forked from Mirrors/openclonk
1752 lines
62 KiB
C++
1752 lines
62 KiB
C++
/*
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* PCG Random Number Generation for C++
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*
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* Copyright 2014 Melissa O'Neill <oneill@pcg-random.org>
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*
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* For additional information about the PCG random number generation scheme,
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* including its license and other licensing options, visit
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*
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* http://www.pcg-random.org
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*/
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/*
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* This code provides the reference implementation of the PCG family of
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* random number generators. The code is complex because it implements
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*
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* - several members of the PCG family, specifically members corresponding
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* to the output functions:
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* - XSH RR (good for 64-bit state, 32-bit output)
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* - XSH RS (good for 64-bit state, 32-bit output)
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* - XSL RR (good for 128-bit state, 64-bit output)
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* - RXS M XS (statistically most powerful generator)
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* - XSL RR RR (good for 128-bit state, 128-bit output)
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* - and RXS, RXS M, XSH, XSL (mostly for testing)
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* - at potentially *arbitrary* bit sizes
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* - with four different techniques for random streams (MCG, one-stream
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* LCG, settable-stream LCG, unique-stream LCG)
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* - and the extended generation schemes allowing arbitrary periods
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* - with all features of C++11 random number generation (and more),
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* some of which are somewhat painful, including
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* - initializing with a SeedSequence which writes 32-bit values
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* to memory, even though the state of the generator may not
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* use 32-bit values (it might use smaller or larger integers)
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* - I/O for RNGs and a prescribed format, which needs to handle
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* the issue that 8-bit and 128-bit integers don't have working
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* I/O routines (e.g., normally 8-bit = char, not integer)
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* - equality and inequality for RNGs
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* - and a number of convenience typedefs to mask all the complexity
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*
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* The code employes a fairly heavy level of abstraction, and has to deal
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* with various C++ minutia. If you're looking to learn about how the PCG
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* scheme works, you're probably best of starting with one of the other
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* codebases (see www.pcg-random.org). But if you're curious about the
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* constants for the various output functions used in those other, simpler,
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* codebases, this code shows how they are calculated.
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*
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* On the positive side, at least there are convenience typedefs so that you
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* can say
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*
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* pcg32 myRNG;
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*
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* rather than:
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*
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* pcg_detail::engine<
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* uint32_t, // Output Type
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* uint64_t, // State Type
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* pcg_detail::xsh_rr_mixin<uint32_t, uint64_t>, true, // Output Func
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* pcg_detail::specific_stream<uint64_t>, // Stream Kind
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* pcg_detail::default_multiplier<uint64_t> // LCG Mult
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* > myRNG;
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*
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*/
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#ifndef PCG_RAND_HPP_INCLUDED
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#define PCG_RAND_HPP_INCLUDED 1
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#include <cinttypes>
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#include <cstddef>
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#include <cstdlib>
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#include <cstring>
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#include <cassert>
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#include <limits>
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#include <iostream>
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#include <type_traits>
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#include <utility>
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#include <locale>
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#include <new>
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#include <stdexcept>
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/*
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* The pcg_extras namespace contains some support code that is likley to
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* be useful for a variety of RNGs, including:
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* - 128-bit int support for platforms where it isn't available natively
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* - bit twiddling operations
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* - I/O of 128-bit and 8-bit integers
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* - Handling the evilness of SeedSeq
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* - Support for efficiently producing random numbers less than a given
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* bound
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*/
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#include "pcg_extras.hpp"
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namespace pcg_detail {
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using namespace pcg_extras;
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/*
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* The LCG generators need some constants to function. This code lets you
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* look up the constant by *type*. For example
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*
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* default_multiplier<uint32_t>::multiplier()
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*
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* gives you the default multipler for 32-bit integers. We use the name
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* of the constant and not a generic word like value to allow these classes
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* to be used as mixins.
