Add include crap

include/pcg_extras.hpp

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+/*
+ * PCG Random Number Generation for C++
+ *
+ * Copyright 2014 Melissa O'Neill <oneill@pcg-random.org>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * For additional information about the PCG random number generation scheme,
+ * including its license and other licensing options, visit
+ *
+ *     http://www.pcg-random.org
+ */
+
+/*
+ * This file provides support code that is useful for random-number generation
+ * but not specific to the PCG generation scheme, 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
+ */
+
+#ifndef PCG_EXTRAS_HPP_INCLUDED
+#define PCG_EXTRAS_HPP_INCLUDED 1
+
+#include <cinttypes>
+#include <cstddef>
+#include <cstdlib>
+#include <cstring>
+#include <cassert>
+#include <limits>
+#include <iostream>
+#include <type_traits>
+#include <utility>
+#include <locale>
+#include <iterator>
+#include <utility>
+
+#ifdef __GNUC__
+    #include <cxxabi.h>
+#endif
+
+/*
+ * Abstractions for compiler-specific directives
+ */
+
+#ifdef __GNUC__
+    #define PCG_NOINLINE __attribute__((noinline))
+#else
+    #define PCG_NOINLINE
+#endif
+
+/*
+ * Some members of the PCG library use 128-bit math.  When compiling on 64-bit
+ * platforms, both GCC and Clang provide 128-bit integer types that are ideal
+ * for the job.
+ *
+ * On 32-bit platforms (or with other compilers), we fall back to a C++
+ * class that provides 128-bit unsigned integers instead.  It may seem
+ * like we're reinventing the wheel here, because libraries already exist
+ * that support large integers, but most existing libraries provide a very
+ * generic multiprecision code, but here we're operating at a fixed size.
+ * Also, most other libraries are fairly heavyweight.  So we use a direct
+ * implementation.  Sadly, it's much slower than hand-coded assembly or
+ * direct CPU support.
+ *
+ */
+#if __SIZEOF_INT128__
+    namespace pcg_extras {
+        typedef __uint128_t pcg128_t;
+    }
+    #define PCG_128BIT_CONSTANT(high,low) \
+            ((pcg128_t(high) << 64) + low)
+#else
+    #include "pcg_uint128.hpp"
+    namespace pcg_extras {
+        typedef pcg_extras::uint_x4<uint32_t,uint64_t> pcg128_t;
+    }
+    #define PCG_128BIT_CONSTANT(high,low) \
+            pcg128_t(high,low)
+    #define PCG_EMULATED_128BIT_MATH 1
+#endif
+
+
+namespace pcg_extras {
+
+/*
+ * We often need to represent a "number of bits".  When used normally, these
+ * numbers are never greater than 128, so an unsigned char is plenty.
+ * If you're using a nonstandard generator of a larger size, you can set
+ * PCG_BITCOUNT_T to have it define it as a larger size.  (Some compilers
+ * might produce faster code if you set it to an unsigned int.)
+ */
+
+#ifndef PCG_BITCOUNT_T
+    typedef uint8_t bitcount_t;
+#else
+    typedef PCG_BITCOUNT_T bitcount_t;
+#endif
+
+/*
+ * C++ requires us to be able to serialize RNG state by printing or reading
+ * it from a stream.  Because we use 128-bit ints, we also need to be able
+ * ot print them, so here is code to do so.
+ *
+ * This code provides enough functionality to print 128-bit ints in decimal
+ * and zero-padded in hex.  It's not a full-featured implementation.
+ */
+
+template <typename CharT, typename Traits>
+std::basic_ostream<CharT,Traits>&
+operator<<(std::basic_ostream<CharT,Traits>& out, pcg128_t value)
+{
+    auto desired_base = out.flags() & out.basefield;
+    bool want_hex = desired_base == out.hex;
+
+    if (want_hex) {
+        uint64_t highpart = uint64_t(value >> 64);
+        uint64_t lowpart  = uint64_t(value);
+        auto desired_width = out.width();
+        if (desired_width > 16) {
+            out.width(desired_width - 16);
+        }
+        if (highpart != 0 || desired_width > 16)
+            out << highpart;
+        CharT oldfill;
+        if (highpart != 0) {
+            out.width(16);
+            oldfill = out.fill('0');
+        }
+        auto oldflags = out.setf(decltype(desired_base){}, out.showbase);
+        out << lowpart;
+        out.setf(oldflags);
+        if (highpart != 0) {
+            out.fill(oldfill);
+        }
+        return out;
+    }
+    constexpr size_t MAX_CHARS_128BIT = 40;
+
+    char buffer[MAX_CHARS_128BIT];
+    char* pos = buffer+sizeof(buffer);
+    *(--pos) = '\0';
+    constexpr auto BASE = pcg128_t(10ULL);
+    do {
+        auto div = value / BASE;
+        auto mod = uint32_t(value - (div * BASE));
+        *(--pos) = '0' + mod;
+        value = div;
+    } while(value != pcg128_t(0ULL));
+    return out << pos;
+}
+
+template <typename CharT, typename Traits>
+std::basic_istream<CharT,Traits>&
+operator>>(std::basic_istream<CharT,Traits>& in, pcg128_t& value)
+{
+    typename std::basic_istream<CharT,Traits>::sentry s(in);
+
+    if (!s)
+         return in;
+
+    constexpr auto BASE = pcg128_t(10ULL);
+    pcg128_t current(0ULL);
+    bool did_nothing = true;
+    bool overflow = false;
+    for(;;) {
+        CharT wide_ch = in.get();
+        if (!in.good())
+            break;
+        auto ch = in.narrow(wide_ch, '\0');
+        if (ch < '0' || ch > '9') {
+            in.unget();
+            break;
+        }
+        did_nothing = false;
+        pcg128_t digit(uint32_t(ch - '0'));
+        pcg128_t timesbase = current*BASE;
+        overflow = overflow || timesbase < current;
+        current = timesbase + digit;
+        overflow = overflow || current < digit;
+    }
+
+    if (did_nothing || overflow) {
+        in.setstate(std::ios::failbit);
+        if (overflow)
+            current = ~pcg128_t(0ULL);
+    }
+
+    value = current;
+
+    return in;
+}
+
+/*
+ * Likewise, if people use tiny rngs, we'll be serializing uint8_t.
