Arbutils/extern/pcg_random.hpp

/*
 * 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 <cassert>
#include <cinttypes>
#include <cstddef>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <iterator>
#include <limits>
#include <locale>
#include <new>
#include <stdexcept>
#include <type_traits>
#include <utility>

#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 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 multiplier_mixin::multiplier;
        using stream_mixin::increment;

    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 = {})
            : engine(generate_one<itype, 1, 2>(seedSeq), generate_one<itype, 0, 2>(seedSeq)) {
            // Nothing else to do.
        }

        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) {
        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;

        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 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 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;

#ifdef _MSC_VER
#pragma warning(default : 4146)
#endif

#endif // PCG_RAND_HPP_INCLUDED