/* * PCG Random Number Generation for C++ * * Copyright 2014-2017 Melissa O'Neill <oneill@pcg-random.org>, * and the PCG Project contributors. * * SPDX-License-Identifier: (Apache-2.0 OR MIT) * * Licensed under the Apache License, Version 2.0 (provided in * LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0) * or under the MIT license (provided in LICENSE-MIT.txt and at * http://opensource.org/licenses/MIT), at your option. This file may not * be copied, modified, or distributed except according to those terms. * * Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either * express or implied. See your chosen license for details. * * For additional information about the PCG random number generation scheme, * visit http://www.pcg-random.org/. */ /* * This code provides the reference implementation of the PCG family of * random number generators. The code is complex because it implements * * - several members of the PCG family, specifically members corresponding * to the output functions: * - XSH RR (good for 64-bit state, 32-bit output) * - XSH RS (good for 64-bit state, 32-bit output) * - XSL RR (good for 128-bit state, 64-bit output) * - RXS M XS (statistically most powerful generator) * - XSL RR RR (good for 128-bit state, 128-bit output) * - and RXS, RXS M, XSH, XSL (mostly for testing) * - at potentially *arbitrary* bit sizes * - with four different techniques for random streams (MCG, one-stream * LCG, settable-stream LCG, unique-stream LCG) * - and the extended generation schemes allowing arbitrary periods * - with all features of C++11 random number generation (and more), * some of which are somewhat painful, including * - initializing with a SeedSequence which writes 32-bit values * to memory, even though the state of the generator may not * use 32-bit values (it might use smaller or larger integers) * - I/O for RNGs and a prescribed format, which needs to handle * the issue that 8-bit and 128-bit integers don't have working * I/O routines (e.g., normally 8-bit = char, not integer) * - equality and inequality for RNGs * - and a number of convenience typedefs to mask all the complexity * * The code employes a fairly heavy level of abstraction, and has to deal * with various C++ minutia. If you're looking to learn about how the PCG * scheme works, you're probably best of starting with one of the other * codebases (see www.pcg-random.org). But if you're curious about the * constants for the various output functions used in those other, simpler, * codebases, this code shows how they are calculated. * * On the positive side, at least there are convenience typedefs so that you * can say * * pcg32 myRNG; * * rather than: * * pcg_detail::engine< * uint32_t, // Output Type * uint64_t, // State Type * pcg_detail::xsh_rr_mixin<uint32_t, uint64_t>, true, // Output Func * pcg_detail::specific_stream<uint64_t>, // Stream Kind * pcg_detail::default_multiplier<uint64_t> // LCG Mult * > myRNG; * */ #ifndef PCG_RAND_HPP_INCLUDED #define PCG_RAND_HPP_INCLUDED 1 #include <algorithm> #include <cinttypes> #include <cstddef> #include <cstdlib> #include <cstring> #include <cassert> #include <limits> #include <iostream> #include <iterator> #include <type_traits> #include <utility> #include <locale> #include <new> #include <stdexcept> #ifdef _MSC_VER #pragma warning(disable:4146) #endif #ifdef _MSC_VER #define PCG_ALWAYS_INLINE _forceinline #elif __GNUC__ #define PCG_ALWAYS_INLINE __attribute__((always_inline)) #else #define PCG_ALWAYS_INLINE inline #endif /* * The pcg_extras namespace contains some support code that is 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" // NOLINTBEGIN(*) namespace DB { struct PcgSerializer; struct PcgDeserializer; } namespace pcg_detail { using namespace pcg_extras; /* * The LCG generators need some constants to function. This code lets you * look up the constant by *type*. For example * * default_multiplier<uint32_t>::multiplier() * * gives you the default 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 <typename T> struct default_multiplier { // Not defined for an arbitrary type }; template <typename T> struct default_increment { // Not defined for an arbitrary type }; #define PCG_DEFINE_CONSTANT(type, what, kind, constant) \ template <> \ struct what ## _ ## kind<type> { \ static constexpr type kind() { \ return constant; \ } \ }; PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U) PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U) PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U) PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U) PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U) PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U) PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL) PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL) PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier, PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL)) PCG_DEFINE_CONSTANT(pcg128_t, default, increment, PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL)) /* * Each PCG generator is available in four variants, based on how it applies * the additive constant for its underlying LCG; the variations are: * * single stream - all instances use the same fixed constant, thus * the RNG always somewhere in same sequence * mcg - adds zero, resulting in a single stream and reduced * period * specific stream - the constant can be changed at any time, selecting * a different random sequence * unique stream - the constant is based on the memory address of the * object, thus every RNG has its own unique sequence * * This variation is provided though mixin classes which define a function * value called increment() that returns the nesessary additive constant. */ /* * unique stream */ template <typename itype> class unique_stream { protected: static constexpr bool is_mcg = false; // Is never called, but is provided for symmetry with specific_stream void set_stream(...) { abort(); } public: typedef itype state_type; constexpr itype increment() const { return itype(reinterpret_cast<unsigned long>(this) | 1); } constexpr itype stream() const { return increment() >> 1; } static constexpr bool can_specify_stream = false; static constexpr size_t streams_pow2() { return (sizeof(itype) < sizeof(size_t) ? sizeof(itype) : sizeof(size_t))*8 - 1u; } protected: constexpr unique_stream() = default; }; /* * no stream (mcg) */ template <typename itype> class no_stream { protected: static constexpr bool is_mcg = true; // Is never called, but is provided for symmetry with specific_stream void set_stream(...) { abort(); } public: typedef itype state_type; static constexpr itype increment() { return 0; } static constexpr bool can_specify_stream = false; static constexpr size_t streams_pow2() { return 0u; } protected: constexpr no_stream() = default; }; /* * single stream/sequence (oneseq) */ template <typename itype> class oneseq_stream : public default_increment<itype> { protected: static constexpr bool is_mcg = false; // Is never called, but is provided for symmetry with specific_stream void set_stream(...) { abort(); } public: typedef itype state_type; static constexpr itype stream() { return default_increment<itype>::increment() >> 1; } static constexpr bool can_specify_stream = false; static constexpr size_t streams_pow2() { return 0u; } protected: constexpr oneseq_stream() = default; }; /* * specific stream */ template <typename itype> class specific_stream { protected: static constexpr bool is_mcg = false; itype inc_ = default_increment<itype>::increment(); public: typedef itype state_type; typedef itype stream_state; constexpr itype increment() const { return inc_; } itype stream() { return inc_ >> 1; } void set_stream(itype specific_seq) { inc_ = (specific_seq << 1) | 1; } static constexpr bool can_specify_stream = true; static constexpr size_t streams_pow2() { return (sizeof(itype)*8) - 1u; } protected: specific_stream() = default; specific_stream(itype specific_seq) : inc_(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 xtype, typename itype, typename output_mixin, bool output_previous = true, typename stream_mixin = oneseq_stream<itype>, typename multiplier_mixin = default_multiplier<itype> > class engine : protected output_mixin, public stream_mixin, protected multiplier_mixin { protected: itype state_; struct can_specify_stream_tag {}; struct no_specifiable_stream_tag {}; using stream_mixin::increment; using multiplier_mixin::multiplier; public: typedef xtype result_type; typedef itype state_type; static constexpr size_t period_pow2() { return sizeof(state_type)*8 - 2*stream_mixin::is_mcg; } // It would be nice to use std::numeric_limits for these, but // we can't be sure that it'd be defined for the 128-bit types. static constexpr result_type min() { return result_type(0UL); } static constexpr result_type max() { return result_type(~result_type(0UL)); } protected: itype bump(itype state) { return state * multiplier() + increment(); } itype base_generate() { return state_ = bump(state_); } itype base_generate0() { itype old_state = state_; state_ = bump(state_); return old_state; } public: result_type operator()() { if (output_previous) return this->output(base_generate0()); else return this->output(base_generate()); } result_type operator()(result_type upper_bound) { return bounded_rand(*this, upper_bound); } protected: static itype advance(itype state, itype delta, itype cur_mult, itype cur_plus); static itype distance(itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask = ~itype(0U)); itype distance(itype newstate, itype mask = itype(~itype(0U))) const { return distance(state_, newstate, multiplier(), increment(), mask); } public: void advance(itype delta) { state_ = advance(state_, delta, this->multiplier(), this->increment()); } void backstep(itype delta) { advance(-delta); } void discard(itype delta) { advance(delta); } bool wrapped() { if (stream_mixin::is_mcg) { // For MCGs, the low order two bits never change. In this // implementation, we keep them fixed at 3 to make this test // easier. return state_ == 3; } else { return state_ == 0; } } engine(itype state = itype(0xcafef00dd15ea5e5ULL)) : state_(this->is_mcg ? state|state_type(3U) : bump(state + this->increment())) { // Nothing else to do. } // This function may or may not exist. It thus has to be a template // to use SFINAE; users don't have to worry about its template-ness. template <typename sm = stream_mixin> engine(itype state, typename sm::stream_state stream_seed) : stream_mixin(stream_seed), state_(this->is_mcg ? state|state_type(3U) : bump(state + this->increment())) { // Nothing else to do. } template<typename SeedSeq> engine(SeedSeq&& seedSeq, typename std::enable_if< !stream_mixin::can_specify_stream && !std::is_convertible<SeedSeq, itype>::value && !std::is_convertible<SeedSeq, engine>::value, no_specifiable_stream_tag>::type = {}) : engine(generate_one<itype>(std::forward<SeedSeq>(seedSeq))) { // Nothing else to do. } template<typename SeedSeq> engine(SeedSeq&& seedSeq, typename std::enable_if< stream_mixin::can_specify_stream && !std::is_convertible<SeedSeq, itype>::value && !std::is_convertible<SeedSeq, engine>::value, can_specify_stream_tag>::type = {}) : engine(generate_one<itype,1,2>(seedSeq), generate_one<itype,0,2>(seedSeq)) { // Nothing else to do. } template<typename... Args> void seed(Args&&... args) { new (this) engine(std::forward<Args>(args)...); } template <typename xtype1, typename itype1, typename output_mixin1, bool output_previous1, typename stream_mixin_lhs, typename multiplier_mixin_lhs, typename stream_mixin_rhs, typename multiplier_mixin_rhs> friend bool operator==(const engine<xtype1,itype1, output_mixin1,output_previous1, stream_mixin_lhs, multiplier_mixin_lhs>&, const engine<xtype1,itype1, output_mixin1,output_previous1, stream_mixin_rhs, multiplier_mixin_rhs>&); template <typename xtype1, typename itype1, typename output_mixin1, bool output_previous1, typename stream_mixin_lhs, typename multiplier_mixin_lhs, typename stream_mixin_rhs, typename multiplier_mixin_rhs> friend itype1 operator-(const engine<xtype1,itype1, output_mixin1,output_previous1, stream_mixin_lhs, multiplier_mixin_lhs>&, const engine<xtype1,itype1, output_mixin1,output_previous1, stream_mixin_rhs, multiplier_mixin_rhs>&); template <typename CharT, typename Traits, typename xtype1, typename itype1, typename output_mixin1, bool output_previous1, typename stream_mixin1, typename multiplier_mixin1> friend std::basic_ostream<CharT,Traits>& operator<<(std::basic_ostream<CharT,Traits>& out, const engine<xtype1,itype1, output_mixin1,output_previous1, stream_mixin1, multiplier_mixin1>&); template <typename CharT, typename Traits, typename xtype1, typename itype1, typename output_mixin1, bool output_previous1, typename stream_mixin1, typename multiplier_mixin1> friend std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& in, engine<xtype1, itype1, output_mixin1, output_previous1, stream_mixin1, multiplier_mixin1>& rng); friend ::DB::PcgSerializer; friend ::DB::PcgDeserializer; }; template <typename CharT, typename Traits, typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin, typename multiplier_mixin> std::basic_ostream<CharT,Traits>& operator<<(std::basic_ostream<CharT,Traits>& out, const engine<xtype,itype, output_mixin,output_previous, stream_mixin, multiplier_mixin>& rng) { auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); auto space = out.widen(' '); auto orig_fill = out.fill(); out << rng.multiplier() << space << rng.increment() << space << rng.state_; out.flags(orig_flags); out.fill(orig_fill); return out; } template <typename CharT, typename Traits, typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin, typename multiplier_mixin> std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& in, engine<xtype,itype, output_mixin,output_previous, stream_mixin, multiplier_mixin>& rng) { auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); itype multiplier, increment, state; in >> multiplier >> increment >> state; if (!in.fail()) { bool good = true; if (multiplier != rng.multiplier()) { good = false; } else if (rng.can_specify_stream) { rng.set_stream(increment >> 1); } else if (increment != rng.increment()) { good = false; } if (good) { rng.state_ = state; } else { in.clear(std::ios::failbit); } } in.flags(orig_flags); return in; } template <typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin, typename multiplier_mixin> itype engine<xtype,itype,output_mixin,output_previous,stream_mixin, multiplier_mixin>::advance( itype state, itype delta, itype cur_mult, itype cur_plus) { // The method used here is based on Brown, "Random Number Generation // with Arbitrary Stride,", Transactions of the American Nuclear // Society (Nov. 1994). The algorithm is very similar to fast // exponentiation. // // Even though delta is an unsigned integer, we can pass a // signed integer to go backwards, it just goes "the long way round". constexpr itype ZERO = 0u; // itype may be a non-trivial types, so constexpr itype ONE = 1u; // we define some ugly constants. itype acc_mult = 1; itype acc_plus = 0; while (delta > ZERO) { if (delta & ONE) { acc_mult *= cur_mult; acc_plus = acc_plus*cur_mult + cur_plus; } cur_plus = (cur_mult+ONE)*cur_plus; cur_mult *= cur_mult; delta >>= 1; } return acc_mult * state + acc_plus; } template <typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin, typename multiplier_mixin> itype engine<xtype,itype,output_mixin,output_previous,stream_mixin, multiplier_mixin>::distance( itype cur_state, itype newstate, itype cur_mult, itype cur_plus, itype mask) { constexpr itype ONE = 1u; // itype could be weird, so use constant itype the_bit = stream_mixin::is_mcg ? itype(4u) : itype(1u); itype distance = 0u; while ((cur_state & mask) != (newstate & mask)) { if ((cur_state & the_bit) != (newstate & the_bit)) { cur_state = cur_state * cur_mult + cur_plus; distance |= the_bit; } assert((cur_state & the_bit) == (newstate & the_bit)); the_bit <<= 1; cur_plus = (cur_mult+ONE)*cur_plus; cur_mult *= cur_mult; } return stream_mixin::is_mcg ? distance >> 2 : distance; } template <typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin_lhs, typename multiplier_mixin_lhs, typename stream_mixin_rhs, typename multiplier_mixin_rhs> itype operator-(const engine<xtype,itype, output_mixin,output_previous, stream_mixin_lhs, multiplier_mixin_lhs>& lhs, const engine<xtype,itype, output_mixin,output_previous, stream_mixin_rhs, multiplier_mixin_rhs>& rhs) { static_assert( std::is_same<stream_mixin_lhs, stream_mixin_rhs>::value && std::is_same<multiplier_mixin_lhs, multiplier_mixin_rhs>::value, "Incomparable generators"); return rhs.distance(lhs.state_); } template <typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin_lhs, typename multiplier_mixin_lhs, typename stream_mixin_rhs, typename multiplier_mixin_rhs> bool operator==(const engine<xtype,itype, output_mixin,output_previous, stream_mixin_lhs, multiplier_mixin_lhs>& lhs, const engine<xtype,itype, output_mixin,output_previous, stream_mixin_rhs, multiplier_mixin_rhs>& rhs) { return (lhs.multiplier() == rhs.multiplier()) && (lhs.increment() == rhs.increment()) && (lhs.state_ == rhs.state_); } template <typename xtype, typename itype, typename output_mixin, bool output_previous, typename stream_mixin_lhs, typename multiplier_mixin_lhs, typename stream_mixin_rhs, typename multiplier_mixin_rhs> inline bool operator!=(const engine<xtype,itype, output_mixin,output_previous, stream_mixin_lhs, multiplier_mixin_lhs>& lhs, const engine<xtype,itype, output_mixin,output_previous, stream_mixin_rhs, multiplier_mixin_rhs>& rhs) { return !operator==(lhs,rhs); } template <typename xtype, typename itype, template<typename XT,typename IT> class output_mixin, bool output_previous = (sizeof(itype) <= 8)> using oneseq_base = engine<xtype, itype, output_mixin<xtype, itype>, output_previous, oneseq_stream<itype> >; template <typename xtype, typename itype, template<typename XT,typename IT> class output_mixin, bool output_previous = (sizeof(itype) <= 8)> using unique_base = engine<xtype, itype, output_mixin<xtype, itype>, output_previous, unique_stream<itype> >; template <typename xtype, typename itype, template<typename XT,typename IT> class output_mixin, bool output_previous = (sizeof(itype) <= 8)> using setseq_base = engine<xtype, itype, output_mixin<xtype, itype>, output_previous, specific_stream<itype> >; template <typename xtype, typename itype, template<typename XT,typename IT> class output_mixin, bool output_previous = (sizeof(itype) <= 8)> using mcg_base = engine<xtype, itype, output_mixin<xtype, itype>, output_previous, no_stream<itype> >; /* * OUTPUT FUNCTIONS. * * These are the core of the PCG generation scheme. They specify how to * turn the base LCG's internal state into the output value of the final * generator. * * They're implemented as mixin classes. * * All of the classes have code that is written to allow it to be applied * at *arbitrary* bit sizes, although in practice they'll only be used at * standard sizes supported by C++. */ /* * XSH RS -- high xorshift, followed by a random shift * * Fast. A good performer. */ template <typename xtype, typename itype> struct xsh_rs_mixin { static xtype output(itype internal) { constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t sparebits = bits - xtypebits; constexpr bitcount_t opbits = sparebits-5 >= 64 ? 