/*
* PCG Random Number Generation for C++
*
* Copyright 2014 Melissa O'Neill <oneill@pcg-random.org>
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* For additional information about the PCG random number generation scheme,
* including its license and other licensing options, visit
*
* http://www.pcg-random.org
*/
/*
* This file provides support code that is useful for random-number generation
* but not specific to the PCG generation scheme, 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
*/
#ifndef PCG_EXTRAS_HPP_INCLUDED
#define PCG_EXTRAS_HPP_INCLUDED 1
#include <cinttypes>
#include <cstddef>
#include <cstdlib>
#include <cstring>
#include <cassert>
#include <limits>
#include <iostream>
#include <type_traits>
#include <utility>
#include <locale>
#include <iterator>
#include <utility>
#ifdef __GNUC__
#include <cxxabi.h>
#endif
/*
* Abstractions for compiler-specific directives
*/
#ifdef __GNUC__
#define PCG_NOINLINE __attribute__((noinline))
#else
#define PCG_NOINLINE
#endif
/*
* Some members of the PCG library use 128-bit math. When compiling on 64-bit
* platforms, both GCC and Clang provide 128-bit integer types that are ideal
* for the job.
*
* On 32-bit platforms (or with other compilers), we fall back to a C++
* class that provides 128-bit unsigned integers instead. It may seem
* like we're reinventing the wheel here, because libraries already exist
* that support large integers, but most existing libraries provide a very
* generic multiprecision code, but here we're operating at a fixed size.
* Also, most other libraries are fairly heavyweight. So we use a direct
* implementation. Sadly, it's much slower than hand-coded assembly or
* direct CPU support.
*
*/
#if __SIZEOF_INT128__
namespace pcg_extras {
typedef __uint128_t pcg128_t;
}
#define PCG_128BIT_CONSTANT(high,low) \
((pcg128_t(high) << 64) + low)
#else
#include "pcg_uint128.hpp"
namespace pcg_extras {
typedef pcg_extras::uint_x4<uint32_t,uint64_t> pcg128_t;
}
#define PCG_128BIT_CONSTANT(high,low) \
pcg128_t(high,low)
#define PCG_EMULATED_128BIT_MATH 1
#endif
namespace pcg_extras {
/*
* We often need to represent a "number of bits". When used normally, these
* numbers are never greater than 128, so an unsigned char is plenty.
* If you're using a nonstandard generator of a larger size, you can set
* PCG_BITCOUNT_T to have it define it as a larger size. (Some compilers
* might produce faster code if you set it to an unsigned int.)
*/
#ifndef PCG_BITCOUNT_T
typedef uint8_t bitcount_t;
#else
typedef PCG_BITCOUNT_T bitcount_t;
#endif
/*
* C++ requires us to be able to serialize RNG state by printing or reading
* it from a stream. Because we use 128-bit ints, we also need to be able
* ot print them, so here is code to do so.
*
* This code provides enough functionality to print 128-bit ints in decimal
* and zero-padded in hex. It's not a full-featured implementation.
*/
template <typename CharT, typename Traits>
std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>& out, pcg128_t value)
{
auto desired_base = out.flags() & out.basefield;
bool want_hex = desired_base == out.hex;
if (want_hex) {
uint64_t highpart = uint64_t(value >> 64);
uint64_t lowpart = uint64_t(value);
auto desired_width = out.width();
if (desired_width > 16) {
out.width(desired_width - 16);
}
if (highpart != 0 || desired_width > 16)
out << highpart;
CharT oldfill;
if (highpart != 0) {
out.width(16);
oldfill = out.fill('0');
}
auto oldflags = out.setf(decltype(desired_base){}, out.showbase);
out << lowpart;
out.setf(oldflags);
if (highpart != 0) {
out.fill(oldfill);
}
return out;
}
constexpr size_t MAX_CHARS_128BIT = 40;
char buffer[MAX_CHARS_128BIT];
char* pos = buffer+sizeof(buffer);
*(--pos) = '\0';
constexpr auto BASE = pcg128_t(10ULL);
do {
auto div = value / BASE;
auto mod = uint32_t(value - (div * BASE));
*(--pos) = '0' + mod;
value = div;
} while(value != pcg128_t(0ULL));
return out << pos;
}
template <typename CharT, typename Traits>
std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& in, pcg128_t& value)
{
typename std::basic_istream<CharT,Traits>::sentry s(in);
if (!s)
return in;
constexpr auto BASE = pcg128_t(10ULL);
pcg128_t current(0ULL);
bool did_nothing = true;
bool overflow = false;
for(;;) {
CharT wide_ch = in.get();
if (!in.good())
break;
auto ch = in.narrow(wide_ch, '\0');
if (ch < '0' || ch > '9') {
in.unget();
break;
}
did_nothing = false;
pcg128_t digit(uint32_t(ch - '0'));
pcg128_t timesbase = current*BASE;
overflow = overflow || timesbase < current;
current = timesbase + digit;
overflow = overflow || current < digit;
}
if (did_nothing || overflow) {
in.setstate(std::ios::failbit);
if (overflow)
current = ~pcg128_t(0ULL);
}
value = current;
return in;
}
/*
* Likewise, if people use tiny rngs, we'll be serializing uint8_t.