+ * If we just used the provided IO operators, they'd read/write chars,
+ * not ints, so we need to define our own.  We *can* redefine this operator
+ * here because we're in our own namespace.
+ */
+
+template <typename CharT, typename Traits>
+std::basic_ostream<CharT,Traits>&
+operator<<(std::basic_ostream<CharT,Traits>&out, uint8_t value)
+{
+    return out << uint32_t(value);
+}
+
+template <typename CharT, typename Traits>
+std::basic_istream<CharT,Traits>&
+operator>>(std::basic_istream<CharT,Traits>& in, uint8_t target)
+{
+    uint32_t value = 0xdecea5edU;
+    in >> value;
+    if (!in && value == 0xdecea5edU)
+        return in;
+    if (value > uint8_t(~0)) {
+        in.setstate(std::ios::failbit);
+        value = ~0U;
+    }
+    target = uint8_t(value);
+    return in;
+}
+
+/* Unfortunately, the above functions don't get found in preference to the
+ * built in ones, so we create some more specific overloads that will.
+ * Ugh.
+ */
+
+inline std::ostream& operator<<(std::ostream& out, uint8_t value)
+{
+    return pcg_extras::operator<< <char>(out, value);
+}
+
+inline std::istream& operator>>(std::istream& in, uint8_t& value)
+{
+    return pcg_extras::operator>> <char>(in, value);
+}
+
+
+
+/*
+ * Useful bitwise operations.
+ */
+
+/*
+ * XorShifts are invertable, but they are someting of a pain to invert.
+ * This function backs them out.  It's used by the whacky "inside out"
+ * generator defined later.
+ */
+
+template <typename itype>
+inline itype unxorshift(itype x, bitcount_t bits, bitcount_t shift)
+{
+    if (2*shift >= bits) {
+        return x ^ (x >> shift);
+    }
+    itype lowmask1 = (itype(1U) << (bits - shift*2)) - 1;
+    itype highmask1 = ~lowmask1;
+    itype top1 = x;
+    itype bottom1 = x & lowmask1;
+    top1 ^= top1 >> shift;
+    top1 &= highmask1;
+    x = top1 | bottom1;
+    itype lowmask2 = (itype(1U) << (bits - shift)) - 1;
+    itype bottom2 = x & lowmask2;
+    bottom2 = unxorshift(bottom2, bits - shift, shift);
+    bottom2 &= lowmask1;
+    return top1 | bottom2;
+}
+
+/*
+ * Rotate left and right.
+ *
+ * In ideal world, compilers would spot idiomatic rotate code and convert it
+ * to a rotate instruction.  Of course, opinions vary on what the correct
+ * idiom is and how to spot it.  For clang, sometimes it generates better
+ * (but still crappy) code if you define PCG_USE_ZEROCHECK_ROTATE_IDIOM.
+ */
+
+template <typename itype>
+inline itype rotl(itype value, bitcount_t rot)
+{
+    constexpr bitcount_t bits = sizeof(itype) * 8;
+    constexpr bitcount_t mask = bits - 1;
+#if PCG_USE_ZEROCHECK_ROTATE_IDIOM
+    return rot ? (value << rot) | (value >> (bits - rot)) : value;
+#else
+    return (value << rot) | (value >> ((- rot) & mask));
+#endif
+}
+
+template <typename itype>
+inline itype rotr(itype value, bitcount_t rot)
+{
+    constexpr bitcount_t bits = sizeof(itype) * 8;
+    constexpr bitcount_t mask = bits - 1;
+#if PCG_USE_ZEROCHECK_ROTATE_IDIOM
+    return rot ? (value >> rot) | (value << (bits - rot)) : value;
+#else
+    return (value >> rot) | (value << ((- rot) & mask));
+#endif
+}
+
+/* Unfortunately, both Clang and GCC sometimes perform poorly when it comes
+ * to properly recognizing idiomatic rotate code, so for we also provide
+ * assembler directives (enabled with PCG_USE_INLINE_ASM).  Boo, hiss.
+ * (I hope that these compilers get better so that this code can die.)
+ *
+ * These overloads will be preferred over the general template code above.
+ */
+#if PCG_USE_INLINE_ASM && __GNUC__ && (__x86_64__  || __i386__)
+
+inline uint8_t rotr(uint8_t value, bitcount_t rot)
+{
+    asm ("rorb   %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
+    return value;
+}
+
+inline uint16_t rotr(uint16_t value, bitcount_t rot)
+{
+    asm ("rorw   %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
+    return value;
+}
+
+inline uint32_t rotr(uint32_t value, bitcount_t rot)
+{
+    asm ("rorl   %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
+    return value;
+}
+
+#if __x86_64__
+inline uint64_t rotr(uint64_t value, bitcount_t rot)
+{
+    asm ("rorq   %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
+    return value;
+}
+#endif // __x86_64__
+
+#endif // PCG_USE_INLINE_ASM
+
+
+/*
+ * The C++ SeedSeq concept (modelled by seed_seq) can fill an array of
+ * 32-bit integers with seed data, but sometimes we want to produce
+ * larger or smaller integers.