5 : sparebits-4 >= 32 ? 4 : sparebits-3 >= 16 ? 3 : sparebits-2 >= 4 ? 2 : sparebits-1 >= 1 ? 1 : 0; constexpr bitcount_t mask = (1 << opbits) - 1; constexpr bitcount_t maxrandshift = mask; constexpr bitcount_t topspare = opbits; constexpr bitcount_t bottomspare = sparebits - topspare; constexpr bitcount_t xshift = topspare + (xtypebits+maxrandshift)/2; bitcount_t rshift = opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0; internal ^= internal >> xshift; xtype result = xtype(internal >> (bottomspare - maxrandshift + rshift)); return result; } }; /* * XSH RR -- high xorshift, followed by a random rotate * * Fast. A good performer. Slightly better statistically than XSH RS. */ template <typename xtype, typename itype> struct xsh_rr_mixin { static xtype output(itype internal) { constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype)*8); constexpr bitcount_t sparebits = bits - xtypebits; constexpr bitcount_t wantedopbits = xtypebits >= 128 ? 7 : xtypebits >= 64 ? 6 : xtypebits >= 32 ? 5 : xtypebits >= 16 ? 4 : 3; constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits : sparebits; constexpr bitcount_t amplifier = wantedopbits - opbits; constexpr bitcount_t mask = (1 << opbits) - 1; constexpr bitcount_t topspare = opbits; constexpr bitcount_t bottomspare = sparebits - topspare; constexpr bitcount_t xshift = (topspare + xtypebits)/2; bitcount_t rot = opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0; bitcount_t amprot = (rot << amplifier) & mask; internal ^= internal >> xshift; xtype result = xtype(internal >> bottomspare); result = rotr(result, amprot); return result; } }; /* * RXS -- random xorshift */ template <typename xtype, typename itype> struct rxs_mixin { static xtype output_rxs(itype internal) { constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype)*8); constexpr bitcount_t shift = bits - xtypebits; constexpr bitcount_t extrashift = (xtypebits - shift)/2; bitcount_t rshift = shift > 64+8 ? (internal >> (bits - 6)) & 63 : shift > 32+4 ? (internal >> (bits - 5)) & 31 : shift > 16+2 ? (internal >> (bits - 4)) & 15 : shift > 8+1 ? (internal >> (bits - 3)) & 7 : shift > 4+1 ? (internal >> (bits - 2)) & 3 : shift > 2+1 ? (internal >> (bits - 1)) & 1 : 0; internal ^= internal >> (shift + extrashift - rshift); xtype result = internal >> rshift; return result; } }; /* * RXS M XS -- random xorshift, mcg multiply, fixed xorshift * * The most statistically powerful generator, but all those steps * make it slower than some of the others. We give it the rottenest jobs. * * Because it's usually used in contexts where the state type and the * result type are the same, it is a permutation and is thus invertable. * We thus provide a function to invert it. This function is used to * for the "inside out" generator used by the extended generator. */ /* Defined type-based concepts for the multiplication step. They're actually * all derived by truncating the 128-bit, which was computed to be a good * "universal" constant. */ template <typename T> struct mcg_multiplier { // Not defined for an arbitrary type }; template <typename T> struct mcg_unmultiplier { // Not defined for an arbitrary type }; PCG_DEFINE_CONSTANT(uint8_t, mcg, multiplier, 217U) PCG_DEFINE_CONSTANT(uint8_t, mcg, unmultiplier, 105U) PCG_DEFINE_CONSTANT(uint16_t, mcg, multiplier, 62169U) PCG_DEFINE_CONSTANT(uint16_t, mcg, unmultiplier, 28009U) PCG_DEFINE_CONSTANT(uint32_t, mcg, multiplier, 277803737U) PCG_DEFINE_CONSTANT(uint32_t, mcg, unmultiplier, 2897767785U) PCG_DEFINE_CONSTANT(uint64_t, mcg, multiplier, 12605985483714917081ULL) PCG_DEFINE_CONSTANT(uint64_t, mcg, unmultiplier, 15009553638781119849ULL) PCG_DEFINE_CONSTANT(pcg128_t, mcg, multiplier, PCG_128BIT_CONSTANT(17766728186571221404ULL, 12605985483714917081ULL)) PCG_DEFINE_CONSTANT(pcg128_t, mcg, unmultiplier, PCG_128BIT_CONSTANT(14422606686972528997ULL, 15009553638781119849ULL)) template <typename xtype, typename itype> struct rxs_m_xs_mixin { static xtype output(itype internal) { constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t opbits = xtypebits >= 128 ? 6 : xtypebits >= 64 ? 5 : xtypebits >= 32 ? 4 : xtypebits >= 16 ? 3 : 2; constexpr bitcount_t shift = bits - xtypebits; constexpr bitcount_t mask = (1 << opbits) - 1; bitcount_t rshift = opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0; //-V547 internal ^= internal >> (opbits + rshift); internal *= mcg_multiplier<itype>::multiplier(); xtype result = internal >> shift; result ^= result >> ((2U*xtypebits+2U)/3U); return result; } static itype unoutput(itype internal) { constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t opbits = bits >= 128 ? 6 : bits >= 64 ? 5 : bits >= 32 ? 4 : bits >= 16 ? 3 : 2; constexpr bitcount_t mask = (1 << opbits) - 1; internal = unxorshift(internal, bits, (2U*bits+2U)/3U); internal *= mcg_unmultiplier<itype>::unmultiplier(); bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0; //-V547 internal = unxorshift(internal, bits, opbits + rshift); return internal; } }; /* * RXS M -- random xorshift, mcg multiply */ template <typename xtype, typename itype> struct rxs_m_mixin { static xtype output(itype internal) { constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t opbits = xtypebits >= 128 ? 6 : xtypebits >= 64 ? 5 : xtypebits >= 32 ? 4 : xtypebits >= 16 ? 3 : 2; constexpr bitcount_t shift = bits - xtypebits; constexpr bitcount_t mask = (1 << opbits) - 1; bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0; //-V547 internal ^= internal >> (opbits + rshift); internal *= mcg_multiplier<itype>::multiplier(); xtype result = internal >> shift; return result; } }; /* * XSL RR -- fixed xorshift (to low bits), random rotate * * Useful for 128-bit types that are split across two CPU registers. */ template <typename xtype, typename itype> struct xsl_rr_mixin { static xtype output(itype internal) { constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t sparebits = bits - xtypebits; constexpr bitcount_t wantedopbits = xtypebits >= 128 ? 