base = engine<xtype, itype,
                       output_mixin<xtype, itype>, output_previous,
                       no_stream<itype>,
                       multiplier_mixin<itype> >;
 
 /*
  * OUTPUT FUNCTIONS.
  *
  * These are the core of the PCG generation scheme.  They specify how to
  * turn the base LCG's internal state into the output value of the final
  * generator.
  *
  * They're implemented as mixin classes.
  *
  * All of the classes have code that is written to allow it to be applied
  * at *arbitrary* bit sizes, although in practice they'll only be used at
  * standard sizes supported by C++.
  */
 
 /*
  * XSH RS -- high xorshift, followed by a random shift
  *
  * Fast.  A good performer.
  */
 
 template <typename xtype, typename itype>
 struct xsh_rs_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t bits        = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t xtypebits   = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t sparebits   = bits - xtypebits;
         constexpr bitcount_t opbits =
                               sparebits-5 >= 64 ? 5
                             : sparebits-4 >= 32 ? 4
                             : sparebits-3 >= 16 ? 3
                             : sparebits-2 >= 4  ? 2
                             : sparebits-1 >= 1  ? 1
                             :                     0;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         constexpr bitcount_t maxrandshift  = mask;
         constexpr bitcount_t topspare     = opbits;
         constexpr bitcount_t bottomspare = sparebits - topspare;
         constexpr bitcount_t xshift     = topspare + (xtypebits+maxrandshift)/2;
         bitcount_t rshift =
             opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
         internal ^= internal >> xshift;
         xtype result = xtype(internal >> (bottomspare - maxrandshift + rshift));
         return result;
     }
 };
 
 /*
  * XSH RR -- high xorshift, followed by a random rotate
  *
  * Fast.  A good performer.  Slightly better statistically than XSH RS.
  */
 
 template <typename xtype, typename itype>
 struct xsh_rr_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t bits        = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t xtypebits   = bitcount_t(sizeof(xtype)*8);
         constexpr bitcount_t sparebits   = bits - xtypebits;
         constexpr bitcount_t wantedopbits =
                               xtypebits >= 128 ? 7
                             : xtypebits >=  64 ? 6
                             : xtypebits >=  32 ? 5
                             : xtypebits >=  16 ? 4
                             :                    3;
         constexpr bitcount_t opbits =
                               sparebits >= wantedopbits ? wantedopbits
                                                         : sparebits;
         constexpr bitcount_t amplifier = wantedopbits - opbits;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         constexpr bitcount_t topspare    = opbits;
         constexpr bitcount_t bottomspare = sparebits - topspare;
         constexpr bitcount_t xshift      = (topspare + xtypebits)/2;
         bitcount_t rot = opbits ? bitcount_t(internal >> (bits - opbits)) & mask
                                 : 0;
         bitcount_t amprot = (rot << amplifier) & mask;
         internal ^= internal >> xshift;
         xtype result = xtype(internal >> bottomspare);
         result = rotr(result, amprot);
         return result;
     }
 };
 
 /*
  * RXS -- random xorshift
  */
 
 template <typename xtype, typename itype>
 struct rxs_mixin {
 static xtype output_rxs(itype internal)
     {
         constexpr bitcount_t bits        = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t xtypebits   = bitcount_t(sizeof(xtype)*8);
         constexpr bitcount_t shift       = bits - xtypebits;
         constexpr bitcount_t extrashift  = (xtypebits - shift)/2;
         bitcount_t rshift = shift > 64+8 ? (internal >> (bits - 6)) & 63
                        : shift > 32+4 ? (internal >> (bits - 5)) & 31
                        : shift > 16+2 ? (internal >> (bits - 4)) & 15
                        : shift >  8+1 ? (internal >> (bits - 3)) & 7
                        : shift >  4+1 ? (internal >> (bits - 2)) & 3
                        : shift >  2+1 ? (internal >> (bits - 1)) & 1
                        :              0;
         internal ^= internal >> (shift + extrashift - rshift);
         xtype result = internal >> rshift;
         return result;
     }
 };
 
 /*
  * RXS M XS -- random xorshift, mcg multiply, fixed xorshift
  *
  * The most statistically powerful generator, but all those steps
  * make it slower than some of the others.  We give it the rottenest jobs.
  *
  * Because it's usually used in contexts where the state type and the
  * result type are the same, it is a permutation and is thus invertable.
  * We thus provide a function to invert it.  This function is used to
  * for the "inside out" generator used by the extended generator.
  */
 
 /* Defined type-based concepts for the multiplication step.  They're actually
  * all derived by truncating the 128-bit, which was computed to be a good
  * "universal" constant.
  */
 
 template <typename T>
 struct mcg_multiplier {
     // Not defined for an arbitrary type
 };
 
 template <typename T>
 struct mcg_unmultiplier {
     // Not defined for an arbitrary type
 };
 
 PCG_DEFINE_CONSTANT(uint8_t,  mcg, multiplier,   217U)
 PCG_DEFINE_CONSTANT(uint8_t,  mcg, unmultiplier, 105U)
 
 PCG_DEFINE_CONSTANT(uint16_t, mcg, multiplier,   62169U)
 PCG_DEFINE_CONSTANT(uint16_t, mcg, unmultiplier, 28009U)
 
 PCG_DEFINE_CONSTANT(uint32_t, mcg, multiplier,   277803737U)
 PCG_DEFINE_CONSTANT(uint32_t, mcg, unmultiplier, 2897767785U)
 
 PCG_DEFINE_CONSTANT(uint64_t, mcg, multiplier,   12605985483714917081ULL)
 PCG_DEFINE_CONSTANT(uint64_t, mcg, unmultiplier, 15009553638781119849ULL)
 
