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glm/test/external/boost/random/mersenne_twister.hpp

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/* boost random/mersenne_twister.hpp header file
*
* Copyright Jens Maurer 2000-2001
* Copyright Steven Watanabe 2010
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* See http://www.boost.org for most recent version including documentation.
*
* $Id: mersenne_twister.hpp 74867 2011-10-09 23:13:31Z steven_watanabe $
*
* Revision history
* 2001-02-18 moved to individual header files
*/
#ifndef BOOST_RANDOM_MERSENNE_TWISTER_HPP
#define BOOST_RANDOM_MERSENNE_TWISTER_HPP
#include <iosfwd>
#include <istream>
#include <stdexcept>
#include <boost/config.hpp>
#include <boost/cstdint.hpp>
#include <boost/integer/integer_mask.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/ptr_helper.hpp>
#include <boost/random/detail/seed.hpp>
#include <boost/random/detail/seed_impl.hpp>
#include <boost/random/detail/generator_seed_seq.hpp>
namespace boost {
namespace random {
/**
* Instantiations of class template mersenne_twister_engine model a
* \pseudo_random_number_generator. It uses the algorithm described in
*
* @blockquote
* "Mersenne Twister: A 623-dimensionally equidistributed uniform
* pseudo-random number generator", Makoto Matsumoto and Takuji Nishimura,
* ACM Transactions on Modeling and Computer Simulation: Special Issue on
* Uniform Random Number Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
* @endblockquote
*
* @xmlnote
* The boost variant has been implemented from scratch and does not
* derive from or use mt19937.c provided on the above WWW site. However, it
* was verified that both produce identical output.
* @endxmlnote
*
* The seeding from an integer was changed in April 2005 to address a
* <a href="http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html">weakness</a>.
*
* The quality of the generator crucially depends on the choice of the
* parameters. User code should employ one of the sensibly parameterized
* generators such as \mt19937 instead.
*
* The generator requires considerable amounts of memory for the storage of
* its state array. For example, \mt11213b requires about 1408 bytes and
* \mt19937 requires about 2496 bytes.
*/
template<class UIntType,
std::size_t w, std::size_t n, std::size_t m, std::size_t r,
UIntType a, std::size_t u, UIntType d, std::size_t s,
UIntType b, std::size_t t,
UIntType c, std::size_t l, UIntType f>
class mersenne_twister_engine
{
public:
typedef UIntType result_type;
BOOST_STATIC_CONSTANT(std::size_t, word_size = w);
BOOST_STATIC_CONSTANT(std::size_t, state_size = n);
BOOST_STATIC_CONSTANT(std::size_t, shift_size = m);
BOOST_STATIC_CONSTANT(std::size_t, mask_bits = r);
BOOST_STATIC_CONSTANT(UIntType, xor_mask = a);
BOOST_STATIC_CONSTANT(std::size_t, tempering_u = u);
BOOST_STATIC_CONSTANT(UIntType, tempering_d = d);
BOOST_STATIC_CONSTANT(std::size_t, tempering_s = s);
BOOST_STATIC_CONSTANT(UIntType, tempering_b = b);
BOOST_STATIC_CONSTANT(std::size_t, tempering_t = t);
BOOST_STATIC_CONSTANT(UIntType, tempering_c = c);
BOOST_STATIC_CONSTANT(std::size_t, tempering_l = l);
BOOST_STATIC_CONSTANT(UIntType, initialization_multiplier = f);
BOOST_STATIC_CONSTANT(UIntType, default_seed = 5489u);
// backwards compatibility
BOOST_STATIC_CONSTANT(UIntType, parameter_a = a);
BOOST_STATIC_CONSTANT(std::size_t, output_u = u);
BOOST_STATIC_CONSTANT(std::size_t, output_s = s);
BOOST_STATIC_CONSTANT(UIntType, output_b = b);
BOOST_STATIC_CONSTANT(std::size_t, output_t = t);
BOOST_STATIC_CONSTANT(UIntType, output_c = c);
BOOST_STATIC_CONSTANT(std::size_t, output_l = l);
// old Boost.Random concept requirements
BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
/**
* Constructs a @c mersenne_twister_engine and calls @c seed().
*/
mersenne_twister_engine() { seed(); }
/**
* Constructs a @c mersenne_twister_engine and calls @c seed(value).