* If we just used the provided IO operators, they'd read/write chars,
* not ints, so we need to define our own. We *can* redefine this operator
* here because we're in our own namespace.
*/
template <typename CharT, typename Traits>
std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>&out, uint8_t value)
{
return out << uint32_t(value);
}
template <typename CharT, typename Traits>
std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& in, uint8_t target)
{
uint32_t value = 0xdecea5edU;
in >> value;
if (!in && value == 0xdecea5edU)
return in;
if (value > uint8_t(~0)) {
in.setstate(std::ios::failbit);
value = ~0U;
}
target = uint8_t(value);
return in;
}
/* Unfortunately, the above functions don't get found in preference to the
* built in ones, so we create some more specific overloads that will.
* Ugh.
*/
inline std::ostream& operator<<(std::ostream& out, uint8_t value)
{
return pcg_extras::operator<< <char>(out, value);
}
inline std::istream& operator>>(std::istream& in, uint8_t& value)
{
return pcg_extras::operator>> <char>(in, value);
}
/*
* Useful bitwise operations.
*/
/*
* XorShifts are invertable, but they are someting of a pain to invert.
* This function backs them out. It's used by the whacky "inside out"
* generator defined later.
*/
template <typename itype>
inline itype unxorshift(itype x, bitcount_t bits, bitcount_t shift)
{
if (2*shift >= bits) {
return x ^ (x >> shift);
}
itype lowmask1 = (itype(1U) << (bits - shift*2)) - 1;
itype highmask1 = ~lowmask1;
itype top1 = x;
itype bottom1 = x & lowmask1;
top1 ^= top1 >> shift;
top1 &= highmask1;
x = top1 | bottom1;
itype lowmask2 = (itype(1U) << (bits - shift)) - 1;
itype bottom2 = x & lowmask2;
bottom2 = unxorshift(bottom2, bits - shift, shift);
bottom2 &= lowmask1;
return top1 | bottom2;
}
/*
* Rotate left and right.
*
* In ideal world, compilers would spot idiomatic rotate code and convert it
* to a rotate instruction. Of course, opinions vary on what the correct
* idiom is and how to spot it. For clang, sometimes it generates better
* (but still crappy) code if you define PCG_USE_ZEROCHECK_ROTATE_IDIOM.
*/
template <typename itype>
inline itype rotl(itype value, bitcount_t rot)
{
constexpr bitcount_t bits = sizeof(itype) * 8;
constexpr bitcount_t mask = bits - 1;
#if PCG_USE_ZEROCHECK_ROTATE_IDIOM
return rot ? (value << rot) | (value >> (bits - rot)) : value;
#else
return (value << rot) | (value >> ((- rot) & mask));
#endif
}
template <typename itype>
inline itype rotr(itype value, bitcount_t rot)
{
constexpr bitcount_t bits = sizeof(itype) * 8;
constexpr bitcount_t mask = bits - 1;
#if PCG_USE_ZEROCHECK_ROTATE_IDIOM
return rot ? (value >> rot) | (value << (bits - rot)) : value;
#else
return (value >> rot) | (value << ((- rot) & mask));
#endif
}
/* Unfortunately, both Clang and GCC sometimes perform poorly when it comes
* to properly recognizing idiomatic rotate code, so for we also provide
* assembler directives (enabled with PCG_USE_INLINE_ASM). Boo, hiss.
* (I hope that these compilers get better so that this code can die.)
*
* These overloads will be preferred over the general template code above.
*/
#if PCG_USE_INLINE_ASM && __GNUC__ && (__x86_64__ || __i386__)
inline uint8_t rotr(uint8_t value, bitcount_t rot)
{
asm ("rorb %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
return value;
}
inline uint16_t rotr(uint16_t value, bitcount_t rot)
{
asm ("rorw %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
return value;
}
inline uint32_t rotr(uint32_t value, bitcount_t rot)
{
asm ("rorl %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
return value;
}
#if __x86_64__
inline uint64_t rotr(uint64_t value, bitcount_t rot)
{
asm ("rorq %%cl, %0" : "=r" (value) : "0" (value), "c" (rot));
return value;
}
#endif // __x86_64__
#endif // PCG_USE_INLINE_ASM
/*
* The C++ SeedSeq concept (modelled by seed_seq) can fill an array of
* 32-bit integers with seed data, but sometimes we want to produce
* larger or smaller integers.