 PCG_DEFINE_CONSTANT(pcg128_t, mcg, multiplier,
         PCG_128BIT_CONSTANT(17766728186571221404ULL, 12605985483714917081ULL))
 PCG_DEFINE_CONSTANT(pcg128_t, mcg, unmultiplier,
         PCG_128BIT_CONSTANT(14422606686972528997ULL, 15009553638781119849ULL))
 
 
 template <typename xtype, typename itype>
 struct rxs_m_xs_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t opbits = xtypebits >= 128 ? 6
                                  : xtypebits >=  64 ? 5
                                  : xtypebits >=  32 ? 4
                                  : xtypebits >=  16 ? 3
                                  :                    2;
         constexpr bitcount_t shift = bits - xtypebits;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         bitcount_t rshift =
             opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
         internal ^= internal >> (opbits + rshift);
         internal *= mcg_multiplier<itype>::multiplier();
         xtype result = internal >> shift;
         result ^= result >> ((2U*xtypebits+2U)/3U);
         return result;
     }
 
     static itype unoutput(itype internal)
     {
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t opbits = bits >= 128 ? 6
                                  : bits >=  64 ? 5
                                  : bits >=  32 ? 4
                                  : bits >=  16 ? 3
                                  :               2;
         constexpr bitcount_t mask = (1 << opbits) - 1;
 
         internal = unxorshift(internal, bits, (2U*bits+2U)/3U);
 
         internal *= mcg_unmultiplier<itype>::unmultiplier();
 
         bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
         internal = unxorshift(internal, bits, opbits + rshift);
 
         return internal;
     }
 };
 
 
 /*
  * RXS M -- random xorshift, mcg multiply
  */
 
 template <typename xtype, typename itype>
 struct rxs_m_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t opbits = xtypebits >= 128 ? 6
                                  : xtypebits >=  64 ? 5
                                  : xtypebits >=  32 ? 4
                                  : xtypebits >=  16 ? 3
                                  :                    2;
         constexpr bitcount_t shift = bits - xtypebits;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
         internal ^= internal >> (opbits + rshift);
         internal *= mcg_multiplier<itype>::multiplier();
         xtype result = internal >> shift;
         return result;
     }
 };
 
 
 /*
  * DXSM -- double xorshift multiply
  *
  * This is a new, more powerful output permutation (added in 2019).  It's
  * a more comprehensive scrambling than RXS M, but runs faster on 128-bit
  * types.  Although primarily intended for use at large sizes, also works
  * at smaller sizes as well.
  *
  * This permutation is similar to xorshift multiply hash functions, except
  * that one of the multipliers is the LCG multiplier (to avoid needing to
  * have a second constant) and the other is based on the low-order bits.
  * This latter aspect means that the scrambling applied to the high bits
  * depends on the low bits, and makes it (to my eye) impractical to back
  * out the permutation without having the low-order bits.
  */
 
 template <typename xtype, typename itype>
 struct dxsm_mixin {
     inline xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t itypebits = bitcount_t(sizeof(itype) * 8);
         static_assert(xtypebits <= itypebits/2,
                       "Output type must be half the size of the state type.");
         
         xtype hi = xtype(internal >> (itypebits - xtypebits));
         xtype lo = xtype(internal);
 
         lo |= 1;
         hi ^= hi >> (xtypebits/2);
     hi *= xtype(cheap_multiplier<itype>::multiplier());
     hi ^= hi >> (3*(xtypebits/4));
     hi *= lo;
     return hi;
     }
 };
 
 
 /*
  * XSL RR -- fixed xorshift (to low bits), random rotate
  *
  * Useful for 128-bit types that are split across two CPU registers.
  */
 
 template <typename xtype, typename itype>
 struct xsl_rr_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t sparebits = bits - xtypebits;
         constexpr bitcount_t wantedopbits = xtypebits >= 128 ? 7
                                        : xtypebits >=  64 ? 6
                                        : xtypebits >=  32 ? 5
                                        : xtypebits >=  16 ? 4
                                        :                    3;
         constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
                                                              : sparebits;
         constexpr bitcount_t amplifier = wantedopbits - opbits;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         constexpr bitcount_t topspare = sparebits;
         constexpr bitcount_t bottomspare = sparebits - topspare;
         constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
 
         bitcount_t rot =
             opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
         bitcount_t amprot = (rot << amplifier) & mask;
         internal ^= internal >> xshift;
         xtype result = xtype(internal >> bottomspare);
         result = rotr(result, amprot);
         return result;
     }
 };
 
 
 /*
  * XSL RR RR -- fixed xorshift (to low bits), random rotate (both parts)
  *
  * Useful for 128-bit types that are split across two CPU registers.
  * If you really want an invertable 128-bit RNG, I guess this is the one.
  */
 
 template <typename T> struct halfsize_trait {};
 template <> struct halfsize_trait<pcg128_t>  { typedef uint64_t type; };
 template <> struct halfsize_trait<uint64_t>  { typedef uint32_t type; };
 template <> struct halfsize_trait<uint32_t>  { typedef uint16_t type; };
 template <> struct halfsize_trait<uint16_t>  { typedef uint8_t type;  };
 
 template <typename xtype, typename itype>
 struct xsl_rr_rr_mixin {
     typedef typename halfsize_trait<itype>::type htype;
 
     static itype output(itype internal)
     {
         constexpr bitcount_t htypebits = bitcount_t(sizeof(htype) * 8);
         constexpr bitcount_t bits      = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t sparebits = bits - htypebits;
         constexpr bitcount_t wantedopbits = htypebits >= 128 ? 7
                                        : htypebits >=  64 ? 6
                                        : htypebits >=  32 ? 5
                                        : htypebits >=  16 ? 4
                                        :                    3;
         constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
                                                                 : sparebits;
         constexpr bitcount_t amplifier = wantedopbits - opbits;
         constexpr bitcount_t mask = (1 << opbits) - 1;
         constexpr bitcount_t topspare = sparebits;
         constexpr bitcount_t xshift = (topspare + htypebits) / 2;
 
         bitcount_t rot =
             opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
         bitcount_t amprot = (rot << amplifier) & mask;
         internal ^= internal >> xshift;
         htype lowbits = htype(internal);
         lowbits = rotr(lowbits, amprot);
         htype highbits = htype(internal >> topspare);
         bitcount_t rot2 = lowbits & mask;
         bitcount_t amprot2 = (rot2 << amplifier) & mask;
         highbits = rotr(highbits, amprot2);
         return (itype(highbits) << topspare) ^ itype(lowbits);
     }
 };
 