7 : xtypebits >= 64 ? 6 : xtypebits >= 32 ? 5 : xtypebits >= 16 ? 4 : 3; constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits : sparebits; constexpr bitcount_t amplifier = wantedopbits - opbits; constexpr bitcount_t mask = (1 << opbits) - 1; constexpr bitcount_t topspare = sparebits; constexpr bitcount_t bottomspare = sparebits - topspare; constexpr bitcount_t xshift = (topspare + xtypebits) / 2; bitcount_t rot = opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0; bitcount_t amprot = (rot << amplifier) & mask; internal ^= internal >> xshift; xtype result = xtype(internal >> bottomspare); result = rotr(result, amprot); return result; } }; /* * XSL RR RR -- fixed xorshift (to low bits), random rotate (both parts) * * Useful for 128-bit types that are split across two CPU registers. * If you really want an invertable 128-bit RNG, I guess this is the one. */ template <typename T> struct halfsize_trait {}; template <> struct halfsize_trait<pcg128_t> { typedef uint64_t type; }; template <> struct halfsize_trait<uint64_t> { typedef uint32_t type; }; template <> struct halfsize_trait<uint32_t> { typedef uint16_t type; }; template <> struct halfsize_trait<uint16_t> { typedef uint8_t type; }; template <typename xtype, typename itype> struct xsl_rr_rr_mixin { typedef typename halfsize_trait<itype>::type htype; static itype output(itype internal) { constexpr bitcount_t htypebits = bitcount_t(sizeof(htype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t sparebits = bits - htypebits; constexpr bitcount_t wantedopbits = htypebits >= 128 ? 7 : htypebits >= 64 ? 6 : htypebits >= 32 ? 5 : htypebits >= 16 ? 4 : 3; constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits : sparebits; constexpr bitcount_t amplifier = wantedopbits - opbits; constexpr bitcount_t mask = (1 << opbits) - 1; constexpr bitcount_t topspare = sparebits; constexpr bitcount_t xshift = (topspare + htypebits) / 2; bitcount_t rot = opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0; bitcount_t amprot = (rot << amplifier) & mask; internal ^= internal >> xshift; htype lowbits = htype(internal); lowbits = rotr(lowbits, amprot); htype highbits = htype(internal >> topspare); bitcount_t rot2 = lowbits & mask; bitcount_t amprot2 = (rot2 << amplifier) & mask; highbits = rotr(highbits, amprot2); return (itype(highbits) << topspare) ^ itype(lowbits); } }; /* * XSH -- fixed xorshift (to high bits) * * You shouldn't use this at 64-bits or less. */ template <typename xtype, typename itype> struct xsh_mixin { static xtype output(itype internal) { constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t sparebits = bits - xtypebits; constexpr bitcount_t topspare = 0; constexpr bitcount_t bottomspare = sparebits - topspare; constexpr bitcount_t xshift = (topspare + xtypebits) / 2; internal ^= internal >> xshift; xtype result = internal >> bottomspare; return result; } }; /* * XSL -- fixed xorshift (to low bits) * * You shouldn't use this at 64-bits or less. */ template <typename xtype, typename itype> struct xsl_mixin { inline xtype output(itype internal) { constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8); constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8); constexpr bitcount_t sparebits = bits - xtypebits; constexpr bitcount_t topspare = sparebits; constexpr bitcount_t bottomspare = sparebits - topspare; constexpr bitcount_t xshift = (topspare + xtypebits) / 2; internal ^= internal >> xshift; xtype result = internal >> bottomspare; return result; } }; /* ---- End of Output Functions ---- */ template <typename baseclass> struct inside_out : private baseclass { inside_out() = delete; typedef typename baseclass::result_type result_type; typedef typename baseclass::state_type state_type; static_assert(sizeof(result_type) == sizeof(state_type), "Require a RNG whose output function is a permutation"); static bool external_step(result_type& randval, size_t i) { state_type state = baseclass::unoutput(randval); state = state * baseclass::multiplier() + baseclass::increment() + state_type(i*2); result_type result = baseclass::output(state); randval = result; state_type zero = baseclass::is_mcg ? state & state_type(3U) : state_type(0U); return result == zero; } static bool external_advance(result_type& randval, size_t i, result_type delta, bool forwards = true) { state_type state = baseclass::unoutput(randval); state_type mult = baseclass::multiplier(); state_type inc = baseclass::increment() + state_type(i*2); state_type zero = baseclass::is_mcg ? state & state_type(3U) : state_type(0U); state_type dist_to_zero = baseclass::distance(state, zero, mult, inc); bool crosses_zero = forwards ? dist_to_zero <= delta : (-dist_to_zero) <= delta; if (!forwards) delta = -delta; state = baseclass::advance(state, delta, mult, inc); randval = baseclass::output(state); return crosses_zero; } }; template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd = true> class extended : public baseclass { public: typedef typename baseclass::state_type state_type; typedef typename baseclass::result_type result_type; typedef inside_out<extvalclass> insideout; private: static constexpr bitcount_t rtypebits = sizeof(result_type)*8; static constexpr bitcount_t stypebits = sizeof(state_type)*8; static constexpr bitcount_t tick_limit_pow2 = 64U; static constexpr size_t table_size = 1UL << table_pow2; static constexpr size_t table_shift = stypebits - table_pow2; static constexpr state_type table_mask = (state_type(1U) << table_pow2) - state_type(1U); static constexpr bool may_tick = (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2); static constexpr size_t tick_shift = stypebits - advance_pow2; static constexpr state_type tick_mask = may_tick ? state_type( (uint64_t(1) << (advance_pow2*may_tick)) - 1) // ^-- stupidity to appease GCC warnings : ~state_type(0U); static constexpr bool may_tock = stypebits < tick_limit_pow2; result_type data_[table_size]; PCG_NOINLINE void advance_table(); PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true); result_type& get_extended_value() { state_type state = this->state_; if (kdd && baseclass::is_mcg) { // The low order bits of an MCG are constant, so drop them. state >>= 2; } size_t