diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..2b9b79e --- /dev/null +++ b/.gitattributes @@ -0,0 +1,2 @@ +* text=auto eol=lf + diff --git a/include/pcg_extras.hpp b/include/pcg_extras.hpp index ce8fd6c..7e7bef4 100644 --- a/include/pcg_extras.hpp +++ b/include/pcg_extras.hpp @@ -1,681 +1,681 @@ -/* - * PCG Random Number Generation for C++ - * - * Copyright 2014-2017 Melissa O'Neill , - * 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 - */ -#pragma once -#ifndef PCG_EXTRAS_HPP_INCLUDED -#define PCG_EXTRAS_HPP_INCLUDED 1 - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - -#if __cplusplus >= 202002L || (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L) || defined(PCG_USE_BIT_HEADER) - #include - #define PCG_BIT_SUPPORT 1 -#endif - -#ifdef __GNUC__ - #include -#endif - -/* - * Abstractions for compiler-specific directives - */ - -#ifdef __GNUC__ - #define PCG_NOINLINE __attribute__((noinline)) -#elif defined(_MSC_VER) - #define PCG_NOINLINE __declspec(noinline) - #pragma warning(disable:4127) // conditional expression is constant -#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__ && !PCG_FORCE_EMULATED_128BIT_MATH - namespace pcg_extras { - using pcg128_t = __uint128_t; - } - #define PCG_128BIT_CONSTANT(high,low) \ - ((pcg_extras::pcg128_t(high) << 64) + low) -#else - #include "pcg_uint128.hpp" - namespace pcg_extras { - using pcg128_t = pcg_extras::uint_x4; - } - #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 - using bitcount_t = uint8_t; -#else - using bitcount_t = PCG_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 -std::basic_ostream& -operator<<(std::basic_ostream& 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 -std::basic_istream& -operator>>(std::basic_istream& in, pcg128_t& value) -{ - typename std::basic_istream::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()) { - in.clear(std::ios::eofbit); - 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 -std::basic_ostream& -operator<<(std::basic_ostream&out, uint8_t value) -{ - return out << uint32_t(value); -} - -template -std::basic_istream& -operator>>(std::basic_istream& 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<< (out, value); -} - -inline std::istream& operator>>(std::istream& in, uint8_t& value) -{ - return pcg_extras::operator>> (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. - * - * This optimized implementation is from imneme/pcg-cpp PR #82. - */ - -template -inline itype unxorshift(itype x, bitcount_t bits, bitcount_t shift) -{ - do { - x ^= x >> shift; - shift *= 2u; - } while(shift < bits); - return x; -} - -/* - * 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 -inline itype rotl(itype value, bitcount_t rot) -{ -#if PCG_BIT_SUPPORT - if constexpr (std::is_integral_v && std::is_unsigned_v) { - return std::rotl(value, (int)rot); - } -#endif - 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 -inline itype rotr(itype value, bitcount_t rot) -{ -#if PCG_BIT_SUPPORT - if constexpr (std::is_integral_v && std::is_unsigned_v) { - return std::rotr(value, (int)rot); - } -#endif - 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 -SrcIter uneven_copy_impl( - SrcIter src_first, DestIter dest_first, DestIter dest_last, - std::true_type) -{ - using src_t = typename std::iterator_traits::value_type; - using dest_t = typename std::iterator_traits::value_type; - - constexpr size_t SRC_SIZE = sizeof(src_t); - constexpr size_t DEST_SIZE = sizeof(dest_t); - constexpr bitcount_t DEST_BITS = bitcount_t(DEST_SIZE * 8); - constexpr size_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 -SrcIter uneven_copy_impl( - SrcIter src_first, DestIter dest_first, DestIter dest_last, - std::false_type) -{ - using src_t = typename std::iterator_traits::value_type; - using dest_t = typename std::iterator_traits::value_type; - - 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); - size_t shift = 0; - - for (size_t i = 0; i < SCALE; ++i) { - value |= dest_t(*src_first++) << bitcount_t(shift); - shift += SRC_BITS; - } - - *dest_first++ = value; - } - return src_first; -} - -/* uneven_copy, call the right code for larger vs. smaller */ - -template -inline SrcIter uneven_copy(SrcIter src_first, - DestIter dest_first, DestIter dest_last) -{ - using src_t = typename std::iterator_traits::value_type; - using dest_t = typename std::iterator_traits::value_type; - - constexpr bool DEST_IS_SMALLER = sizeof(dest_t) < sizeof(src_t); - - return uneven_copy_impl(src_first, dest_first, dest_last, - std::integral_constant{}); -} - -/* generate_to, fill in a fixed-size array of integral type using a SeedSeq - * (actually works for any random-access iterator) - */ - -template -inline void generate_to_impl(SeedSeq&& generator, DestIter dest, - std::true_type) -{ - generator.generate(dest, dest+size); -} - -template -void generate_to_impl(SeedSeq&& generator, DestIter dest, - std::false_type) -{ - using dest_t = typename std::iterator_traits::value_type; - 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(malloc(GEN_SIZE * FROM_ELEMS)); - generator.generate(buffer, buffer+FROM_ELEMS); - uneven_copy(buffer, dest, dest+size); - free(static_cast(buffer)); - } -} - -template -inline void generate_to(SeedSeq&& generator, DestIter dest) -{ - using dest_t = typename std::iterator_traits::value_type; - constexpr bool IS_32BIT = sizeof(dest_t) == sizeof(uint32_t); - - generate_to_impl(std::forward(generator), dest, - std::integral_constant{}); -} - -/* 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 -PCG_NODISCARD inline UInt generate_one(SeedSeq&& generator) -{ - UInt result[N]; - generate_to(std::forward(generator), result); - return result[i]; -} - -template -PCG_NODISCARD auto bounded_rand(RngType& rng, typename RngType::result_type upper_bound) - -> typename RngType::result_type -{ - using rtype = typename RngType::result_type; - 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 -void shuffle(Iter from, Iter to, RandType&& rng) -{ - using delta_t = typename std::iterator_traits::difference_type; - using result_t = typename std::remove_reference::type::result_type; - 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 -class seed_seq_from { -private: - RngType rng_; - -public: - // This fix is from imneme/pcg-cpp PR #83 - using result_type = uint_least32_t; - - template - seed_seq_from(Args&&... args) : - rng_(std::forward(args)...) - { - // Nothing (else) to do... - } - - template - 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 -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__); - - //Prevent creation, while keeping GCC from giving a warning - static_arbitrary_seed() = delete; -}; - -// 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() -// -// to print out my_foo_type_t (or its concrete type if it is a synonym) - -#if __cpp_rtti || __GXX_RTTI - -template -struct printable_typename {}; - -template -std::ostream& operator<<(std::ostream& out, printable_typename) { - 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(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 +/* + * PCG Random Number Generation for C++ + * + * Copyright 2014-2017 Melissa O'Neill , + * 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 + */ +#pragma once +#ifndef PCG_EXTRAS_HPP_INCLUDED +#define PCG_EXTRAS_HPP_INCLUDED 1 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#if __cplusplus >= 202002L || (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L) || defined(PCG_USE_BIT_HEADER) + #include + #define PCG_BIT_SUPPORT 1 +#endif + +#ifdef __GNUC__ + #include +#endif + +/* + * Abstractions for compiler-specific directives + */ + +#ifdef __GNUC__ + #define PCG_NOINLINE __attribute__((noinline)) +#elif defined(_MSC_VER) + #define PCG_NOINLINE __declspec(noinline) + #pragma warning(disable:4127) // conditional expression is constant +#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__ && !PCG_FORCE_EMULATED_128BIT_MATH + namespace pcg_extras { + using pcg128_t = __uint128_t; + } + #define PCG_128BIT_CONSTANT(high,low) \ + ((pcg_extras::pcg128_t(high) << 64) + low) +#else + #include "pcg_uint128.hpp" + namespace pcg_extras { + using pcg128_t = pcg_extras::uint_x4; + } + #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 + using bitcount_t = uint8_t; +#else + using bitcount_t = PCG_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 +std::basic_ostream& +operator<<(std::basic_ostream& 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 +std::basic_istream& +operator>>(std::basic_istream& in, pcg128_t& value) +{ + typename std::basic_istream::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()) { + in.clear(std::ios::eofbit); + 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 +std::basic_ostream& +operator<<(std::basic_ostream&out, uint8_t value) +{ + return out << uint32_t(value); +} + +template +std::basic_istream& +operator>>(std::basic_istream& 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<< (out, value); +} + +inline std::istream& operator>>(std::istream& in, uint8_t& value) +{ + return pcg_extras::operator>> (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. + * + * This optimized implementation is from imneme/pcg-cpp PR #82. + */ + +template +inline itype unxorshift(itype x, bitcount_t bits, bitcount_t shift) +{ + do { + x ^= x >> shift; + shift *= 2u; + } while(shift < bits); + return x; +} + +/* + * 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 +inline itype rotl(itype value, bitcount_t rot) +{ +#if PCG_BIT_SUPPORT + if constexpr (std::is_integral_v && std::is_unsigned_v) { + return std::rotl(value, (int)rot); + } +#endif + 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 +inline itype rotr(itype value, bitcount_t rot) +{ +#if PCG_BIT_SUPPORT + if constexpr (std::is_integral_v && std::is_unsigned_v) { + return std::rotr(value, (int)rot); + } +#endif + 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 +SrcIter uneven_copy_impl( + SrcIter src_first, DestIter dest_first, DestIter dest_last, + std::true_type) +{ + using src_t = typename std::iterator_traits::value_type; + using dest_t = typename std::iterator_traits::value_type; + + constexpr size_t SRC_SIZE = sizeof(src_t); + constexpr size_t DEST_SIZE = sizeof(dest_t); + constexpr bitcount_t DEST_BITS = bitcount_t(DEST_SIZE * 8); + constexpr size_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 +SrcIter uneven_copy_impl( + SrcIter src_first, DestIter dest_first, DestIter dest_last, + std::false_type) +{ + using src_t = typename std::iterator_traits::value_type; + using dest_t = typename std::iterator_traits::value_type; + + 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); + size_t shift = 0; + + for (size_t i = 0; i < SCALE; ++i) { + value |= dest_t(*src_first++) << bitcount_t(shift); + shift += SRC_BITS; + } + + *dest_first++ = value; + } + return src_first; +} + +/* uneven_copy, call the right code for larger vs. smaller */ + +template +inline SrcIter uneven_copy(SrcIter src_first, + DestIter dest_first, DestIter dest_last) +{ + using src_t = typename std::iterator_traits::value_type; + using dest_t = typename std::iterator_traits::value_type; + + constexpr bool DEST_IS_SMALLER = sizeof(dest_t) < sizeof(src_t); + + return uneven_copy_impl(src_first, dest_first, dest_last, + std::integral_constant{}); +} + +/* generate_to, fill in a fixed-size array of integral type using a SeedSeq + * (actually works for any random-access iterator) + */ + +template +inline void generate_to_impl(SeedSeq&& generator, DestIter dest, + std::true_type) +{ + generator.generate(dest, dest+size); +} + +template +void generate_to_impl(SeedSeq&& generator, DestIter dest, + std::false_type) +{ + using dest_t = typename std::iterator_traits::value_type; + 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(malloc(GEN_SIZE * FROM_ELEMS)); + generator.generate(buffer, buffer+FROM_ELEMS); + uneven_copy(buffer, dest, dest+size); + free(static_cast(buffer)); + } +} + +template +inline void generate_to(SeedSeq&& generator, DestIter dest) +{ + using dest_t = typename std::iterator_traits::value_type; + constexpr bool IS_32BIT = sizeof(dest_t) == sizeof(uint32_t); + + generate_to_impl(std::forward(generator), dest, + std::integral_constant{}); +} + +/* 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 +PCG_NODISCARD inline UInt generate_one(SeedSeq&& generator) +{ + UInt result[N]; + generate_to(std::forward(generator), result); + return result[i]; +} + +template +PCG_NODISCARD auto bounded_rand(RngType& rng, typename RngType::result_type upper_bound) + -> typename RngType::result_type +{ + using rtype = typename RngType::result_type; + 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 +void shuffle(Iter from, Iter to, RandType&& rng) +{ + using delta_t = typename std::iterator_traits::difference_type; + using result_t = typename std::remove_reference::type::result_type; + 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 +class seed_seq_from { +private: + RngType rng_; + +public: + // This fix is from imneme/pcg-cpp PR #83 + using result_type = uint_least32_t; + + template + seed_seq_from(Args&&... args) : + rng_(std::forward(args)...) + { + // Nothing (else) to do... + } + + template + 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 +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__); + + //Prevent creation, while keeping GCC from giving a warning + static_arbitrary_seed() = delete; +}; + +// 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() +// +// to print out my_foo_type_t (or its concrete type if it is a synonym) + +#if __cpp_rtti || __GXX_RTTI + +template +struct printable_typename {}; + +template +std::ostream& operator<<(std::ostream& out, printable_typename) { + 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(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 