boost/random/niederreiter_base2.hpp
/* boost random/nierderreiter_base2.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_NIEDERREITER_BASE2_HPP
#define BOOST_RANDOM_NIEDERREITER_BASE2_HPP
#include <boost/random/detail/niederreiter_base2_table.hpp>
#include <boost/random/detail/gray_coded_qrng.hpp>
#include <boost/dynamic_bitset.hpp>
namespace boost {
namespace random {
/** @cond */
namespace qrng_detail {
namespace nb2 {
// Return the base 2 logarithm for a given bitset v
template <typename DynamicBitset>
inline typename DynamicBitset::size_type
bitset_log2(const DynamicBitset& v)
{
if (v.none())
boost::throw_exception( std::invalid_argument("bitset_log2") );
typename DynamicBitset::size_type hibit = v.size() - 1;
while (!v.test(hibit))
--hibit;
return hibit;
}
// Multiply polynomials over Z_2.
template <typename PolynomialT, typename DynamicBitset>
inline void modulo2_multiply(PolynomialT P, DynamicBitset& v, DynamicBitset& pt)
{
pt.reset(); // pt == 0
for (; P; P >>= 1, v <<= 1)
if (P & 1) pt ^= v;
pt.swap(v);
}
// Calculate the values of the constants V(J,R) as
// described in BFN section 3.3.
//
// pb = polynomial defined in section 2.3 of BFN.
template <typename DynamicBitset>
inline void calculate_v(const DynamicBitset& pb,
typename DynamicBitset::size_type kj,
typename DynamicBitset::size_type pb_degree,
DynamicBitset& v)
{
typedef typename DynamicBitset::size_type size_type;
// Now choose values of V in accordance with
// the conditions in section 3.3.
size_type r = 0;
for ( ; r != kj; ++r)
v.reset(r);
// Quoting from BFN: "Our program currently sets each K_q
// equal to eq. This has the effect of setting all unrestricted
// values of v to 1."
for ( ; r < pb_degree; ++r)
v.set(r);
// Calculate the remaining V's using the recursion of section 2.3,
// remembering that the B's have the opposite sign.
for ( ; r != v.size(); ++r)
{
bool term = false;
for (typename DynamicBitset::size_type k = 0; k < pb_degree; ++k)
{
term ^= pb.test(k) & v[r + k - pb_degree];
}
v[r] = term;
}
}
} // namespace nb2
template<typename UIntType, unsigned w, typename Nb2Table>
struct niederreiter_base2_lattice
{
typedef UIntType value_type;
BOOST_STATIC_ASSERT(w > 0u);
BOOST_STATIC_CONSTANT(unsigned, bit_count = w);
private:
typedef std::vector<value_type> container_type;
public:
explicit niederreiter_base2_lattice(std::size_t dimension)
{
resize(dimension);
}
void resize(std::size_t dimension)
{
typedef boost::dynamic_bitset<> bitset_type;
dimension_assert("Niederreiter base 2", dimension, Nb2Table::max_dimension);
// Initialize the bit array
container_type cj(bit_count * dimension);
// Reserve temporary space for lattice computation
bitset_type v, pb, tmp;
// Compute Niedderreiter base 2 lattice
for (std::size_t dim = 0; dim != dimension; ++dim)
{
const typename Nb2Table::value_type poly = Nb2Table::polynomial(dim);
if (poly > std::numeric_limits<value_type>::max()) {
boost::throw_exception( std::range_error("niederreiter_base2: polynomial value outside the given value type range") );
}
const unsigned degree = multiprecision::msb(poly); // integer log2(poly)
const unsigned space_required = degree * ((bit_count / degree) + 1); // ~ degree + bit_count
v.resize(degree + bit_count - 1);
// For each dimension, we need to calculate powers of an
// appropriate irreducible polynomial, see Niederreiter
// page 65, just below equation (19).
// Copy the appropriate irreducible polynomial into PX,
// and its degree into E. Set polynomial B = PX ** 0 = 1.
// M is the degree of B. Subsequently B will hold higher
// powers of PX.
pb.resize(space_required); tmp.resize(space_required);
typename bitset_type::size_type kj, pb_degree = 0;
pb.reset(); // pb == 0
pb.set(pb_degree); // set the proper bit for the pb_degree
value_type j = high_bit_mask_t<bit_count - 1>::high_bit;
do
{
// Now choose a value of Kj as defined in section 3.3.
// We must have 0 <= Kj < E*J = M.
// The limit condition on Kj does not seem to be very relevant
// in this program.
kj = pb_degree;
// Now multiply B by PX so B becomes PX**J.
// In section 2.3, the values of Bi are defined with a minus sign :
// don't forget this if you use them later!
nb2::modulo2_multiply(poly, pb, tmp);
pb_degree += degree;
if (pb_degree >= pb.size()) {
// Note that it is quite possible for kj to become bigger than
// the new computed value of pb_degree.
pb_degree = nb2::bitset_log2(pb);
}
// If U = 0, we need to set B to the next power of PX
// and recalculate V.
nb2::calculate_v(pb, kj, pb_degree, v);
// Niederreiter (page 56, after equation (7), defines two
// variables Q and U. We do not need Q explicitly, but we
// do need U.