index = kdd ? state & table_mask : state >> table_shift; if (may_tick) { bool tick = kdd ? (state & tick_mask) == state_type(0u) : (state >> tick_shift) == state_type(0u); if (tick) advance_table(); } if (may_tock) { bool tock = state == state_type(0u); if (tock) advance_table(); } return data_[index]; } public: static constexpr size_t period_pow2() { return baseclass::period_pow2() + table_size*extvalclass::period_pow2(); } PCG_ALWAYS_INLINE result_type operator()() { result_type rhs = get_extended_value(); result_type lhs = this->baseclass::operator()(); return lhs ^ rhs; } result_type operator()(result_type upper_bound) { return bounded_rand(*this, upper_bound); } void set(result_type wanted) { result_type& rhs = get_extended_value(); result_type lhs = this->baseclass::operator()(); rhs = lhs ^ wanted; } void advance(state_type distance, bool forwards = true); void backstep(state_type distance) { advance(distance, false); } extended(const result_type* data) : baseclass() { datainit(data); } extended(const result_type* data, state_type seed) : baseclass(seed) { datainit(data); } // This function may or may not exist. It thus has to be a template // to use SFINAE; users don't have to worry about its template-ness. template <typename bc = baseclass> extended(const result_type* data, state_type seed, typename bc::stream_state stream_seed) : baseclass(seed, stream_seed) { datainit(data); } extended() : baseclass() { selfinit(); } extended(state_type seed) : baseclass(seed) { selfinit(); } // This function may or may not exist. It thus has to be a template // to use SFINAE; users don't have to worry about its template-ness. template <typename bc = baseclass> extended(state_type seed, typename bc::stream_state stream_seed) : baseclass(seed, stream_seed) { selfinit(); } private: void selfinit(); void datainit(const result_type* data); public: template<typename SeedSeq, typename = typename std::enable_if< !std::is_convertible<SeedSeq, result_type>::value && !std::is_convertible<SeedSeq, extended>::value>::type> extended(SeedSeq&& seedSeq) : baseclass(seedSeq) { generate_to<table_size>(seedSeq, data_); } template<typename... Args> void seed(Args&&... args) { new (this) extended(std::forward<Args>(args)...); } template <bitcount_t table_pow2_, bitcount_t advance_pow2_, typename baseclass_, typename extvalclass_, bool kdd_> friend bool operator==(const extended<table_pow2_, advance_pow2_, baseclass_, extvalclass_, kdd_>&, const extended<table_pow2_, advance_pow2_, baseclass_, extvalclass_, kdd_>&); template <typename CharT, typename Traits, bitcount_t table_pow2_, bitcount_t advance_pow2_, typename baseclass_, typename extvalclass_, bool kdd_> friend std::basic_ostream<CharT,Traits>& operator<<(std::basic_ostream<CharT,Traits>& out, const extended<table_pow2_, advance_pow2_, baseclass_, extvalclass_, kdd_>&); template <typename CharT, typename Traits, bitcount_t table_pow2_, bitcount_t advance_pow2_, typename baseclass_, typename extvalclass_, bool kdd_> friend std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& in, extended<table_pow2_, advance_pow2_, baseclass_, extvalclass_, kdd_>&); }; template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::datainit( const result_type* data) { for (size_t i = 0; i < table_size; ++i) data_[i] = data[i]; } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::selfinit() { // We need to fill the extended table with something, and we have // very little provided data, so we use the base generator to // produce values. Although not ideal (use a seed sequence, folks!), // unexpected correlations are mitigated by // - using XOR differences rather than the number directly // - the way the table is accessed, its values *won't* be accessed // in the same order the were written. // - any strange correlations would only be apparent if we // were to backstep the generator so that the base generator // was generating the same values again result_type xdiff = baseclass::operator()() - baseclass::operator()(); //-V501 for (size_t i = 0; i < table_size; ++i) { data_[i] = baseclass::operator()() ^ xdiff; } } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> bool operator==(const extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& lhs, const extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& rhs) { auto& base_lhs = static_cast<const baseclass&>(lhs); auto& base_rhs = static_cast<const baseclass&>(rhs); return base_lhs == base_rhs && std::equal( std::begin(lhs.data_), std::end(lhs.data_), std::begin(rhs.data_) ); } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> inline bool operator!=(const extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& lhs, const extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& rhs) { return !operator==(lhs, rhs); } template <typename CharT, typename Traits, bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> std::basic_ostream<CharT,Traits>& operator<<(std::basic_ostream<CharT,Traits>& out, const extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& rng) { auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left); auto space = out.widen(' '); auto orig_fill = out.fill(); out << rng.multiplier() << space << rng.increment() << space << rng.state_; for (const auto& datum : rng.data_) out << space << datum; out.flags(orig_flags); out.fill(orig_fill); return out; } template <typename CharT, typename Traits, bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& in, extended<table_pow2, advance_pow2, baseclass, extvalclass, kdd>& rng) { extended<table_pow2, advance_pow2, baseclass, extvalclass> new_rng; auto& base_rng = static_cast<baseclass&>(new_rng); in >> base_rng; if (in.fail()) return in; auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws); for (auto& datum : new_rng.data_) { in >> datum; if (in.fail()) goto bail; } rng = new_rng; bail: in.flags(orig_flags); return in; } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table() { bool carry = false; for (size_t i = 0; i < table_size; ++i) { if (carry) { carry = insideout::external_step(data_[i],i+1); } bool carry2 = insideout::external_step(data_[i],i+1); carry = carry || carry2; } } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance_table( state_type delta, bool isForwards) { typedef typename baseclass::state_type base_state_t; typedef typename