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*/
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template <typename T>
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struct default_multiplier {
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// Not defined for an arbitrary type
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};
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template <typename T>
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struct default_increment {
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// Not defined for an arbitrary type
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};
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#define PCG_DEFINE_CONSTANT(type, what, kind, constant) \
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template <> \
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struct what ## _ ## kind<type> { \
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static constexpr type kind() { \
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return constant; \
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} \
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};
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PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U)
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PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U)
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PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U)
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PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U)
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PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U)
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PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U)
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PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL)
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PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL)
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PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier,
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PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL))
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PCG_DEFINE_CONSTANT(pcg128_t, default, increment,
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PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL))
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/*
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* Each PCG generator is available in four variants, based on how it applies
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* the additive constant for its underlying LCG; the variations are:
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*
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* single stream - all instances use the same fixed constant, thus
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* the RNG always somewhere in same sequence
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* mcg - adds zero, resulting in a single stream and reduced
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* period
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* specific stream - the constant can be changed at any time, selecting
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* a different random sequence
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* unique stream - the constant is based on the memory addresss of the
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* object, thus every RNG has its own unique sequence
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*
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* This variation is provided though mixin classes which define a function
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* value called increment() that returns the nesessary additive constant.
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*/
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/*
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* unique stream
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*/
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template <typename itype>
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class unique_stream {
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protected:
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static constexpr bool is_mcg = false;
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// Is never called, but is provided for symmetry with specific_stream
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void set_stream(...)
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{
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abort();
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}
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public:
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typedef itype state_type;
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constexpr itype increment() const {
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return itype(reinterpret_cast<unsigned long>(this) | 1);
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}
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constexpr itype stream() const
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{
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return increment() >> 1;
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}
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static constexpr bool can_specify_stream = false;
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static constexpr size_t streams_pow2()
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{
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return (sizeof(itype) < sizeof(size_t) ? sizeof(itype)
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: sizeof(size_t))*8 - 1u;
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}
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protected:
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constexpr unique_stream() = default;
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};
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/*
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* no stream (mcg)
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*/
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template <typename itype>
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class no_stream {
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protected:
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static constexpr bool is_mcg = true;
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// Is never called, but is provided for symmetry with specific_stream
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void set_stream(...)
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{
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abort();
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}
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public:
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typedef itype state_type;
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static constexpr itype increment() {
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return 0;
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}
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static constexpr bool can_specify_stream = false;
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static constexpr size_t streams_pow2()
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{
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return 0u;
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}
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protected:
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constexpr no_stream() = default;
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};
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/*
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* single stream/sequence (oneseq)
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*/
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template <typename itype>
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class oneseq_stream : public default_increment<itype> {
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protected:
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static constexpr bool is_mcg = false;
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// Is never called, but is provided for symmetry with specific_stream
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void set_stream(...)
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{
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abort();
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}
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public:
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typedef itype state_type;
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static constexpr itype stream()
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{
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return default_increment<itype>::increment() >> 1;
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}
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static constexpr bool can_specify_stream = false;
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static constexpr size_t streams_pow2()
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{
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return 0u;
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}
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protected:
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constexpr oneseq_stream() = default;
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};
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/*
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* specific stream
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*/
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template <typename itype>
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class specific_stream {
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protected:
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static constexpr bool is_mcg = false;
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itype inc_ = default_increment<itype>::increment();
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public:
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typedef itype state_type;
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typedef itype stream_state;
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constexpr itype increment() const {
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return inc_;
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}
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itype stream()
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{
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return inc_ >> 1;
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}
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void set_stream(itype specific_seq)
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{
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inc_ = (specific_seq << 1) | 1;
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}
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static constexpr bool can_specify_stream = true;
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static constexpr size_t streams_pow2()
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{
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return (sizeof(itype)*8) - 1u;
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}
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protected:
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specific_stream() = default;
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specific_stream(itype specific_seq)
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: inc_((specific_seq << 1) | itype(1U))
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{
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// Nothing (else) to do.
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}
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};
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/*
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* This is where it all comes together. This function joins together three
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* mixin classes which define
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* - the LCG additive constant (the stream)
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* - the LCG multiplier
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* - the output function
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* in addition, we specify the type of the LCG state, and the result type,
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* and whether to use the pre-advance version of the state for the output
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* (increasing instruction-level parallelism) or the post-advance version
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* (reducing register pressure).
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*
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* Given the high level of parameterization, the code has to use some
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* template-metaprogramming tricks to handle some of the suble variations
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* involved.
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*/
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template <typename xtype, typename itype,
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typename output_mixin,
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bool output_previous = true,
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typename stream_mixin = oneseq_stream<itype>,
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typename multiplier_mixin = default_multiplier<itype> >
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class engine : protected output_mixin,
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public stream_mixin,
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protected multiplier_mixin {
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protected:
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itype state_;
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struct can_specify_stream_tag {};
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struct no_specifiable_stream_tag {};
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using stream_mixin::increment;
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using multiplier_mixin::multiplier;
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public:
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typedef xtype result_type;
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typedef itype state_type;
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static constexpr size_t period_pow2()
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{
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return sizeof(state_type)*8 - 2*stream_mixin::is_mcg;
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}
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// It would be nice to use std::numeric_limits for these, but
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// we can't be sure that it'd be defined for the 128-bit types.