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister_engine,
UIntType, value)
{ seed(value); }
template<class It> mersenne_twister_engine(It& first, It last)
{ seed(first,last); }
/**
* Constructs a mersenne_twister_engine and calls @c seed(gen).
*
* @xmlnote
* The copy constructor will always be preferred over
* the templated constructor.
* @endxmlnote
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(mersenne_twister_engine,
SeedSeq, seq)
{ seed(seq); }
// compiler-generated copy ctor and assignment operator are fine
/** Calls @c seed(default_seed). */
void seed() { seed(default_seed); }
/**
* Sets the state x(0) to v mod 2w. Then, iteratively,
* sets x(i) to
* (i + f * (x(i-1) xor (x(i-1) rshift w-2))) mod 2<sup>w</sup>
* for i = 1 .. n-1. x(n) is the first value to be returned by operator().
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister_engine, UIntType, value)
{
// New seeding algorithm from
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/emt19937ar.html
// In the previous versions, MSBs of the seed affected only MSBs of the
// state x[].
const UIntType mask = (max)();
x[0] = value & mask;
for (i = 1; i < n; i++) {
// See Knuth "The Art of Computer Programming"
// Vol. 2, 3rd ed., page 106
x[i] = (f * (x[i-1] ^ (x[i-1] >> (w-2))) + i) & mask;
}
}
/**
* Seeds a mersenne_twister_engine using values produced by seq.generate().
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(mersenne_twister_engine, SeeqSeq, seq)
{
detail::seed_array_int<w>(seq, x);
i = n;
// fix up the state if it's all zeroes.
if((x[0] & (~static_cast<UIntType>(0) << r)) == 0) {
for(std::size_t j = 1; j < n; ++j) {
if(x[j] != 0) return;
}
x[0] = static_cast<UIntType>(1) << (w-1);
}
}
/** Sets the state of the generator using values from an iterator range. */
template<class It>
void seed(It& first, It last)
{
detail::fill_array_int<w>(first, last, x);
i = n;
// fix up the state if it's all zeroes.
if((x[0] & (~static_cast<UIntType>(0) << r)) == 0) {
for(std::size_t j = 1; j < n; ++j) {
if(x[j] != 0) return;
}
x[0] = static_cast<UIntType>(1) << (w-1);
}
}
/** Returns the smallest value that the generator can produce. */
static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return 0; }
/** Returns the largest value that the generator can produce. */
static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return boost::low_bits_mask_t<w>::sig_bits; }
/** Produces the next value of the generator. */
result_type operator()();
/** Fills a range with random values */
template<class Iter>
void generate(Iter first, Iter last)
{ detail::generate_from_int(*this, first, last); }
/**
* Advances the state of the generator by @c z steps. Equivalent to
*
* @code
* for(unsigned long long i = 0; i < z; ++i) {
* gen();
* }
* @endcode
*/
void discard(boost::uintmax_t z)
{
for(boost::uintmax_t j = 0; j < z; ++j) {
(*this)();
}
}
#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
/** Writes a mersenne_twister_engine to a @c std::ostream */
template<class CharT, class Traits>
friend std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>& os,
const mersenne_twister_engine& mt)
{
mt.print(os);
return os;
}
/** Reads a mersenne_twister_engine from a @c std::istream */
template<class CharT, class Traits>
friend std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& is,
mersenne_twister_engine& mt)
{
for(std::size_t j = 0; j < mt.state_size; ++j)
is >> mt.x[j] >> std::ws;
// MSVC (up to 7.1) and Borland (up to 5.64) don't handle the template
// value parameter "n" available from the class template scope, so use
// the static constant with the same value
mt.i = mt.state_size;
return is;
}
#endif
/**
* Returns true if the two generators are in the same state,
* and will thus produce identical sequences.
*/
friend bool operator==(const mersenne_twister_engine& x,
const mersenne_twister_engine& y)
{
if(x.i < y.i) return x.equal_imp(y);
else return y.equal_imp(x);
}
/**
* Returns true if the two generators are in different states.
*/
friend bool operator!=(const mersenne_twister_engine& x,
const mersenne_twister_engine& y)
{ return !(x == y); }
private:
/// \cond show_private
void twist();
/**
* Does the work of operator==. This is in a member function
* for portability. Some compilers, such as msvc 7.1 and
* Sun CC 5.10 can't access template parameters or static
* members of the class from inline friend functions.