 
 /*
  * XSH -- fixed xorshift (to high bits)
  *
  * You shouldn't use this at 64-bits or less.
  */
 
 template <typename xtype, typename itype>
 struct xsh_mixin {
     static xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t sparebits = bits - xtypebits;
         constexpr bitcount_t topspare = 0;
         constexpr bitcount_t bottomspare = sparebits - topspare;
         constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
 
         internal ^= internal >> xshift;
         xtype result = internal >> bottomspare;
         return result;
     }
 };
 
 /*
  * XSL -- fixed xorshift (to low bits)
  *
  * You shouldn't use this at 64-bits or less.
  */
 
 template <typename xtype, typename itype>
 struct xsl_mixin {
     inline xtype output(itype internal)
     {
         constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
         constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
         constexpr bitcount_t sparebits = bits - xtypebits;
         constexpr bitcount_t topspare = sparebits;
         constexpr bitcount_t bottomspare = sparebits - topspare;
         constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
 
         internal ^= internal >> xshift;
         xtype result = internal >> bottomspare;
         return result;
     }
 };
 
 
 /* ---- End of Output Functions ---- */
 
 
 template <typename baseclass>
 struct inside_out : private baseclass {
     inside_out() = delete;
 
     typedef typename baseclass::result_type result_type;
     typedef typename baseclass::state_type  state_type;
     static_assert(sizeof(result_type) == sizeof(state_type),
                   "Require a RNG whose output function is a permutation");
 
     static bool external_step(result_type& randval, size_t i)
     {
         state_type state = baseclass::unoutput(randval);
         state = state * baseclass::multiplier() + baseclass::increment()
                 + state_type(i*2);
         result_type result = baseclass::output(state);
         randval = result;
         state_type zero =
             baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
         return result == zero;
     }
 
     static bool external_advance(result_type& randval, size_t i,
                                  result_type delta, bool forwards = true)
     {
         state_type state = baseclass::unoutput(randval);
         state_type mult  = baseclass::multiplier();
         state_type inc   = baseclass::increment() + state_type(i*2);
         state_type zero =
             baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
         state_type dist_to_zero = baseclass::distance(state, zero, mult, inc);
         bool crosses_zero =
             forwards ? dist_to_zero <= delta
                      : (-dist_to_zero) <= delta;
         if (!forwards)
             delta = -delta;
         state = baseclass::advance(state, delta, mult, inc);
         randval = baseclass::output(state);
         return crosses_zero;
     }
 };
 
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd = true>
 class extended : public baseclass {
 public:
     typedef typename baseclass::state_type  state_type;
     typedef typename baseclass::result_type result_type;
     typedef inside_out<extvalclass> insideout;
 
 private:
     static constexpr bitcount_t rtypebits = sizeof(result_type)*8;
     static constexpr bitcount_t stypebits = sizeof(state_type)*8;
 
     static constexpr bitcount_t tick_limit_pow2 = 64U;
 
     static constexpr size_t table_size  = 1UL << table_pow2;
     static constexpr size_t table_shift = stypebits - table_pow2;
     static constexpr state_type table_mask =
         (state_type(1U) << table_pow2) - state_type(1U);
 
     static constexpr bool   may_tick  =
         (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2);
     static constexpr size_t tick_shift = stypebits - advance_pow2;
     static constexpr state_type tick_mask  =
         may_tick ? state_type(
                        (uint64_t(1) << (advance_pow2*may_tick)) - 1)
                                         // ^-- stupidity to appease GCC warnings
                  : ~state_type(0U);
 
     static constexpr bool may_tock = stypebits < tick_limit_pow2;
 
     result_type data_[table_size];
 
     PCG_NOINLINE void advance_table();
 
     PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true);
 
     result_type& get_extended_value()
     {
         state_type state = this->state_;
         if (kdd && baseclass::is_mcg) {
             // The low order bits of an MCG are constant, so drop them.
             state >>= 2;
         }
         size_t index       = kdd ? state &  table_mask
                                  : state >> table_shift;
 
         if (may_tick) {
             bool tick = kdd ? (state & tick_mask) == state_type(0u)
                             : (state >> tick_shift) == state_type(0u);
             if (tick)
                     advance_table();
         }
         if (may_tock) {
             bool tock = state == state_type(0u);
             if (tock)
                 advance_table();
         }
         return data_[index];
     }
 
 public:
     static constexpr size_t period_pow2()
     {
         return baseclass::period_pow2() + table_size*extvalclass::period_pow2();
     }
 
     PCG_ALWAYS_INLINE result_type operator()()
     {
         result_type rhs = get_extended_value();
         result_type lhs = this->baseclass::operator()();
         return lhs ^ rhs;
     }
 
     result_type operator()(result_type upper_bound)
     {
         return bounded_rand(*this, upper_bound);
     }
 
     void set(result_type wanted)
     {
         result_type& rhs = get_extended_value();
         result_type lhs = this->baseclass::operator()();
         rhs = lhs ^ wanted;
     }
 
     void advance(state_type distance, bool forwards = true);
 
     void backstep(state_type distance)
     {
         advance(distance, false);
     }
 
     extended(const result_type* data)
         : baseclass()
     {
         datainit(data);
     }
 
     extended(const result_type* data, state_type seed)
         : baseclass(seed)
     {
         datainit(data);
     }
 
     // This function may or may not exist.  It thus has to be a template
     // to use SFINAE; users don't have to worry about its template-ness.
 