extvalclass::state_type ext_state_t; constexpr bitcount_t basebits = sizeof(base_state_t)*8; constexpr bitcount_t extbits = sizeof(ext_state_t)*8; static_assert(basebits <= extbits || advance_pow2 > 0, "Current implementation might overflow its carry"); base_state_t carry = 0; for (size_t i = 0; i < table_size; ++i) { base_state_t total_delta = carry + delta; ext_state_t trunc_delta = ext_state_t(total_delta); if (basebits > extbits) { carry = total_delta >> extbits; } else { carry = 0; } carry += insideout::external_advance(data_[i],i+1, trunc_delta, isForwards); } } template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd> void extended<table_pow2,advance_pow2,baseclass,extvalclass,kdd>::advance( state_type distance, bool forwards) { static_assert(kdd, "Efficient advance is too hard for non-kdd extension. " "For a weak advance, cast to base class"); state_type zero = baseclass::is_mcg ? this->state_ & state_type(3U) : state_type(0U); if (may_tick) { state_type ticks = distance >> (advance_pow2*may_tick); // ^-- stupidity to appease GCC // warnings state_type adv_mask = baseclass::is_mcg ? tick_mask << 2 : tick_mask; state_type next_advance_distance = this->distance(zero, adv_mask); if (!forwards) next_advance_distance = (-next_advance_distance) & tick_mask; if (next_advance_distance < (distance & tick_mask)) { ++ticks; } if (ticks) advance_table(ticks, forwards); } if (forwards) { if (may_tock && this->distance(zero) <= distance) advance_table(); baseclass::advance(distance); } else { if (may_tock && -(this->distance(zero)) <= distance) advance_table(state_type(1U), false); baseclass::advance(-distance); } } } // namespace pcg_detail namespace pcg_engines { using namespace pcg_detail; /* Predefined types for XSH RS */ typedef oneseq_base<uint8_t, uint16_t, xsh_rs_mixin> oneseq_xsh_rs_16_8; typedef oneseq_base<uint16_t, uint32_t, xsh_rs_mixin> oneseq_xsh_rs_32_16; typedef oneseq_base<uint32_t, uint64_t, xsh_rs_mixin> oneseq_xsh_rs_64_32; typedef oneseq_base<uint64_t, pcg128_t, xsh_rs_mixin> oneseq_xsh_rs_128_64; typedef unique_base<uint8_t, uint16_t, xsh_rs_mixin> unique_xsh_rs_16_8; typedef unique_base<uint16_t, uint32_t, xsh_rs_mixin> unique_xsh_rs_32_16; typedef unique_base<uint32_t, uint64_t, xsh_rs_mixin> unique_xsh_rs_64_32; typedef unique_base<uint64_t, pcg128_t, xsh_rs_mixin> unique_xsh_rs_128_64; typedef setseq_base<uint8_t, uint16_t, xsh_rs_mixin> setseq_xsh_rs_16_8; typedef setseq_base<uint16_t, uint32_t, xsh_rs_mixin> setseq_xsh_rs_32_16; typedef setseq_base<uint32_t, uint64_t, xsh_rs_mixin> setseq_xsh_rs_64_32; typedef setseq_base<uint64_t, pcg128_t, xsh_rs_mixin> setseq_xsh_rs_128_64; typedef mcg_base<uint8_t, uint16_t, xsh_rs_mixin> mcg_xsh_rs_16_8; typedef mcg_base<uint16_t, uint32_t, xsh_rs_mixin> mcg_xsh_rs_32_16; typedef mcg_base<uint32_t, uint64_t, xsh_rs_mixin> mcg_xsh_rs_64_32; typedef mcg_base<uint64_t, pcg128_t, xsh_rs_mixin> mcg_xsh_rs_128_64; /* Predefined types for XSH RR */ typedef oneseq_base<uint8_t, uint16_t, xsh_rr_mixin> oneseq_xsh_rr_16_8; typedef oneseq_base<uint16_t, uint32_t, xsh_rr_mixin> oneseq_xsh_rr_32_16; typedef oneseq_base<uint32_t, uint64_t, xsh_rr_mixin> oneseq_xsh_rr_64_32; typedef oneseq_base<uint64_t, pcg128_t, xsh_rr_mixin> oneseq_xsh_rr_128_64; typedef unique_base<uint8_t, uint16_t, xsh_rr_mixin> unique_xsh_rr_16_8; typedef unique_base<uint16_t, uint32_t, xsh_rr_mixin> unique_xsh_rr_32_16; typedef unique_base<uint32_t, uint64_t, xsh_rr_mixin> unique_xsh_rr_64_32; typedef unique_base<uint64_t, pcg128_t, xsh_rr_mixin> unique_xsh_rr_128_64; typedef setseq_base<uint8_t, uint16_t, xsh_rr_mixin> setseq_xsh_rr_16_8; typedef setseq_base<uint16_t, uint32_t, xsh_rr_mixin> setseq_xsh_rr_32_16; typedef setseq_base<uint32_t, uint64_t, xsh_rr_mixin> setseq_xsh_rr_64_32; typedef setseq_base<uint64_t, pcg128_t, xsh_rr_mixin> setseq_xsh_rr_128_64; typedef mcg_base<uint8_t, uint16_t, xsh_rr_mixin> mcg_xsh_rr_16_8; typedef mcg_base<uint16_t, uint32_t, xsh_rr_mixin> mcg_xsh_rr_32_16; typedef mcg_base<uint32_t, uint64_t, xsh_rr_mixin> mcg_xsh_rr_64_32; typedef mcg_base<uint64_t, pcg128_t, xsh_rr_mixin> mcg_xsh_rr_128_64; /* Predefined types for RXS M XS */ typedef oneseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_8_8; typedef oneseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_16_16; typedef oneseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_32_32; typedef oneseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_64_64; typedef oneseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_128_128; typedef unique_base<uint8_t, uint8_t, rxs_m_xs_mixin> unique_rxs_m_xs_8_8; typedef unique_base<uint16_t, uint16_t, rxs_m_xs_mixin> unique_rxs_m_xs_16_16; typedef unique_base<uint32_t, uint32_t, rxs_m_xs_mixin> unique_rxs_m_xs_32_32; typedef unique_base<uint64_t, uint64_t, rxs_m_xs_mixin> unique_rxs_m_xs_64_64; typedef unique_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> unique_rxs_m_xs_128_128; typedef setseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> setseq_rxs_m_xs_8_8; typedef setseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> setseq_rxs_m_xs_16_16; typedef setseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> setseq_rxs_m_xs_32_32; typedef setseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> setseq_rxs_m_xs_64_64; typedef setseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> setseq_rxs_m_xs_128_128; // MCG versions don't make sense here, so aren't defined. /* Predefined types for XSL RR (only defined for "large" types) */ typedef oneseq_base<uint32_t, uint64_t, xsl_rr_mixin> oneseq_xsl_rr_64_32; typedef oneseq_base<uint64_t, pcg128_t, xsl_rr_mixin> oneseq_xsl_rr_128_64; typedef unique_base<uint32_t, uint64_t, xsl_rr_mixin> unique_xsl_rr_64_32; typedef unique_base<uint64_t, pcg128_t, xsl_rr_mixin> unique_xsl_rr_128_64; typedef setseq_base<uint32_t, uint64_t, xsl_rr_mixin> setseq_xsl_rr_64_32; typedef setseq_base<uint64_t, pcg128_t, xsl_rr_mixin> setseq_xsl_rr_128_64; typedef mcg_base<uint32_t, uint64_t, xsl_rr_mixin> mcg_xsl_rr_64_32; typedef mcg_base<uint64_t, pcg128_t, xsl_rr_mixin> mcg_xsl_rr_128_64; /* Predefined types for XSL RR RR (only defined for "large" types) */ typedef oneseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin> oneseq_xsl_rr_rr_64_64; typedef oneseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin> oneseq_xsl_rr_rr_128_128; typedef unique_base<uint64_t, uint64_t, xsl_rr_rr_mixin> unique_xsl_rr_rr_64_64; typedef unique_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin> unique_xsl_rr_rr_128_128; typedef setseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin> setseq_xsl_rr_rr_64_64; typedef setseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin> setseq_xsl_rr_rr_128_128; // MCG versions don't make sense here, so aren't defined. /* Extended generators */ template <bitcount_t table_pow2, bitcount_t advance_pow2, typename BaseRNG, bool kdd = true> using ext_std8 = pcg_detail::extended<table_pow2, advance_pow2, BaseRNG, oneseq_rxs_m_xs_8_8, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, typename BaseRNG, bool kdd = true> using ext_std16 = pcg_detail::extended<table_pow2, advance_pow2, BaseRNG, oneseq_rxs_m_xs_16_16, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, typename BaseRNG, bool kdd = true> using ext_std32 = pcg_detail::extended<table_pow2, advance_pow2, BaseRNG, oneseq_rxs_m_xs_32_32, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, typename BaseRNG, bool kdd = true> using ext_std64 = pcg_detail::extended<table_pow2, advance_pow2, BaseRNG, oneseq_rxs_m_xs_64_64, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_oneseq_rxs_m_xs_32_32 = ext_std32<table_pow2, advance_pow2, oneseq_rxs_m_xs_32_32, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_mcg_xsh_rs_64_32 = ext_std32<table_pow2, advance_pow2, mcg_xsh_rs_64_32, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_oneseq_xsh_rs_64_32 = ext_std32<table_pow2, advance_pow2, oneseq_xsh_rs_64_32, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_setseq_xsh_rr_64_32 = ext_std32<table_pow2, advance_pow2, setseq_xsh_rr_64_32, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_mcg_xsl_rr_128_64 = ext_std64<table_pow2, advance_pow2, mcg_xsl_rr_128_64, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_oneseq_xsl_rr_128_64 = ext_std64<table_pow2, advance_pow2, oneseq_xsl_rr_128_64, kdd>; template <bitcount_t table_pow2, bitcount_t advance_pow2, bool kdd = true> using ext_setseq_xsl_rr_128_64 = ext_std64<table_pow2, advance_pow2, setseq_xsl_rr_128_64, kdd>; } // namespace pcg_engines typedef pcg_engines::setseq_xsh_rr_64_32 pcg32; typedef pcg_engines::oneseq_xsh_rr_64_32 pcg32_oneseq; typedef pcg_engines::unique_xsh_rr_64_32 pcg32_unique; typedef pcg_engines::mcg_xsh_rs_64_32 pcg32_fast; typedef pcg_engines::setseq_xsl_rr_128_64 pcg64; typedef pcg_engines::oneseq_xsl_rr_128_64 pcg64_oneseq; typedef pcg_engines::unique_xsl_rr_128_64 pcg64_unique; typedef pcg_engines::mcg_xsl_rr_128_64 pcg64_fast; typedef pcg_engines::setseq_rxs_m_xs_8_8 pcg8_once_insecure; typedef pcg_engines::setseq_rxs_m_xs_16_16 pcg16_once_insecure; typedef pcg_engines::setseq_rxs_m_xs_32_32 pcg32_once_insecure; typedef pcg_engines::setseq_rxs_m_xs_64_64 pcg64_once_insecure; typedef pcg_engines::setseq_xsl_rr_rr_128_128 pcg128_once_insecure; typedef pcg_engines::oneseq_rxs_m_xs_8_8 pcg8_oneseq_once_insecure; typedef pcg_engines::oneseq_rxs_m_xs_16_16 pcg16_oneseq_once_insecure; typedef pcg_engines::oneseq_rxs_m_xs_32_32 pcg32_oneseq_once_insecure; typedef pcg_engines::oneseq_rxs_m_xs_64_64 pcg64_oneseq_once_insecure; typedef pcg_engines::oneseq_xsl_rr_rr_128_128 pcg128_oneseq_once_insecure; // These two extended RNGs provide two-dimensionally equidistributed // 32-bit generators. pcg32_k2_fast occupies the same space as pcg64, // and can be called twice to generate 64 bits, but does not required // 128-bit math; on 32-bit systems, it's faster than pcg64 as well. typedef pcg_engines::ext_setseq_xsh_rr_64_32<1,16,true> pcg32_k2; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<1,32,true> pcg32_k2_fast; // These eight extended RNGs have about as much state as arc4random // // - the k variants are k-dimensionally equidistributed // - the c variants offer better crypographic security // // (just how good the cryptographic security is is an open question) typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,true> pcg32_k64; typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,true> pcg32_k64_oneseq; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,true> pcg32_k64_fast; typedef pcg_engines::ext_setseq_xsh_rr_64_32<6,16,false> pcg32_c64; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<6,32,false> pcg32_c64_oneseq; typedef pcg_engines::ext_mcg_xsh_rs_64_32<6,32,false> pcg32_c64_fast; typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,true> pcg64_k32; typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,true> pcg64_k32_oneseq; typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,true> pcg64_k32_fast; typedef pcg_engines::ext_setseq_xsl_rr_128_64<5,16,false> pcg64_c32; typedef pcg_engines::ext_oneseq_xsl_rr_128_64<5,128,false> pcg64_c32_oneseq; typedef pcg_engines::ext_mcg_xsl_rr_128_64<5,128,false> pcg64_c32_fast; // These eight extended RNGs have more state than the Mersenne twister // // - the k variants are k-dimensionally equidistributed // - the c variants offer better crypographic security // // (just how good the cryptographic security is is an open question) typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,true> pcg32_k1024; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,true> pcg32_k1024_fast; typedef pcg_engines::ext_setseq_xsh_rr_64_32<10,16,false> pcg32_c1024; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<10,32,false> pcg32_c1024_fast; typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,true> pcg64_k1024; typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,true> pcg64_k1024_fast; typedef pcg_engines::ext_setseq_xsl_rr_128_64<10,16,false> pcg64_c1024; typedef pcg_engines::ext_oneseq_xsl_rr_128_64<10,128,false> pcg64_c1024_fast; // These generators have an insanely huge period (2^524352), and is suitable // for silly party tricks, such as dumping out 64 KB ZIP files at an arbitrary // point in the future. [Actually, over the full period of the generator, it // will produce every 64 KB ZIP file 2^64 times!] typedef pcg_engines::ext_setseq_xsh_rr_64_32<14,16,true> pcg32_k16384; typedef pcg_engines::ext_oneseq_xsh_rs_64_32<14,32,true> pcg32_k16384_fast; #ifdef _MSC_VER #pragma warning(default:4146) #endif // NOLINTEND(*) #endif // PCG_RAND_HPP_INCLUDED