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static constexpr result_type min()
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{
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return result_type(0UL);
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}
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static constexpr result_type max()
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{
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return ~result_type(0UL);
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}
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protected:
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itype bump(itype state)
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{
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return state * multiplier() + increment();
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}
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itype base_generate()
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{
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return state_ = bump(state_);
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}
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itype base_generate0()
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{
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itype old_state = state_;
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state_ = bump(state_);
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return old_state;
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}
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public:
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result_type operator()()
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{
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if (output_previous)
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return this->output(base_generate0());
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else
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return this->output(base_generate());
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}
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result_type operator()(result_type upper_bound)
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{
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return bounded_rand(*this, upper_bound);
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}
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protected:
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static itype advance(itype state, itype delta,
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itype cur_mult, itype cur_plus);
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static itype distance(itype cur_state, itype newstate, itype cur_mult,
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itype cur_plus, itype mask = ~itype(0U));
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itype distance(itype newstate, itype mask = ~itype(0U)) const
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{
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return distance(state_, newstate, multiplier(), increment(), mask);
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}
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public:
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void advance(itype delta)
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{
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state_ = advance(state_, delta, this->multiplier(), this->increment());
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}
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void backstep(itype delta)
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{
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advance(-delta);
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}
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void discard(itype delta)
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{
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advance(delta);
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}
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bool wrapped()
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{
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if (stream_mixin::is_mcg) {
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// For MCGs, the low order two bits never change. In this
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// implementation, we keep them fixed at 3 to make this test
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// easier.
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return state_ == 3;
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} else {
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return state_ == 0;
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}
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}
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engine(itype state = itype(0xcafef00dd15ea5e5ULL))
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: state_(this->is_mcg ? state|state_type(3U)
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: bump(state + this->increment()))
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{
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// Nothing else to do.
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}
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// This function may or may not exist. It thus has to be a template
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// to use SFINAE; users don't have to worry about its template-ness.
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template <typename sm = stream_mixin>
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engine(itype state, typename sm::stream_state stream_seed)
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: stream_mixin(stream_seed),
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state_(this->is_mcg ? state|state_type(3U)
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: bump(state + this->increment()))
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{
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// Nothing else to do.
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}
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template<typename SeedSeq>
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engine(SeedSeq&& seedSeq, typename std::enable_if<
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!stream_mixin::can_specify_stream
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&& !std::is_convertible<SeedSeq, itype>::value
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&& !std::is_convertible<SeedSeq, engine>::value,
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no_specifiable_stream_tag>::type = {})
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: engine(generate_one<itype>(std::forward<SeedSeq>(seedSeq)))
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{
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// Nothing else to do.
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}
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template<typename SeedSeq>
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engine(SeedSeq&& seedSeq, typename std::enable_if<
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stream_mixin::can_specify_stream
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&& !std::is_convertible<SeedSeq, itype>::value
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&& !std::is_convertible<SeedSeq, engine>::value,
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can_specify_stream_tag>::type = {})
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: engine(generate_one<itype,1,2>(seedSeq),
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generate_one<itype,0,2>(seedSeq))
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{
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// Nothing else to do.