+ *
+ * The following code handles this annoyance.
+ *
+ * uneven_copy will copy an array of 32-bit ints to an array of larger or
+ * smaller ints (actually, the code is general it only needing forward
+ * iterators).  The copy is identical to the one that would be performed if
+ * we just did memcpy on a standard little-endian machine, but works
+ * regardless of the endian of the machine (or the weirdness of the ints
+ * involved).
+ *
+ * generate_to initializes an array of integers using a SeedSeq
+ * object.  It is given the size as a static constant at compile time and
+ * tries to avoid memory allocation.  If we're filling in 32-bit constants
+ * we just do it directly.  If we need a separate buffer and it's small,
+ * we allocate it on the stack.  Otherwise, we fall back to heap allocation.
+ * Ugh.
+ *
+ * generate_one produces a single value of some integral type using a
+ * SeedSeq object.
+ */
+
+ /* uneven_copy helper, case where destination ints are less than 32 bit. */
+
+template<class SrcIter, class DestIter>
+SrcIter uneven_copy_impl(
+    SrcIter src_first, DestIter dest_first, DestIter dest_last,
+    std::true_type)
+{
+    typedef typename std::iterator_traits<SrcIter>::value_type  src_t;
+    typedef typename std::iterator_traits<DestIter>::value_type dest_t;
+
+    constexpr bitcount_t SRC_SIZE  = sizeof(src_t);
+    constexpr bitcount_t DEST_SIZE = sizeof(dest_t);
+    constexpr bitcount_t DEST_BITS = DEST_SIZE * 8;
+    constexpr bitcount_t SCALE     = SRC_SIZE / DEST_SIZE;
+
+    size_t count = 0;
+    src_t value;
+
+    while (dest_first != dest_last) {
+        if ((count++ % SCALE) == 0)
+            value = *src_first++;       // Get more bits
+        else
+            value >>= DEST_BITS;        // Move down bits
+
+        *dest_first++ = dest_t(value);  // Truncates, ignores high bits.
+    }
+    return src_first;
+}
+
+ /* uneven_copy helper, case where destination ints are more than 32 bit. */
+
+template<class SrcIter, class DestIter>
+SrcIter uneven_copy_impl(
+    SrcIter src_first, DestIter dest_first, DestIter dest_last,
+    std::false_type)
+{
+    typedef typename std::iterator_traits<SrcIter>::value_type  src_t;
+    typedef typename std::iterator_traits<DestIter>::value_type dest_t;
+
+    constexpr auto SRC_SIZE  = sizeof(src_t);
+    constexpr auto SRC_BITS  = SRC_SIZE * 8;
+    constexpr auto DEST_SIZE = sizeof(dest_t);
+    constexpr auto SCALE     = (DEST_SIZE+SRC_SIZE-1) / SRC_SIZE;
+
+    while (dest_first != dest_last) {
+        dest_t value(0UL);
+        unsigned int shift = 0;
+
+        for (size_t i = 0; i < SCALE; ++i) {
+            value |= dest_t(*src_first++) << shift;
+            shift += SRC_BITS;
+        }
+
+        *dest_first++ = value;
+    }
+    return src_first;
+}
+
+/* uneven_copy, call the right code for larger vs. smaller */
+
+template<class SrcIter, class DestIter>
+inline SrcIter uneven_copy(SrcIter src_first,
+                           DestIter dest_first, DestIter dest_last)
+{
+    typedef typename std::iterator_traits<SrcIter>::value_type  src_t;
+    typedef typename std::iterator_traits<DestIter>::value_type dest_t;
+
+    constexpr bool DEST_IS_SMALLER = sizeof(dest_t) < sizeof(src_t);
+
+    return uneven_copy_impl(src_first, dest_first, dest_last,
+                            std::integral_constant<bool, DEST_IS_SMALLER>{});
+}
+
+/* generate_to, fill in a fixed-size array of integral type using a SeedSeq
+ * (actually works for any random-access iterator)
+ */
+
+template <size_t size, typename SeedSeq, typename DestIter>
+inline void generate_to_impl(SeedSeq&& generator, DestIter dest,
+                             std::true_type)
+{
+    generator.generate(dest, dest+size);
+}
+
+template <size_t size, typename SeedSeq, typename DestIter>
+void generate_to_impl(SeedSeq&& generator, DestIter dest,
+                      std::false_type)
+{
+    typedef typename std::iterator_traits<DestIter>::value_type dest_t;
+    constexpr auto DEST_SIZE = sizeof(dest_t);
+    constexpr auto GEN_SIZE  = sizeof(uint32_t);
+
+    constexpr bool GEN_IS_SMALLER = GEN_SIZE < DEST_SIZE;
+    constexpr size_t FROM_ELEMS =
+        GEN_IS_SMALLER
+            ? size * ((DEST_SIZE+GEN_SIZE-1) / GEN_SIZE)
+            : (size + (GEN_SIZE / DEST_SIZE) - 1)
+                / ((GEN_SIZE / DEST_SIZE) + GEN_IS_SMALLER);
+                        //  this odd code ^^^^^^^^^^^^^^^^^ is work-around for
+                        //  a bug: http://llvm.org/bugs/show_bug.cgi?id=21287
+
+    if (FROM_ELEMS <= 1024) {
+        uint32_t buffer[FROM_ELEMS];
+        generator.generate(buffer, buffer+FROM_ELEMS);
+        uneven_copy(buffer, dest, dest+size);
+    } else {
+        uint32_t* buffer = (uint32_t*) malloc(GEN_SIZE * FROM_ELEMS);
+        generator.generate(buffer, buffer+FROM_ELEMS);
+        uneven_copy(buffer, dest, dest+size);
+        free(buffer);
+    }
+}
+
+template <size_t size, typename SeedSeq, typename DestIter>
+inline void generate_to(SeedSeq&& generator, DestIter dest)
+{
+    typedef typename std::iterator_traits<DestIter>::value_type dest_t;
+    constexpr bool IS_32BIT = sizeof(dest_t) == sizeof(uint32_t);
+
+    generate_to_impl<size>(std::forward<SeedSeq>(generator), dest,
+                           std::integral_constant<bool, IS_32BIT>{});
+}
+
+/* generate_one, produce a value of integral type using a SeedSeq
+ * (optionally, we can have it produce more than one and pick which one
+ * we want)
+ */
+
+template <typename UInt, size_t i = 0UL, size_t N = i+1UL, typename SeedSeq>
+inline UInt generate_one(SeedSeq&& generator)
+{
+    UInt result[N];
