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pcg_random.hpp
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pcg_random.hpp
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/*
* PCG Random Number Generation for C++
*
* Copyright 2014-2022 Melissa O'Neill <oneill@pcg-random.org>,
* and the PCG Project contributors.
*
* SPDX-License-Identifier: (Apache-2.0 OR MIT)
*
* Licensed under the Apache License, Version 2.0 (provided in
* LICENSE-APACHE.txt and at http://www.apache.org/licenses/LICENSE-2.0)
* or under the MIT license (provided in LICENSE-MIT.txt and at
* http://opensource.org/licenses/MIT), at your option. This file may not
* be copied, modified, or distributed except according to those terms.
*
* Distributed on an "AS IS" BASIS, WITHOUT WARRANTY OF ANY KIND, either
* express or implied. See your chosen license for details.
*
* For additional information about the PCG random number generation scheme,
* visit http://www.pcg-random.org/.
*/
/*
* This code provides the reference implementation of the PCG family of
* random number generators. The code is complex because it implements
*
* - several members of the PCG family, specifically members corresponding
* to the output functions:
* - XSH RR (good for 64-bit state, 32-bit output)
* - XSH RS (good for 64-bit state, 32-bit output)
* - XSL RR (good for 128-bit state, 64-bit output)
* - RXS M XS (statistically most powerful generator)
* - XSL RR RR (good for 128-bit state, 128-bit output)
* - and RXS, RXS M, XSH, XSL (mostly for testing)
* - at potentially *arbitrary* bit sizes
* - with four different techniques for random streams (MCG, one-stream
* LCG, settable-stream LCG, unique-stream LCG)
* - and the extended generation schemes allowing arbitrary periods
* - with all features of C++11 random number generation (and more),
* some of which are somewhat painful, including
* - initializing with a SeedSequence which writes 32-bit values
* to memory, even though the state of the generator may not
* use 32-bit values (it might use smaller or larger integers)
* - I/O for RNGs and a prescribed format, which needs to handle
* the issue that 8-bit and 128-bit integers don't have working
* I/O routines (e.g., normally 8-bit = char, not integer)
* - equality and inequality for RNGs
* - and a number of convenience typedefs to mask all the complexity
*
* The code employees a fairly heavy level of abstraction, and has to deal
* with various C++ minutia. If you're looking to learn about how the PCG
* scheme works, you're probably best of starting with one of the other
* codebases (see www.pcg-random.org). But if you're curious about the
* constants for the various output functions used in those other, simpler,
* codebases, this code shows how they are calculated.
*
* On the positive side, at least there are convenience typedefs so that you
* can say
*
* pcg32 myRNG;
*
* rather than:
*
* pcg_detail::engine<
* uint32_t, // Output Type
* uint64_t, // State Type
* pcg_detail::xsh_rr_mixin<uint32_t, uint64_t>, true, // Output Func
* pcg_detail::specific_stream<uint64_t>, // Stream Kind
* pcg_detail::default_multiplier<uint64_t> // LCG Mult
* > myRNG;
*
*/
#ifndef PCG_RAND_HPP_INCLUDED
#define PCG_RAND_HPP_INCLUDED 1
#include <algorithm>
#include <cinttypes>
#include <cstddef>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <limits>
#include <iostream>
#include <iterator>
#include <type_traits>
#include <utility>
#include <locale>
#include <new>
#include <stdexcept>
#ifdef _MSC_VER
#pragma warning(disable:4146)
#endif
#ifdef _MSC_VER
#define PCG_ALWAYS_INLINE __forceinline
#elif __GNUC__
#define PCG_ALWAYS_INLINE __attribute__((always_inline))
#else
#define PCG_ALWAYS_INLINE inline
#endif
/*
* The pcg_extras namespace contains some support code that is likely to
* be useful for a variety of RNGs, including:
* - 128-bit int support for platforms where it isn't available natively
* - bit twiddling operations
* - I/O of 128-bit and 8-bit integers
* - Handling the evilness of SeedSeq
* - Support for efficiently producing random numbers less than a given
* bound
*/
#include "pcg_extras.hpp"
namespace pcg_detail {
using namespace pcg_extras;
/*
* The LCG generators need some constants to function. This code lets you
* look up the constant by *type*. For example
*
* default_multiplier<uint32_t>::multiplier()
*
* gives you the default multiplier for 32-bit integers. We use the name
* of the constant and not a generic word like value to allow these classes
* to be used as mixins.
