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/* boost random/faure.hpp header file
*
* Copyright Justinas Vygintas Daugmaudis 2010-2018
* 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)
*/
#ifndef BOOST_RANDOM_FAURE_HPP
#define BOOST_RANDOM_FAURE_HPP
#include <boost/random/detail/qrng_base.hpp>
#include <cmath>
#include <vector>
#include <algorithm>
#include <boost/assert.hpp>
namespace boost {
namespace random {
/** @cond */
namespace detail {
namespace qrng_tables {
// There is no particular reason why 187 first primes were chosen
// to be put into this table. The only reason was, perhaps, that
// the number of dimensions for Faure generator would be around
// the same order of magnitude as the number of dimensions supported
// by the Sobol qrng.
struct primes
{
typedef unsigned short value_type;
BOOST_STATIC_CONSTANT(int, number_of_primes = 187);
// A function that returns lower bound prime for a given n
static value_type lower_bound(std::size_t n)
{
static const value_type prim_a[number_of_primes] = {
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787,
797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031,
1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093,
1097, 1103, 1109, 1117 };
qrng_detail::dimension_assert("Faure", n, prim_a[number_of_primes - 1]);
return *std::lower_bound(prim_a, prim_a + number_of_primes, n);
}
};
} // namespace qrng_tables
} // namespace detail
namespace qrng_detail {
namespace fr {
// Returns the integer part of the logarithm base Base of arg.
// In erroneous situations, e.g., integer_log(base, 0) the function
// returns 0 and does not report the error. This is the intended
// behavior.
template <typename T>
inline T integer_log(T base, T arg)
{
T ilog = T();
while (base <= arg)
{
arg /= base; ++ilog;
}
return ilog;
}
// Perform exponentiation by squaring (potential for code reuse in multiprecision::powm)
template <typename T>
inline T integer_pow(T base, T e)
{
T result = static_cast<T>(1);
while (e)
{
if (e & static_cast<T>(1))
result *= base;
e >>= 1;
base *= base;
}
return result;
}
} // namespace fr
// Computes a table of binomial coefficients modulo qs.
template<typename RealType, typename SeqSizeT, typename PrimeTable>
struct binomial_coefficients
{
typedef RealType value_type;
typedef SeqSizeT size_type;
// Binomial values modulo qs_base will never be bigger than qs_base.
// We can choose an appropriate integer type to hold modulo values and
// shave off memory footprint.
typedef typename PrimeTable::value_type packed_uint_t;
// default copy c-tor is fine
explicit binomial_coefficients(std::size_t dimension)
{
resize(dimension);
}
void resize(std::size_t dimension)
{
qs_base = PrimeTable::lower_bound(dimension);
// Throw away previously computed coefficients.
// This will trigger recomputation on next update
coeff.clear();
}
template <typename Iterator>
void update(size_type seq, Iterator first, Iterator last)
{
if (first != last)
{
const size_type ilog = fr::integer_log(static_cast<size_type>(qs_base), seq);
const size_type hisum = ilog + 1;
if (coeff.size() != size_hint(hisum)) {
ytemp.resize(static_cast<std::size_t>(hisum)); // cast safe because log is small
compute_coefficients(hisum);
qs_pow = fr::integer_pow(static_cast<size_type>(qs_base), ilog);
}
*first = compute_recip(seq, ytemp.rbegin());
// Find other components using the Faure method.
++first;
for ( ; first != last; ++first)
{
*first = RealType();
RealType r = static_cast<RealType>(1);
for (size_type i = 0; i != hisum; ++i)
{
RealType ztemp = ytemp[static_cast<std::size_t>(i)] * upper_element(i, i, hisum);
for (size_type j = i + 1; j != hisum; ++j)
ztemp += ytemp[static_cast<std::size_t>(j)] * upper_element(i, j, hisum);
// Sum ( J <= I <= HISUM ) ( old ytemp(i) * binom(i,j) ) mod QS.
ytemp[static_cast<std::size_t>(i)] = std::fmod(ztemp, static_cast<RealType>(qs_base));
r *= static_cast<RealType>(qs_base);
*first += ytemp[static_cast<std::size_t>(i)] / r;
}
}
}
}
private:
inline static size_type size_hint(size_type n)
{
return n * (n + 1) / 2;
}
packed_uint_t& upper_element(size_type i, size_type j, size_type dim)
{
BOOST_ASSERT( i < dim );
BOOST_ASSERT( j < dim );
BOOST_ASSERT( i <= j );
return coeff[static_cast<std::size_t>((i * (2 * dim - i + 1)) / 2 + j - i)];
}
template<typename Iterator>
RealType compute_recip(size_type seq, Iterator out) const
{
// Here we do
// Sum ( 0 <= J <= HISUM ) YTEMP(J) * QS**J
// Sum ( 0 <= J <= HISUM ) YTEMP(J) / QS**(J+1)
// in one go
RealType r = RealType();
size_type m, k = qs_pow;
for( ; k != 0; ++out, seq = m, k /= qs_base )
{
m = seq % k;
RealType v = static_cast<RealType>((seq - m) / k); // RealType <- size type
r += v;
r /= static_cast<RealType>(qs_base);
*out = v; // saves double dereference
}
return r;
}
void compute_coefficients(const size_type n)
{
// Resize and initialize to zero
coeff.resize(static_cast<std::size_t>(size_hint(n)));
std::fill(coeff.begin(), coeff.end(), packed_uint_t());
// The first row and the diagonal is assigned to 1
upper_element(0, 0, n) = 1;
for (size_type i = 1; i < n; ++i)
{
upper_element(0, i, n) = 1;
upper_element(i, i, n) = 1;
}
// Computes binomial coefficients MOD qs_base
for (size_type i = 1; i < n; ++i)
{
for (size_type j = i + 1; j < n; ++j)
{
upper_element(i, j, n) = ( upper_element(i, j-1, n) +
upper_element(i-1, j-1, n) ) % qs_base;
}
}
}
private:
packed_uint_t qs_base;
// here we cache precomputed data; note that binomial coefficients have
// to be recomputed iff the integer part of the logarithm of seq changes,
// which happens relatively rarely.