// Advance Niederreiter's state variables.
for (unsigned u = 0; j && u != degree; ++u, j >>= 1)
{
// Now C is obtained from V. Niederreiter
// obtains A from V (page 65, near the bottom), and then gets
// C from A (page 56, equation (7)). However this can be done
// in one step. Here CI(J,R) corresponds to
// Niederreiter's C(I,J,R), whose values we pack into array
// CJ so that CJ(I,R) holds all the values of C(I,J,R) for J from 1 to NBITS.
for (unsigned r = 0; r != bit_count; ++r) {
value_type& num = cj[dimension * r + dim];
// set the jth bit in num
num = (num & ~j) | (-v[r + u] & j);
}
}
} while (j != 0);
}
bits.swap(cj);
}
typename container_type::const_iterator iter_at(std::size_t n) const
{
BOOST_ASSERT(!(n > bits.size()));
return bits.begin() + n;
}
private:
container_type bits;
};
} // namespace qrng_detail
typedef detail::qrng_tables::niederreiter_base2 default_niederreiter_base2_table;
/** @endcond */
//!Instantiations of class template niederreiter_base2_engine model a \quasi_random_number_generator.
//!The niederreiter_base2_engine uses the algorithm described in
//! \blockquote
//!Bratley, Fox, Niederreiter, ACM Trans. Model. Comp. Sim. 2, 195 (1992).
//! \endblockquote
//!
//!\attention niederreiter_base2_engine skips trivial zeroes at the start of the sequence. For example,
//!the beginning of the 2-dimensional Niederreiter base 2 sequence in @c uniform_01 distribution will look
//!like this:
//!\code{.cpp}
//!0.5, 0.5,
//!0.75, 0.25,
//!0.25, 0.75,
//!0.375, 0.375,
//!0.875, 0.875,
//!...
//!\endcode
//!
//!In the following documentation @c X denotes the concrete class of the template
//!niederreiter_base2_engine returning objects of type @c UIntType, u and v are the values of @c X.
//!
//!Some member functions may throw exceptions of type std::range_error. This
//!happens when the quasi-random domain is exhausted and the generator cannot produce
//!any more values. The length of the low discrepancy sequence is given by
//! \f$L=Dimension \times (2^{w} - 1)\f$.
template<typename UIntType, unsigned w, typename Nb2Table = default_niederreiter_base2_table>
class niederreiter_base2_engine
: public qrng_detail::gray_coded_qrng<
qrng_detail::niederreiter_base2_lattice<UIntType, w, Nb2Table>
>
{
typedef qrng_detail::niederreiter_base2_lattice<UIntType, w, Nb2Table> lattice_t;
typedef qrng_detail::gray_coded_qrng<lattice_t> base_t;
public:
//!Effects: Constructs the default `s`-dimensional Niederreiter base 2 quasi-random number generator.
//!
//!Throws: bad_alloc, invalid_argument, range_error.
explicit niederreiter_base2_engine(std::size_t s)
: base_t(s) // initialize lattice here
{}
#ifdef BOOST_RANDOM_DOXYGEN
//=========================Doxygen needs this!==============================
typedef UIntType result_type;
//!Returns: Tight lower bound on the set of values returned by operator().
//!
//!Throws: nothing.
static BOOST_CONSTEXPR result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return (base_t::min)(); }
//!Returns: Tight upper bound on the set of values returned by operator().
//!
//!Throws: nothing.
static BOOST_CONSTEXPR result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return (base_t::max)(); }
//!Returns: The dimension of of the quasi-random domain.
//!
//!Throws: nothing.
std::size_t dimension() const { return base_t::dimension(); }
//!Effects: Resets the quasi-random number generator state to
//!the one given by the default construction. Equivalent to u.seed(0).
//!
//!\brief Throws: nothing.
void seed()
{
base_t::seed();
}
//!Effects: Effectively sets the quasi-random number generator state to the `init`-th
//!vector in the `s`-dimensional quasi-random domain, where `s` == X::dimension().
//!\code
//!X u, v;
//!for(int i = 0; i < N; ++i)
//! for( std::size_t j = 0; j < u.dimension(); ++j )
//! u();
//!v.seed(N);
//!assert(u() == v());
//!\endcode
//!
//!\brief Throws: range_error.
void seed(UIntType init)
{
base_t::seed(init);
}
//!Returns: Returns a successive element of an `s`-dimensional
//!(s = X::dimension()) vector at each invocation. When all elements are
//!exhausted, X::operator() begins anew with the starting element of a
//!subsequent `s`-dimensional vector.
//!
//!Throws: range_error.
result_type operator()()
{
return base_t::operator()();
}
//!Effects: Advances *this state as if `z` consecutive
//!X::operator() invocations were executed.
//!\code
//!X u = v;
//!for(int i = 0; i < N; ++i)
//! u();
//!v.discard(N);
//!assert(u() == v());
//!\endcode
//!
//!Throws: range_error.
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(niederreiter_base2_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(niederreiter_base2_engine)
//!Writes the textual representation of the generator to a @c std::ostream.
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, niederreiter_base2_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, niederreiter_base2_engine, s)
{ return is >> static_cast<base_t&>(s); }
#endif // BOOST_RANDOM_DOXYGEN
};
/**
* @attention This specialization of \niederreiter_base2_engine supports up to 4720 dimensions.
*
* Binary irreducible polynomials (primes in the ring `GF(2)[X]`, evaluated at `X=2`) were generated
* while condition `max(prime)` < 2<sup>16</sup> was satisfied.
*
* There are exactly 4720 such primes, which yields a Niederreiter base 2 table for 4720 dimensions.
*
* However, it is possible to provide your own table to \niederreiter_base2_engine should the default one be insufficient.
*/
typedef niederreiter_base2_engine<boost::uint_least64_t, 64u, default_niederreiter_base2_table> niederreiter_base2;
} // namespace random
} // namespace boost
#endif // BOOST_RANDOM_NIEDERREITER_BASE2_HPP