diff --git a/include/pcg_random.hpp b/include/pcg_random.hpp index bbfb88e..c9c8d9a 100644 --- a/include/pcg_random.hpp +++ b/include/pcg_random.hpp @@ -1,1982 +1,1982 @@ -/* - * PCG Random Number Generation for C++ - * - * Copyright 2014-2022 Melissa O'Neill , - * and the PCG Project contributors. - * - * SPDX-License-Identifier: (Apache-2.0 OR MIT) - * - * Licensed under the Apache License, Version 2.0 (provided in - * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0) - * or under the MIT license (provided in LICENSE-MIT.txt and at - * http://opensource.org/licenses/MIT), at your option. This file may not - * be copied, modified, or distributed except according to those terms. - * - * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either - * express or implied. See your chosen license for details. - * - * For additional information about the PCG random number generation scheme, - * visit http://www.pcg-random.org/. - */ - -/* - * This code provides the reference implementation of the PCG family of - * random number generators. The code is complex because it implements - * - * - several members of the PCG family, specifically members corresponding - * to the output functions: - * - XSH RR (good for 64-bit state, 32-bit output) - * - XSH RS (good for 64-bit state, 32-bit output) - * - XSL RR (good for 128-bit state, 64-bit output) - * - RXS M XS (statistically most powerful generator) - * - XSL RR RR (good for 128-bit state, 128-bit output) - * - and RXS, RXS M, XSH, XSL (mostly for testing) - * - at potentially *arbitrary* bit sizes - * - with four different techniques for random streams (MCG, one-stream - * LCG, settable-stream LCG, unique-stream LCG) - * - and the extended generation schemes allowing arbitrary periods - * - with all features of C++11 random number generation (and more), - * some of which are somewhat painful, including - * - initializing with a SeedSequence which writes 32-bit values - * to memory, even though the state of the generator may not - * use 32-bit values (it might use smaller or larger integers) - * - I/O for RNGs and a prescribed format, which needs to handle - * the issue that 8-bit and 128-bit integers don't have working - * I/O routines (e.g., normally 8-bit = char, not integer) - * - equality and inequality for RNGs - * - and a number of convenience typedefs to mask all the complexity - * - * The code employees 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, true, // Output Func - * pcg_detail::specific_stream, // Stream Kind - * pcg_detail::default_multiplier // LCG Mult - * > myRNG; - * - */ - -#pragma once -#ifndef PCG_RAND_HPP_INCLUDED -#define PCG_RAND_HPP_INCLUDED 1 - -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include -#include - -#ifdef _MSC_VER - #pragma warning(disable:4146) - #pragma warning(disable:4127) // conditional expression is constant -#endif - -#ifdef _MSC_VER - #define PCG_ALWAYS_INLINE __forceinline - #if defined(_MSC_FULL_VER) && _MSC_FULL_VER >= 190024210 - // available since VS 2015 Update 2/3 - // This fix is from imneme/pcg-cpp PR #66 - #define PCG_EBO __declspec(empty_bases) - #else - #define PCG_EBO - #endif -#elif __GNUC__ - #define PCG_ALWAYS_INLINE __attribute__((always_inline)) - #define PCG_EBO -#else - #define PCG_ALWAYS_INLINE inline - #define PCG_EBO -#endif - -#if __cplusplus >= 201703L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) - #define PCG_NODISCARD [[nodiscard]] -#elif defined(__GNUC__) || defined(__clang__) - #define PCG_NODISCARD __attribute__((warn_unused_result)) -#else - #define PCG_NODISCARD -#endif - -/* - * The pcg_extras namespace contains some support code that is likely 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::multiplier() - * - * gives you the default multiplier 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 -struct default_multiplier { - // Not defined for an arbitrary type -}; - -template -struct default_increment { - // Not defined for an arbitrary type -}; - -#define PCG_DEFINE_CONSTANT(type, what, kind, constant) \ - template <> \ - struct what ## _ ## kind { \ - static constexpr type kind() { \ - return constant; \ - } \ - }; - -PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U) -PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U) - -PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U) -PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U) - -PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U) -PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U) - -PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL) -PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL) - -PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier, - PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL)) -PCG_DEFINE_CONSTANT(pcg128_t, default, increment, - PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL)) - -/* Alternative (cheaper) multipliers for 128-bit */ - -template -struct cheap_multiplier : public default_multiplier { - // For most types just use the default. -}; - -template <> -struct cheap_multiplier { - static constexpr uint64_t multiplier() { - return 0xda942042e4dd58b5ULL; - } -}; - - -/* - * Each PCG generator is available in four variants, based on how it applies - * the additive constant for its underlying LCG; the variations are: - * - * single stream - all instances use the same fixed constant, thus - * the RNG always somewhere in same sequence - * mcg - adds zero, resulting in a single stream and reduced - * period - * specific stream - the constant can be changed at any time, selecting - * a different random sequence - * unique stream - the constant is based on the memory address of the - * object, thus every RNG has its own unique sequence - * - * This variation is provided though mixin classes which define a function - * value called increment() that returns the necessary additive constant. - */ - - - -/* - * unique stream - */ - - -template -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: - using state_type = itype; - - constexpr itype increment() const { - return itype(reinterpret_cast(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 -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: - using state_type = itype; - - 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 -class oneseq_stream : public default_increment { -protected: - static constexpr bool is_mcg = false; - - // Is never called, but is provided for symmetry with specific_stream - void set_stream(...) - { - abort(); - } - -public: - using state_type = itype; - - static constexpr itype stream() - { - return default_increment::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 -class specific_stream { -protected: - static constexpr bool is_mcg = false; - - itype inc_ = default_increment::increment(); - -public: - using state_type = itype; - using stream_state = itype; - - constexpr itype increment() const { - return inc_; - } - - itype stream() - { - return inc_ >> 1; - } - - void set_stream(itype specific_seq) - { - inc_ = (specific_seq << 1) | itype(1U); - } - - static constexpr bool can_specify_stream = true; - - static constexpr size_t streams_pow2() - { - return (sizeof(itype)*8) - 1u; - } - -protected: - specific_stream() = default; - - specific_stream(itype specific_seq) - : inc_(itype(specific_seq << 1) | itype(1U)) - { - // Nothing (else) to do. - } -}; - - -/* - * This is where it all comes together. This function joins together three - * mixin classes which define - * - the LCG additive constant (the stream) - * - the LCG multiplier - * - the output function - * in addition, we specify the type of the LCG state, and the result type, - * and whether to use the pre-advance version of the state for the output - * (increasing instruction-level parallelism) or the post-advance version - * (reducing register pressure). - * - * Given the high level of parameterization, the code has to use some - * template-metaprogramming tricks to handle some of the subtle variations - * involved. - */ - -template , - typename multiplier_mixin = default_multiplier > -class PCG_EBO 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: - using result_type = xtype; - using state_type = itype; - - 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. - - PCG_NODISCARD static constexpr result_type min() - { - return result_type(0UL); - } - - PCG_NODISCARD static constexpr result_type max() - { - return result_type(~result_type(0UL)); - } - -protected: - itype bump(itype state) - { - return state * multiplier() + increment(); - } - - itype base_generate() - { - return state_ = bump(state_); - } - - itype base_generate0() - { - itype old_state = state_; - state_ = bump(state_); - return old_state; - } - -public: - PCG_NODISCARD result_type operator()() - { - if (output_previous) - return this->output(base_generate0()); - else - return this->output(base_generate()); - } - - PCG_NODISCARD result_type operator()(result_type upper_bound) - { - return bounded_rand(*this, upper_bound); - } - -protected: - static itype advance(itype state, itype delta, - itype cur_mult, itype cur_plus); - - static itype distance(itype cur_state, itype newstate, itype cur_mult, - itype cur_plus, itype mask = ~itype(0U)); - - itype distance(itype newstate, itype mask = itype(~itype(0U))) const - { - return distance(state_, newstate, multiplier(), increment(), mask); - } - -public: - void advance(itype delta) - { - state_ = advance(state_, delta, this->multiplier(), this->increment()); - } - - void backstep(itype delta) - { - advance(-delta); - } - - void discard(itype delta) - { - advance(delta); - } - - bool wrapped() - { - if (stream_mixin::is_mcg) { - // For MCGs, the low order two bits never change. In this - // implementation, we keep them fixed at 3 to make this test - // easier. - return state_ == 3; - } else { - return state_ == 0; - } - } - - engine(itype state = itype(0xcafef00dd15ea5e5ULL)) - : state_(this->is_mcg ? state|state_type(3U) - : bump(state + this->increment())) - { - // Nothing else to do. - } - - // This function may or may not exist. It thus has to be a template - // to use SFINAE; users don't have to worry about its template-ness. - - template - 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 - engine(SeedSeq&& seedSeq, typename std::enable_if< - !stream_mixin::can_specify_stream - && !std::is_convertible::value - && !std::is_convertible::value, - no_specifiable_stream_tag>::type = {}) - : engine(generate_one(std::forward(seedSeq))) - { - // Nothing else to do. - } - - template - engine(SeedSeq&& seedSeq, typename std::enable_if< - stream_mixin::can_specify_stream - && !std::is_convertible::value - && !std::is_convertible::value, - can_specify_stream_tag>::type = {}) - { - itype seeddata[2]; - generate_to<2>(std::forward(seedSeq), seeddata); - seed(seeddata[1], seeddata[0]); - } - - - template - void seed(Args&&... args) - { - new (this) engine(std::forward(args)...); - } - - template - friend bool operator==(const engine&, - const engine&); - - template - friend itype1 operator-(const engine&, - const engine&); - - template - friend std::basic_ostream& - operator<<(std::basic_ostream& out, - const engine&); - - template - friend std::basic_istream& - operator>>(std::basic_istream& in, - engine& rng); -}; - -template -std::basic_ostream& -operator<<(std::basic_ostream& out, - const engine& rng) -{ - using pcg_extras::operator<<; - - auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); - auto space = out.widen(' '); - auto orig_fill = out.fill(); - - out << rng.multiplier() << space - << rng.increment() << space - << rng.state_; - - out.flags(orig_flags); - out.fill(orig_fill); - return out; -} - - -template -std::basic_istream& -operator>>(std::basic_istream& in, - engine& rng) -{ - using pcg_extras::operator>>; - - auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); - - itype multiplier, increment, state; - in >> multiplier >> increment >> state; - - if (!in.fail()) { - bool good = true; - if (multiplier != itype(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 -itype engine::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 -itype engine::distance( - itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask) -{ - constexpr itype ONE = 1u; // itype could be weird, so use constant - bool is_mcg_internal = cur_plus == itype(0); - itype the_bit = is_mcg_internal ? itype(4u) : itype(1u); - itype distance = 0u; - while ((cur_state & mask) != (newstate & mask)) { - if ((cur_state & the_bit) != (newstate & the_bit)) { - cur_state = cur_state * cur_mult + cur_plus; - distance |= the_bit; - } - assert((cur_state & the_bit) == (newstate & the_bit)); - the_bit <<= 1; - cur_plus = (cur_mult+ONE)*cur_plus; - cur_mult *= cur_mult; - } - return is_mcg_internal ? distance >> 2 : distance; -} - -template -itype operator-(const engine& lhs, - const engine& rhs) -{ - static_assert( - std::is_same::value && - std::is_same::value, - "Incomparable generators"); - if (lhs.increment() == rhs.increment()) { - return rhs.distance(lhs.state_); - } else { - constexpr itype ONE = 1u; - itype lhs_diff = lhs.increment() + (lhs.multiplier()-ONE) * lhs.state_; - itype rhs_diff = rhs.increment() + (rhs.multiplier()-ONE) * rhs.state_; - if ((lhs_diff & itype(3u)) != (rhs_diff & itype(3u))) { - rhs_diff = -rhs_diff; - } - return rhs.distance(rhs_diff, lhs_diff, rhs.multiplier(), itype(0u)); - } -} - - -template -bool operator==(const engine& lhs, - const engine& rhs) -{ - return (lhs.multiplier() == rhs.multiplier()) - && (lhs.increment() == rhs.increment()) - && (lhs.state_ == rhs.state_); -} - -template -inline bool operator!