     template <typename bc = baseclass>
     extended(const result_type* data, state_type seed,
             typename bc::stream_state stream_seed)
         : baseclass(seed, stream_seed)
     {
         datainit(data);
     }
 
     extended()
         : baseclass()
     {
         selfinit();
     }
 
     extended(state_type seed)
         : baseclass(seed)
     {
         selfinit();
     }
 
     // This function may or may not exist.  It thus has to be a template
     // to use SFINAE; users don't have to worry about its template-ness.
 
     template <typename bc = baseclass>
     extended(state_type seed, typename bc::stream_state stream_seed)
         : baseclass(seed, stream_seed)
     {
         selfinit();
     }
 
 private:
     void selfinit();
     void datainit(const result_type* data);
 
 public:
 
     template<typename SeedSeq, typename = typename std::enable_if<
            !std::is_convertible<SeedSeq, result_type>::value
         && !std::is_convertible<SeedSeq, extended>::value>::type>
     extended(SeedSeq&& seedSeq)
         : baseclass(seedSeq)
     {
         generate_to<table_size>(seedSeq, data_);
     }
 
     template<typename... Args>
     void seed(Args&&... args)
     {
         new (this) extended(std::forward<Args>(args)...);
     }
 
     template <bitcount_t table_pow2_, bitcount_t advance_pow2_,
               typename baseclass_, typename extvalclass_, bool kdd_>
     friend bool operator==(const extended<table_pow2_, advance_pow2_,
                                               baseclass_, extvalclass_, kdd_>&,
                            const extended<table_pow2_, advance_pow2_,
                                               baseclass_, extvalclass_, kdd_>&);
 
     template <typename CharT, typename Traits,
               bitcount_t table_pow2_, bitcount_t advance_pow2_,
               typename baseclass_, typename extvalclass_, bool kdd_>
     friend std::basic_ostream<CharT,Traits>&
     operator<<(std::basic_ostream<CharT,Traits>& out,
                const extended<table_pow2_, advance_pow2_,
                               baseclass_, extvalclass_, kdd_>&);
 
     template <typename CharT, typename Traits,
               bitcount_t table_pow2_, bitcount_t advance_pow2_,
               typename baseclass_, typename extvalclass_, bool kdd_>
     friend std::basic_istream<CharT,Traits>&
     operator>>(std::basic_istream<CharT,Traits>& in,
                extended<table_pow2_, advance_pow2_,
                         baseclass_, extvalclass_, kdd_>&);
 
 };
 
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::datainit(
          const result_type* data)
 {
     for (size_t i = 0; i < table_size; ++i)
         data_[i] = data[i];
 }
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::selfinit()
 {
     // We need to fill the extended table with something, and we have
     // very little provided data, so we use the base generator to
     // produce values.  Although not ideal (use a seed sequence, folks!),
     // unexpected correlations are mitigated by
     //      - using XOR differences rather than the number directly
     //      - the way the table is accessed, its values *won't* be accessed
     //        in the same order the were written.
     //      - any strange correlations would only be apparent if we
     //        were to backstep the generator so that the base generator
     //        was generating the same values again
     result_type lhs = baseclass::operator()();
     result_type rhs = baseclass::operator()();
     result_type xdiff = lhs - rhs;
     for (size_t i = 0; i < table_size; ++i) {
         data_[i] = baseclass::operator()() ^ xdiff;
     }
 }
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 bool operator==(const extended<table_pow2, advance_pow2,
                                baseclass, extvalclass, kdd>& lhs,
                 const extended<table_pow2, advance_pow2,
                                baseclass, extvalclass, kdd>& rhs)
 {
     auto& base_lhs = static_cast<const baseclass&>(lhs);
     auto& base_rhs = static_cast<const baseclass&>(rhs);
     return base_lhs == base_rhs
         && std::equal(
                std::begin(lhs.data_), std::end(lhs.data_),
                std::begin(rhs.data_)
            );
 }
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 inline bool operator!=(const extended<table_pow2, advance_pow2,
                                       baseclass, extvalclass, kdd>& lhs,
                        const extended<table_pow2, advance_pow2,
                                       baseclass, extvalclass, kdd>& rhs)
 {
     return !operator==(lhs, rhs);
 }
 
 template <typename CharT, typename Traits,
           bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 std::basic_ostream<CharT,Traits>&
 operator<<(std::basic_ostream<CharT,Traits>& out,
            const extended<table_pow2, advance_pow2,
                           baseclass, extvalclass, kdd>& rng)
 {
     using pcg_extras::operator<<;
 
     auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left);
     auto space = out.widen(' ');
     auto orig_fill = out.fill();
 
     out << rng.multiplier() << space
         << rng.increment() << space
         << rng.state_;
 
     for (const auto& datum : rng.data_)
         out << space << datum;
 
     out.flags(orig_flags);
     out.fill(orig_fill);
     return out;
 }
 
 template <typename CharT, typename Traits,
           bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 std::basic_istream<CharT,Traits>&
 operator>>(std::basic_istream<CharT,Traits>& in,
            extended<table_pow2, advance_pow2,
                     baseclass, extvalclass, kdd>& rng)
 {
     extended<table_pow2, advance_pow2, baseclass, extvalclass> new_rng;
     auto& base_rng = static_cast<baseclass&>(new_rng);
     in >> base_rng;
 
     if (in.fail())
         return in;
 
     using pcg_extras::operator>>;
 
     auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws);
 
     for (auto& datum : new_rng.data_) {
         in >> datum;
         if (in.fail())
             goto bail;
     }
 
     rng = new_rng;
 
 bail:
     in.flags(orig_flags);
     return in;
 }
 
 
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 void
 extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table()
 {
     bool carry = false;
     for (size_t i = 0; i < table_size; ++i) {
         if (carry) {
             carry = insideout::external_step(data_[i],i+1);
         }
         bool carry2 = insideout::external_step(data_[i],i+1);
         carry = carry || carry2;
     }
 }
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 void
 extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table(
         state_type delta, bool isForwards)
 {
     typedef typename baseclass::state_type   base_state_t;
     typedef typename extvalclass::state_type ext_state_t;
     constexpr bitcount_t basebits = sizeof(base_state_t)*8;
     constexpr bitcount_t extbits  = sizeof(ext_state_t)*8;
     static_assert(basebits <= extbits || advance_pow2 > 0,
                   "Current implementation might overflow its carry");
 