+    generate_to<N>(std::forward<SeedSeq>(generator), result);
+    return result[i];
+}
+
+template <typename RngType>
+auto bounded_rand(RngType& rng, typename RngType::result_type upper_bound)
+        -> typename RngType::result_type
+{
+    typedef typename RngType::result_type rtype;
+    rtype threshold = (RngType::max() - RngType::min() + rtype(1) - upper_bound)
+                    % upper_bound;
+    for (;;) {
+        rtype r = rng() - RngType::min();
+        if (r >= threshold)
+            return r % upper_bound;
+    }
+}
+
+template <typename Iter, typename RandType>
+void shuffle(Iter from, Iter to, RandType&& rng)
+{
+    typedef typename std::iterator_traits<Iter>::difference_type delta_t;
+    auto count = to - from;
+    while (count > 1) {
+        delta_t chosen(bounded_rand(rng, count));
+        --count;
+        --to;
+        using std::swap;
+        swap(*(from+chosen), *to);
+    }
+}
+
+/*
+ * Although std::seed_seq is useful, it isn't everything.  Often we want to
+ * initialize a random-number generator some other way, such as from a random
+ * device.
+ *
+ * Technically, it does not meet the requirements of a SeedSequence because
+ * it lacks some of the rarely-used member functions (some of which would
+ * be impossible to provide).  However the C++ standard is quite specific
+ * that actual engines only called the generate method, so it ought not to be
+ * a problem in practice.
+ */
+
+template <typename RngType>
+class seed_seq_from {
+private:
+    RngType rng_;
+
+    typedef uint_least32_t result_type;
+
+public:
+    template<typename... Args>
+    seed_seq_from(Args&&... args) :
+        rng_(std::forward<Args>(args)...)
+    {
+        // Nothing (else) to do...
+    }
+
+    template<typename Iter>
+    void generate(Iter start, Iter finish)
+    {
+        for (auto i = start; i != finish; ++i)
+            *i = result_type(rng_());
+    }
+
+    constexpr size_t size() const
+    {
+        return (sizeof(typename RngType::result_type) > sizeof(result_type)
+                && RngType::max() > ~size_t(0UL))
+             ? ~size_t(0UL)
+             : size_t(RngType::max());
+    }
+};
+
+/*
+ * Sometimes you might want a distinct seed based on when the program
+ * was compiled.  That way, a particular instance of the program will
+ * behave the same way, but when recompiled it'll produce a different
+ * value.
+ */
+
+template <typename IntType>
+struct static_arbitrary_seed {
+private:
+    static constexpr IntType fnv(IntType hash, const char* pos) {
+        return *pos == '\0'
+             ? hash
+             : fnv((hash * IntType(16777619U)) ^ *pos, (pos+1));
+    }
+
+public:
+    static constexpr IntType value = fnv(IntType(2166136261U ^ sizeof(IntType)),
+                        __DATE__ __TIME__ __FILE__);
+};
+
+// Sometimes, when debugging or testing, it's handy to be able print the name
+// of a (in human-readable form).  This code allows the idiom:
+//
+//      cout << printable_typename<my_foo_type_t>()
+//
+// to print out my_foo_type_t (or its concrete type if it is a synonym)
+
+template <typename T>
+struct printable_typename {};
+
+template <typename T>
+std::ostream& operator<<(std::ostream& out, printable_typename<T>) {
+    const char *implementation_typename = typeid(T).name();
+#ifdef __GNUC__
+    int status;
+    const char* pretty_name =
+        abi::__cxa_demangle(implementation_typename, NULL, NULL, &status);
+    if (status == 0)
+        out << pretty_name;
+    free((void*) pretty_name);
+    if (status == 0)
+        return out;
+#endif
+    out << implementation_typename;
+    return out;
+}
+
+} // namespace pcg_extras
+
+#endif // PCG_EXTRAS_HPP_INCLUDED

include/pcg_random.hpp

@@ -0,0 +1,1751 @@
+/*
+ * PCG Random Number Generation for C++
+ *
+ * Copyright 2014 Melissa O'Neill <oneill@pcg-random.org>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * For additional information about the PCG random number generation scheme,
+ * including its license and other licensing options, 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 <cinttypes>
+#include <cstddef>
+#include <cstdlib>
+#include <cstring>
+#include <cassert>
+#include <limits>
+#include <iostream>
+#include <type_traits>
+#include <utility>
+#include <locale>
+#include <new>
+#include <stdexcept>
+
+/*
+ * 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))
+
+
+/*
+ * 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 addresss 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<unsigned long>(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_((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(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(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)
+{
+    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)
+{
+    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
+    itype the_bit = stream_mixin::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 stream_mixin::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)
+{
+    if (lhs.multiplier() != rhs.multiplier()
+        || lhs.increment() != rhs.increment())
+        throw std::logic_error("incomparable generators");
+    return rhs.distance(lhs.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>
+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)>
+using oneseq_base  = engine<xtype, itype,
+                        output_mixin<xtype, itype>, output_previous,
+                        oneseq_stream<itype> >;
+
+template <typename xtype, typename itype,
+         template<typename XT,typename IT> class output_mixin,
+         bool output_previous = (sizeof(itype) <= 8)>