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}
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|
|
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template<typename... Args>
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void seed(Args&&... args)
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{
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new (this) engine(std::forward<Args>(args)...);
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}
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template <typename xtype1, typename itype1,
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typename output_mixin1, bool output_previous1,
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typename stream_mixin_lhs, typename multiplier_mixin_lhs,
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typename stream_mixin_rhs, typename multiplier_mixin_rhs>
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friend bool operator==(const engine<xtype1,itype1,
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output_mixin1,output_previous1,
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stream_mixin_lhs, multiplier_mixin_lhs>&,
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const engine<xtype1,itype1,
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output_mixin1,output_previous1,
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stream_mixin_rhs, multiplier_mixin_rhs>&);
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template <typename xtype1, typename itype1,
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typename output_mixin1, bool output_previous1,
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typename stream_mixin_lhs, typename multiplier_mixin_lhs,
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typename stream_mixin_rhs, typename multiplier_mixin_rhs>
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|
friend itype1 operator-(const engine<xtype1,itype1,
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output_mixin1,output_previous1,
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stream_mixin_lhs, multiplier_mixin_lhs>&,
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const engine<xtype1,itype1,
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output_mixin1,output_previous1,
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stream_mixin_rhs, multiplier_mixin_rhs>&);
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|
template <typename CharT, typename Traits,
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|
typename xtype1, typename itype1,
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typename output_mixin1, bool output_previous1,
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typename stream_mixin1, typename multiplier_mixin1>
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|
friend std::basic_ostream<CharT,Traits>&
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operator<<(std::basic_ostream<CharT,Traits>& out,
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const engine<xtype1,itype1,
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output_mixin1,output_previous1,
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stream_mixin1, multiplier_mixin1>&);
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|
|
|
template <typename CharT, typename Traits,
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typename xtype1, typename itype1,
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typename output_mixin1, bool output_previous1,
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typename stream_mixin1, typename multiplier_mixin1>
|
|
friend std::basic_istream<CharT,Traits>&
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|
operator>>(std::basic_istream<CharT,Traits>& in,
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|
engine<xtype1, itype1,
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output_mixin1, output_previous1,
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|
stream_mixin1, multiplier_mixin1>& rng);
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|
};
|
|
|
|
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;
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typedef oneseq_base<uint16_t, uint32_t, xsh_rs_mixin> oneseq_xsh_rs_32_16;
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typedef oneseq_base<uint32_t, uint64_t, xsh_rs_mixin> oneseq_xsh_rs_64_32;
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typedef oneseq_base<uint64_t, pcg128_t, xsh_rs_mixin> oneseq_xsh_rs_128_64;
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typedef unique_base<uint8_t, uint16_t, xsh_rs_mixin> unique_xsh_rs_16_8;
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typedef unique_base<uint16_t, uint32_t, xsh_rs_mixin> unique_xsh_rs_32_16;
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typedef unique_base<uint32_t, uint64_t, xsh_rs_mixin> unique_xsh_rs_64_32;
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typedef unique_base<uint64_t, pcg128_t, xsh_rs_mixin> unique_xsh_rs_128_64;
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typedef setseq_base<uint8_t, uint16_t, xsh_rs_mixin> setseq_xsh_rs_16_8;
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typedef setseq_base<uint16_t, uint32_t, xsh_rs_mixin> setseq_xsh_rs_32_16;
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typedef setseq_base<uint32_t, uint64_t, xsh_rs_mixin> setseq_xsh_rs_64_32;
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typedef setseq_base<uint64_t, pcg128_t, xsh_rs_mixin> setseq_xsh_rs_128_64;
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typedef mcg_base<uint8_t, uint16_t, xsh_rs_mixin> mcg_xsh_rs_16_8;
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typedef mcg_base<uint16_t, uint32_t, xsh_rs_mixin> mcg_xsh_rs_32_16;
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typedef mcg_base<uint32_t, uint64_t, xsh_rs_mixin> mcg_xsh_rs_64_32;
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typedef mcg_base<uint64_t, pcg128_t, xsh_rs_mixin> mcg_xsh_rs_128_64;
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/* Predefined types for XSH RR */
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typedef oneseq_base<uint8_t, uint16_t, xsh_rr_mixin> oneseq_xsh_rr_16_8;
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typedef oneseq_base<uint16_t, uint32_t, xsh_rr_mixin> oneseq_xsh_rr_32_16;
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typedef oneseq_base<uint32_t, uint64_t, xsh_rr_mixin> oneseq_xsh_rr_64_32;
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typedef oneseq_base<uint64_t, pcg128_t, xsh_rr_mixin> oneseq_xsh_rr_128_64;
