/*
 * PCG Random Number Generation for C++
 *
 * Copyright 2014-2017 Melissa O'Neill <oneill@pcg-random.org>,
 *                     and the PCG Project contributors.
 *
 * SPDX-License-Identifier: (Apache-2.0 OR MIT)
 *
 * Licensed under the Apache License, Version 2.0 (provided in
 * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0)
 * or under the MIT license (provided in LICENSE-MIT.txt and at
 * http://opensource.org/licenses/MIT), at your option. This file may not
 * be copied, modified, or distributed except according to those terms.
 *
 * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either
 * express or implied.  See your chosen license for details.
 *
 * For additional information about the PCG random number generation scheme,
 * visit http://www.pcg-random.org/.
 */

/*
 * This 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>

#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) \
            ((pcg_extras::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) \
            pcg_extras::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 = '\0';
        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' + char(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__

#elif defined(_MSC_VER)
  // Use MSVC++ bit rotation intrinsics

#pragma intrinsic(_rotr, _rotr64, _rotr8, _rotr16)

inline uint8_t rotr(uint8_t value, bitcount_t rot)
{
    return _rotr8(value, rot);
}

inline uint16_t rotr(uint16_t value, bitcount_t rot)
{
    return _rotr16(value, rot);
}

inline uint32_t rotr(uint32_t value, bitcount_t rot)
{
    return _rotr(value, rot);
}

inline uint64_t rotr(uint64_t value, bitcount_t rot)
{
    return _rotr64(value, rot);
}

#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 = 0;

    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 = static_cast<uint32_t*>(malloc(GEN_SIZE * FROM_ELEMS));
        generator.generate(buffer, buffer+FROM_ELEMS);
        uneven_copy(buffer, dest, dest+size);
        free(static_cast<void*>(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;
    typedef typename std::remove_reference<RandType>::type::result_type result_t;
    auto count = to - from;
    while (count > 1) {
        delta_t chosen = delta_t(bounded_rand(rng, result_t(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)

#if __cpp_rtti || __GXX_RTTI

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;
    char* pretty_name =
        abi::__cxa_demangle(implementation_typename, nullptr, nullptr, &status);
    if (status == 0)
        out << pretty_name;
    free(static_cast<void*>(pretty_name));
    if (status == 0)
        return out;
#endif
    out << implementation_typename;
    return out;
}

#endif  // __cpp_rtti || __GXX_RTTI

} // namespace pcg_extras

#endif // PCG_EXTRAS_HPP_INCLUDED