+using unique_base = engine<xtype, itype,
+                         output_mixin<xtype, itype>, output_previous,
+                         unique_stream<itype> >;
+
+template <typename xtype, typename itype,
+         template<typename XT,typename IT> class output_mixin,
+         bool output_previous = (sizeof(itype) <= 8)>
+using setseq_base = engine<xtype, itype,
+                         output_mixin<xtype, itype>, output_previous,
+                         specific_stream<itype> >;
+
+template <typename xtype, typename itype,
+         template<typename XT,typename IT> class output_mixin,
+         bool output_previous = (sizeof(itype) <= 8)>
+using mcg_base = engine<xtype, itype,
+                      output_mixin<xtype, itype>, output_previous,
+                      no_stream<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;
+    }
+};
+
+/*
+ * 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();
+    }
+
+    __attribute__((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 xdiff = baseclass::operator()() - baseclass::operator()();
+    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
+        && !memcmp((void*) lhs.data_, (void*) rhs.data_, sizeof(lhs.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 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 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 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 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;
+
+/* 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 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 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 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;
+
+
+/* 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 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 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;
+
+                // MCG versions don't make sense here, so aren't defined.
+
+/* 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 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 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 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;
+
+
+/* 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 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 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;
+
+                // 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<6,16,true>     pcg32_k2;
+typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,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;
+
+#endif // PCG_RAND_HPP_INCLUDED

include/pcg_uint128.hpp

@@ -0,0 +1,750 @@
+/*
+ * PCG Random Number Generation for C++
+ *
+ * Copyright 2014 Melissa O'Neill <oneill@pcg-random.org>
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * For additional information about the PCG random number generation scheme,
+ * including its license and other licensing options, visit
+ *
+ *     http://www.pcg-random.org
+ */
+
+/*
+ * This code provides a a C++ class that can provide 128-bit (or higher)
+ * integers.  To produce 2K-bit integers, it uses two K-bit integers,
+ * placed in a union that allowes the code to also see them as four K/2 bit
+ * integers (and access them either directly name, or by index).
+ *
+ * It may seem like we're reinventing the wheel here, because several
+ * libraries already exist that support large integers, but most existing
+ * libraries provide a very generic multiprecision code, but here we're
+ * operating at a fixed size.  Also, most other libraries are fairly
+ * heavyweight.  So we use a direct implementation.  Sadly, it's much slower
+ * than hand-coded assembly or direct CPU support.
+ */
+
+#ifndef PCG_UINT128_HPP_INCLUDED
+#define PCG_UINT128_HPP_INCLUDED 1
+
+#include <cstdint>
+#include <cstdio>
+#include <cassert>
+#include <climits>
+#include <utility>
+#include <initializer_list>
+#include <type_traits>
+
+/*
+ * We want to lay the type out the same way that a native type would be laid
+ * out, which means we must know the machine's endian, at compile time.
+ * This ugliness attempts to do so.
+ */
+
+#ifndef PCG_LITTLE_ENDIAN
+    #if defined(__BYTE_ORDER__)
+        #if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
+            #define PCG_LITTLE_ENDIAN 1
+        #elif __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
+            #define PCG_LITTLE_ENDIAN 0
+        #else
+            #error __BYTE_ORDER__ does not match a standard endian, pick a side
+        #endif
+    #elif __LITTLE_ENDIAN__ || _LITTLE_ENDIAN
+        #define PCG_LITTLE_ENDIAN 1
+    #elif __BIG_ENDIAN__ || _BIG_ENDIAN
+        #define PCG_LITTLE_ENDIAN 0
+    #elif __x86_64 || __x86_64__ || __i386 || __i386__
+        #define PCG_LITTLE_ENDIAN 1
+    #elif __powerpc__ || __POWERPC__ || __ppc__ || __PPC__ \
+          || __m68k__ || __mc68000__
+        #define PCG_LITTLE_ENDIAN 0
+    #else
+        #error Unable to determine target endianness
+    #endif
+#endif
+
+namespace pcg_extras {
+
+// Recent versions of GCC have intrinsics we can use to quickly calculate
+// the number of leading and trailing zeros in a number.  If possible, we
+// use them, otherwise we fall back to old-fashioned bit twiddling to figure
+// them out.
+
+#ifndef PCG_BITCOUNT_T
+    typedef uint8_t bitcount_t;
+#else
+    typedef PCG_BITCOUNT_T bitcount_t;
+#endif
+
+/*
+ * Provide some useful helper functions
+ *      * flog2                 floor(log2(x))
+ *      * trailingzeros         number of trailing zero bits
+ */
+
+#ifdef __GNUC__         // Any GNU-compatible compiler supporting C++11 has
+                        // some useful intrinsics we can use.