*
* requires i <= other.i
*/
bool equal_imp(const mersenne_twister_engine& other) const
{
UIntType back[n];
std::size_t offset = other.i - i;
for(std::size_t j = 0; j + offset < n; ++j)
if(x[j] != other.x[j+offset])
return false;
rewind(&back[n-1], offset);
for(std::size_t j = 0; j < offset; ++j)
if(back[j + n - offset] != other.x[j])
return false;
return true;
}
/**
* Does the work of operator<<. This is in a member function
* for portability.
*/
template<class CharT, class Traits>
void print(std::basic_ostream<CharT, Traits>& os) const
{
UIntType data[n];
for(std::size_t j = 0; j < i; ++j) {
data[j + n - i] = x[j];
}
if(i != n) {
rewind(&data[n - i - 1], n - i);
}
os << data[0];
for(std::size_t j = 1; j < n; ++j) {
os << ' ' << data[j];
}
}
/**
* Copies z elements of the state preceding x[0] into
* the array whose last element is last.
*/
void rewind(UIntType* last, std::size_t z) const
{
const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
const UIntType lower_mask = ~upper_mask;
UIntType y0 = x[m-1] ^ x[n-1];
if(y0 & (static_cast<UIntType>(1) << (w-1))) {
y0 = ((y0 ^ a) << 1) | 1;
} else {
y0 = y0 << 1;
}
for(std::size_t sz = 0; sz < z; ++sz) {
UIntType y1 =
rewind_find(last, sz, m-1) ^ rewind_find(last, sz, n-1);
if(y1 & (static_cast<UIntType>(1) << (w-1))) {
y1 = ((y1 ^ a) << 1) | 1;
} else {
y1 = y1 << 1;
}
*(last - sz) = (y0 & upper_mask) | (y1 & lower_mask);
y0 = y1;
}
}
/**
* Given a pointer to the last element of the rewind array,
* and the current size of the rewind array, finds an element
* relative to the next available slot in the rewind array.
*/
UIntType
rewind_find(UIntType* last, std::size_t size, std::size_t j) const
{
std::size_t index = (j + n - size + n - 1) % n;
if(index < n - size) {
return x[index];
} else {
return *(last - (n - 1 - index));
}
}
/// \endcond
// state representation: next output is o(x(i))
// x[0] ... x[k] x[k+1] ... x[n-1] represents
// x(i-k) ... x(i) x(i+1) ... x(i-k+n-1)
UIntType x[n];
std::size_t i;
};
/// \cond show_private
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
// A definition is required even for integral static constants
#define BOOST_RANDOM_MT_DEFINE_CONSTANT(type, name) \
template<class UIntType, std::size_t w, std::size_t n, std::size_t m, \
std::size_t r, UIntType a, std::size_t u, UIntType d, std::size_t s, \
UIntType b, std::size_t t, UIntType c, std::size_t l, UIntType f> \
const type mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::name
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, word_size);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, state_size);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, shift_size);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, mask_bits);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, xor_mask);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_u);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_d);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_s);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_b);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_t);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, tempering_c);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, tempering_l);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, initialization_multiplier);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, default_seed);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, parameter_a);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_u );
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_s);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_b);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_t);
BOOST_RANDOM_MT_DEFINE_CONSTANT(UIntType, output_c);
BOOST_RANDOM_MT_DEFINE_CONSTANT(std::size_t, output_l);
BOOST_RANDOM_MT_DEFINE_CONSTANT(bool, has_fixed_range);
#undef BOOST_RANDOM_MT_DEFINE_CONSTANT
#endif
template<class UIntType,
std::size_t w, std::size_t n, std::size_t m, std::size_t r,
UIntType a, std::size_t u, UIntType d, std::size_t s,
UIntType b, std::size_t t,
UIntType c, std::size_t l, UIntType f>
void
mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::twist()
{
const UIntType upper_mask = (~static_cast<UIntType>(0)) << r;