=(const engine& lhs, - const engine& rhs) -{ - return !operator==(lhs,rhs); -} - - -template class output_mixin, - bool output_previous = (sizeof(itype) <= 8), - template class multiplier_mixin = default_multiplier> -using oneseq_base = engine, output_previous, - oneseq_stream, - multiplier_mixin >; - -template class output_mixin, - bool output_previous = (sizeof(itype) <= 8), - template class multiplier_mixin = default_multiplier> -using unique_base = engine, output_previous, - unique_stream, - multiplier_mixin >; - -template class output_mixin, - bool output_previous = (sizeof(itype) <= 8), - template class multiplier_mixin = default_multiplier> -using setseq_base = engine, output_previous, - specific_stream, - multiplier_mixin >; - -template class output_mixin, - bool output_previous = (sizeof(itype) <= 8), - template class multiplier_mixin = default_multiplier> -using mcg_base = engine, output_previous, - no_stream, - multiplier_mixin >; - -/* - * 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 -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 -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 -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 -struct mcg_multiplier { - // Not defined for an arbitrary type -}; - -template -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 -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::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::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 -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::multiplier(); - xtype result = internal >> shift; - return result; - } -}; - - -/* - * DXSM -- double xorshift multiply - * - * This is a new, more powerful output permutation (added in 2019). It's - * a more comprehensive scrambling than RXS M, but runs faster on 128-bit - * types. Although primarily intended for use at large sizes, also works - * at smaller sizes as well. - * - * This permutation is similar to xorshift multiply hash functions, except - * that one of the multipliers is the LCG multiplier (to avoid needing to - * have a second constant) and the other is based on the low-order bits. - * This latter aspect means that the scrambling applied to the high bits - * depends on the low bits, and makes it (to my eye) impractical to back - * out the permutation without having the low-order bits. - */ - -template -struct dxsm_mixin { - inline xtype output(itype internal) - { - constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); - constexpr bitcount_t itypebits = bitcount_t(sizeof(itype) * 8); - static_assert(xtypebits <= itypebits/2, - "Output type must be half the size of the state type."); - - xtype hi = xtype(internal >> (itypebits - xtypebits)); - xtype lo = xtype(internal); - - lo |= 1; - hi ^= hi >> (xtypebits/2); - hi *= xtype(cheap_multiplier::multiplier()); - hi ^= hi >> (3*(xtypebits/4)); - hi *= lo; - return hi; - } -}; - - -/* - * XSL RR -- fixed xorshift (to low bits), random rotate - * - * Useful for 128-bit types that are split across two CPU registers. - */ - -template -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 struct halfsize_trait {}; -template <> struct halfsize_trait { using type = uint64_t; }; -template <> struct halfsize_trait { using type = uint32_t; }; -template <> struct halfsize_trait { using type = uint16_t; }; -template <> struct halfsize_trait { using type = uint8_t; }; - -template -struct xsl_rr_rr_mixin { - using htype = typename halfsize_trait::type; - - 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 -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 -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 -struct PCG_EBO inside_out : private baseclass { - inside_out() = delete; - - using result_type = typename baseclass::result_type; - using state_type = typename baseclass::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 -class PCG_EBO extended : public baseclass { -public: - using state_type = typename baseclass::state_type; - using result_type = typename baseclass::result_type; - using insideout = inside_out; - -private: - static constexpr bitcount_t rtypebits = sizeof(result_type)*8; - static constexpr bitcount_t stypebits = sizeof(state_type)*8; - - static constexpr bitcount_t tick_limit_pow2 = 64U; - - static constexpr size_t table_size = 1UL << table_pow2; - static constexpr size_t table_shift = stypebits - table_pow2; - static constexpr state_type table_mask = - (state_type(1U) << table_pow2) - state_type(1U); - - static constexpr bool may_tick = - (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2); - static constexpr size_t tick_shift = stypebits - advance_pow2; - static constexpr state_type tick_mask = - may_tick ? state_type( - (uint64_t(1) << (advance_pow2*may_tick)) - 1) - // ^-- stupidity to appease GCC warnings - : ~state_type(0U); - - static constexpr bool may_tock = stypebits < tick_limit_pow2; - - result_type data_[table_size]; - - PCG_NOINLINE void advance_table(); - - PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true); - - result_type& get_extended_value() - { - state_type state = this->state_; - if (kdd && baseclass::is_mcg) { - // The low order bits of an MCG are constant, so drop them. - state >>= 2; - } - size_t index = kdd ? state & table_mask - : state >> table_shift; - - if (may_tick) { - bool tick = kdd ? (state & tick_mask) == state_type(0u) - : (state >> tick_shift) == state_type(0u); - if (tick) - advance_table(); - } - if (may_tock) { - bool tock = state == state_type(0u); - if (tock) - advance_table(); - } - return data_[index]; - } - -public: - static constexpr size_t period_pow2() - { - return baseclass::period_pow2() + table_size*extvalclass::period_pow2(); - } - - PCG_NODISCARD PCG_ALWAYS_INLINE result_type operator()() - { - result_type rhs = get_extended_value(); - result_type lhs = this->baseclass::operator()(); - return lhs ^ rhs; - } - - PCG_NODISCARD 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 - 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 - 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::value - && !std::is_convertible::value>::type> - extended(SeedSeq&& seedSeq) - : baseclass(seedSeq) - { - generate_to(seedSeq, data_); - } - - template - void seed(Args&&... args) - { - new (this) extended(std::forward(args)...); - } - - template - friend bool operator==(const extended&, - const extended&); - - template - friend std::basic_ostream& - operator<<(std::basic_ostream& out, - const extended&); - - template - friend std::basic_istream& - operator>>(std::basic_istream& in, - extended&); - -}; - - -template -void extended::datainit( - const result_type* data) -{ - for (size_t i = 0; i < table_size; ++i) - data_[i] = data[i]; -} - -template -void extended::selfinit() -{ - // We need to fill the extended table with something, and we have - // very little provided data, so we use the base generator to - // produce values. Although not ideal (use a seed sequence, folks!), - // unexpected correlations are mitigated by - // - using XOR differences rather than the number directly - // - the way the table is accessed, its values *won't* be accessed - // in the same order the were written. - // - any strange correlations would only be apparent if we - // were to backstep the generator so that the base generator - // was generating the same values again - result_type lhs = baseclass::operator()(); - result_type rhs = baseclass::operator()(); - result_type xdiff = lhs - rhs; - for (size_t i = 0; i < table_size; ++i) { - data_[i] = baseclass::operator()() ^ xdiff; - } -} - -template -bool operator==(const extended& lhs, - const extended& rhs) -{ - auto& base_lhs = static_cast(lhs); - auto& base_rhs = static_cast(rhs); - return base_lhs == base_rhs - && std::equal( - std::begin(lhs.data_), std::end(lhs.data_), - std::begin(rhs.data_) - ); -} - -template -inline bool operator!=(const extended& lhs, - const extended& rhs) -{ - return !operator==(lhs, rhs); -} - -template -std::basic_ostream& -operator<<(std::basic_ostream& out, - const extended& rng) -{ - using pcg_extras::operator<<; - - auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); - auto space = out.widen(' '); - auto orig_fill = out.fill(); - - out << rng.multiplier() << space - << rng.increment() << space - << rng.state_; - - for (const auto& datum : rng.data_) - out << space << datum; - - out.flags(orig_flags); - out.fill(orig_fill); - return out; -} - -template -std::basic_istream& -operator>>(std::basic_istream& in, - extended& rng) -{ - extended new_rng; - auto& base_rng = static_cast(new_rng); - in >> base_rng; - - if (in.fail()) - return in; - - using pcg_extras::operator>>; - - auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); - - for (auto& datum : new_rng.data_) { - in >> datum; - if (in.fail()) - goto bail; - } - - rng = new_rng; - -bail: - in.flags(orig_flags); - return in; -} - - - -template -void -extended::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 -void -extended::advance_table( - state_type delta, bool isForwards) -{ - using base_state_t = typename baseclass::state_type; - using ext_state_t = typename extvalclass::state_type; - 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 -void extended::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 */ - -using oneseq_xsh_rs_16_8 = oneseq_base; -using oneseq_xsh_rs_32_16 = oneseq_base; -using oneseq_xsh_rs_64_32 = oneseq_base; -using oneseq_xsh_rs_128_64 = oneseq_base; -using cm_oneseq_xsh_rs_128_64 = - oneseq_base; - -using unique_xsh_rs_16_8 = unique_base; -using unique_xsh_rs_32_16 = unique_base; -using unique_xsh_rs_64_32 = unique_base; -using unique_xsh_rs_128_64 = unique_base; -using cm_unique_xsh_rs_128_64 = - unique_base; - -using setseq_xsh_rs_16_8 = setseq_base; -using setseq_xsh_rs_32_16 = setseq_base; -using setseq_xsh_rs_64_32 = setseq_base; -using setseq_xsh_rs_128_64 = setseq_base; -using cm_setseq_xsh_rs_128_64 = - setseq_base; - -using mcg_xsh_rs_16_8 = mcg_base; -using mcg_xsh_rs_32_16 = mcg_base; -using mcg_xsh_rs_64_32 = mcg_base; -using mcg_xsh_rs_128_64 = mcg_base; -using cm_mcg_xsh_rs_128_64 = - mcg_base; - -/* Predefined types for XSH RR */ - -using oneseq_xsh_rr_16_8 = oneseq_base; -using oneseq_xsh_rr_32_16 = oneseq_base; -using oneseq_xsh_rr_64_32 = oneseq_base; -using oneseq_xsh_rr_128_64 = oneseq_base; -using cm_oneseq_xsh_rr_128_64 = - oneseq_base; - -using unique_xsh_rr_16_8 = unique_base; -using unique_xsh_rr_32_16 = unique_base; -using unique_xsh_rr_64_32 = unique_base; -using unique_xsh_rr_128_64 = unique_base; -using cm_unique_xsh_rr_128_64 = - unique_base; - -using setseq_xsh_rr_16_8 = setseq_base; -using setseq_xsh_rr_32_16 = setseq_base; -using setseq_xsh_rr_64_32 = setseq_base; -using setseq_xsh_rr_128_64 = setseq_base; -using cm_setseq_xsh_rr_128_64 = - setseq_base; - -using mcg_xsh_rr_16_8 = mcg_base; -using mcg_xsh_rr_32_16 = mcg_base; -using mcg_xsh_rr_64_32 = mcg_base; -using mcg_xsh_rr_128_64 = mcg_base; -using cm_mcg_xsh_rr_128_64 = - mcg_base; - - -/* Predefined types for RXS M XS */ - -using oneseq_rxs_m_xs_8_8 = oneseq_base; -using oneseq_rxs_m_xs_16_16 = oneseq_base; -using oneseq_rxs_m_xs_32_32 = oneseq_base; -using oneseq_rxs_m_xs_64_64 = oneseq_base; -using oneseq_rxs_m_xs_128_128 = - oneseq_base; -using cm_oneseq_rxs_m_xs_128_128 = - oneseq_base; - -using unique_rxs_m_xs_8_8 = unique_base; -using unique_rxs_m_xs_16_16 = unique_base; -using unique_rxs_m_xs_32_32 = unique_base; -using unique_rxs_m_xs_64_64 = unique_base; -using unique_rxs_m_xs_128_128 = unique_base; -using cm_unique_rxs_m_xs_128_128 = - unique_base; - -using setseq_rxs_m_xs_8_8 = setseq_base; -using setseq_rxs_m_xs_16_16 = setseq_base; -using setseq_rxs_m_xs_32_32 = setseq_base; -using setseq_rxs_m_xs_64_64 = setseq_base; -using setseq_rxs_m_xs_128_128 = setseq_base; -using cm_setseq_rxs_m_xs_128_128 = - setseq_base; - - // MCG versions don't make sense here, so aren't defined. - -/* Predefined types for RXS M */ - -using oneseq_rxs_m_16_8 = oneseq_base; -using oneseq_rxs_m_32_16 = oneseq_base; -using oneseq_rxs_m_64_32 = oneseq_base; -using oneseq_rxs_m_128_64 = oneseq_base; -using cm_oneseq_rxs_m_128_64 = - oneseq_base; - -using unique_rxs_m_16_8 = unique_base; -using unique_rxs_m_32_16 = unique_base; -using unique_rxs_m_64_32 = unique_base; -using unique_rxs_m_128_64 = unique_base; -using cm_unique_rxs_m_128_64 = - unique_base; - -using setseq_rxs_m_16_8 = setseq_base; -using setseq_rxs_m_32_16 = setseq_base; -using setseq_rxs_m_64_32 = setseq_base; -using setseq_rxs_m_128_64 = setseq_base; -using cm_setseq_rxs_m_128_64 = - setseq_base; - -using mcg_rxs_m_16_8 = mcg_base; -using mcg_rxs_m_32_16 = mcg_base; -using mcg_rxs_m_64_32 = mcg_base; -using mcg_rxs_m_128_64 = mcg_base; -using cm_mcg_rxs_m_128_64 = - mcg_base; - -/* Predefined types for DXSM */ - -using oneseq_dxsm_16_8 = oneseq_base; -using oneseq_dxsm_32_16 = oneseq_base; -using oneseq_dxsm_64_32 = oneseq_base; -using oneseq_dxsm_128_64 = oneseq_base; -using cm_oneseq_dxsm_128_64 = - oneseq_base; - -using unique_dxsm_16_8 = unique_base; -using unique_dxsm_32_16 = unique_base; -using unique_dxsm_64_32 = unique_base; -using unique_dxsm_128_64 = unique_base; -using cm_unique_dxsm_128_64 = - unique_base; - -using setseq_dxsm_16_8 = setseq_base; -using setseq_dxsm_32_16 = setseq_base; -using setseq_dxsm_64_32 = setseq_base; -using setseq_dxsm_128_64 = setseq_base; -using cm_setseq_dxsm_128_64 = - setseq_base; - -using mcg_dxsm_16_8 = mcg_base; -using mcg_dxsm_32_16 = mcg_base; -using mcg_dxsm_64_32 = mcg_base; -using mcg_dxsm_128_64 = mcg_base; -using cm_mcg_dxsm_128_64 = - mcg_base; - -/* Predefined types for DXSM (Convenience) */ - -using pcg32_dxsm = setseq_dxsm_64_32; -using pcg32_dxsm_oneseq = oneseq_dxsm_64_32; -using pcg32_dxsm_unique = unique_dxsm_64_32; -using pcg32_dxsm_fast = mcg_dxsm_64_32; - -using pcg64_dxsm = setseq_dxsm_128_64; -using pcg64_dxsm_oneseq = oneseq_dxsm_128_64; -using pcg64_dxsm_unique = unique_dxsm_128_64; -using pcg64_dxsm_fast = mcg_dxsm_128_64; - -/* Predefined types for XSL RR (only defined for "large" types) */ - -using oneseq_xsl_rr_64_32 = oneseq_base; -using oneseq_xsl_rr_128_64 = oneseq_base; -using cm_oneseq_xsl_rr_128_64 = - oneseq_base; - -using unique_xsl_rr_64_32 = unique_base; -using unique_xsl_rr_128_64 = unique_base; -using cm_unique_xsl_rr_128_64 = - unique_base; - -using setseq_xsl_rr_64_32 = setseq_base; -using setseq_xsl_rr_128_64 = setseq_base; -using cm_setseq_xsl_rr_128_64 = - setseq_base; - -using mcg_xsl_rr_64_32 = mcg_base; -using mcg_xsl_rr_128_64 = mcg_base; -using cm_mcg_xsl_rr_128_64 = - mcg_base; - - -/* Predefined types for XSL RR RR (only defined for "large" types) */ - -using oneseq_xsl_rr_rr_64_64 = - oneseq_base; -using oneseq_xsl_rr_rr_128_128 = - oneseq_base; -using cm_oneseq_xsl_rr_rr_128_128 = - oneseq_base; - -using unique_xsl_rr_rr_64_64 = - unique_base; -using unique_xsl_rr_rr_128_128 = - unique_base; -using cm_unique_xsl_rr_rr_128_128 = - unique_base; - -using setseq_xsl_rr_rr_64_64 = - setseq_base; -using setseq_xsl_rr_rr_128_128 = - setseq_base; -using cm_setseq_xsl_rr_rr_128_128 = - setseq_base; - - // MCG versions don't make sense here, so aren't defined. - -/* Extended generators */ - -template -using ext_std8 = extended; - -template -using ext_std16 = extended; - -template -using ext_std32 = extended; - -template -using ext_std64 = extended; - - -template -using ext_oneseq_rxs_m_xs_32_32 = - ext_std32; - -template -using ext_mcg_xsh_rs_64_32 = - ext_std32; - -template -using ext_oneseq_xsh_rs_64_32 = - ext_std32; - -template -using ext_setseq_xsh_rr_64_32 = - ext_std32; - -template -using ext_mcg_xsl_rr_128_64 = - ext_std64; - -template -using ext_oneseq_xsl_rr_128_64 = - ext_std64; - -template -using ext_setseq_xsl_rr_128_64 = - ext_std64; - -} // namespace pcg_engines - -using pcg32 = pcg_engines::setseq_xsh_rr_64_32; -using pcg32_oneseq = pcg_engines::oneseq_xsh_rr_64_32; -using pcg32_unique = pcg_engines::unique_xsh_rr_64_32; -using pcg32_fast = pcg_engines::mcg_xsh_rs_64_32; - -using pcg64 = pcg_engines::setseq_xsl_rr_128_64; -using pcg64_oneseq = pcg_engines::oneseq_xsl_rr_128_64; -using pcg64_unique = pcg_engines::unique_xsl_rr_128_64; -using pcg64_fast = pcg_engines::mcg_xsl_rr_128_64; - -using pcg8_once_insecure = pcg_engines::setseq_rxs_m_xs_8_8; -using pcg16_once_insecure = pcg_engines::setseq_rxs_m_xs_16_16; -using pcg32_once_insecure = pcg_engines::setseq_rxs_m_xs_32_32; -using pcg64_once_insecure = pcg_engines::setseq_rxs_m_xs_64_64; -using pcg128_once_insecure = pcg_engines::setseq_xsl_rr_rr_128_128; - -using pcg8_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_8_8; -using pcg16_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_16_16; -using pcg32_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_32_32; -using pcg64_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_64_64; -using pcg128_oneseq_once_insecure = pcg_engines::oneseq_xsl_rr_rr_128_128; - - -// 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. - -using pcg32_k2 = pcg_engines::ext_setseq_xsh_rr_64_32<1,16,true>; -using pcg32_k2_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<1,32,true>; - -// These eight extended RNGs have about as much state as arc4random -// -// - the k variants are k-dimensionally equidistributed -// - the c variants offer are intended to be harder to predict -// -// (neither is intended for use in cryptographic applications) - -using pcg32_k64 = pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true>; -using pcg32_k64_oneseq = pcg_engines::ext_mcg_xsh_rs_64_32<6,32,true>; -using pcg32_k64_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true>; - -using pcg32_c64 = pcg_engines::ext_setseq_xsh_rr_64_32<6,16,false>; -using pcg32_c64_oneseq = pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,false>; -using pcg32_c64_fast = pcg_engines::ext_mcg_xsh_rs_64_32<6,32,false>; - -using pcg64_k32 = pcg_engines::ext_setseq_xsl_rr_128_64<5,16,true>; -using pcg64_k32_oneseq = pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,true>; -using pcg64_k32_fast = pcg_engines::ext_mcg_xsl_rr_128_64<5,128,true>; - -using pcg64_c32 = pcg_engines::ext_setseq_xsl_rr_128_64<5,16,false>; -using pcg64_c32_oneseq = pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,false>; -using pcg64_c32_fast = pcg_engines::ext_mcg_xsl_rr_128_64<5,128,false>; - -// These eight extended RNGs have more state than the Mersenne twister -// -// - the k variants are k-dimensionally equidistributed -// - the c variants offer are intended to be harder to predict -// -// (neither is intended for use in cryptographic applications) - -using pcg32_k1024 = pcg_engines::ext_setseq_xsh_rr_64_32<10,16,true>; -using pcg32_k1024_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,true>; - -using pcg32_c1024 = pcg_engines::ext_setseq_xsh_rr_64_32<10,16,false>; -using pcg32_c1024_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,false>; - -using pcg64_k1024 = pcg_engines::ext_setseq_xsl_rr_128_64<10,16,true>; -using pcg64_k1024_fast = pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,true>; - -using pcg64_c1024 = pcg_engines::ext_setseq_xsl_rr_128_64<10,16,false>; -using pcg64_c1024_fast = pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,false>; - -// 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!] - -using pcg32_k16384 = pcg_engines::ext_setseq_xsh_rr_64_32<14,16,true>; -using pcg32_k16384_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<14,32,true>; - -#ifdef _MSC_VER - #pragma warning(default:4146) -#endif - -#endif // PCG_RAND_HPP_INCLUDED +/* + * PCG Random Number Generation for C++ + * + * Copyright 2014-2022 Melissa O'Neill , + * and the PCG Project contributors. + * + * SPDX-License-Identifier: (Apache-2.0 OR MIT) + * + * Licensed under the Apache License, Version 2.0 (provided in + * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0) + * or under the MIT license (provided in LICENSE-MIT.txt and at + * http://opensource.org/licenses/MIT), at your option. This file may not + * be copied, modified, or distributed except according to those terms. + * + * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either + * express or implied. See your chosen license for details. + * + * For additional information about the PCG random number generation scheme, + * visit http://www.pcg-random.org/. + */ + +/* + * This code provides the reference implementation of the PCG family of + * random number generators. The code is complex because it implements + * + * - several members of the PCG family, specifically members corresponding + * to the output functions: + * - XSH RR (good for 64-bit state, 32-bit output) + * - XSH RS (good for 64-bit state, 32-bit output) + * - XSL RR (good for 128-bit state, 64-bit output) + * - RXS M XS (statistically most powerful generator) + * - XSL RR RR (good for 128-bit state, 128-bit output) + * - and RXS, RXS M, XSH, XSL (mostly for testing) + * - at potentially *arbitrary* bit sizes + * - with four different techniques for random streams (MCG, one-stream + * LCG, settable-stream LCG, unique-stream LCG) + * - and the extended generation schemes allowing arbitrary periods + * - with all features of C++11 random number generation (and more), + * some of which are somewhat painful, including + * - initializing with a SeedSequence which writes 32-bit values + * to memory, even though the state of the generator may not + * use 32-bit values (it might use smaller or larger integers) + * - I/O for RNGs and a prescribed format, which needs to handle + * the issue that 8-bit and 128-bit integers don't have working + * I/O routines (e.g., normally 8-bit = char, not integer) + * - equality and inequality for RNGs + * - and a number of convenience typedefs to mask all the complexity + * + * The code employees 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, true, // Output Func + * pcg_detail::specific_stream, // Stream Kind + * pcg_detail::default_multiplier // LCG Mult + * > myRNG; + * + */ + +#pragma once +#ifndef PCG_RAND_HPP_INCLUDED +#define PCG_RAND_HPP_INCLUDED 1 + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#ifdef _MSC_VER + #pragma warning(disable:4146) + #pragma warning(disable:4127) // conditional expression is constant +#endif + +#ifdef _MSC_VER + #define PCG_ALWAYS_INLINE __forceinline + #if defined(_MSC_FULL_VER) && _MSC_FULL_VER >= 190024210 + // available since VS 2015 Update 2/3 + // This fix is from imneme/pcg-cpp PR #66 + #define PCG_EBO __declspec(empty_bases) + #else + #define PCG_EBO + #endif +#elif __GNUC__ + #define PCG_ALWAYS_INLINE __attribute__((always_inline)) + #define PCG_EBO +#else + #define PCG_ALWAYS_INLINE inline + #define PCG_EBO +#endif + +#if __cplusplus >= 201703L || (defined(_MSVC_LANG) && _MSVC_LANG >= 201703L) + #define PCG_NODISCARD [[nodiscard]] +#elif defined(__GNUC__) || defined(__clang__) + #define PCG_NODISCARD __attribute__((warn_unused_result)) +#else + #define PCG_NODISCARD +#endif + +/* + * The pcg_extras namespace contains some support code that is likely 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::multiplier() + * + * gives you the default multiplier 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 +struct default_multiplier { + // Not defined for an arbitrary type +}; + +template +struct default_increment { + // Not defined for an arbitrary type +}; + +#define PCG_DEFINE_CONSTANT(type, what, kind, constant) \ + template <> \ + struct what ## _ ## kind { \ + static constexpr type kind() { \ + return constant; \ + } \ + }; + +PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U) +PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U) + +PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U) +PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U) + +PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U) +PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U) + +PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL) +PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL) + +PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier, + PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL)) +PCG_DEFINE_CONSTANT(pcg128_t, default, increment, + PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL)) + +/* Alternative (cheaper) multipliers for 128-bit */ + +template +struct cheap_multiplier : public default_multiplier { + // For most types just use the default. +}; + +template <> +struct cheap_multiplier { + static constexpr uint64_t multiplier() { + return 0xda942042e4dd58b5ULL; + } +}; + + +/* + * Each PCG generator is available in four variants, based on how it applies + * the additive constant for its underlying LCG; the variations are: + * + * single stream - all instances use the same fixed constant, thus + * the RNG always somewhere in same sequence + * mcg - adds zero, resulting in a single stream and reduced + * period + * specific stream - the constant can be changed at any time, selecting + * a different random sequence + * unique stream - the constant is based on the memory address of the + * object, thus every RNG has its own unique sequence + * + * This variation is provided though mixin classes which define a function + * value called increment() that returns the necessary additive constant. + */ + + + +/* + * unique stream + */ + + +template +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: + using state_type = itype; + + constexpr itype increment() const { + return itype(reinterpret_cast(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 +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: + using state_type = itype; + + 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 +class oneseq_stream : public default_increment { +protected: + static constexpr bool is_mcg = false; + + // Is never called, but is provided for symmetry with specific_stream + void set_stream(...) + { + abort(); + } + +public: + using state_type = itype; + + static constexpr itype stream() + { + return default_increment::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 +class specific_stream { +protected: + static constexpr bool is_mcg = false; + + itype inc_ = default_increment::increment(); + +public: + using state_type = itype; + using stream_state = itype; + + constexpr itype increment() const { + return inc_; + } + + itype stream() + { + return inc_ >> 1; + } + + void set_stream(itype specific_seq) + { + inc_ = (specific_seq << 1) | itype(1U); + } + + static constexpr bool can_specify_stream = true; + + static constexpr size_t streams_pow2() + { + return (sizeof(itype)*8) - 1u; + } + +protected: + specific_stream() = default; + + specific_stream(itype specific_seq) + : inc_(itype(specific_seq << 1) | itype(1U)) + { + // Nothing (else) to do. + } +}; + + +/* + * This is where it all comes together. This function joins together three + * mixin classes which define + * - the LCG additive constant (the stream) + * - the LCG multiplier + * - the output function + * in addition, we specify the type of the LCG state, and the result type, + * and whether to use the pre-advance version of the state for the output + * (increasing instruction-level parallelism) or the post-advance version + * (reducing register pressure). + * + * Given the high level of parameterization, the code has to use some + * template-metaprogramming tricks to handle some of the subtle variations + * involved. + */ + +template , + typename multiplier_mixin = default_multiplier > +class PCG_EBO 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: + using result_type = xtype; + using state_type = itype; + + 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. + + PCG_NODISCARD static constexpr result_type min() + { + return result_type(0UL); + } + + PCG_NODISCARD static constexpr result_type max() + { + return result_type(~result_type(0UL)); + } + +protected: + itype bump(itype state) + { + return state * multiplier() + increment(); + } + + itype base_generate() + { + return state_ = bump(state_); + } + + itype base_generate0() + { + itype old_state = state_; + state_ = bump(state_); + return old_state; + } + +public: + PCG_NODISCARD result_type operator()() + { + if (output_previous) + return this->output(base_generate0()); + else + return this->output(base_generate()); + } + + PCG_NODISCARD result_type operator()(result_type upper_bound) + { + return bounded_rand(*this, upper_bound); + } + +protected: + static itype advance(itype state, itype delta, + itype cur_mult, itype cur_plus); + + static itype distance(itype cur_state, itype newstate, itype cur_mult, + itype cur_plus, itype mask = ~itype(0U)); + + itype distance(itype newstate, itype mask = itype(~itype(0U))) const + { + return distance(state_, newstate, multiplier(), increment(), mask); + } + +public: + void advance(itype delta) + { + state_ = advance(state_, delta, this->multiplier(), this->increment()); + } + + void backstep(itype delta) + { + advance(-delta); + } + + void discard(itype delta) + { + advance(delta); + } + + bool wrapped() + { + if (stream_mixin::is_mcg) { + // For MCGs, the low order two bits never change. In this + // implementation, we keep them fixed at 3 to make this test + // easier. + return state_ == 3; + } else { + return state_ == 0; + } + } + + engine(itype state = itype(0xcafef00dd15ea5e5ULL)) + : state_(this->is_mcg ? state|state_type(3U) + : bump(state + this->increment())) + { + // Nothing else to do. + } + + // This function may or may not exist. It thus has to be a template + // to use SFINAE; users don't have to worry about its template-ness. + + template + 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 + engine(SeedSeq&& seedSeq, typename std::enable_if< + !stream_mixin::can_specify_stream + && !std::is_convertible::value + && !std::is_convertible::value, + no_specifiable_stream_tag>::type = {}) + : engine(generate_one(std::forward(seedSeq))) + { + // Nothing else to do. + } + + template + engine(SeedSeq&& seedSeq, typename std::enable_if< + stream_mixin::can_specify_stream + && !std::is_convertible::value + && !std::is_convertible::value, + can_specify_stream_tag>::type = {}) + { + itype seeddata[2]; + generate_to<2>(std::forward(seedSeq), seeddata); + seed(seeddata[1], seeddata[0]); + } + + + template + void seed(Args&&... args) + { + new (this) engine(std::forward(args)...); + } + + template + friend bool operator==(const engine&, + const engine&); + + template + friend itype1 operator-(const engine&, + const engine&); + + template + friend std::basic_ostream& + operator<<(std::basic_ostream& out, + const engine&); + + template + friend std::basic_istream& + operator>>(std::basic_istream& in, + engine& rng); +}; + +template +std::basic_ostream& +operator<<(std::basic_ostream& out, + const engine& rng) +{ + using pcg_extras::operator<<; + + auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); + auto space = out.widen(' '); + auto orig_fill = out.fill(); + + out << rng.multiplier() << space + << rng.increment() << space + << rng.state_; + + out.flags(orig_flags); + out.fill(orig_fill); + return out; +} + + +template +std::basic_istream& +operator>>(std::basic_istream& in, + engine& rng) +{ + using pcg_extras::operator>>; + + auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); + + itype multiplier, increment, state; + in >> multiplier >> increment >> state; + + if (!in.fail()) { + bool good = true; + if (multiplier != itype(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 +itype engine::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 +itype engine::distance( + itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask) +{ + constexpr itype ONE = 1u; // itype could be weird, so use constant + bool is_mcg_internal = cur_plus == itype(0); + itype the_bit = is_mcg_internal ? itype(4u) : itype(1u); + itype distance = 0u; + while ((cur_state & mask) != (newstate & mask)) { + if ((cur_state & the_bit) != (newstate & the_bit)) { + cur_state = cur_state * cur_mult + cur_plus; + distance |= the_bit; + } + assert((cur_state & the_bit) == (newstate & the_bit)); + the_bit <<= 1; + cur_plus = (cur_mult+ONE)*cur_plus; + cur_mult *= cur_mult; + } + return is_mcg_internal ? distance >> 2 : distance; +} + +template +itype operator-(const engine& lhs, + const engine& rhs) +{ + static_assert( + std::is_same::value && + std::is_same::value, + "Incomparable generators"); + if (lhs.increment() == rhs.increment()) { + return rhs.distance(lhs.state_); + } else { + constexpr itype ONE = 1u; + itype lhs_diff = lhs.increment() + (lhs.multiplier()-ONE) * lhs.state_; + itype rhs_diff = rhs.increment() + (rhs.multiplier()-ONE) * rhs.state_; + if ((lhs_diff & itype(3u)) != (rhs_diff & itype(3u))) { + rhs_diff = -rhs_diff; + } + return rhs.distance(rhs_diff, lhs_diff, rhs.multiplier(), itype(0u)); + } +} + + +template +bool operator==(const engine& lhs, + const engine& rhs) +{ + return (lhs.multiplier() == rhs.multiplier()) + && (lhs.increment() == rhs.increment()) + && (lhs.state_ == rhs.state_); +} + +template +inline bool operator!=(const engine& lhs, + const engine& rhs) +{ + return !operator==(lhs,rhs); +} + + +template class output_mixin, + bool output_previous = (sizeof(itype) <= 8), + template class multiplier_mixin = default_multiplier> +using oneseq_base = engine, output_previous, + oneseq_stream, + multiplier_mixin >; + +template class output_mixin, + bool output_previous = (sizeof(itype) <= 8), + template class multiplier_mixin = default_multiplier> +using unique_base = engine, output_previous, + unique_stream, + multiplier_mixin >; + +template class output_mixin, + bool output_previous = (sizeof(itype) <= 8), + template class multiplier_mixin = default_multiplier> +using setseq_base = engine, output_previous, + specific_stream, + multiplier_mixin >; + +template class output_mixin, + bool output_previous = (sizeof(itype) <= 8), + template class multiplier_mixin = default_multiplier> +using mcg_base = engine, output_previous, + no_stream, + multiplier_mixin >; + +/* + * 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 +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 +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 +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 +struct mcg_multiplier { + // Not defined for an arbitrary type +}; + +template +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 +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::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::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 +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::multiplier(); + xtype result = internal >> shift; + return result; + } +}; + + +/* + * DXSM -- double xorshift multiply + * + * This is a new, more powerful output permutation (added in 2019). It's + * a more comprehensive scrambling than RXS M, but runs faster on 128-bit + * types. Although primarily intended for use at large sizes, also works + * at smaller sizes as well. + * + * This permutation is similar to xorshift multiply hash functions, except + * that one of the multipliers is the LCG multiplier (to avoid needing to + * have a second constant) and the other is based on the low-order bits. + * This latter aspect means that the scrambling applied to the high bits + * depends on the low bits, and makes it (to my eye) impractical to back + * out the permutation without having the low-order bits. + */ + +template +struct dxsm_mixin { + inline xtype output(itype internal) + { + constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); + constexpr bitcount_t itypebits = bitcount_t(sizeof(itype) * 8); + static_assert(xtypebits <= itypebits/2, + "Output type must be half the size of the state type."); + + xtype hi = xtype(internal >> (itypebits - xtypebits)); + xtype lo = xtype(internal); + + lo |= 1; + hi ^= hi >> (xtypebits/2); + hi *= xtype(cheap_multiplier::multiplier()); + hi ^= hi >> (3*(xtypebits/4)); + hi *= lo; + return hi; + } +}; + + +/* + * XSL RR -- fixed xorshift (to low bits), random rotate + * + * Useful for 128-bit types that are split across two CPU registers. + */ + +template +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 struct halfsize_trait {}; +template <> struct halfsize_trait { using type = uint64_t; }; +template <> struct halfsize_trait { using type = uint32_t; }; +template <> struct halfsize_trait { using type = uint16_t; }; +template <> struct halfsize_trait { using type = uint8_t; }; + +template +struct xsl_rr_rr_mixin { + using htype = typename halfsize_trait::type; + + 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 +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 +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 +struct PCG_EBO inside_out : private baseclass { + inside_out() = delete; + + using result_type = typename baseclass::result_type; + using state_type = typename baseclass::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 +class PCG_EBO extended : public baseclass { +public: + using state_type = typename baseclass::state_type; + using result_type = typename baseclass::result_type; + using insideout = inside_out; + +private: + static constexpr bitcount_t rtypebits = sizeof(result_type)*8; + static constexpr bitcount_t stypebits = sizeof(state_type)*8; + + static constexpr bitcount_t tick_limit_pow2 = 64U; + + static constexpr size_t table_size = 1UL << table_pow2; + static constexpr size_t table_shift = stypebits - table_pow2; + static constexpr state_type table_mask = + (state_type(1U) << table_pow2) - state_type(1U); + + static constexpr bool may_tick = + (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2); + static constexpr size_t tick_shift = stypebits - advance_pow2; + static constexpr state_type tick_mask = + may_tick ? state_type( + (uint64_t(1) << (advance_pow2*may_tick)) - 1) + // ^-- stupidity to appease GCC warnings + : ~state_type(0U); + + static constexpr bool may_tock = stypebits < tick_limit_pow2; + + result_type data_[table_size]; + + PCG_NOINLINE void advance_table(); + + PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true); + + result_type& get_extended_value() + { + state_type state = this->state_; + if (kdd && baseclass::is_mcg) { + // The low order bits of an MCG are constant, so drop them. + state >>= 2; + } + size_t index = kdd ? state & table_mask + : state >> table_shift; + + if (may_tick) { + bool tick = kdd ? (state & tick_mask) == state_type(0u) + : (state >> tick_shift) == state_type(0u); + if (tick) + advance_table(); + } + if (may_tock) { + bool tock = state == state_type(0u); + if (tock) + advance_table(); + } + return data_[index]; + } + +public: + static constexpr size_t period_pow2() + { + return baseclass::period_pow2() + table_size*extvalclass::period_pow2(); + } + + PCG_NODISCARD PCG_ALWAYS_INLINE result_type operator()() + { + result_type rhs = get_extended_value(); + result_type lhs = this->baseclass::operator()(); + return lhs ^ rhs; + } + + PCG_NODISCARD 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 + 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 + 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::value + && !std::is_convertible::value>::type> + extended(SeedSeq&& seedSeq) + : baseclass(seedSeq) + { + generate_to(seedSeq, data_); + } + + template + void seed(Args&&... args) + { + new (this) extended(std::forward(args)...); + } + + template + friend bool operator==(const extended&, + const extended&); + + template + friend std::basic_ostream& + operator<<(std::basic_ostream& out, + const extended&); + + template + friend std::basic_istream& + operator>>(std::basic_istream& in, + extended&); + +}; + + +template +void extended::datainit( + const result_type* data) +{ + for (size_t i = 0; i < table_size; ++i) + data_[i] = data[i]; +} + +template +void extended::selfinit() +{ + // We need to fill the extended table with something, and we have + // very little provided data, so we use the base generator to + // produce values. Although not ideal (use a seed sequence, folks!), + // unexpected correlations are mitigated by + // - using XOR differences rather than the number directly + // - the way the table is accessed, its values *won't* be accessed + // in the same order the were written. + // - any strange correlations would only be apparent if we + // were to backstep the generator so that the base generator + // was generating the same values again + result_type lhs = baseclass::operator()(); + result_type rhs = baseclass::operator()(); + result_type xdiff = lhs - rhs; + for (size_t i = 0; i < table_size; ++i) { + data_[i] = baseclass::operator()() ^ xdiff; + } +} + +template +bool operator==(const extended& lhs, + const extended& rhs) +{ + auto& base_lhs = static_cast(lhs); + auto& base_rhs = static_cast(rhs); + return base_lhs == base_rhs + && std::equal( + std::begin(lhs.data_), std::end(lhs.data_), + std::begin(rhs.data_) + ); +} + +template +inline bool operator!