+
+inline bitcount_t flog2(uint32_t v)
+{
+    return 31 - __builtin_clz(v);
+}
+
+inline bitcount_t trailingzeros(uint32_t v)
+{
+    return __builtin_ctz(v);
+}
+
+inline bitcount_t flog2(uint64_t v)
+{
+#if UINT64_MAX == ULONG_MAX
+    return 63 - __builtin_clzl(v);
+#elif UINT64_MAX == ULLONG_MAX
+    return 63 - __builtin_clzll(v);
+#else
+    #error Cannot find a function for uint64_t
+#endif
+}
+
+inline bitcount_t trailingzeros(uint64_t v)
+{
+#if UINT64_MAX == ULONG_MAX
+    return __builtin_ctzl(v);
+#elif UINT64_MAX == ULLONG_MAX
+    return __builtin_ctzll(v);
+#else
+    #error Cannot find a function for uint64_t
+#endif
+}
+
+#else                   // Otherwise, we fall back to bit twiddling
+                        // implementations
+
+inline bitcount_t flog2(uint32_t v)
+{
+    // Based on code by Eric Cole and Mark Dickinson, which appears at
+    // https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogDeBruijn
+
+    static const uint8_t multiplyDeBruijnBitPos[32] = {
+      0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30,
+      8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31
+    };
+
+    v |= v >> 1; // first round down to one less than a power of 2
+    v |= v >> 2;
+    v |= v >> 4;
+    v |= v >> 8;
+    v |= v >> 16;
+
+    return multiplyDeBruijnBitPos[(uint32_t)(v * 0x07C4ACDDU) >> 27];
+}
+
+inline bitcount_t trailingzeros(uint32_t v)
+{
+    static const uint8_t multiplyDeBruijnBitPos[32] = {
+      0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8,
+      31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
+    };
+
+    return multiplyDeBruijnBitPos[((uint32_t)((v & -v) * 0x077CB531U)) >> 27];
+}
+
+inline bitcount_t flog2(uint64_t v)
+{
+    uint32_t high = v >> 32;
+    uint32_t low  = uint32_t(v);
+
+    return high ? 32+flog2(high) : flog2(low);
+}
+
+inline bitcount_t trailingzeros(uint64_t v)
+{
+    uint32_t high = v >> 32;
+    uint32_t low  = uint32_t(v);
+
+    return low ? trailingzeros(low) : trailingzeros(high)+32;
+}
+
+#endif
+
+template <typename UInt>
+inline bitcount_t clog2(UInt v)
+{
+    return flog2(v) + ((v & (-v)) != v);
+}
+
+template <typename UInt>
+inline UInt addwithcarry(UInt x, UInt y, bool carryin, bool* carryout)
+{
+    UInt half_result = y + carryin;
+    UInt result = x + half_result;
+    *carryout = (half_result < y) || (result < x);
+    return result;
+}
+
+template <typename UInt>
+inline UInt subwithcarry(UInt x, UInt y, bool carryin, bool* carryout)
+{
+    UInt half_result = y + carryin;
+    UInt result = x - half_result;
+    *carryout = (half_result < y) || (result > x);
+    return result;
+}
+
+
+template <typename UInt, typename UIntX2>
+class uint_x4 {
+// private:
+public:
+    union {
+#if PCG_LITTLE_ENDIAN
+        struct {
+            UInt v0, v1, v2, v3;
+        } w;
+        struct {
+            UIntX2 v01, v23;
+        } d;
+#else
+        struct {
+            UInt v3, v2, v1, v0;
+        } w;
+        struct {
+            UIntX2 v23, v01;
+        } d;
+#endif
+        // For the array access versions, the code that uses the array
+        // must handle endian itself.  Yuck.
+        UInt wa[4];
+        UIntX2 da[2];
+    };
+
+public:
+    uint_x4() = default;
+
+    constexpr uint_x4(UInt v3, UInt v2, UInt v1, UInt v0)
+#if PCG_LITTLE_ENDIAN
+       : w{v0, v1, v2, v3}
+#else
+       : w{v3, v2, v1, v0}
+#endif
+    {
+        // Nothing (else) to do
+    }
+
+    constexpr uint_x4(UIntX2 v23, UIntX2 v01)
+#if PCG_LITTLE_ENDIAN
+       : d{v01,v23}
+#else
+       : d{v23,v01}
+#endif
+    {
+        // Nothing (else) to do
+    }
+
+    template<class Integral,
+             typename std::enable_if<(std::is_integral<Integral>::value
+                                      && sizeof(Integral) <= sizeof(UIntX2))
+                                    >::type* = nullptr>
+    constexpr uint_x4(Integral v01)
+#if PCG_LITTLE_ENDIAN
+       : d{UIntX2(v01),0UL}
+#else
+       : d{0UL,UIntX2(v01)}
+#endif
+    {
+        // Nothing (else) to do
+    }
+
+    explicit constexpr operator uint64_t() const
+    {
+        return d.v01;
+    }
+
+    explicit constexpr operator uint32_t() const
+    {
+        return w.v0;
+    }
+
+    explicit constexpr operator int() const
+    {
+        return w.v0;
+    }
+
+    explicit constexpr operator uint16_t() const
+    {
+        return w.v0;
+    }
+
+    explicit constexpr operator uint8_t() const
+    {
+        return w.v0;
+    }
+
+    typedef typename std::conditional<std::is_same<uint64_t,
+                                                   unsigned long>::value,
+                                      unsigned long long,
+                                      unsigned long>::type
+            uint_missing_t;
+
+    explicit constexpr operator uint_missing_t() const
+    {
+        return d.v01;
+    }
+
+    explicit constexpr operator bool() const
+    {
+        return d.v01 || d.v23;
+    }
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator*(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend std::pair< uint_x4<U,V>,uint_x4<U,V> >