const UIntType lower_mask = ~upper_mask;
const std::size_t unroll_factor = 6;
const std::size_t unroll_extra1 = (n-m) % unroll_factor;
const std::size_t unroll_extra2 = (m-1) % unroll_factor;
// split loop to avoid costly modulo operations
{ // extra scope for MSVC brokenness w.r.t. for scope
for(std::size_t j = 0; j < n-m-unroll_extra1; j++) {
UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
}
}
{
for(std::size_t j = n-m-unroll_extra1; j < n-m; j++) {
UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
x[j] = x[j+m] ^ (y >> 1) ^ ((x[j+1]&1) * a);
}
}
{
for(std::size_t j = n-m; j < n-1-unroll_extra2; j++) {
UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
}
}
{
for(std::size_t j = n-1-unroll_extra2; j < n-1; j++) {
UIntType y = (x[j] & upper_mask) | (x[j+1] & lower_mask);
x[j] = x[j-(n-m)] ^ (y >> 1) ^ ((x[j+1]&1) * a);
}
}
// last iteration
UIntType y = (x[n-1] & upper_mask) | (x[0] & lower_mask);
x[n-1] = x[m-1] ^ (y >> 1) ^ ((x[0]&1) * a);
i = 0;
}
/// \endcond
template<class UIntType,
std::size_t w, std::size_t n, std::size_t m, std::size_t r,
UIntType a, std::size_t u, UIntType d, std::size_t s,
UIntType b, std::size_t t,
UIntType c, std::size_t l, UIntType f>
inline typename
mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::result_type
mersenne_twister_engine<UIntType,w,n,m,r,a,u,d,s,b,t,c,l,f>::operator()()
{
if(i == n)
twist();
// Step 4
UIntType z = x[i];
++i;
z ^= ((z >> u) & d);
z ^= ((z << s) & b);
z ^= ((z << t) & c);
z ^= (z >> l);
return z;
}
/**
* The specializations \mt11213b and \mt19937 are from
*
* @blockquote
* "Mersenne Twister: A 623-dimensionally equidistributed
* uniform pseudo-random number generator", Makoto Matsumoto
* and Takuji Nishimura, ACM Transactions on Modeling and
* Computer Simulation: Special Issue on Uniform Random Number
* Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
* @endblockquote
*/
typedef mersenne_twister_engine<uint32_t,32,351,175,19,0xccab8ee7,
11,0xffffffff,7,0x31b6ab00,15,0xffe50000,17,1812433253> mt11213b;
/**
* The specializations \mt11213b and \mt19937 are from
*
* @blockquote
* "Mersenne Twister: A 623-dimensionally equidistributed
* uniform pseudo-random number generator", Makoto Matsumoto
* and Takuji Nishimura, ACM Transactions on Modeling and
* Computer Simulation: Special Issue on Uniform Random Number
* Generation, Vol. 8, No. 1, January 1998, pp. 3-30.
* @endblockquote
*/
typedef mersenne_twister_engine<uint32_t,32,624,397,31,0x9908b0df,
11,0xffffffff,7,0x9d2c5680,15,0xefc60000,18,1812433253> mt19937;
#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
typedef mersenne_twister_engine<uint64_t,64,312,156,31,
UINT64_C(0xb5026f5aa96619e9),29,UINT64_C(0x5555555555555555),17,
UINT64_C(0x71d67fffeda60000),37,UINT64_C(0xfff7eee000000000),43,
UINT64_C(6364136223846793005)> mt19937_64;
#endif
/// \cond show_deprecated
template<class UIntType,
int w, int n, int m, int r,
UIntType a, int u, std::size_t s,
UIntType b, int t,
UIntType c, int l, UIntType v>
class mersenne_twister :
public mersenne_twister_engine<UIntType,
w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253>
{
typedef mersenne_twister_engine<UIntType,
w, n, m, r, a, u, ~(UIntType)0, s, b, t, c, l, 1812433253> base_type;
public:
mersenne_twister() {}
BOOST_RANDOM_DETAIL_GENERATOR_CONSTRUCTOR(mersenne_twister, Gen, gen)
{ seed(gen); }
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(mersenne_twister, UIntType, val)
{ seed(val); }
template<class It>
mersenne_twister(It& first, It last) : base_type(first, last) {}
void seed() { base_type::seed(); }
BOOST_RANDOM_DETAIL_GENERATOR_SEED(mersenne_twister, Gen, gen)
{
detail::generator_seed_seq<Gen> seq(gen);
base_type::seed(seq);
}
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(mersenne_twister, UIntType, val)
{ base_type::seed(val); }
template<class It>
void seed(It& first, It last) { base_type::seed(first, last); }
};
/// \endcond
} // namespace random
using random::mt11213b;
using random::mt19937;
using random::mt19937_64;
} // namespace boost
BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt11213b)
BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937)
BOOST_RANDOM_PTR_HELPER_SPEC(boost::mt19937_64)
#endif // BOOST_RANDOM_MERSENNE_TWISTER_HPP