boost/random/inversive_congruential.hpp
/* boost random/inversive_congruential.hpp header file
*
* Copyright Jens Maurer 2000-2001
* 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: inversive_congruential.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $
*
* Revision history
* 2001-02-18 moved to individual header files
*/
#ifndef BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
#define BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP
#include <iosfwd>
#include <stdexcept>
#include <boost/assert.hpp>
#include <boost/config.hpp>
#include <boost/cstdint.hpp>
#include <boost/integer/static_log2.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/const_mod.hpp>
#include <boost/random/detail/seed.hpp>
#include <boost/random/detail/operators.hpp>
#include <boost/random/detail/seed_impl.hpp>
#include <boost/random/detail/disable_warnings.hpp>
namespace boost {
namespace random {
// Eichenauer and Lehn 1986
/**
* Instantiations of class template @c inversive_congruential_engine model a
* \pseudo_random_number_generator. It uses the inversive congruential
* algorithm (ICG) described in
*
* @blockquote
* "Inversive pseudorandom number generators: concepts, results and links",
* Peter Hellekalek, In: "Proceedings of the 1995 Winter Simulation
* Conference", C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman
* (editors), 1995, pp. 255-262. ftp://random.mat.sbg.ac.at/pub/data/wsc95.ps
* @endblockquote
*
* The output sequence is defined by x(n+1) = (a*inv(x(n)) - b) (mod p),
* where x(0), a, b, and the prime number p are parameters of the generator.
* The expression inv(k) denotes the multiplicative inverse of k in the
* field of integer numbers modulo p, with inv(0) := 0.
*
* The template parameter IntType shall denote a signed integral type large
* enough to hold p; a, b, and p are the parameters of the generators. The
* template parameter val is the validation value checked by validation.
*
* @xmlnote
* The implementation currently uses the Euclidian Algorithm to compute
* the multiplicative inverse. Therefore, the inversive generators are about
* 10-20 times slower than the others (see section"performance"). However,
* the paper talks of only 3x slowdown, so the Euclidian Algorithm is probably
* not optimal for calculating the multiplicative inverse.
* @endxmlnote
*/
template<class IntType, IntType a, IntType b, IntType p>
class inversive_congruential_engine
{
public:
typedef IntType result_type;
BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
BOOST_STATIC_CONSTANT(result_type, multiplier = a);
BOOST_STATIC_CONSTANT(result_type, increment = b);
BOOST_STATIC_CONSTANT(result_type, modulus = p);
BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return b == 0 ? 1 : 0; }
static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () { return p-1; }
/**
* Constructs an @c inversive_congruential_engine, seeding it with
* the default seed.
*/
inversive_congruential_engine() { seed(); }
/**
* Constructs an @c inversive_congruential_engine, seeding it with @c x0.
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(inversive_congruential_engine,
IntType, x0)
{ seed(x0); }
/**
* Constructs an @c inversive_congruential_engine, seeding it with values
* produced by a call to @c seq.generate().
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(inversive_congruential_engine,
SeedSeq, seq)
{ seed(seq); }
/**
* Constructs an @c inversive_congruential_engine, seeds it
* with values taken from the itrator range [first, last),
* and adjusts first to point to the element after the last one
* used. If there are not enough elements, throws @c std::invalid_argument.
*
* first and last must be input iterators.
*/
template<class It> inversive_congruential_engine(It& first, It last)
{ seed(first, last); }
/**
* Calls seed(default_seed)
*/
void seed() { seed(default_seed); }
/**
* If c mod m is zero and x0 mod m is zero, changes the current value of
* the generator to 1. Otherwise, changes it to x0 mod m. If c is zero,
* distinct seeds in the range [1,m) will leave the generator in distinct
* states. If c is not zero, the range is [0,m).