*
* The following code handles this annoyance.
*
* uneven_copy will copy an array of 32-bit ints to an array of larger or
* smaller ints (actually, the code is general it only needing forward
* iterators). The copy is identical to the one that would be performed if
* we just did memcpy on a standard little-endian machine, but works
* regardless of the endian of the machine (or the weirdness of the ints
* involved).
*
* generate_to initializes an array of integers using a SeedSeq
* object. It is given the size as a static constant at compile time and
* tries to avoid memory allocation. If we're filling in 32-bit constants
* we just do it directly. If we need a separate buffer and it's small,
* we allocate it on the stack. Otherwise, we fall back to heap allocation.
* Ugh.
*
* generate_one produces a single value of some integral type using a
* SeedSeq object.
*/
/* uneven_copy helper, case where destination ints are less than 32 bit. */
template<class SrcIter, class DestIter>
SrcIter uneven_copy_impl(
SrcIter src_first, DestIter dest_first, DestIter dest_last,
std::true_type)
{
typedef typename std::iterator_traits<SrcIter>::value_type src_t;
typedef typename std::iterator_traits<DestIter>::value_type dest_t;
constexpr bitcount_t SRC_SIZE = sizeof(src_t);
constexpr bitcount_t DEST_SIZE = sizeof(dest_t);
constexpr bitcount_t DEST_BITS = DEST_SIZE * 8;
constexpr bitcount_t SCALE = SRC_SIZE / DEST_SIZE;
size_t count = 0;
src_t value;
while (dest_first != dest_last) {
if ((count++ % SCALE) == 0)
value = *src_first++; // Get more bits
else
value >>= DEST_BITS; // Move down bits
*dest_first++ = dest_t(value); // Truncates, ignores high bits.
}
return src_first;
}
/* uneven_copy helper, case where destination ints are more than 32 bit. */
template<class SrcIter, class DestIter>
SrcIter uneven_copy_impl(
SrcIter src_first, DestIter dest_first, DestIter dest_last,
std::false_type)
{
typedef typename std::iterator_traits<SrcIter>::value_type src_t;
typedef typename std::iterator_traits<DestIter>::value_type dest_t;
constexpr auto SRC_SIZE = sizeof(src_t);
constexpr auto SRC_BITS = SRC_SIZE * 8;
constexpr auto DEST_SIZE = sizeof(dest_t);
constexpr auto SCALE = (DEST_SIZE+SRC_SIZE-1) / SRC_SIZE;
while (dest_first != dest_last) {
dest_t value(0UL);
unsigned int shift = 0;
for (size_t i = 0; i < SCALE; ++i) {
value |= dest_t(*src_first++) << shift;
shift += SRC_BITS;
}
*dest_first++ = value;
}
return src_first;
}
/* uneven_copy, call the right code for larger vs. smaller */
template<class SrcIter, class DestIter>
inline SrcIter uneven_copy(SrcIter src_first,
DestIter dest_first, DestIter dest_last)
{
typedef typename std::iterator_traits<SrcIter>::value_type src_t;
typedef typename std::iterator_traits<DestIter>::value_type dest_t;
constexpr bool DEST_IS_SMALLER = sizeof(dest_t) < sizeof(src_t);
return uneven_copy_impl(src_first, dest_first, dest_last,
std::integral_constant<bool, DEST_IS_SMALLER>{});
}
/* generate_to, fill in a fixed-size array of integral type using a SeedSeq
* (actually works for any random-access iterator)
*/
template <size_t size, typename SeedSeq, typename DestIter>
inline void generate_to_impl(SeedSeq&& generator, DestIter dest,
std::true_type)
{
generator.generate(dest, dest+size);
}
template <size_t size, typename SeedSeq, typename DestIter>
void generate_to_impl(SeedSeq&& generator, DestIter dest,
std::false_type)
{
typedef typename std::iterator_traits<DestIter>::value_type dest_t;
constexpr auto DEST_SIZE = sizeof(dest_t);
constexpr auto GEN_SIZE = sizeof(uint32_t);
constexpr bool GEN_IS_SMALLER = GEN_SIZE < DEST_SIZE;
constexpr size_t FROM_ELEMS =
GEN_IS_SMALLER
? size * ((DEST_SIZE+GEN_SIZE-1) / GEN_SIZE)
: (size + (GEN_SIZE / DEST_SIZE) - 1)
/ ((GEN_SIZE / DEST_SIZE) + GEN_IS_SMALLER);
// this odd code ^^^^^^^^^^^^^^^^^ is work-around for
// a bug: http://llvm.org/bugs/show_bug.cgi?id=21287
if (FROM_ELEMS <= 1024) {
uint32_t buffer[FROM_ELEMS];
generator.generate(buffer, buffer+FROM_ELEMS);