+        divmod(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator+(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator-(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator<<(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator>>(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator&(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator|(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator^(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator==(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator!=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator<(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator<=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator>(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bool operator>=(const uint_x4<U,V>&, const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator~(const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend uint_x4<U,V> operator-(const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bitcount_t flog2(const uint_x4<U,V>&);
+
+    template<typename U, typename V>
+    friend bitcount_t trailingzeros(const uint_x4<U,V>&);
+
+    uint_x4& operator*=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this * rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator/=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this / rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator%=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this % rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator+=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this + rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator-=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this - rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator&=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this & rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator|=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this | rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator^=(const uint_x4& rhs)
+    {
+        uint_x4 result = *this ^ rhs;
+        return *this = result;
+    }
+
+    uint_x4& operator>>=(bitcount_t shift)
+    {
+        uint_x4 result = *this >> shift;
+        return *this = result;
+    }
+
+    uint_x4& operator<<=(bitcount_t shift)
+    {
+        uint_x4 result = *this << shift;
+        return *this = result;
+    }
+
+};
+
+template<typename U, typename V>
+bitcount_t flog2(const uint_x4<U,V>& v)
+{
+#if PCG_LITTLE_ENDIAN
+    for (uint8_t i = 4; i !=0; /* dec in loop */) {
+        --i;
+#else
+    for (uint8_t i = 0; i < 4; ++i) {
+#endif
+        if (v.wa[i] == 0)
+             continue;
+        return flog2(v.wa[i]) + (sizeof(U)*CHAR_BIT)*i;
+    }
+    abort();
+}
+
+template<typename U, typename V>
+bitcount_t trailingzeros(const uint_x4<U,V>& v)
+{
+#if PCG_LITTLE_ENDIAN
+    for (uint8_t i = 0; i < 4; ++i) {
+#else
+    for (uint8_t i = 4; i !=0; /* dec in loop */) {
+        --i;
+#endif
+        if (v.wa[i] != 0)
+            return trailingzeros(v.wa[i]) + (sizeof(U)*CHAR_BIT)*i;
+    }
+    return (sizeof(U)*CHAR_BIT)*4;
+}
+
+template <typename UInt, typename UIntX2>
+std::pair< uint_x4<UInt,UIntX2>, uint_x4<UInt,UIntX2> >
+    divmod(const uint_x4<UInt,UIntX2>& orig_dividend,
+           const uint_x4<UInt,UIntX2>& divisor)
+{
+    // If the dividend is less than the divisor, the answer is always zero.
+    // This takes care of boundary cases like 0/x (which would otherwise be
+    // problematic because we can't take the log of zero.  (The boundary case
+    // of division by zero is undefined.)
+    if (orig_dividend < divisor)
+        return { uint_x4<UInt,UIntX2>(0UL), orig_dividend };
+
+    auto dividend = orig_dividend;
+
+    auto log2_divisor  = flog2(divisor);
+    auto log2_dividend = flog2(dividend);
+    // assert(log2_dividend >= log2_divisor);
+    bitcount_t logdiff = log2_dividend - log2_divisor;
+
+    constexpr uint_x4<UInt,UIntX2> ONE(1UL);
+    if (logdiff == 0)
+        return { ONE, dividend - divisor };
+
+    // Now we change the log difference to
+    //  floor(log2(divisor)) - ceil(log2(dividend))
+    // to ensure that we *underestimate* the result.
+    logdiff -= 1;
+
+    uint_x4<UInt,UIntX2> quotient(0UL);
+
+    auto qfactor = ONE << logdiff;
+    auto factor  = divisor << logdiff;
+
+    do {
+        dividend -= factor;
+        quotient += qfactor;
+        while (dividend < factor) {
+            factor  >>= 1;
+            qfactor >>= 1;
+        }
+    } while (dividend >= divisor);
+
+    return { quotient, dividend };
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator/(const uint_x4<UInt,UIntX2>& dividend,
+                               const uint_x4<UInt,UIntX2>& divisor)
+{
+    return divmod(dividend, divisor).first;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator%(const uint_x4<UInt,UIntX2>& dividend,
+                               const uint_x4<UInt,UIntX2>& divisor)
+{
+    return divmod(dividend, divisor).second;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator*(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+    bool carryin = false;
+    bool carryout;
+    UIntX2 a0b0 = UIntX2(a.w.v0) * UIntX2(b.w.v0);
+    r.w.v0 = UInt(a0b0);
+    r.w.v1 = UInt(a0b0 >> 32);
+
+    UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(b.w.v0);
+    r.w.v2 = UInt(a1b0 >> 32);
+    r.w.v1 = addwithcarry(r.w.v1, UInt(a1b0), carryin, &carryout);
+    carryin = carryout;
+    r.w.v2 = addwithcarry(r.w.v2, UInt(0U), carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+    UIntX2 a0b1 = UIntX2(a.w.v0) * UIntX2(b.w.v1);
+    carryin = false;
+    r.w.v2 = addwithcarry(r.w.v2, UInt(a0b1 >> 32), carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+    carryin = false;
+    r.w.v1 = addwithcarry(r.w.v1, UInt(a0b1), carryin, &carryout);
+    carryin = carryout;
+    r.w.v2 = addwithcarry(r.w.v2, UInt(0U), carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = addwithcarry(r.w.v3, UInt(0U), carryin, &carryout);
+
