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- /*
- * 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;
- internal ^= internal >> (opbits + rshift);
- internal *= mcg_multiplier<itype>::multiplier();
- xtype result = internal >> shift;
- result ^= result >> ((2U*xtypebits+2U)/3U);
- return result;
- }
- static itype unoutput(itype internal)
- {
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t opbits = bits >= 128 ? 6
- : bits >= 64 ? 5
- : bits >= 32 ? 4
- : bits >= 16 ? 3
- : 2;
- constexpr bitcount_t mask = (1 << opbits) - 1;
- internal = unxorshift(internal, bits, (2U*bits+2U)/3U);
- internal *= mcg_unmultiplier<itype>::unmultiplier();
- bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
- internal = unxorshift(internal, bits, opbits + rshift);
- return internal;
- }
- };
- /*
- * RXS M -- random xorshift, mcg multiply
- */
- template <typename xtype, typename itype>
- struct rxs_m_mixin {
- static xtype output(itype internal)
- {
- constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t opbits = xtypebits >= 128 ? 6
- : xtypebits >= 64 ? 5
- : xtypebits >= 32 ? 4
- : xtypebits >= 16 ? 3
- : 2;
- constexpr bitcount_t shift = bits - xtypebits;
- constexpr bitcount_t mask = (1 << opbits) - 1;
- bitcount_t rshift = opbits ? (internal >> (bits - opbits)) & mask : 0;
- internal ^= internal >> (opbits + rshift);
- internal *= mcg_multiplier<itype>::multiplier();
- xtype result = internal >> shift;
- return result;
- }
- };
- /*
- * XSL RR -- fixed xorshift (to low bits), random rotate
- *
- * Useful for 128-bit types that are split across two CPU registers.
- */
- template <typename xtype, typename itype>
- struct xsl_rr_mixin {
- static xtype output(itype internal)
- {
- constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t sparebits = bits - xtypebits;
- constexpr bitcount_t wantedopbits = xtypebits >= 128 ? 7
- : xtypebits >= 64 ? 6
- : xtypebits >= 32 ? 5
- : xtypebits >= 16 ? 4
- : 3;
- constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
- : sparebits;
- constexpr bitcount_t amplifier = wantedopbits - opbits;
- constexpr bitcount_t mask = (1 << opbits) - 1;
- constexpr bitcount_t topspare = sparebits;
- constexpr bitcount_t bottomspare = sparebits - topspare;
- constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
- bitcount_t rot =
- opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
- bitcount_t amprot = (rot << amplifier) & mask;
- internal ^= internal >> xshift;
- xtype result = xtype(internal >> bottomspare);
- result = rotr(result, amprot);
- return result;
- }
- };
- /*
- * XSL RR RR -- fixed xorshift (to low bits), random rotate (both parts)
- *
- * Useful for 128-bit types that are split across two CPU registers.
- * If you really want an invertable 128-bit RNG, I guess this is the one.
- */
- template <typename T> struct halfsize_trait {};
- template <> struct halfsize_trait<pcg128_t> { typedef uint64_t type; };
- template <> struct halfsize_trait<uint64_t> { typedef uint32_t type; };
- template <> struct halfsize_trait<uint32_t> { typedef uint16_t type; };
- template <> struct halfsize_trait<uint16_t> { typedef uint8_t type; };
- template <typename xtype, typename itype>
- struct xsl_rr_rr_mixin {
- typedef typename halfsize_trait<itype>::type htype;
- static itype output(itype internal)
- {
- constexpr bitcount_t htypebits = bitcount_t(sizeof(htype) * 8);
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t sparebits = bits - htypebits;
- constexpr bitcount_t wantedopbits = htypebits >= 128 ? 7
- : htypebits >= 64 ? 6
- : htypebits >= 32 ? 5
- : htypebits >= 16 ? 4
- : 3;
- constexpr bitcount_t opbits = sparebits >= wantedopbits ? wantedopbits
- : sparebits;
- constexpr bitcount_t amplifier = wantedopbits - opbits;
- constexpr bitcount_t mask = (1 << opbits) - 1;
- constexpr bitcount_t topspare = sparebits;
- constexpr bitcount_t xshift = (topspare + htypebits) / 2;
- bitcount_t rot =
- opbits ? bitcount_t(internal >> (bits - opbits)) & mask : 0;
- bitcount_t amprot = (rot << amplifier) & mask;
- internal ^= internal >> xshift;
- htype lowbits = htype(internal);
- lowbits = rotr(lowbits, amprot);
- htype highbits = htype(internal >> topspare);
- bitcount_t rot2 = lowbits & mask;
- bitcount_t amprot2 = (rot2 << amplifier) & mask;
- highbits = rotr(highbits, amprot2);
- return (itype(highbits) << topspare) ^ itype(lowbits);
- }
- };
- /*
- * XSH -- fixed xorshift (to high bits)
- *
- * You shouldn't use this at 64-bits or less.