     base_state_t carry = 0;
     for (size_t i = 0; i < table_size; ++i) {
         base_state_t total_delta = carry + delta;
         ext_state_t  trunc_delta = ext_state_t(total_delta);
         if (basebits > extbits) {
             carry = total_delta >> extbits;
         } else {
             carry = 0;
         }
         carry +=
             insideout::external_advance(data_[i],i+1, trunc_delta, isForwards);
     }
 }
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename baseclass, typename extvalclass, bool kdd>
 void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance(
     state_type distance, bool forwards)
 {
     static_assert(kdd,
         "Efficient advance is too hard for non-kdd extension. "
         "For a weak advance, cast to base class");
     state_type zero =
         baseclass::is_mcg ? this->state_ & state_type(3U) : state_type(0U);
     if (may_tick) {
         state_type ticks = distance >> (advance_pow2*may_tick);
                                         // ^-- stupidity to appease GCC
                                         // warnings
         state_type adv_mask =
             baseclass::is_mcg ? tick_mask << 2 : tick_mask;
         state_type next_advance_distance = this->distance(zero, adv_mask);
         if (!forwards)
             next_advance_distance = (-next_advance_distance) & tick_mask;
         if (next_advance_distance < (distance & tick_mask)) {
             ++ticks;
         }
         if (ticks)
             advance_table(ticks, forwards);
     }
     if (forwards) {
         if (may_tock && this->distance(zero) <= distance)
             advance_table();
         baseclass::advance(distance);
     } else {
         if (may_tock && -(this->distance(zero)) <= distance)
             advance_table(state_type(1U), false);
         baseclass::advance(-distance);
     }
 }
 
 } // namespace pcg_detail
 
 namespace pcg_engines {
 
 using namespace pcg_detail;
 
 /* Predefined types for XSH RS */
 
 typedef oneseq_base<uint8_t,  uint16_t, xsh_rs_mixin>  oneseq_xsh_rs_16_8;
 typedef oneseq_base<uint16_t, uint32_t, xsh_rs_mixin>  oneseq_xsh_rs_32_16;
 typedef oneseq_base<uint32_t, uint64_t, xsh_rs_mixin>  oneseq_xsh_rs_64_32;
 typedef oneseq_base<uint64_t, pcg128_t, xsh_rs_mixin>  oneseq_xsh_rs_128_64;
 typedef oneseq_base<uint64_t, pcg128_t, xsh_rs_mixin, true, cheap_multiplier>
                                                        cm_oneseq_xsh_rs_128_64;
 
 typedef unique_base<uint8_t,  uint16_t, xsh_rs_mixin>  unique_xsh_rs_16_8;
 typedef unique_base<uint16_t, uint32_t, xsh_rs_mixin>  unique_xsh_rs_32_16;
 typedef unique_base<uint32_t, uint64_t, xsh_rs_mixin>  unique_xsh_rs_64_32;
 typedef unique_base<uint64_t, pcg128_t, xsh_rs_mixin>  unique_xsh_rs_128_64;
 typedef unique_base<uint64_t, pcg128_t, xsh_rs_mixin, true, cheap_multiplier>
                                                        cm_unique_xsh_rs_128_64;
 
 typedef setseq_base<uint8_t,  uint16_t, xsh_rs_mixin>  setseq_xsh_rs_16_8;
 typedef setseq_base<uint16_t, uint32_t, xsh_rs_mixin>  setseq_xsh_rs_32_16;
 typedef setseq_base<uint32_t, uint64_t, xsh_rs_mixin>  setseq_xsh_rs_64_32;
 typedef setseq_base<uint64_t, pcg128_t, xsh_rs_mixin>  setseq_xsh_rs_128_64;
 typedef setseq_base<uint64_t, pcg128_t, xsh_rs_mixin, true, cheap_multiplier>
                                                        cm_setseq_xsh_rs_128_64;
 
 typedef mcg_base<uint8_t,  uint16_t, xsh_rs_mixin>  mcg_xsh_rs_16_8;
 typedef mcg_base<uint16_t, uint32_t, xsh_rs_mixin>  mcg_xsh_rs_32_16;
 typedef mcg_base<uint32_t, uint64_t, xsh_rs_mixin>  mcg_xsh_rs_64_32;
 typedef mcg_base<uint64_t, pcg128_t, xsh_rs_mixin>  mcg_xsh_rs_128_64;
 typedef mcg_base<uint64_t, pcg128_t, xsh_rs_mixin, true, cheap_multiplier>
                                                     cm_mcg_xsh_rs_128_64;
 
 /* Predefined types for XSH RR */
 
 typedef oneseq_base<uint8_t,  uint16_t, xsh_rr_mixin>  oneseq_xsh_rr_16_8;
 typedef oneseq_base<uint16_t, uint32_t, xsh_rr_mixin>  oneseq_xsh_rr_32_16;
 typedef oneseq_base<uint32_t, uint64_t, xsh_rr_mixin>  oneseq_xsh_rr_64_32;
 typedef oneseq_base<uint64_t, pcg128_t, xsh_rr_mixin>  oneseq_xsh_rr_128_64;
 typedef oneseq_base<uint64_t, pcg128_t, xsh_rr_mixin, true, cheap_multiplier>
                                                        cm_oneseq_xsh_rr_128_64;
 
 typedef unique_base<uint8_t,  uint16_t, xsh_rr_mixin>  unique_xsh_rr_16_8;
 typedef unique_base<uint16_t, uint32_t, xsh_rr_mixin>  unique_xsh_rr_32_16;
 typedef unique_base<uint32_t, uint64_t, xsh_rr_mixin>  unique_xsh_rr_64_32;
 typedef unique_base<uint64_t, pcg128_t, xsh_rr_mixin>  unique_xsh_rr_128_64;
 typedef unique_base<uint64_t, pcg128_t, xsh_rr_mixin, true, cheap_multiplier>
                                                        cm_unique_xsh_rr_128_64;
 