*/
template <typename T>
struct default_multiplier {
// Not defined for an arbitrary type
};
template <typename T>
struct default_increment {
// Not defined for an arbitrary type
};
#define PCG_DEFINE_CONSTANT(type, what, kind, constant) \
template <> \
struct what ## _ ## kind<type> { \
static constexpr type kind() { \
return constant; \
} \
};
PCG_DEFINE_CONSTANT(uint8_t, default, multiplier, 141U)
PCG_DEFINE_CONSTANT(uint8_t, default, increment, 77U)
PCG_DEFINE_CONSTANT(uint16_t, default, multiplier, 12829U)
PCG_DEFINE_CONSTANT(uint16_t, default, increment, 47989U)
PCG_DEFINE_CONSTANT(uint32_t, default, multiplier, 747796405U)
PCG_DEFINE_CONSTANT(uint32_t, default, increment, 2891336453U)
PCG_DEFINE_CONSTANT(uint64_t, default, multiplier, 6364136223846793005ULL)
PCG_DEFINE_CONSTANT(uint64_t, default, increment, 1442695040888963407ULL)
PCG_DEFINE_CONSTANT(pcg128_t, default, multiplier,
PCG_128BIT_CONSTANT(2549297995355413924ULL,4865540595714422341ULL))
PCG_DEFINE_CONSTANT(pcg128_t, default, increment,
PCG_128BIT_CONSTANT(6364136223846793005ULL,1442695040888963407ULL))
/* Alternative (cheaper) multipliers for 128-bit */
template <typename T>
struct cheap_multiplier : public default_multiplier<T> {
// For most types just use the default.
};
template <>
struct cheap_multiplier<pcg128_t> {
static constexpr uint64_t multiplier() {
return 0xda942042e4dd58b5ULL;
}
};
/*
* Each PCG generator is available in four variants, based on how it applies
* the additive constant for its underlying LCG; the variations are:
*
* single stream - all instances use the same fixed constant, thus
* the RNG always somewhere in same sequence
* mcg - adds zero, resulting in a single stream and reduced
* period
* specific stream - the constant can be changed at any time, selecting
* a different random sequence
* unique stream - the constant is based on the memory address of the
* object, thus every RNG has its own unique sequence
*
* This variation is provided though mixin classes which define a function
* value called increment() that returns the necessary additive constant.
*/
/*
* unique stream
*/
template <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<uintptr_t>(this) | 1);
}
constexpr itype stream() const
{
return increment() >> 1;
}
static constexpr bool can_specify_stream = false;
static constexpr size_t streams_pow2()
{
return (sizeof(itype) < sizeof(size_t) ? sizeof(itype)
: sizeof(size_t))*8 - 1u;
}
protected:
constexpr unique_stream() = default;
};
/*
* no stream (mcg)
*/
template <typename itype>
class no_stream {
protected:
static constexpr bool is_mcg = true;
// Is never called, but is provided for symmetry with specific_stream
void set_stream(...)
{
abort();
}
public:
typedef itype state_type;
static constexpr itype increment() {
return 0;
}
static constexpr bool can_specify_stream = false;
static constexpr size_t streams_pow2()
{
return 0u;
}
protected:
constexpr no_stream() = default;
};
/*
* single stream/sequence (oneseq)
*/
template <typename itype>
class oneseq_stream : public default_increment<itype> {
protected:
static constexpr bool is_mcg = false;
// Is never called, but is provided for symmetry with specific_stream
void set_stream(...)