std::vector<packed_uint_t> coeff; // packed upper (!) triangular matrix
std::vector<RealType> ytemp;
size_type qs_pow;
};
} // namespace qrng_detail
typedef detail::qrng_tables::primes default_faure_prime_table;
/** @endcond */
//!Instantiations of class template faure_engine model a \quasi_random_number_generator.
//!The faure_engine uses the algorithm described in
//! \blockquote
//!Henri Faure,
//!Discrepance de suites associees a un systeme de numeration (en dimension s),
//!Acta Arithmetica,
//!Volume 41, 1982, pages 337-351.
//! \endblockquote
//
//! \blockquote
//!Bennett Fox,
//!Algorithm 647:
//!Implementation and Relative Efficiency of Quasirandom
//!Sequence Generators,
//!ACM Transactions on Mathematical Software,
//!Volume 12, Number 4, December 1986, pages 362-376.
//! \endblockquote
//!
//!In the following documentation @c X denotes the concrete class of the template
//!faure_engine returning objects of type @c RealType, u and v are the values of @c X.
//!
//!Some member functions may throw exceptions of type @c std::bad_alloc.
template<typename RealType, typename SeqSizeT, typename PrimeTable = default_faure_prime_table>
class faure_engine
: public qrng_detail::qrng_base<
faure_engine<RealType, SeqSizeT, PrimeTable>
, qrng_detail::binomial_coefficients<RealType, SeqSizeT, PrimeTable>
, SeqSizeT
>
{
typedef faure_engine<RealType, SeqSizeT, PrimeTable> self_t;
typedef qrng_detail::binomial_coefficients<RealType, SeqSizeT, PrimeTable> lattice_t;
typedef qrng_detail::qrng_base<self_t, lattice_t, SeqSizeT> base_t;
friend class qrng_detail::qrng_base<self_t, lattice_t, SeqSizeT>;
public:
typedef RealType result_type;
/** @copydoc boost::random::niederreiter_base2_engine::min() */
static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return static_cast<result_type>(0); }
/** @copydoc boost::random::niederreiter_base2_engine::max() */
static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return static_cast<result_type>(1); }
//!Effects: Constructs the `s`-dimensional default Faure quasi-random number generator.
//!
//!Throws: bad_alloc, invalid_argument.
explicit faure_engine(std::size_t s)
: base_t(s) // initialize the binomial table here
{}
/** @copydetails boost::random::niederreiter_base2_engine::seed(UIntType)
* Throws: bad_alloc.
*/
void seed(SeqSizeT init = 0)
{
compute_seq(init);
base_t::reset_seq(init);
}
#ifdef BOOST_RANDOM_DOXYGEN
//=========================Doxygen needs this!==============================
/** @copydoc boost::random::niederreiter_base2_engine::dimension() */
std::size_t dimension() const { return base_t::dimension(); }
/** @copydoc boost::random::niederreiter_base2_engine::operator()() */
result_type operator()()
{
return base_t::operator()();
}
/** @copydoc boost::random::niederreiter_base2_engine::discard(boost::uintmax_t)
* Throws: bad_alloc.
*/
void discard(boost::uintmax_t z)
{
base_t::discard(z);
}
/** Returns true if the two generators will produce identical sequences of outputs. */
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(faure_engine, x, y)
{ return static_cast<const base_t&>(x) == y; }
/** Returns true if the two generators will produce different sequences of outputs. */
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(faure_engine)
/** Writes the textual representation of the generator to a @c std::ostream. */
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, faure_engine, s)
{ return os << static_cast<const base_t&>(s); }
/** Reads the textual representation of the generator from a @c std::istream. */
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, faure_engine, s)
{ return is >> static_cast<base_t&>(s); }
#endif // BOOST_RANDOM_DOXYGEN
private:
/** @cond hide_private_members */
void compute_seq(SeqSizeT seq)
{
qrng_detail::check_seed_sign(seq);
this->lattice.update(seq, this->state_begin(), this->state_end());
}
/** @endcond */
};
/**
* @attention This specialization of \faure_engine supports up to 1117 dimensions.
*
* However, it is possible to provide your own prime table to \faure_engine should the default one be insufficient.
*/
typedef faure_engine<double, boost::uint_least64_t, default_faure_prime_table> faure;
} // namespace random
} // namespace boost
#endif // BOOST_RANDOM_FAURE_HPP