uneven_copy(buffer, dest, dest+size);
} else {
uint32_t* buffer = (uint32_t*) malloc(GEN_SIZE * FROM_ELEMS);
generator.generate(buffer, buffer+FROM_ELEMS);
uneven_copy(buffer, dest, dest+size);
free(buffer);
}
}
template <size_t size, typename SeedSeq, typename DestIter>
inline void generate_to(SeedSeq&& generator, DestIter dest)
{
typedef typename std::iterator_traits<DestIter>::value_type dest_t;
constexpr bool IS_32BIT = sizeof(dest_t) == sizeof(uint32_t);
generate_to_impl<size>(std::forward<SeedSeq>(generator), dest,
std::integral_constant<bool, IS_32BIT>{});
}
/* generate_one, produce a value of integral type using a SeedSeq
* (optionally, we can have it produce more than one and pick which one
* we want)
*/
template <typename UInt, size_t i = 0UL, size_t N = i+1UL, typename SeedSeq>
inline UInt generate_one(SeedSeq&& generator)
{
UInt result[N];
generate_to<N>(std::forward<SeedSeq>(generator), result);
return result[i];
}
template <typename RngType>
auto bounded_rand(RngType& rng, typename RngType::result_type upper_bound)
-> typename RngType::result_type
{
typedef typename RngType::result_type rtype;
rtype threshold = (RngType::max() - RngType::min() + rtype(1) - upper_bound)
% upper_bound;
for (;;) {
rtype r = rng() - RngType::min();
if (r >= threshold)
return r % upper_bound;
}
}
template <typename Iter, typename RandType>
void shuffle(Iter from, Iter to, RandType&& rng)
{
typedef typename std::iterator_traits<Iter>::difference_type delta_t;
auto count = to - from;
while (count > 1) {
delta_t chosen(bounded_rand(rng, count));
--count;
--to;
using std::swap;
swap(*(from+chosen), *to);
}
}
/*
* Although std::seed_seq is useful, it isn't everything. Often we want to
* initialize a random-number generator some other way, such as from a random
* device.
*
* Technically, it does not meet the requirements of a SeedSequence because
* it lacks some of the rarely-used member functions (some of which would
* be impossible to provide). However the C++ standard is quite specific
* that actual engines only called the generate method, so it ought not to be
* a problem in practice.
*/
template <typename RngType>
class seed_seq_from {
private:
RngType rng_;
typedef uint_least32_t result_type;
public:
template<typename... Args>
seed_seq_from(Args&&... args) :
rng_(std::forward<Args>(args)...)
{
// Nothing (else) to do...
}
template<typename Iter>
void generate(Iter start, Iter finish)
{
for (auto i = start; i != finish; ++i)
*i = result_type(rng_());
}
constexpr size_t size() const
{
return (sizeof(typename RngType::result_type) > sizeof(result_type)
&& RngType::max() > ~size_t(0UL))
? ~size_t(0UL)
: size_t(RngType::max());
}
};
/*
* Sometimes you might want a distinct seed based on when the program
* was compiled. That way, a particular instance of the program will
* behave the same way, but when recompiled it'll produce a different
* value.
*/
template <typename IntType>
struct static_arbitrary_seed {
private:
static constexpr IntType fnv(IntType hash, const char* pos) {
return *pos == '\0'
? hash
: fnv((hash * IntType(16777619U)) ^ *pos, (pos+1));
}
public:
static constexpr IntType value = fnv(IntType(2166136261U ^ sizeof(IntType)),
__DATE__ __TIME__ __FILE__);
};
// Sometimes, when debugging or testing, it's handy to be able print the name
// of a (in human-readable form). This code allows the idiom:
//
// cout << printable_typename<my_foo_type_t>()
//
// to print out my_foo_type_t (or its concrete type if it is a synonym)
template <typename T>
struct printable_typename {};
template <typename T>
std::ostream& operator<<(std::ostream& out, printable_typename<T>) {
const char *implementation_typename = typeid(T).name();
#ifdef __GNUC__
int status;
const char* pretty_name =
abi::__cxa_demangle(implementation_typename, NULL, NULL, &status);
if (status == 0)
out << pretty_name;
free((void*) pretty_name);
if (status == 0)
return out;
#endif
out << implementation_typename;
return out;
}
} // namespace pcg_extras
#endif // PCG_EXTRAS_HPP_INCLUDED