 typedef setseq_base<uint8_t,  uint16_t, xsh_rr_mixin>  setseq_xsh_rr_16_8;
 typedef setseq_base<uint16_t, uint32_t, xsh_rr_mixin>  setseq_xsh_rr_32_16;
 typedef setseq_base<uint32_t, uint64_t, xsh_rr_mixin>  setseq_xsh_rr_64_32;
 typedef setseq_base<uint64_t, pcg128_t, xsh_rr_mixin>  setseq_xsh_rr_128_64;
 typedef setseq_base<uint64_t, pcg128_t, xsh_rr_mixin, true, cheap_multiplier>
                                                        cm_setseq_xsh_rr_128_64;
 
 typedef mcg_base<uint8_t,  uint16_t, xsh_rr_mixin>  mcg_xsh_rr_16_8;
 typedef mcg_base<uint16_t, uint32_t, xsh_rr_mixin>  mcg_xsh_rr_32_16;
 typedef mcg_base<uint32_t, uint64_t, xsh_rr_mixin>  mcg_xsh_rr_64_32;
 typedef mcg_base<uint64_t, pcg128_t, xsh_rr_mixin>  mcg_xsh_rr_128_64;
 typedef mcg_base<uint64_t, pcg128_t, xsh_rr_mixin, true, cheap_multiplier>
                                                     cm_mcg_xsh_rr_128_64;
 
 
 /* Predefined types for RXS M XS */
 
 typedef oneseq_base<uint8_t,  uint8_t, rxs_m_xs_mixin>   oneseq_rxs_m_xs_8_8;
 typedef oneseq_base<uint16_t, uint16_t, rxs_m_xs_mixin>  oneseq_rxs_m_xs_16_16;
 typedef oneseq_base<uint32_t, uint32_t, rxs_m_xs_mixin>  oneseq_rxs_m_xs_32_32;
 typedef oneseq_base<uint64_t, uint64_t, rxs_m_xs_mixin>  oneseq_rxs_m_xs_64_64;
 typedef oneseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin>
                                                         oneseq_rxs_m_xs_128_128;
 typedef oneseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin, true, cheap_multiplier>
                                                      cm_oneseq_rxs_m_xs_128_128;
 
 typedef unique_base<uint8_t,  uint8_t, rxs_m_xs_mixin>  unique_rxs_m_xs_8_8;
 typedef unique_base<uint16_t, uint16_t, rxs_m_xs_mixin> unique_rxs_m_xs_16_16;
 typedef unique_base<uint32_t, uint32_t, rxs_m_xs_mixin> unique_rxs_m_xs_32_32;
 typedef unique_base<uint64_t, uint64_t, rxs_m_xs_mixin> unique_rxs_m_xs_64_64;
 typedef unique_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> unique_rxs_m_xs_128_128;
 typedef unique_base<pcg128_t, pcg128_t, rxs_m_xs_mixin, true, cheap_multiplier>
                                                      cm_unique_rxs_m_xs_128_128;
 
 typedef setseq_base<uint8_t,  uint8_t, rxs_m_xs_mixin>  setseq_rxs_m_xs_8_8;
 typedef setseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> setseq_rxs_m_xs_16_16;
 typedef setseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> setseq_rxs_m_xs_32_32;
 typedef setseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> setseq_rxs_m_xs_64_64;
 typedef setseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> setseq_rxs_m_xs_128_128;
 typedef setseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin, true, cheap_multiplier>
                                                      cm_setseq_rxs_m_xs_128_128;
 
                 // MCG versions don't make sense here, so aren't defined.
 
 /* Predefined types for RXS M */
 
 typedef oneseq_base<uint8_t,  uint16_t, rxs_m_mixin>  oneseq_rxs_m_16_8;
 typedef oneseq_base<uint16_t, uint32_t, rxs_m_mixin>  oneseq_rxs_m_32_16;
 typedef oneseq_base<uint32_t, uint64_t, rxs_m_mixin>  oneseq_rxs_m_64_32;
 typedef oneseq_base<uint64_t, pcg128_t, rxs_m_mixin>  oneseq_rxs_m_128_64;
 typedef oneseq_base<uint64_t, pcg128_t, rxs_m_mixin, true, cheap_multiplier>
                                                       cm_oneseq_rxs_m_128_64;
 
 typedef unique_base<uint8_t,  uint16_t, rxs_m_mixin>  unique_rxs_m_16_8;
 typedef unique_base<uint16_t, uint32_t, rxs_m_mixin>  unique_rxs_m_32_16;
 typedef unique_base<uint32_t, uint64_t, rxs_m_mixin>  unique_rxs_m_64_32;
 typedef unique_base<uint64_t, pcg128_t, rxs_m_mixin>  unique_rxs_m_128_64;
 typedef unique_base<uint64_t, pcg128_t, rxs_m_mixin, true, cheap_multiplier>
                                                       cm_unique_rxs_m_128_64;
 
 typedef setseq_base<uint8_t,  uint16_t, rxs_m_mixin>  setseq_rxs_m_16_8;
 typedef setseq_base<uint16_t, uint32_t, rxs_m_mixin>  setseq_rxs_m_32_16;
 typedef setseq_base<uint32_t, uint64_t, rxs_m_mixin>  setseq_rxs_m_64_32;
 typedef setseq_base<uint64_t, pcg128_t, rxs_m_mixin>  setseq_rxs_m_128_64;
 typedef setseq_base<uint64_t, pcg128_t, rxs_m_mixin, true, cheap_multiplier>
                                                       cm_setseq_rxs_m_128_64;
 
 typedef mcg_base<uint8_t,  uint16_t, rxs_m_mixin>  mcg_rxs_m_16_8;
 typedef mcg_base<uint16_t, uint32_t, rxs_m_mixin>  mcg_rxs_m_32_16;
 typedef mcg_base<uint32_t, uint64_t, rxs_m_mixin>  mcg_rxs_m_64_32;
 typedef mcg_base<uint64_t, pcg128_t, rxs_m_mixin>  mcg_rxs_m_128_64;
 typedef mcg_base<uint64_t, pcg128_t, rxs_m_mixin, true, cheap_multiplier>
                                                    cm_mcg_rxs_m_128_64;
 