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typedef unique_base<uint8_t, uint16_t, xsh_rr_mixin> unique_xsh_rr_16_8;
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typedef unique_base<uint16_t, uint32_t, xsh_rr_mixin> unique_xsh_rr_32_16;
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typedef unique_base<uint32_t, uint64_t, xsh_rr_mixin> unique_xsh_rr_64_32;
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typedef unique_base<uint64_t, pcg128_t, xsh_rr_mixin> unique_xsh_rr_128_64;
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typedef setseq_base<uint8_t, uint16_t, xsh_rr_mixin> setseq_xsh_rr_16_8;
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typedef setseq_base<uint16_t, uint32_t, xsh_rr_mixin> setseq_xsh_rr_32_16;
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typedef setseq_base<uint32_t, uint64_t, xsh_rr_mixin> setseq_xsh_rr_64_32;
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typedef setseq_base<uint64_t, pcg128_t, xsh_rr_mixin> setseq_xsh_rr_128_64;
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typedef mcg_base<uint8_t, uint16_t, xsh_rr_mixin> mcg_xsh_rr_16_8;
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typedef mcg_base<uint16_t, uint32_t, xsh_rr_mixin> mcg_xsh_rr_32_16;
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typedef mcg_base<uint32_t, uint64_t, xsh_rr_mixin> mcg_xsh_rr_64_32;
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typedef mcg_base<uint64_t, pcg128_t, xsh_rr_mixin> mcg_xsh_rr_128_64;
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/* Predefined types for RXS M XS */
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typedef oneseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_8_8;
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typedef oneseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_16_16;
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typedef oneseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_32_32;
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typedef oneseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_64_64;
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typedef oneseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> oneseq_rxs_m_xs_128_128;
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typedef unique_base<uint8_t, uint8_t, rxs_m_xs_mixin> unique_rxs_m_xs_8_8;
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typedef unique_base<uint16_t, uint16_t, rxs_m_xs_mixin> unique_rxs_m_xs_16_16;
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typedef unique_base<uint32_t, uint32_t, rxs_m_xs_mixin> unique_rxs_m_xs_32_32;
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typedef unique_base<uint64_t, uint64_t, rxs_m_xs_mixin> unique_rxs_m_xs_64_64;
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typedef unique_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> unique_rxs_m_xs_128_128;
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typedef setseq_base<uint8_t, uint8_t, rxs_m_xs_mixin> setseq_rxs_m_xs_8_8;
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typedef setseq_base<uint16_t, uint16_t, rxs_m_xs_mixin> setseq_rxs_m_xs_16_16;
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typedef setseq_base<uint32_t, uint32_t, rxs_m_xs_mixin> setseq_rxs_m_xs_32_32;
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typedef setseq_base<uint64_t, uint64_t, rxs_m_xs_mixin> setseq_rxs_m_xs_64_64;
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typedef setseq_base<pcg128_t, pcg128_t, rxs_m_xs_mixin> setseq_rxs_m_xs_128_128;
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// MCG versions don't make sense here, so aren't defined.
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/* Predefined types for XSL RR (only defined for "large" types) */
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typedef oneseq_base<uint32_t, uint64_t, xsl_rr_mixin> oneseq_xsl_rr_64_32;
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typedef oneseq_base<uint64_t, pcg128_t, xsl_rr_mixin> oneseq_xsl_rr_128_64;
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typedef unique_base<uint32_t, uint64_t, xsl_rr_mixin> unique_xsl_rr_64_32;
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typedef unique_base<uint64_t, pcg128_t, xsl_rr_mixin> unique_xsl_rr_128_64;
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typedef setseq_base<uint32_t, uint64_t, xsl_rr_mixin> setseq_xsl_rr_64_32;
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typedef setseq_base<uint64_t, pcg128_t, xsl_rr_mixin> setseq_xsl_rr_128_64;
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typedef mcg_base<uint32_t, uint64_t, xsl_rr_mixin> mcg_xsl_rr_64_32;
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typedef mcg_base<uint64_t, pcg128_t, xsl_rr_mixin> mcg_xsl_rr_128_64;
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/* Predefined types for XSL RR RR (only defined for "large" types) */
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typedef oneseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
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oneseq_xsl_rr_rr_64_64;
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typedef oneseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
|
|
oneseq_xsl_rr_rr_128_128;
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typedef unique_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
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unique_xsl_rr_rr_64_64;
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typedef unique_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
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unique_xsl_rr_rr_128_128;
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typedef setseq_base<uint64_t, uint64_t, xsl_rr_rr_mixin>
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setseq_xsl_rr_rr_64_64;
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typedef setseq_base<pcg128_t, pcg128_t, xsl_rr_rr_mixin>
|
|
setseq_xsl_rr_rr_128_128;
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// MCG versions don't make sense here, so aren't defined.
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/* Extended generators */
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template <bitcount_t table_pow2, bitcount_t advance_pow2,
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typename BaseRNG, bool kdd = true>
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using ext_std8 = extended<table_pow2, advance_pow2, BaseRNG,
|
|
oneseq_rxs_m_xs_8_8, kdd>;
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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>;
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|
|
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
|