{
abort();
}
public:
typedef itype state_type;
static constexpr itype stream()
{
return default_increment<itype>::increment() >> 1;
}
static constexpr bool can_specify_stream = false;
static constexpr size_t streams_pow2()
{
return 0u;
}
protected:
constexpr oneseq_stream() = default;
};
/*
* specific stream
*/
template <typename itype>
class specific_stream {
protected:
static constexpr bool is_mcg = false;
itype inc_ = default_increment<itype>::increment();
public:
typedef itype state_type;
typedef itype stream_state;
constexpr itype increment() const {
return inc_;
}
itype stream()
{
return inc_ >> 1;
}
void set_stream(itype specific_seq)
{
inc_ = (specific_seq << 1) | 1;
}
static constexpr bool can_specify_stream = true;
static constexpr size_t streams_pow2()
{
return (sizeof(itype)*8) - 1u;
}
protected:
specific_stream() = default;
specific_stream(itype specific_seq)
: inc_(itype(specific_seq << 1) | itype(1U))
{
// Nothing (else) to do.
}
};
/*
* This is where it all comes together. This function joins together three
* mixin classes which define
* - the LCG additive constant (the stream)
* - the LCG multiplier
* - the output function
* in addition, we specify the type of the LCG state, and the result type,
* and whether to use the pre-advance version of the state for the output
* (increasing instruction-level parallelism) or the post-advance version
* (reducing register pressure).
*
* Given the high level of parameterization, the code has to use some
* template-metaprogramming tricks to handle some of the subtle variations
* involved.
*/
template <typename xtype, typename itype,
typename output_mixin,
bool output_previous = true,
typename stream_mixin = oneseq_stream<itype>,
typename multiplier_mixin = default_multiplier<itype> >
class engine : protected output_mixin,
public stream_mixin,
protected multiplier_mixin {
protected:
itype state_;
struct can_specify_stream_tag {};
struct no_specifiable_stream_tag {};
using stream_mixin::increment;
using multiplier_mixin::multiplier;
public:
typedef xtype result_type;
typedef itype state_type;
static constexpr size_t period_pow2()
{
return sizeof(state_type)*8 - 2*stream_mixin::is_mcg;
}
// It would be nice to use std::numeric_limits for these, but
// we can't be sure that it'd be defined for the 128-bit types.
static constexpr result_type min()
{
return result_type(0UL);
}
static constexpr result_type max()
{
return result_type(~result_type(0UL));
}
protected:
itype bump(itype state)
{
return state * multiplier() + increment();
}
itype base_generate()
{
return state_ = bump(state_);
}
itype base_generate0()
{
itype old_state = state_;
state_ = bump(state_);
return old_state;
}
public:
result_type operator()()
{
if (output_previous)
return this->output(base_generate0());
else
return this->output(base_generate());
}
result_type operator()(result_type upper_bound)
{
return bounded_rand(*this, upper_bound);
}
protected:
static itype advance(itype state, itype delta,
itype cur_mult, itype cur_plus);
static itype distance(itype cur_state, itype newstate, itype cur_mult,
itype cur_plus, itype mask = ~itype(0U));
itype distance(itype newstate, itype mask = itype(~itype(0U))) const
{
return distance(state_, newstate, multiplier(), increment(), mask);
}
public:
void advance(itype delta)
{
state_ = advance(state_, delta, this->multiplier(), this->increment());
}
void backstep(itype delta)
{
advance(-delta);
}
void discard(itype delta)
{
advance(delta);
}
bool wrapped()
{
if (stream_mixin::is_mcg) {
// For MCGs, the low order two bits never change. In this
// implementation, we keep them fixed at 3 to make this test
// easier.
return state_ == 3;
} else {
return state_ == 0;
}
}
engine(itype state = itype(0xcafef00dd15ea5e5ULL))
: state_(this->is_mcg ? state|state_type(3U)
: bump(state + this->increment()))
{
// Nothing else to do.
}
// This function may or may not exist. It thus has to be a template
// to use SFINAE; users don't have to worry about its template-ness.
template <typename sm = stream_mixin>
engine(itype state, typename sm::stream_state stream_seed)
: stream_mixin(stream_seed),
state_(this->is_mcg ? state|state_type(3U)
: bump(state + this->increment()))
{
// Nothing else to do.