=(const extended& lhs, + const extended& rhs) +{ + return !operator==(lhs, rhs); +} + +template +std::basic_ostream& +operator<<(std::basic_ostream& out, + const extended& rng) +{ + using pcg_extras::operator<<; + + auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); + auto space = out.widen(' '); + auto orig_fill = out.fill(); + + out << rng.multiplier() << space + << rng.increment() << space + << rng.state_; + + for (const auto& datum : rng.data_) + out << space << datum; + + out.flags(orig_flags); + out.fill(orig_fill); + return out; +} + +template +std::basic_istream& +operator>>(std::basic_istream& in, + extended& rng) +{ + extended new_rng; + auto& base_rng = static_cast(new_rng); + in >> base_rng; + + if (in.fail()) + return in; + + using pcg_extras::operator>>; + + auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); + + for (auto& datum : new_rng.data_) { + in >> datum; + if (in.fail()) + goto bail; + } + + rng = new_rng; + +bail: + in.flags(orig_flags); + return in; +} + + + +template +void +extended::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 +void +extended::advance_table( + state_type delta, bool isForwards) +{ + using base_state_t = typename baseclass::state_type; + using ext_state_t = typename extvalclass::state_type; + 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 +void extended::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 */ + +using oneseq_xsh_rs_16_8 = oneseq_base; +using oneseq_xsh_rs_32_16 = oneseq_base; +using oneseq_xsh_rs_64_32 = oneseq_base; +using oneseq_xsh_rs_128_64 = oneseq_base; +using cm_oneseq_xsh_rs_128_64 = + oneseq_base; + +using unique_xsh_rs_16_8 = unique_base; +using unique_xsh_rs_32_16 = unique_base; +using unique_xsh_rs_64_32 = unique_base; +using unique_xsh_rs_128_64 = unique_base; +using cm_unique_xsh_rs_128_64 = + unique_base; + +using setseq_xsh_rs_16_8 = setseq_base; +using setseq_xsh_rs_32_16 = setseq_base; +using setseq_xsh_rs_64_32 = setseq_base; +using setseq_xsh_rs_128_64 = setseq_base; +using cm_setseq_xsh_rs_128_64 = + setseq_base; + +using mcg_xsh_rs_16_8 = mcg_base; +using mcg_xsh_rs_32_16 = mcg_base; +using mcg_xsh_rs_64_32 = mcg_base; +using mcg_xsh_rs_128_64 = mcg_base; +using cm_mcg_xsh_rs_128_64 = + mcg_base; + +/* Predefined types for XSH RR */ + +using oneseq_xsh_rr_16_8 = oneseq_base; +using oneseq_xsh_rr_32_16 = oneseq_base; +using oneseq_xsh_rr_64_32 = oneseq_base; +using oneseq_xsh_rr_128_64 = oneseq_base; +using cm_oneseq_xsh_rr_128_64 = + oneseq_base; + +using unique_xsh_rr_16_8 = unique_base; +using unique_xsh_rr_32_16 = unique_base; +using unique_xsh_rr_64_32 = unique_base; +using unique_xsh_rr_128_64 = unique_base; +using cm_unique_xsh_rr_128_64 = + unique_base; + +using setseq_xsh_rr_16_8 = setseq_base; +using setseq_xsh_rr_32_16 = setseq_base; +using setseq_xsh_rr_64_32 = setseq_base; +using setseq_xsh_rr_128_64 = setseq_base; +using cm_setseq_xsh_rr_128_64 = + setseq_base; + +using mcg_xsh_rr_16_8 = mcg_base; +using mcg_xsh_rr_32_16 = mcg_base; +using mcg_xsh_rr_64_32 = mcg_base; +using mcg_xsh_rr_128_64 = mcg_base; +using cm_mcg_xsh_rr_128_64 = + mcg_base; + + +/* Predefined types for RXS M XS */ + +using oneseq_rxs_m_xs_8_8 = oneseq_base; +using oneseq_rxs_m_xs_16_16 = oneseq_base; +using oneseq_rxs_m_xs_32_32 = oneseq_base; +using oneseq_rxs_m_xs_64_64 = oneseq_base; +using oneseq_rxs_m_xs_128_128 = + oneseq_base; +using cm_oneseq_rxs_m_xs_128_128 = + oneseq_base; + +using unique_rxs_m_xs_8_8 = unique_base; +using unique_rxs_m_xs_16_16 = unique_base; +using unique_rxs_m_xs_32_32 = unique_base; +using unique_rxs_m_xs_64_64 = unique_base; +using unique_rxs_m_xs_128_128 = unique_base; +using cm_unique_rxs_m_xs_128_128 = + unique_base; + +using setseq_rxs_m_xs_8_8 = setseq_base; +using setseq_rxs_m_xs_16_16 = setseq_base; +using setseq_rxs_m_xs_32_32 = setseq_base; +using setseq_rxs_m_xs_64_64 = setseq_base; +using setseq_rxs_m_xs_128_128 = setseq_base; +using cm_setseq_rxs_m_xs_128_128 = + setseq_base; + + // MCG versions don't make sense here, so aren't defined. + +/* Predefined types for RXS M */ + +using oneseq_rxs_m_16_8 = oneseq_base; +using oneseq_rxs_m_32_16 = oneseq_base; +using oneseq_rxs_m_64_32 = oneseq_base; +using oneseq_rxs_m_128_64 = oneseq_base; +using cm_oneseq_rxs_m_128_64 = + oneseq_base; + +using unique_rxs_m_16_8 = unique_base; +using unique_rxs_m_32_16 = unique_base; +using unique_rxs_m_64_32 = unique_base; +using unique_rxs_m_128_64 = unique_base; +using cm_unique_rxs_m_128_64 = + unique_base; + +using setseq_rxs_m_16_8 = setseq_base; +using setseq_rxs_m_32_16 = setseq_base; +using setseq_rxs_m_64_32 = setseq_base; +using setseq_rxs_m_128_64 = setseq_base; +using cm_setseq_rxs_m_128_64 = + setseq_base; + +using mcg_rxs_m_16_8 = mcg_base; +using mcg_rxs_m_32_16 = mcg_base; +using mcg_rxs_m_64_32 = mcg_base; +using mcg_rxs_m_128_64 = mcg_base; +using cm_mcg_rxs_m_128_64 = + mcg_base; + +/* Predefined types for DXSM */ + +using oneseq_dxsm_16_8 = oneseq_base; +using oneseq_dxsm_32_16 = oneseq_base; +using oneseq_dxsm_64_32 = oneseq_base; +using oneseq_dxsm_128_64 = oneseq_base; +using cm_oneseq_dxsm_128_64 = + oneseq_base; + +using unique_dxsm_16_8 = unique_base; +using unique_dxsm_32_16 = unique_base; +using unique_dxsm_64_32 = unique_base; +using unique_dxsm_128_64 = unique_base; +using cm_unique_dxsm_128_64 = + unique_base; + +using setseq_dxsm_16_8 = setseq_base; +using setseq_dxsm_32_16 = setseq_base; +using setseq_dxsm_64_32 = setseq_base; +using setseq_dxsm_128_64 = setseq_base; +using cm_setseq_dxsm_128_64 = + setseq_base; + +using mcg_dxsm_16_8 = mcg_base; +using mcg_dxsm_32_16 = mcg_base; +using mcg_dxsm_64_32 = mcg_base; +using mcg_dxsm_128_64 = mcg_base; +using cm_mcg_dxsm_128_64 = + mcg_base; + +/* Predefined types for DXSM (Convenience) */ + +using pcg32_dxsm = setseq_dxsm_64_32; +using pcg32_dxsm_oneseq = oneseq_dxsm_64_32; +using pcg32_dxsm_unique = unique_dxsm_64_32; +using pcg32_dxsm_fast = mcg_dxsm_64_32; + +using pcg64_dxsm = setseq_dxsm_128_64; +using pcg64_dxsm_oneseq = oneseq_dxsm_128_64; +using pcg64_dxsm_unique = unique_dxsm_128_64; +using pcg64_dxsm_fast = mcg_dxsm_128_64; + +/* Predefined types for XSL RR (only defined for "large" types) */ + +using oneseq_xsl_rr_64_32 = oneseq_base; +using oneseq_xsl_rr_128_64 = oneseq_base; +using cm_oneseq_xsl_rr_128_64 = + oneseq_base; + +using unique_xsl_rr_64_32 = unique_base; +using unique_xsl_rr_128_64 = unique_base; +using cm_unique_xsl_rr_128_64 = + unique_base; + +using setseq_xsl_rr_64_32 = setseq_base; +using setseq_xsl_rr_128_64 = setseq_base; +using cm_setseq_xsl_rr_128_64 = + setseq_base; + +using mcg_xsl_rr_64_32 = mcg_base; +using mcg_xsl_rr_128_64 = mcg_base; +using cm_mcg_xsl_rr_128_64 = + mcg_base; + + +/* Predefined types for XSL RR RR (only defined for "large" types) */ + +using oneseq_xsl_rr_rr_64_64 = + oneseq_base; +using oneseq_xsl_rr_rr_128_128 = + oneseq_base; +using cm_oneseq_xsl_rr_rr_128_128 = + oneseq_base; + +using unique_xsl_rr_rr_64_64 = + unique_base; +using unique_xsl_rr_rr_128_128 = + unique_base; +using cm_unique_xsl_rr_rr_128_128 = + unique_base; + +using setseq_xsl_rr_rr_64_64 = + setseq_base; +using setseq_xsl_rr_rr_128_128 = + setseq_base; +using cm_setseq_xsl_rr_rr_128_128 = + setseq_base; + + // MCG versions don't make sense here, so aren't defined. + +/* Extended generators */ + +template +using ext_std8 = extended; + +template +using ext_std16 = extended; + +template +using ext_std32 = extended; + +template +using ext_std64 = extended; + + +template +using ext_oneseq_rxs_m_xs_32_32 = + ext_std32; + +template +using ext_mcg_xsh_rs_64_32 = + ext_std32; + +template +using ext_oneseq_xsh_rs_64_32 = + ext_std32; + +template +using ext_setseq_xsh_rr_64_32 = + ext_std32; + +template +using ext_mcg_xsl_rr_128_64 = + ext_std64; + +template +using ext_oneseq_xsl_rr_128_64 = + ext_std64; + +template +using ext_setseq_xsl_rr_128_64 = + ext_std64; + +} // namespace pcg_engines + +using pcg32 = pcg_engines::setseq_xsh_rr_64_32; +using pcg32_oneseq = pcg_engines::oneseq_xsh_rr_64_32; +using pcg32_unique = pcg_engines::unique_xsh_rr_64_32; +using pcg32_fast = pcg_engines::mcg_xsh_rs_64_32; + +using pcg64 = pcg_engines::setseq_xsl_rr_128_64; +using pcg64_oneseq = pcg_engines::oneseq_xsl_rr_128_64; +using pcg64_unique = pcg_engines::unique_xsl_rr_128_64; +using pcg64_fast = pcg_engines::mcg_xsl_rr_128_64; + +using pcg8_once_insecure = pcg_engines::setseq_rxs_m_xs_8_8; +using pcg16_once_insecure = pcg_engines::setseq_rxs_m_xs_16_16; +using pcg32_once_insecure = pcg_engines::setseq_rxs_m_xs_32_32; +using pcg64_once_insecure = pcg_engines::setseq_rxs_m_xs_64_64; +using pcg128_once_insecure = pcg_engines::setseq_xsl_rr_rr_128_128; + +using pcg8_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_8_8; +using pcg16_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_16_16; +using pcg32_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_32_32; +using pcg64_oneseq_once_insecure = pcg_engines::oneseq_rxs_m_xs_64_64; +using pcg128_oneseq_once_insecure = pcg_engines::oneseq_xsl_rr_rr_128_128; + + +// 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. + +using pcg32_k2 = pcg_engines::ext_setseq_xsh_rr_64_32<1,16,true>; +using pcg32_k2_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<1,32,true>; + +// These eight extended RNGs have about as much state as arc4random +// +// - the k variants are k-dimensionally equidistributed +// - the c variants offer are intended to be harder to predict +// +// (neither is intended for use in cryptographic applications) + +using pcg32_k64 = pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true>; +using pcg32_k64_oneseq = pcg_engines::ext_mcg_xsh_rs_64_32<6,32,true>; +using pcg32_k64_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true>; + +using pcg32_c64 = pcg_engines::ext_setseq_xsh_rr_64_32<6,16,false>; +using pcg32_c64_oneseq = pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,false>; +using pcg32_c64_fast = pcg_engines::ext_mcg_xsh_rs_64_32<6,32,false>; + +using pcg64_k32 = pcg_engines::ext_setseq_xsl_rr_128_64<5,16,true>; +using pcg64_k32_oneseq = pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,true>; +using pcg64_k32_fast = pcg_engines::ext_mcg_xsl_rr_128_64<5,128,true>; + +using pcg64_c32 = pcg_engines::ext_setseq_xsl_rr_128_64<5,16,false>; +using pcg64_c32_oneseq = pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,false>; +using pcg64_c32_fast = pcg_engines::ext_mcg_xsl_rr_128_64<5,128,false>; + +// These eight extended RNGs have more state than the Mersenne twister +// +// - the k variants are k-dimensionally equidistributed +// - the c variants offer are intended to be harder to predict +// +// (neither is intended for use in cryptographic applications) + +using pcg32_k1024 = pcg_engines::ext_setseq_xsh_rr_64_32<10,16,true>; +using pcg32_k1024_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,true>; + +using pcg32_c1024 = pcg_engines::ext_setseq_xsh_rr_64_32<10,16,false>; +using pcg32_c1024_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,false>; + +using pcg64_k1024 = pcg_engines::ext_setseq_xsl_rr_128_64<10,16,true>; +using pcg64_k1024_fast = pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,true>; + +using pcg64_c1024 = pcg_engines::ext_setseq_xsl_rr_128_64<10,16,false>; +using pcg64_c1024_fast = pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,false>; + +// 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!] + +using pcg32_k16384 = pcg_engines::ext_setseq_xsh_rr_64_32<14,16,true>; +using pcg32_k16384_fast = pcg_engines::ext_oneseq_xsh_rs_64_32<14,32,true>; + +#ifdef _MSC_VER + #pragma warning(default:4146) +#endif + +#endif // PCG_RAND_HPP_INCLUDED diff --git a/include/pcg_uint128.hpp b/include/pcg_uint128.hpp index 6811585..756cd92 100644 --- a/include/pcg_uint128.hpp +++ b/include/pcg_uint128.hpp @@ -1,1051 +1,1051 @@ -/* - * PCG Random Number Generation for C++ - * - * Copyright 2014-2021 Melissa O'Neill , - * and the PCG Project contributors. - * - * SPDX-License-Identifier: (Apache-2.0 OR MIT) - * - * Licensed under the Apache License, Version 2.0 (provided in - * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0) - * or under the MIT license (provided in LICENSE-MIT.txt and at - * http://opensource.org/licenses/MIT), at your option. This file may not - * be copied, modified, or distributed except according to those terms. - * - * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either - * express or implied. See your chosen license for details. - * - * For additional information about the PCG random number generation scheme, - * visit http://www.pcg-random.org/. - */ - -/* - * This code provides 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. - */ -#pragma once -#ifndef PCG_UINT128_HPP_INCLUDED -#define PCG_UINT128_HPP_INCLUDED 1 - -#include -#include -#include -#include - -#if __cplusplus >= 202002L || (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L) || defined(PCG_USE_BIT_HEADER) - #include - #ifndef PCG_BIT_SUPPORT - #define PCG_BIT_SUPPORT 1 - #endif -#endif -#include -#include -#include -#include - -#if defined(_MSC_VER) // Use MSVC++ intrinsics -#include -#endif - -/* - * 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__ || _M_IX86 || _M_AMD64 || _M_ARM64 - #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 - -#if INTPTR_MAX == INT64_MAX && !defined(PCG_64BIT_SPECIALIZATIONS) - #define PCG_64BIT_SPECIALIZATIONS 1 -#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 - using bitcount_t = uint8_t; -#else - using bitcount_t = PCG_BITCOUNT_T; -#endif - -/* - * Provide some useful helper functions - * * flog2 floor(log2(x)) - * * trailingzeros number of trailing zero bits - */ - -#if PCG_BIT_SUPPORT - -inline bitcount_t flog2(uint32_t v) -{ - return bitcount_t(std::bit_width(v) - 1); -} - -inline bitcount_t trailingzeros(uint32_t v) -{ - return bitcount_t(std::countr_zero(v)); -} - -inline bitcount_t flog2(uint64_t v) -{ - return bitcount_t(std::bit_width(v) - 1); -} - -inline bitcount_t trailingzeros(uint64_t v) -{ - return bitcount_t(std::countr_zero(v)); -} - -#elif defined(__GNUC__) // Any GNU-compatible compiler supporting C++11 has - // some useful intrinsics we can use. - // These bitcount_t casts are from SupercriticalSynthesizers/pcg-cpp PR fix-gcc-warnings - -inline bitcount_t flog2(uint32_t v) -{ - return bitcount_t(31 - __builtin_clz(v)); -} - -inline bitcount_t trailingzeros(uint32_t v) -{ - return bitcount_t(__builtin_ctz(v)); -} - -inline bitcount_t flog2(uint64_t v) -{ -#if UINT64_MAX == ULONG_MAX - return bitcount_t(63 - __builtin_clzl(v)); -#elif UINT64_MAX == ULLONG_MAX - return bitcount_t(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 bitcount_t(__builtin_ctzl(v)); -#elif UINT64_MAX == ULLONG_MAX - return bitcount_t(__builtin_ctzll(v)); -#else - #error Cannot find a function for uint64_t -#endif -} - -#elif defined(_MSC_VER) // Use MSVC++ intrinsics - -#pragma intrinsic(_BitScanReverse, _BitScanForward) -#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) -#pragma intrinsic(_BitScanReverse64, _BitScanForward64) -#endif - -inline bitcount_t flog2(uint32_t v) -{ - unsigned long i; - _BitScanReverse(&i, v); - return bitcount_t(i); -} - -inline bitcount_t trailingzeros(uint32_t v) -{ - unsigned long i; - _BitScanForward(&i, v); - return bitcount_t(i); -} - -inline bitcount_t flog2(uint64_t v) -{ -#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) - unsigned long i; - _BitScanReverse64(&i, v); - return bitcount_t(i); -#else - // 32-bit x86 - uint32_t high = v >> 32; - uint32_t low = uint32_t(v); - return high ? 