 /* Predefined types for DXSM */
 
 typedef oneseq_base<uint8_t,  uint16_t, dxsm_mixin>  oneseq_dxsm_16_8;
 typedef oneseq_base<uint16_t, uint32_t, dxsm_mixin>  oneseq_dxsm_32_16;
 typedef oneseq_base<uint32_t, uint64_t, dxsm_mixin>  oneseq_dxsm_64_32;
 typedef oneseq_base<uint64_t, pcg128_t, dxsm_mixin>  oneseq_dxsm_128_64;
 typedef oneseq_base<uint64_t, pcg128_t, dxsm_mixin, true, cheap_multiplier>
                                                      cm_oneseq_dxsm_128_64;
 
 typedef unique_base<uint8_t,  uint16_t, dxsm_mixin>  unique_dxsm_16_8;
 typedef unique_base<uint16_t, uint32_t, dxsm_mixin>  unique_dxsm_32_16;
 typedef unique_base<uint32_t, uint64_t, dxsm_mixin>  unique_dxsm_64_32;
 typedef unique_base<uint64_t, pcg128_t, dxsm_mixin>  unique_dxsm_128_64;
 typedef unique_base<uint64_t, pcg128_t, dxsm_mixin, true, cheap_multiplier>
                                                      cm_unique_dxsm_128_64;
 
 typedef setseq_base<uint8_t,  uint16_t, dxsm_mixin>  setseq_dxsm_16_8;
 typedef setseq_base<uint16_t, uint32_t, dxsm_mixin>  setseq_dxsm_32_16;
 typedef setseq_base<uint32_t, uint64_t, dxsm_mixin>  setseq_dxsm_64_32;
 typedef setseq_base<uint64_t, pcg128_t, dxsm_mixin>  setseq_dxsm_128_64;
 typedef setseq_base<uint64_t, pcg128_t, dxsm_mixin, true, cheap_multiplier>
                                                      cm_setseq_dxsm_128_64;
 
 typedef mcg_base<uint8_t,  uint16_t, dxsm_mixin>  mcg_dxsm_16_8;
 typedef mcg_base<uint16_t, uint32_t, dxsm_mixin>  mcg_dxsm_32_16;
 typedef mcg_base<uint32_t, uint64_t, dxsm_mixin>  mcg_dxsm_64_32;
 typedef mcg_base<uint64_t, pcg128_t, dxsm_mixin>  mcg_dxsm_128_64;
 typedef mcg_base<uint64_t, pcg128_t, dxsm_mixin, true, cheap_multiplier>
                                                   cm_mcg_dxsm_128_64;
 
 /* Predefined types for XSL RR (only defined for "large" types) */
 
 typedef oneseq_base<uint32_t, uint64_t, xsl_rr_mixin>  oneseq_xsl_rr_64_32;
 typedef oneseq_base<uint64_t, pcg128_t, xsl_rr_mixin>  oneseq_xsl_rr_128_64;
 typedef oneseq_base<uint64_t, pcg128_t, xsl_rr_mixin, true, cheap_multiplier>
                                                        cm_oneseq_xsl_rr_128_64;
 
 typedef unique_base<uint32_t, uint64_t, xsl_rr_mixin>  unique_xsl_rr_64_32;
 typedef unique_base<uint64_t, pcg128_t, xsl_rr_mixin>  unique_xsl_rr_128_64;
 typedef unique_base<uint64_t, pcg128_t, xsl_rr_mixin, true, cheap_multiplier>
                                                        cm_unique_xsl_rr_128_64;
 
 typedef setseq_base<uint32_t, uint64_t, xsl_rr_mixin>  setseq_xsl_rr_64_32;
 typedef setseq_base<uint64_t, pcg128_t, xsl_rr_mixin>  setseq_xsl_rr_128_64;
 typedef setseq_base<uint64_t, pcg128_t, xsl_rr_mixin, true, cheap_multiplier>
                                                        cm_setseq_xsl_rr_128_64;
 
 typedef mcg_base<uint32_t, uint64_t, xsl_rr_mixin>  mcg_xsl_rr_64_32;
 typedef mcg_base<uint64_t, pcg128_t, xsl_rr_mixin>  mcg_xsl_rr_128_64;
 typedef mcg_base<uint64_t, pcg128_t, xsl_rr_mixin, true, cheap_multiplier>
                                                     cm_mcg_xsl_rr_128_64;
 
 
 /* Predefined types for XSL RR RR (only defined for "large" types) */
 
 typedef oneseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
     oneseq_xsl_rr_rr_64_64;
 typedef oneseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
     oneseq_xsl_rr_rr_128_128;
 typedef oneseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin, true, cheap_multiplier>
     cm_oneseq_xsl_rr_rr_128_128;
 
 typedef unique_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
     unique_xsl_rr_rr_64_64;
 typedef unique_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
     unique_xsl_rr_rr_128_128;
 typedef unique_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin, true, cheap_multiplier>
     cm_unique_xsl_rr_rr_128_128;
 
 typedef setseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
     setseq_xsl_rr_rr_64_64;
 typedef setseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
     setseq_xsl_rr_rr_128_128;
 typedef setseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin, true, cheap_multiplier>
     cm_setseq_xsl_rr_rr_128_128;
 
                 // MCG versions don't make sense here, so aren't defined.
 