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(inversive_congruential_engine, IntType, x0)
{
// wrap _x if it doesn't fit in the destination
if(modulus == 0) {
_value = x0;
} else {
_value = x0 % modulus;
}
// handle negative seeds
if(_value <= 0 && _value != 0) {
_value += modulus;
}
// adjust to the correct range
if(increment == 0 && _value == 0) {
_value = 1;
}
BOOST_ASSERT(_value >= (min)());
BOOST_ASSERT(_value <= (max)());
}
/**
* Seeds an @c inversive_congruential_engine using values from a SeedSeq.
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(inversive_congruential_engine, SeedSeq, seq)
{ seed(detail::seed_one_int<IntType, modulus>(seq)); }
/**
* seeds an @c inversive_congruential_engine with values taken
* from the itrator range [first, last) and adjusts @c first to
* point to the element after the last one used. If there are
* not enough elements, throws @c std::invalid_argument.
*
* @c first and @c last must be input iterators.
*/
template<class It> void seed(It& first, It last)
{ seed(detail::get_one_int<IntType, modulus>(first, last)); }
/** Returns the next output of the generator. */
IntType operator()()
{
typedef const_mod<IntType, p> do_mod;
_value = do_mod::mult_add(a, do_mod::invert(_value), b);
return _value;
}
/** 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. */
void discard(boost::uintmax_t z)
{
for(boost::uintmax_t j = 0; j < z; ++j) {
(*this)();
}
}
/**
* Writes the textual representation of the generator to a @c std::ostream.
*/
BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, inversive_congruential_engine, x)
{
os << x._value;
return os;
}
/**
* Reads the textual representation of the generator from a @c std::istream.
*/
BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, inversive_congruential_engine, x)
{
is >> x._value;
return is;
}
/**
* Returns true if the two generators will produce identical
* sequences of outputs.
*/
BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(inversive_congruential_engine, x, y)
{ return x._value == y._value; }
/**
* Returns true if the two generators will produce different
* sequences of outputs.
*/
BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(inversive_congruential_engine)
private:
IntType _value;
};
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
// A definition is required even for integral static constants
template<class IntType, IntType a, IntType b, IntType p>
const bool inversive_congruential_engine<IntType, a, b, p>::has_fixed_range;
template<class IntType, IntType a, IntType b, IntType p>
const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::multiplier;
template<class IntType, IntType a, IntType b, IntType p>
const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::increment;
template<class IntType, IntType a, IntType b, IntType p>
const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::modulus;
template<class IntType, IntType a, IntType b, IntType p>
const typename inversive_congruential_engine<IntType, a, b, p>::result_type inversive_congruential_engine<IntType, a, b, p>::default_seed;
#endif
/// \cond show_deprecated
// provided for backwards compatibility
template<class IntType, IntType a, IntType b, IntType p, IntType val = 0>
class inversive_congruential : public inversive_congruential_engine<IntType, a, b, p>
{
typedef inversive_congruential_engine<IntType, a, b, p> base_type;
public:
inversive_congruential(IntType x0 = 1) : base_type(x0) {}
template<class It>
inversive_congruential(It& first, It last) : base_type(first, last) {}
};
/// \endcond
/**
* The specialization hellekalek1995 was suggested in
*
* @blockquote
* "Inversive pseudorandom number generators: concepts, results and links",
* Peter Hellekalek, In: "Proceedings of the 1995 Winter Simulation
* Conference", C. Alexopoulos, K. Kang, W.R. Lilegdon, and D. Goldsman
* (editors), 1995, pp. 255-262. ftp://random.mat.sbg.ac.at/pub/data/wsc95.ps
* @endblockquote
*/
typedef inversive_congruential_engine<uint32_t, 9102, 2147483647-36884165,
2147483647> hellekalek1995;
} // namespace random
using random::hellekalek1995;
} // namespace boost
#include <boost/random/detail/enable_warnings.hpp>
#endif // BOOST_RANDOM_INVERSIVE_CONGRUENTIAL_HPP