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