 /* Extended generators */
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename BaseRNG, bool kdd = true>
 using ext_std8 = extended<table_pow2, advance_pow2, BaseRNG,
                           oneseq_rxs_m_xs_8_8, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename BaseRNG, bool kdd = true>
 using ext_std16 = extended<table_pow2, advance_pow2, BaseRNG,
                            oneseq_rxs_m_xs_16_16, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename BaseRNG, bool kdd = true>
 using ext_std32 = extended<table_pow2, advance_pow2, BaseRNG,
                            oneseq_rxs_m_xs_32_32, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2,
           typename BaseRNG, bool kdd = true>
 using ext_std64 = extended<table_pow2, advance_pow2, BaseRNG,
                            oneseq_rxs_m_xs_64_64, kdd>;
 
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_oneseq_rxs_m_xs_32_32 =
           ext_std32<table_pow2, advance_pow2, oneseq_rxs_m_xs_32_32, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_mcg_xsh_rs_64_32 =
           ext_std32<table_pow2, advance_pow2, mcg_xsh_rs_64_32, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_oneseq_xsh_rs_64_32 =
           ext_std32<table_pow2, advance_pow2, oneseq_xsh_rs_64_32, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_setseq_xsh_rr_64_32 =
           ext_std32<table_pow2, advance_pow2, setseq_xsh_rr_64_32, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_mcg_xsl_rr_128_64 =
           ext_std64<table_pow2, advance_pow2, mcg_xsl_rr_128_64, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_oneseq_xsl_rr_128_64 =
           ext_std64<table_pow2, advance_pow2, oneseq_xsl_rr_128_64, kdd>;
 
 template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true>
 using ext_setseq_xsl_rr_128_64 =
           ext_std64<table_pow2, advance_pow2, setseq_xsl_rr_128_64, kdd>;
 
 } // namespace pcg_engines
 
 typedef pcg_engines::setseq_xsh_rr_64_32        pcg32;
 typedef pcg_engines::oneseq_xsh_rr_64_32        pcg32_oneseq;
 typedef pcg_engines::unique_xsh_rr_64_32        pcg32_unique;
 typedef pcg_engines::mcg_xsh_rs_64_32           pcg32_fast;
 
 typedef pcg_engines::setseq_xsl_rr_128_64       pcg64;
 typedef pcg_engines::oneseq_xsl_rr_128_64       pcg64_oneseq;
 typedef pcg_engines::unique_xsl_rr_128_64       pcg64_unique;
 typedef pcg_engines::mcg_xsl_rr_128_64          pcg64_fast;
 
 typedef pcg_engines::setseq_rxs_m_xs_8_8        pcg8_once_insecure;
 typedef pcg_engines::setseq_rxs_m_xs_16_16      pcg16_once_insecure;
 typedef pcg_engines::setseq_rxs_m_xs_32_32      pcg32_once_insecure;
 typedef pcg_engines::setseq_rxs_m_xs_64_64      pcg64_once_insecure;
 typedef pcg_engines::setseq_xsl_rr_rr_128_128   pcg128_once_insecure;
 
 typedef pcg_engines::oneseq_rxs_m_xs_8_8        pcg8_oneseq_once_insecure;
 typedef pcg_engines::oneseq_rxs_m_xs_16_16      pcg16_oneseq_once_insecure;
 typedef pcg_engines::oneseq_rxs_m_xs_32_32      pcg32_oneseq_once_insecure;
 typedef pcg_engines::oneseq_rxs_m_xs_64_64      pcg64_oneseq_once_insecure;
 typedef pcg_engines::oneseq_xsl_rr_rr_128_128   pcg128_oneseq_once_insecure;
 
 
 // These two extended RNGs provide two-dimensionally equidistributed
 // 32-bit generators.  pcg32_k2_fast occupies the same space as pcg64,
 // and can be called twice to generate 64 bits, but does not required
 // 128-bit math; on 32-bit systems, it's faster than pcg64 as well.
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<1,16,true>     pcg32_k2;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<1,32,true>     pcg32_k2_fast;
 
 // These eight extended RNGs have about as much state as arc4random
 //
 //  - the k variants are k-dimensionally equidistributed
 //  - the c variants offer better crypographic security
 //
 // (just how good the cryptographic security is an open question)
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true>     pcg32_k64;
 typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,true>        pcg32_k64_oneseq;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true>     pcg32_k64_fast;
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,false>    pcg32_c64;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,false>    pcg32_c64_oneseq;
 typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,false>       pcg32_c64_fast;
 
 typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,true>    pcg64_k32;
 typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,true>   pcg64_k32_oneseq;
 typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,true>      pcg64_k32_fast;
 
 typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,false>   pcg64_c32;
 typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,false>  pcg64_c32_oneseq;
 typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,false>     pcg64_c32_fast;
 
 // These eight extended RNGs have more state than the Mersenne twister
 //
 //  - the k variants are k-dimensionally equidistributed
 //  - the c variants offer better crypographic security
 //
 // (just how good the cryptographic security is an open question)
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,true>    pcg32_k1024;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,true>    pcg32_k1024_fast;
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,false>   pcg32_c1024;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,false>   pcg32_c1024_fast;
 
 typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,true>   pcg64_k1024;
 typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,true>  pcg64_k1024_fast;
 
 typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,false>  pcg64_c1024;
 typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,false> pcg64_c1024_fast;
 
 // These generators have an insanely huge period (2^524352), and is suitable
 // for silly party tricks, such as dumping out 64 KB ZIP files at an arbitrary
 // point in the future.   [Actually, over the full period of the generator, it
 // will produce every 64 KB ZIP file 2^64 times!]
 
 typedef pcg_engines::ext_setseq_xsh_rr_64_32<14,16,true>    pcg32_k16384;
 typedef pcg_engines::ext_oneseq_xsh_rs_64_32<14,32,true>    pcg32_k16384_fast;
 
 } // namespace arrow_vendored
 
 #ifdef _MSC_VER
     #pragma warning(default:4146)
 #endif
 
 #endif // PCG_RAND_HPP_INCLUDED

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