}
template<typename SeedSeq>
engine(SeedSeq&& seedSeq, typename std::enable_if<
!stream_mixin::can_specify_stream
&& !std::is_convertible<SeedSeq, itype>::value
&& !std::is_convertible<SeedSeq, engine>::value,
no_specifiable_stream_tag>::type = {})
: engine(generate_one<itype>(std::forward<SeedSeq>(seedSeq)))
{
// Nothing else to do.
}
template<typename SeedSeq>
engine(SeedSeq&& seedSeq, typename std::enable_if<
stream_mixin::can_specify_stream
&& !std::is_convertible<SeedSeq, itype>::value
&& !std::is_convertible<SeedSeq, engine>::value,
can_specify_stream_tag>::type = {})
{
itype seeddata[2];
generate_to<2>(std::forward<SeedSeq>(seedSeq), seeddata);
seed(seeddata[1], seeddata[0]);
}
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)
{
using pcg_extras::operator<<;
auto orig_flags = out.flags(std::ios_base::dec | std::ios_base::left);
auto space = out.widen(' ');
auto orig_fill = out.fill();
out << rng.multiplier() << space
<< rng.increment() << space
<< rng.state_;
out.flags(orig_flags);
out.fill(orig_fill);
return out;
}
template <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)
{
using pcg_extras::operator>>;
auto orig_flags = in.flags(std::ios_base::dec | std::ios_base::skipws);
itype multiplier, increment, state;
in >> multiplier >> increment >> state;
if (!in.fail()) {
bool good = true;
if (multiplier != 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
bool is_mcg = cur_plus == itype(0);
itype the_bit = 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 is_mcg ? distance >> 2 : distance;
}
template <typename xtype, typename itype,
typename output_mixin, bool output_previous,
typename stream_mixin_lhs, typename multiplier_mixin_lhs,
typename stream_mixin_rhs, typename multiplier_mixin_rhs>
itype operator-(const engine<xtype,itype,
output_mixin,output_previous,
stream_mixin_lhs, multiplier_mixin_lhs>& lhs,
const engine<xtype,itype,
output_mixin,output_previous,
stream_mixin_rhs, multiplier_mixin_rhs>& rhs)
{
static_assert(
std::is_same<stream_mixin_lhs, stream_mixin_rhs>::value &&
std::is_same<multiplier_mixin_lhs, multiplier_mixin_rhs>::value,
"Incomparable generators");
if (lhs.increment() == rhs.increment()) {
return rhs.distance(lhs.state_);
} else {
constexpr itype ONE = 1u;
itype lhs_diff = lhs.increment() + (lhs.multiplier()-ONE) * lhs.state_;
itype rhs_diff = rhs.increment() + (rhs.multiplier()-ONE) * rhs.state_;
if ((lhs_diff & itype(3u)) != (rhs_diff & itype(3u))) {
rhs_diff = -rhs_diff;
}
return rhs.distance(rhs_diff, lhs_diff, rhs.multiplier(), itype(0u));
}
}
template <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),
template<typename IT> class multiplier_mixin = default_multiplier>
using oneseq_base = engine<xtype, itype,
output_mixin<xtype, itype>, output_previous,
oneseq_stream<itype>,
multiplier_mixin<itype> >;
template <typename xtype, typename itype,
template<typename XT,typename IT> class output_mixin,
bool output_previous = (sizeof(itype) <= 8),
template<typename IT> class multiplier_mixin = default_multiplier>
using unique_base = engine<xtype, itype,
output_mixin<xtype, itype>, output_previous,
unique_stream<itype>,
multiplier_mixin<itype> >;
template <typename xtype, typename itype,
template<typename XT,typename IT> class output_mixin,
bool output_previous = (sizeof(itype) <= 8),
template<typename IT> class multiplier_mixin = default_multiplier>
using setseq_base = engine<xtype, itype,
output_mixin<xtype, itype>, output_previous,
specific_stream<itype>,
multiplier_mixin<itype> >;
template <typename xtype, typename itype,
template<typename XT,typename IT> class output_mixin,
bool output_previous = (sizeof(itype) <= 8),
template<typename IT> class multiplier_mixin = default_multiplier>
using mcg_base = engine<xtype, itype,
output_mixin<xtype, itype>, output_previous,
no_stream<itype>,
multiplier_mixin<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