- */
- template <typename xtype, typename itype>
- struct xsh_mixin {
- static xtype output(itype internal)
- {
- constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t sparebits = bits - xtypebits;
- constexpr bitcount_t topspare = 0;
- constexpr bitcount_t bottomspare = sparebits - topspare;
- constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
- internal ^= internal >> xshift;
- xtype result = internal >> bottomspare;
- return result;
- }
- };
- /*
- * XSL -- fixed xorshift (to low bits)
- *
- * You shouldn't use this at 64-bits or less.
- */
- template <typename xtype, typename itype>
- struct xsl_mixin {
- inline xtype output(itype internal)
- {
- constexpr bitcount_t xtypebits = bitcount_t(sizeof(xtype) * 8);
- constexpr bitcount_t bits = bitcount_t(sizeof(itype) * 8);
- constexpr bitcount_t sparebits = bits - xtypebits;
- constexpr bitcount_t topspare = sparebits;
- constexpr bitcount_t bottomspare = sparebits - topspare;
- constexpr bitcount_t xshift = (topspare + xtypebits) / 2;
- internal ^= internal >> xshift;
- xtype result = internal >> bottomspare;
- return result;
- }
- };
- /* ---- End of Output Functions ---- */
- template <typename baseclass>
- struct inside_out : private baseclass {
- inside_out() = delete;
- typedef typename baseclass::result_type result_type;
- typedef typename baseclass::state_type state_type;
- static_assert(sizeof(result_type) == sizeof(state_type),
- "Require a RNG whose output function is a permutation");
- static bool external_step(result_type& randval, size_t i)
- {
- state_type state = baseclass::unoutput(randval);
- state = state * baseclass::multiplier() + baseclass::increment()
- + state_type(i*2);
- result_type result = baseclass::output(state);
- randval = result;
- state_type zero =
- baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
- return result == zero;
- }
- static bool external_advance(result_type& randval, size_t i,
- result_type delta, bool forwards = true)
- {
- state_type state = baseclass::unoutput(randval);
- state_type mult = baseclass::multiplier();
- state_type inc = baseclass::increment() + state_type(i*2);
- state_type zero =
- baseclass::is_mcg ? state & state_type(3U) : state_type(0U);
- state_type dist_to_zero = baseclass::distance(state, zero, mult, inc);
- bool crosses_zero =
- forwards ? dist_to_zero <= delta
- : (-dist_to_zero) <= delta;
- if (!forwards)
- delta = -delta;
- state = baseclass::advance(state, delta, mult, inc);
- randval = baseclass::output(state);
- return crosses_zero;
- }
- };
- template <bitcount_t table_pow2, bitcount_t advance_pow2, typename baseclass, typename extvalclass, bool kdd = true>
- class extended : public baseclass {
- public:
- typedef typename baseclass::state_type state_type;
- typedef typename baseclass::result_type result_type;
- typedef inside_out<extvalclass> insideout;
- private:
- static constexpr bitcount_t rtypebits = sizeof(result_type)*8;
- static constexpr bitcount_t stypebits = sizeof(state_type)*8;
- static constexpr bitcount_t tick_limit_pow2 = 64U;
- static constexpr size_t table_size = 1UL << table_pow2;
- static constexpr size_t table_shift = stypebits - table_pow2;
- static constexpr state_type table_mask =
- (state_type(1U) << table_pow2) - state_type(1U);
- static constexpr bool may_tick =
- (advance_pow2 < stypebits) && (advance_pow2 < tick_limit_pow2);
- static constexpr size_t tick_shift = stypebits - advance_pow2;
- static constexpr state_type tick_mask =
- may_tick ? state_type(
- (uint64_t(1) << (advance_pow2*may_tick)) - 1)
- // ^-- stupidity to appease GCC warnings
- : ~state_type(0U);
- static constexpr bool may_tock = stypebits < tick_limit_pow2;
- result_type data_[table_size];
- PCG_NOINLINE void advance_table();
- PCG_NOINLINE void advance_table(state_type delta, bool isForwards = true);
- result_type& get_extended_value()
- {
- state_type state = this->state_;
- if (kdd && baseclass::is_mcg) {
- // The low order bits of an MCG are constant, so drop them.
- state >>= 2;
- }
- size_t index = kdd ? state & table_mask
- : state >> table_shift;
- if (may_tick) {
- bool tick = kdd ? (state & tick_mask) == state_type(0u)
- : (state >> tick_shift) == state_type(0u);
- if (tick)
- advance_table();
- }
- if (may_tock) {
- bool tock = state == state_type(0u);
- if (tock)
- advance_table();
- }
- return data_[index];
- }
- public:
- static constexpr size_t period_pow2()
- {
- return baseclass::period_pow2() + table_size*extvalclass::period_pow2();
- }
- 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()();
- 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
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