32+flog2(high) : flog2(low); -#endif -} - -inline bitcount_t trailingzeros(uint64_t v) -{ -#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) - unsigned long i; - _BitScanForward64(&i, v); - return bitcount_t(i); -#else - // 32-bit x86 - uint32_t high = v >> 32; - uint32_t low = uint32_t(v); - return low ? trailingzeros(low) : trailingzeros(high)+32; -#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 - -inline bitcount_t flog2(uint8_t v) -{ - return flog2(uint32_t(v)); -} - -inline bitcount_t flog2(uint16_t v) -{ - return flog2(uint32_t(v)); -} - -#if __SIZEOF_INT128__ -inline bitcount_t flog2(__uint128_t v) -{ - uint64_t high = uint64_t(v >> 64); - uint64_t low = uint64_t(v); - - return high ? 64+flog2(high) : flog2(low); -} -#endif - -inline bitcount_t trailingzeros(uint8_t v) -{ - return trailingzeros(uint32_t(v)); -} - -inline bitcount_t trailingzeros(uint16_t v) -{ - return trailingzeros(uint32_t(v)); -} - -#if __SIZEOF_INT128__ -inline bitcount_t trailingzeros(__uint128_t v) -{ - uint64_t high = uint64_t(v >> 64); - uint64_t low = uint64_t(v); - return low ? trailingzeros(low) : trailingzeros(high)+64; -} -#endif - -template -inline bitcount_t clog2(UInt v) -{ - return flog2(v) + ((v & (-v)) != v); -} - -template -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 -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 -class uint_x4 { -// private: - static constexpr unsigned int UINT_BITS = sizeof(UInt) * CHAR_BIT; -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]; - }; - -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 - } - - constexpr uint_x4(UIntX2 v01) -#if PCG_LITTLE_ENDIAN - : d{v01, UIntX2(0)} -#else - : d{UIntX2(0),v01} -#endif - { - // Nothing (else) to do - } - - template::value - && sizeof(Integral) <= sizeof(UIntX2)) - >::type* = nullptr> - constexpr uint_x4(Integral v01) -#if PCG_LITTLE_ENDIAN - : d{UIntX2(v01), UIntX2(0)} -#else - : d{UIntX2(0), UIntX2(v01)} -#endif - { - // Nothing (else) to do - } - - explicit constexpr operator UIntX2() const - { - return d.v01; - } - - template::value - && sizeof(Integral) <= sizeof(UIntX2)) - >::type* = nullptr> - explicit constexpr operator Integral() const - { - return Integral(d.v01); - } - - explicit constexpr operator bool() const - { - return d.v01 || d.v23; - } - - template - friend uint_x4 operator*(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator*(const uint_x4&, V); - - template - friend std::pair< uint_x4,uint_x4 > - divmod(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator+(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator-(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator<<(const uint_x4&, const bitcount_t shift); - - template - friend uint_x4 operator>>(const uint_x4&, const bitcount_t shift); - -#if PCG_64BIT_SPECIALIZATIONS - template - friend uint_x4 operator<<(const uint_x4&, const bitcount_t shift); - - template - friend uint_x4 operator>>(const uint_x4&, const bitcount_t shift); -#endif - - template - friend uint_x4 operator&(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator|(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator^(const uint_x4&, const uint_x4&); - - template - friend bool operator==(const uint_x4&, const uint_x4&); - - template - friend bool operator!=(const uint_x4&, const uint_x4&); - - template - friend bool operator<(const uint_x4&, const uint_x4&); - - template - friend bool operator<=(const uint_x4&, const uint_x4&); - - template - friend bool operator>(const uint_x4&, const uint_x4&); - - template - friend bool operator>=(const uint_x4&, const uint_x4&); - - template - friend uint_x4 operator~(const uint_x4&); - - template - friend uint_x4 operator-(const uint_x4&); - - template - friend bitcount_t flog2(const uint_x4&); - - template - friend bitcount_t trailingzeros(const uint_x4&); - -#if PCG_64BIT_SPECIALIZATIONS - template - friend bitcount_t flog2(const uint_x4&); - - template - friend bitcount_t trailingzeros(const uint_x4&); -#endif - - uint_x4& operator*=(const uint_x4& rhs) - { - uint_x4 result = *this * rhs; - return *this = result; - } - - uint_x4& operator*=(UIntX2 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 -bitcount_t flog2(const uint_x4& 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]) + uint_x4::UINT_BITS*i; - } - abort(); -} - -template -bitcount_t trailingzeros(const uint_x4& 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]) + uint_x4::UINT_BITS*i; - } - return uint_x4::UINT_BITS*4; -} - -#if PCG_64BIT_SPECIALIZATIONS -template -bitcount_t flog2(const uint_x4& v) -{ - return v.d.v23 > 0 ? flog2(v.d.v23) + uint_x4::UINT_BITS*2 - : flog2(v.d.v01); -} - -template -bitcount_t trailingzeros(const uint_x4& v) -{ - return v.d.v01 == 0 ? trailingzeros(v.d.v23) + uint_x4::UINT_BITS*2 - : trailingzeros(v.d.v01); -} -#endif - -template -std::pair< uint_x4, uint_x4 > - divmod(const uint_x4& orig_dividend, - const uint_x4& 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(UIntX2(0)), 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 ONE(UIntX2(1)); - 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 quotient(UIntX2(0)); - - 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 -uint_x4 operator/(const uint_x4& dividend, - const uint_x4& divisor) -{ - return divmod(dividend, divisor).first; -} - -template -uint_x4 operator%(const uint_x4& dividend, - const uint_x4& divisor) -{ - return divmod(dividend, divisor).second; -} - - -template -uint_x4 operator*(const uint_x4& a, - const uint_x4& b) -{ - constexpr auto UINT_BITS = uint_x4::UINT_BITS; - uint_x4 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 >> UINT_BITS); - - UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(b.w.v0); - r.w.v2 = UInt(a1b0 >> UINT_BITS); - 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 >> UINT_BITS), 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 >> UINT_BITS), carryin, &carryout); - - r.d.v23 += a.d.v01 * b.d.v23 + a.d.v23 * b.d.v01; - - return r; -} - - -template -uint_x4 operator*(const uint_x4& a, - UIntX2 b01) -{ - constexpr auto UINT_BITS = uint_x4::UINT_BITS; - uint_x4 r = {0U, 0U, 0U, 0U}; - bool carryin = false; - bool carryout; - UIntX2 a0b0 = UIntX2(a.w.v0) * UIntX2(UInt(b01)); - r.w.v0 = UInt(a0b0); - r.w.v1 = UInt(a0b0 >> UINT_BITS); - - UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(UInt(b01)); - r.w.v2 = UInt(a1b0 >> UINT_BITS); - 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(b01 >> UINT_BITS); - carryin = false; - r.w.v2 = addwithcarry(r.w.v2, UInt(a0b1 >> UINT_BITS), 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(b01 >> UINT_BITS); - carryin = false; - r.w.v2 = addwithcarry(r.w.v2, UInt(a1b1), carryin, &carryout); - carryin = carryout; - r.w.v3 = addwithcarry(r.w.v3, UInt(a1b1 >> UINT_BITS), carryin, &carryout); - - r.d.v23 += a.d.v23 * b01; - - return r; -} - -#if PCG_64BIT_SPECIALIZATIONS -#if defined(_MSC_VER) -#if defined(_M_AMD64) || defined(_M_IX86) -#pragma intrinsic(_umul128) -#elif defined(_M_ARM64) -// This fix is from imneme/pcg-cpp PR #99 by Demonese -#pragma intrinsic(__umulh) -#else -#error Unsupported architecture -#endif -#endif - -#if defined(_MSC_VER) || __SIZEOF_INT128__ -template -uint_x4 operator*(const uint_x4& a, - const uint_x4& b) -{ -#if defined(_MSC_VER) -#if defined(_M_AMD64) || defined(_M_IX86) - uint64_t hi; - uint64_t lo = _umul128(a.d.v01, b.d.v01, &hi); -#elif defined(_M_ARM64) - uint64_t lo = a.d.v01 * b.d.v01; - uint64_t hi = __umulh(a.d.v01, b.d.v01); -#else -#error Unsupported architecture -#endif -#else - __uint128_t r = __uint128_t(a.d.v01) * __uint128_t(b.d.v01); - uint64_t lo = uint64_t(r); - uint64_t hi = r >> 64; -#endif - hi += a.d.v23 * b.d.v01 + a.d.v01 * b.d.v23; - return {hi, lo}; -} -#endif -#endif - - -template -uint_x4 operator+(const uint_x4& a, - const uint_x4& b) -{ - uint_x4 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 -uint_x4 operator-(const uint_x4& a, - const uint_x4& b) -{ - uint_x4 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; -} - -#if PCG_64BIT_SPECIALIZATIONS -template -uint_x4 operator+(const uint_x4& a, - const uint_x4& b) -{ - uint_x4 r = {uint64_t(0u), uint64_t(0u)}; - - bool carryin = false; - bool carryout; - r.d.v01 = addwithcarry(a.d.v01, b.d.v01, carryin, &carryout); - carryin = carryout; - r.d.v23 = addwithcarry(a.d.v23, b.d.v23, carryin, &carryout); - - return r; -} - -template -uint_x4 operator-(const uint_x4& a, - const uint_x4& b) -{ - uint_x4 r = {uint64_t(0u), uint64_t(0u)}; - - bool carryin = false; - bool carryout; - r.d.v01 = subwithcarry(a.d.v01, b.d.v01, carryin, &carryout); - carryin = carryout; - r.d.v23 = subwithcarry(a.d.v23, b.d.v23, carryin, &carryout); - - return r; -} -#endif - -template -uint_x4 operator&(const uint_x4& a, - const uint_x4& b) -{ - return uint_x4(a.d.v23 & b.d.v23, a.d.v01 & b.d.v01); -} - -template -uint_x4 operator|(const uint_x4& a, - const uint_x4& b) -{ - return uint_x4(a.d.v23 | b.d.v23, a.d.v01 | b.d.v01); -} - -template -uint_x4 operator^(const uint_x4& a, - const uint_x4& b) -{ - return uint_x4(a.d.v23 ^ b.d.v23, a.d.v01 ^ b.d.v01); -} - -template -uint_x4 operator~(const uint_x4& v) -{ - return uint_x4(~v.d.v23, ~v.d.v01); -} - -template -uint_x4 operator-(const uint_x4& v) -{ - return uint_x4(0UL,0UL) - v; -} - -template -bool operator==(const uint_x4& a, const uint_x4& b) -{ - return (a.d.v01 == b.d.v01) && (a.d.v23 == b.d.v23); -} - -template -bool operator!=(const uint_x4& a, const uint_x4& b) -{ - return !operator==(a,b); -} - - -template -bool operator<(const uint_x4& a, const uint_x4& b) -{ - return (a.d.v23 < b.d.v23) - || ((a.d.v23 == b.d.v23) && (a.d.v01 < b.d.v01)); -} - -template -bool operator>(const uint_x4& a, const uint_x4& b) -{ - return operator<(b,a); -} - -template -bool operator<=(const uint_x4& a, const uint_x4& b) -{ - return !(operator<(b,a)); -} - -template -bool operator>=(const uint_x4& a, const uint_x4& b) -{ - return !(operator<(a,b)); -} - - - -template -uint_x4 operator<<(const uint_x4& v, - const bitcount_t shift) -{ - uint_x4 r = {0U, 0U, 0U, 0U}; - const bitcount_t bits = uint_x4::UINT_BITS; - 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 -uint_x4 operator>>(const uint_x4& v, - const bitcount_t shift) -{ - uint_x4 r = {0U, 0U, 0U, 0U}; - const bitcount_t bits = uint_x4::UINT_BITS; - 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; -} - -#if PCG_64BIT_SPECIALIZATIONS -template -uint_x4 operator<<(const uint_x4& v, - const bitcount_t shift) -{ - constexpr bitcount_t bits2 = uint_x4::UINT_BITS * 2; - - if (shift >= bits2) { - return {v.d.v01 << (shift-bits2), uint64_t(0u)}; - } else { - return {shift ? (v.d.v23 << shift) | (v.d.v01 >> (bits2-shift)) - : v.d.v23, - v.d.v01 << shift}; - } -} - -template -uint_x4 operator>>(const uint_x4& v, - const bitcount_t shift) -{ - constexpr bitcount_t bits2 = uint_x4::UINT_BITS * 2; - - if (shift >= bits2) { - return {uint64_t(0u), v.d.v23 >> (shift-bits2)}; - } else { - return {v.d.v23 >> shift, - shift ? (v.d.v01 >> shift) | (v.d.v23 << (bits2-shift)) - : v.d.v01}; - } -} -#endif - -} // namespace pcg_extras - -#endif // PCG_UINT128_HPP_INCLUDED +/* + * PCG Random Number Generation for C++ + * + * Copyright 2014-2021 Melissa O'Neill , + * and the PCG Project contributors. + * + * SPDX-License-Identifier: (Apache-2.0 OR MIT) + * + * Licensed under the Apache License, Version 2.0 (provided in + * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0) + * or under the MIT license (provided in LICENSE-MIT.txt and at + * http://opensource.org/licenses/MIT), at your option. This file may not + * be copied, modified, or distributed except according to those terms. + * + * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either + * express or implied. See your chosen license for details. + * + * For additional information about the PCG random number generation scheme, + * visit http://www.pcg-random.org/. + */ + +/* + * This code provides 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. + */ +#pragma once +#ifndef PCG_UINT128_HPP_INCLUDED +#define PCG_UINT128_HPP_INCLUDED 1 + +#include +#include +#include +#include + +#if __cplusplus >= 202002L || (defined(_MSVC_LANG) && _MSVC_LANG >= 202002L) || defined(PCG_USE_BIT_HEADER) + #include + #ifndef PCG_BIT_SUPPORT + #define PCG_BIT_SUPPORT 1 + #endif +#endif +#include +#include +#include +#include + +#if defined(_MSC_VER) // Use MSVC++ intrinsics +#include +#endif + +/* + * 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__ || _M_IX86 || _M_AMD64 || _M_ARM64 + #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 + +#if INTPTR_MAX == INT64_MAX && !defined(PCG_64BIT_SPECIALIZATIONS) + #define PCG_64BIT_SPECIALIZATIONS 1 +#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 + using bitcount_t = uint8_t; +#else + using bitcount_t = PCG_BITCOUNT_T; +#endif + +/* + * Provide some useful helper functions + * * flog2 floor(log2(x)) + * * trailingzeros number of trailing zero bits + */ + +#if PCG_BIT_SUPPORT + +inline bitcount_t flog2(uint32_t v) +{ + return bitcount_t(std::bit_width(v) - 1); +} + +inline bitcount_t trailingzeros(uint32_t v) +{ + return bitcount_t(std::countr_zero(v)); +} + +inline bitcount_t flog2(uint64_t v) +{ + return bitcount_t(std::bit_width(v) - 1); +} + +inline bitcount_t trailingzeros(uint64_t v) +{ + return bitcount_t(std::countr_zero(v)); +} + +#elif defined(__GNUC__) // Any GNU-compatible compiler supporting C++11 has + // some useful intrinsics we can use. + // These bitcount_t casts are from SupercriticalSynthesizers/pcg-cpp PR fix-gcc-warnings + +inline bitcount_t flog2(uint32_t v) +{ + return bitcount_t(31 - __builtin_clz(v)); +} + +inline bitcount_t trailingzeros(uint32_t v) +{ + return bitcount_t(__builtin_ctz(v)); +} + +inline bitcount_t flog2(uint64_t v) +{ +#if UINT64_MAX == ULONG_MAX + return bitcount_t(63 - __builtin_clzl(v)); +#elif UINT64_MAX == ULLONG_MAX + return bitcount_t(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 bitcount_t(__builtin_ctzl(v)); +#elif UINT64_MAX == ULLONG_MAX + return bitcount_t(__builtin_ctzll(v)); +#else + #error Cannot find a function for uint64_t +#endif +} + +#elif defined(_MSC_VER) // Use MSVC++ intrinsics + +#pragma intrinsic(_BitScanReverse, _BitScanForward) +#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) +#pragma intrinsic(_BitScanReverse64, _BitScanForward64) +#endif + +inline bitcount_t flog2(uint32_t v) +{ + unsigned long i; + _BitScanReverse(&i, v); + return bitcount_t(i); +} + +inline bitcount_t trailingzeros(uint32_t v) +{ + unsigned long i; + _BitScanForward(&i, v); + return bitcount_t(i); +} + +inline bitcount_t flog2(uint64_t v) +{ +#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) + unsigned long i; + _BitScanReverse64(&i, v); + return bitcount_t(i); +#else + // 32-bit x86 + uint32_t high = v >> 32; + uint32_t low = uint32_t(v); + return high ? 32+flog2(high) : flog2(low); +#endif +} + +inline bitcount_t trailingzeros(uint64_t v) +{ +#if defined(_M_X64) || defined(_M_ARM) || defined(_M_ARM64) + unsigned long i; + _BitScanForward64(&i, v); + return bitcount_t(i); +#else + // 32-bit x86 + uint32_t high = v >> 32; + uint32_t low = uint32_t(v); + return low ? trailingzeros(low) : trailingzeros(high)+32; +#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 + +inline bitcount_t flog2(uint8_t v) +{ + return flog2(uint32_t(v)); +} + +inline bitcount_t flog2(uint16_t v) +{ + return flog2(uint32_t(v)); +} + +#if __SIZEOF_INT128__ +inline bitcount_t flog2(__uint128_t v) +{ + uint64_t high = uint64_t(v >> 64); + uint64_t low = uint64_t(v); + + return high ? 64+flog2(high) : flog2(low); +} +#endif + +inline bitcount_t trailingzeros(uint8_t v) +{ + return trailingzeros(uint32_t(v)); +} + +inline bitcount_t trailingzeros(uint16_t v) +{ + return trailingzeros(uint32_t(v)); +} + +#if __SIZEOF_INT128__ +inline bitcount_t trailingzeros(__uint128_t v) +{ + uint64_t high = uint64_t(v >> 64); + uint64_t low = uint64_t(v); + return low ? trailingzeros(low) : trailingzeros(high)+64; +} +#endif + +template +inline bitcount_t clog2(UInt v) +{ + return flog2(v) + ((v & (-v)) != v); +} + +template +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 +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 +class uint_x4 { +// private: + static constexpr unsigned int UINT_BITS = sizeof(UInt) * CHAR_BIT; +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]; + }; + +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 + } + + constexpr uint_x4(UIntX2 v01) +#if PCG_LITTLE_ENDIAN + : d{v01, UIntX2(0)} +#else + : d{UIntX2(0),v01} +#endif + { + // Nothing (else) to do + } + + template::value + && sizeof(Integral) <= sizeof(UIntX2)) + >::type* = nullptr> + constexpr uint_x4(Integral v01) +#if PCG_LITTLE_ENDIAN + : d{UIntX2(v01), UIntX2(0)} +#else + : d{UIntX2(0), UIntX2(v01)} +#endif + { + // Nothing (else) to do + } + + explicit constexpr operator UIntX2() const + { + return d.v01; + } + + template::value + && sizeof(Integral) <= sizeof(UIntX2)) + >::type* = nullptr> + explicit constexpr operator Integral() const + { + return Integral(d.v01); + } + + explicit constexpr operator bool() const + { + return d.v01 || d.v23; + } + + template + friend uint_x4 operator*(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator*(const uint_x4&, V); + + template + friend std::pair< uint_x4,uint_x4 > + divmod(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator+(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator-(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator<<(const uint_x4&, const bitcount_t shift); + + template + friend uint_x4 operator>>(const uint_x4&, const bitcount_t shift); + +#if PCG_64BIT_SPECIALIZATIONS + template + friend uint_x4 operator<<(const uint_x4&, const bitcount_t shift); + + template + friend uint_x4 operator>>(const uint_x4&, const bitcount_t shift); +#endif + + template + friend uint_x4 operator&(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator|(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator^(const uint_x4&, const uint_x4&); + + template + friend bool operator==(const uint_x4&, const uint_x4&); + + template + friend bool operator!=(const uint_x4&, const uint_x4&); + + template + friend bool operator<(const uint_x4&, const uint_x4&); + + template + friend bool operator<=(const uint_x4&, const uint_x4&); + + template + friend bool operator>(const uint_x4&, const uint_x4&); + + template + friend bool operator>=(const uint_x4&, const uint_x4&); + + template + friend uint_x4 operator~(const uint_x4&); + + template + friend uint_x4 operator-(const uint_x4&); + + template + friend bitcount_t flog2(const uint_x4&); + + template + friend bitcount_t trailingzeros(const uint_x4&); + +#if PCG_64BIT_SPECIALIZATIONS + template + friend bitcount_t flog2(const uint_x4&); + + template + friend bitcount_t trailingzeros(const uint_x4&); +#endif + + uint_x4& operator*=(const uint_x4& rhs) + { + uint_x4 result = *this * rhs; + return *this = result; + } + + uint_x4& operator*=(UIntX2 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 +bitcount_t flog2(const uint_x4& 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]) + uint_x4::UINT_BITS*i; + } + abort(); +} + +template +bitcount_t trailingzeros(const uint_x4& 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]) + uint_x4::UINT_BITS*i; + } + return uint_x4::UINT_BITS*4; +} + +#if PCG_64BIT_SPECIALIZATIONS +template +bitcount_t flog2(const uint_x4& v) +{ + return v.d.v23 > 0 ? flog2(v.d.v23) + uint_x4::UINT_BITS*2 + : flog2(v.d.v01); +} + +template +bitcount_t trailingzeros(const uint_x4& v) +{ + return v.d.v01 == 0 ? trailingzeros(v.d.v23) + uint_x4::UINT_BITS*2 + : trailingzeros(v.d.v01); +} +#endif + +template +std::pair< uint_x4, uint_x4 > + divmod(const uint_x4& orig_dividend, + const uint_x4& 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(UIntX2(0)), 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 ONE(UIntX2(1)); + 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 quotient(UIntX2(0)); + + 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 +uint_x4 operator/(const uint_x4& dividend, + const uint_x4& divisor) +{ + return divmod(dividend, divisor).first; +} + +template +uint_x4 operator%(const uint_x4& dividend, + const uint_x4& divisor) +{ + return divmod(dividend, divisor).second; +} + + +template +uint_x4 operator*(const uint_x4& a, + const uint_x4& b) +{ + constexpr auto UINT_BITS = uint_x4::UINT_BITS; + uint_x4 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 >> UINT_BITS); + + UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(b.w.v0); + r.w.v2 = UInt(a1b0 >> UINT_BITS); + 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 >> UINT_BITS), 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 >> UINT_BITS), carryin, &carryout); + + r.d.v23 += a.d.v01 * b.d.v23 + a.d.v23 * b.d.v01; + + return r; +} + + +template +uint_x4 operator*(const uint_x4& a, + UIntX2 b01) +{ + constexpr auto UINT_BITS = uint_x4::UINT_BITS; + uint_x4 r = {0U, 0U, 0U, 0U}; + bool carryin = false; + bool carryout; + UIntX2 a0b0 = UIntX2(a.w.v0) * UIntX2(UInt(b01)); + r.w.v0 = UInt(a0b0); + r.w.v1 = UInt(a0b0 >> UINT_BITS); + + UIntX2 a1b0 = UIntX2(a.w.v1) * UIntX2(UInt(b01)); + r.w.v2 = UInt(a1b0 >> UINT_BITS); + 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(b01 >> UINT_BITS); + carryin = false; + r.w.v2 = addwithcarry(r.w.v2, UInt(a0b1 >> UINT_BITS), 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(b01 >> UINT_BITS); + carryin = false; + r.w.v2 = addwithcarry(r.w.v2, UInt(a1b1), carryin, &carryout); + carryin = carryout; + r.w.v3 = addwithcarry(r.w.v3, UInt(a1b1 >> UINT_BITS), carryin, &carryout); + + r.d.v23 += a.d.v23 * b01; + + return r; +} + +#if PCG_64BIT_SPECIALIZATIONS +#if defined(_MSC_VER) +#if defined(_M_AMD64) || defined(_M_IX86) +#pragma intrinsic(_umul128) +#elif defined(_M_ARM64) +// This fix is from imneme/pcg-cpp PR #99 by Demonese +#pragma intrinsic(__umulh) +#else +#error Unsupported architecture +#endif +#endif + +#if defined(_MSC_VER) || __SIZEOF_INT128__ +template +uint_x4 operator*(const uint_x4& a, + const uint_x4& b) +{ +#if defined(_MSC_VER) +#if defined(_M_AMD64) || defined(_M_IX86) + uint64_t hi; + uint64_t lo = _umul128(a.d.v01, b.d.v01, &hi); +#elif defined(_M_ARM64) + uint64_t lo = a.d.v01 * b.d.v01; + uint64_t hi = __umulh(a.d.v01, b.d.v01); +#else +#error Unsupported architecture +#endif +#else + __uint128_t r = __uint128_t(a.d.v01) * __uint128_t(b.d.v01); + uint64_t lo = uint64_t(r); + uint64_t hi = r >> 64; +#endif + hi += a.d.v23 * b.d.v01 + a.d.v01 * b.d.v23; + return {hi, lo}; +} +#endif +#endif + + +template +uint_x4 operator+(const uint_x4& a, + const uint_x4& b) +{ + uint_x4 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 +uint_x4 operator-(const uint_x4& a, + const uint_x4& b) +{ + uint_x4 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; +} + +#if PCG_64BIT_SPECIALIZATIONS +template +uint_x4 operator+(const uint_x4& a, + const uint_x4& b) +{ + uint_x4 r = {uint64_t(0u), uint64_t(0u)}; + + bool carryin = false; + bool carryout; + r.d.v01 = addwithcarry(a.d.v01, b.d.v01, carryin, &carryout); + carryin = carryout; + r.d.v23 = addwithcarry(a.d.v23, b.d.v23, carryin, &carryout); + + return r; +} + +template +uint_x4 operator-(const uint_x4& a, + const uint_x4& b) +{ + uint_x4 r = {uint64_t(0u), uint64_t(0u)}; + + bool carryin = false; + bool carryout; + r.d.v01 = subwithcarry(a.d.v01, b.d.v01, carryin, &carryout); + carryin = carryout; + r.d.v23 = subwithcarry(a.d.v23, b.d.v23, carryin, &carryout); + + return r; +} +#endif + +template +uint_x4 operator&(const uint_x4& a, + const uint_x4& b) +{ + return uint_x4(a.d.v23 & b.d.v23, a.d.v01 & b.d.v01); +} + +template +uint_x4 operator|(const uint_x4& a, + const uint_x4& b) +{ + return uint_x4(a.d.v23 | b.d.v23, a.d.v01 | b.d.v01); +} + +template +uint_x4 operator^(const uint_x4& a, + const uint_x4& b) +{ + return uint_x4(a.d.v23 ^ b.d.v23, a.d.v01 ^ b.d.v01); +} + +template +uint_x4 operator~(const uint_x4& v) +{ + return uint_x4(~v.d.v23, ~v.d.v01); +} + +template +uint_x4 operator-(const uint_x4& v) +{ + return uint_x4(0UL,0UL) - v; +} + +template +bool operator==(const uint_x4& a, const uint_x4& b) +{ + return (a.d.v01 == b.d.v01) && (a.d.v23 == b.d.v23); +} + +template +bool operator!=(const uint_x4& a, const uint_x4& b) +{ + return !operator==(a,b); +} + + +template +bool operator<(const uint_x4& a, const uint_x4& b) +{ + return (a.d.v23 < b.d.v23) + || ((a.d.v23 == b.d.v23) && (a.d.v01 < b.d.v01)); +} + +template +bool operator>(const uint_x4& a, const uint_x4& b) +{ + return operator<(b,a); +} + +template +bool operator<=(const uint_x4& a, const uint_x4& b) +{ + return !(operator<(b,a)); +} + +template +bool operator>=(const uint_x4& a, const uint_x4& b) +{ + return !(operator<(a,b)); +} + + + +template +uint_x4 operator<<(const uint_x4& v, + const bitcount_t shift) +{ + uint_x4 r = {0U, 0U, 0U, 0U}; + const bitcount_t bits = uint_x4::UINT_BITS; + 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 +uint_x4 operator>>(const uint_x4& v, + const bitcount_t shift) +{ + uint_x4 r = {0U, 0U, 0U, 0U}; + const bitcount_t bits = uint_x4::UINT_BITS; + 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; +} + +#if PCG_64BIT_SPECIALIZATIONS +template +uint_x4 operator<<(const uint_x4& v, + const bitcount_t shift) +{ + constexpr bitcount_t bits2 = uint_x4::UINT_BITS * 2; + + if (shift >= bits2) { + return {v.d.v01 << (shift-bits2), uint64_t(0u)}; + } else { + return {shift ? (v.d.v23 << shift) | (v.d.v01 >> (bits2-shift)) + : v.d.v23, + v.d.v01 << shift}; + } +} + +template +uint_x4 operator>>(const uint_x4& v, + const bitcount_t shift) +{ + constexpr bitcount_t bits2 = uint_x4::UINT_BITS * 2; + + if (shift >= bits2) { + return {uint64_t(0u), v.d.v23 >> (shift-bits2)}; + } else { + return {v.d.v23 >> shift, + shift ? (v.d.v01 >> shift) | (v.d.v23 << (bits2-shift)) + : v.d.v01}; + } +} +#endif + +} // namespace pcg_extras + +#endif // PCG_UINT128_HPP_INCLUDED