+    UIntX2 a1b1 = UIntX2(a.w.v1) * UIntX2(b.w.v1);
+    carryin = false;
+    r.w.v2 = addwithcarry(r.w.v2, UInt(a1b1), carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = addwithcarry(r.w.v3, UInt(a1b1 >> 32), carryin, &carryout);
+
+    r.d.v23 += a.d.v01 * b.d.v23 + a.d.v23 * b.d.v01;
+
+    return r;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator+(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+
+    bool carryin = false;
+    bool carryout;
+    r.w.v0 = addwithcarry(a.w.v0, b.w.v0, carryin, &carryout);
+    carryin = carryout;
+    r.w.v1 = addwithcarry(a.w.v1, b.w.v1, carryin, &carryout);
+    carryin = carryout;
+    r.w.v2 = addwithcarry(a.w.v2, b.w.v2, carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = addwithcarry(a.w.v3, b.w.v3, carryin, &carryout);
+
+    return r;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator-(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+
+    bool carryin = false;
+    bool carryout;
+    r.w.v0 = subwithcarry(a.w.v0, b.w.v0, carryin, &carryout);
+    carryin = carryout;
+    r.w.v1 = subwithcarry(a.w.v1, b.w.v1, carryin, &carryout);
+    carryin = carryout;
+    r.w.v2 = subwithcarry(a.w.v2, b.w.v2, carryin, &carryout);
+    carryin = carryout;
+    r.w.v3 = subwithcarry(a.w.v3, b.w.v3, carryin, &carryout);
+
+    return r;
+}
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator&(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    return uint_x4<UInt,UIntX2>(a.d.v23 & b.d.v23, a.d.v01 & b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator|(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    return uint_x4<UInt,UIntX2>(a.d.v23 | b.d.v23, a.d.v01 | b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator^(const uint_x4<UInt,UIntX2>& a,
+                               const uint_x4<UInt,UIntX2>& b)
+{
+    return uint_x4<UInt,UIntX2>(a.d.v23 ^ b.d.v23, a.d.v01 ^ b.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator~(const uint_x4<UInt,UIntX2>& v)
+{
+    return uint_x4<UInt,UIntX2>(~v.d.v23, ~v.d.v01);
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator-(const uint_x4<UInt,UIntX2>& v)
+{
+    return uint_x4<UInt,UIntX2>(0UL,0UL) - v;
+}
+
+template <typename UInt, typename UIntX2>
+bool operator==(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return (a.d.v01 == b.d.v01) && (a.d.v23 == b.d.v23);
+}
+
+template <typename UInt, typename UIntX2>
+bool operator!=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return !operator==(a,b);
+}
+
+
+template <typename UInt, typename UIntX2>
+bool operator<(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return (a.d.v23 < b.d.v23)
+           || ((a.d.v23 == b.d.v23) && (a.d.v01 < b.d.v01));
+}
+
+template <typename UInt, typename UIntX2>
+bool operator>(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return operator<(b,a);
+}
+
+template <typename UInt, typename UIntX2>
+bool operator<=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return !(operator<(b,a));
+}
+
+template <typename UInt, typename UIntX2>
+bool operator>=(const uint_x4<UInt,UIntX2>& a, const uint_x4<UInt,UIntX2>& b)
+{
+    return !(operator<(a,b));
+}
+
+
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator<<(const uint_x4<UInt,UIntX2>& v,
+                                const bitcount_t shift)
+{
+    uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+    const bitcount_t bits    = sizeof(UInt) * CHAR_BIT;
+    const bitcount_t bitmask = bits - 1;
+    const bitcount_t shiftdiv = shift / bits;
+    const bitcount_t shiftmod = shift & bitmask;
+
+    if (shiftmod) {
+        UInt carryover = 0;
+#if PCG_LITTLE_ENDIAN
+        for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#else
+        for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+            --out, --in;
+#endif
+            r.wa[out] = (v.wa[in] << shiftmod) | carryover;
+            carryover = (v.wa[in] >> (bits - shiftmod));
+        }
+    } else {
+#if PCG_LITTLE_ENDIAN
+        for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#else
+        for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+            --out, --in;
+#endif
+            r.wa[out] = v.wa[in];
+        }
+    }
+
+    return r;
+}
+
+template <typename UInt, typename UIntX2>
+uint_x4<UInt,UIntX2> operator>>(const uint_x4<UInt,UIntX2>& v,
+                                const bitcount_t shift)
+{
+    uint_x4<UInt,UIntX2> r = {0U, 0U, 0U, 0U};
+    const bitcount_t bits    = sizeof(UInt) * CHAR_BIT;
+    const bitcount_t bitmask = bits - 1;
+    const bitcount_t shiftdiv = shift / bits;
+    const bitcount_t shiftmod = shift & bitmask;
+
+    if (shiftmod) {
+        UInt carryover = 0;
+#if PCG_LITTLE_ENDIAN
+        for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+            --out, --in;
+#else
+        for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#endif
+            r.wa[out] = (v.wa[in] >> shiftmod) | carryover;
+            carryover = (v.wa[in] << (bits - shiftmod));
+        }
+    } else {
+#if PCG_LITTLE_ENDIAN
+        for (uint8_t out = 4-shiftdiv, in = 4; out != 0; /* dec in loop */) {
+            --out, --in;
+#else
+        for (uint8_t out = shiftdiv, in = 0; out < 4; ++out, ++in) {
+#endif
+            r.wa[out] = v.wa[in];
+        }
+    }
+
+    return r;
+}
+
+} // namespace pcg_extras
+
+#endif // PCG_UINT128_HPP_INCLUDED

include/util.hpp

@@ -6,9 +6,9 @@
 #include <string>
 #include <cstring>
 #include <random>
-#include <pcg_random.hpp>
 #include <algorithm>
 #include <iostream>
+#include <pcg_random.hpp>
 #include <fstream>
 #include <iomanip>
 #include <vector>