boost/random/linear_congruential.hpp
/* boost random/linear_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.
*
* $Id$
*
* Revision history
* 2001-02-18 moved to individual header files
*/
#ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
#define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
#include <iostream>
#include <stdexcept>
#include <boost/assert.hpp>
#include <boost/config.hpp>
#include <boost/cstdint.hpp>
#include <boost/limits.hpp>
#include <boost/static_assert.hpp>
#include <boost/integer/static_log2.hpp>
#include <boost/mpl/if.hpp>
#include <boost/type_traits/is_arithmetic.hpp>
#include <boost/random/detail/config.hpp>
#include <boost/random/detail/const_mod.hpp>
#include <boost/random/detail/seed.hpp>
#include <boost/random/detail/seed_impl.hpp>
#include <boost/detail/workaround.hpp>
#include <boost/random/detail/disable_warnings.hpp>
namespace boost {
namespace random {
/**
* Instantiations of class template linear_congruential_engine model a
* \pseudo_random_number_generator. Linear congruential pseudo-random
* number generators are described in:
*
* @blockquote
* "Mathematical methods in large-scale computing units", D. H. Lehmer,
* Proc. 2nd Symposium on Large-Scale Digital Calculating Machines,
* Harvard University Press, 1951, pp. 141-146
* @endblockquote
*
* Let x(n) denote the sequence of numbers returned by some pseudo-random
* number generator. Then for the linear congruential generator,
* x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are
* x(0), a, c, m. The template parameter IntType shall denote an integral
* type. It must be large enough to hold values a, c, and m. The template
* parameters a and c must be smaller than m.
*
* Note: The quality of the generator crucially depends on the choice of
* the parameters. User code should use one of the sensibly parameterized
* generators such as minstd_rand instead.
*/
template<class IntType, IntType a, IntType c, IntType m>
class linear_congruential_engine
{
public:
typedef IntType result_type;
// Required for old Boost.Random concept
BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
BOOST_STATIC_CONSTANT(IntType, multiplier = a);
BOOST_STATIC_CONSTANT(IntType, increment = c);
BOOST_STATIC_CONSTANT(IntType, modulus = m);
BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer);
BOOST_STATIC_ASSERT(m == 0 || a < m);
BOOST_STATIC_ASSERT(m == 0 || c < m);
/**
* Constructs a @c linear_congruential_engine, using the default seed
*/
linear_congruential_engine() { seed(); }
/**
* Constructs a @c linear_congruential_engine, seeding it with @c x0.
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine,
IntType, x0)
{ seed(x0); }
/**
* Constructs a @c linear_congruential_engine, seeding it with values
* produced by a call to @c seq.generate().
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine,
SeedSeq, seq)
{ seed(seq); }
/**
* Constructs a @c linear_congruential_engine and 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>
linear_congruential_engine(It& first, It last)
{
seed(first, last);
}
// compiler-generated copy constructor and assignment operator are fine
/**
* 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(linear_congruential_engine, IntType, x0)
{
// wrap _x if it doesn't fit in the destination
if(modulus == 0) {
_x = x0;
} else {
_x = x0 % modulus;
}
// handle negative seeds
if(_x <= 0 && _x != 0) {
_x += modulus;
}
// adjust to the correct range
if(increment == 0 && _x == 0) {
_x = 1;
}
BOOST_ASSERT(_x >= (min)());
BOOST_ASSERT(_x <= (max)());
}
/**
* Seeds a @c linear_congruential_engine using values from a SeedSeq.
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq)
{ seed(detail::seed_one_int<IntType, m>(seq)); }
/**
* seeds a @c linear_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, m>(first, last)); }
/**
* Returns the smallest value that the @c linear_congruential_engine
* can produce.
*/
static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return c == 0 ? 1 : 0; }
/**
* Returns the largest value that the @c linear_congruential_engine
* can produce.
*/
static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return modulus-1; }
/** Returns the next value of the @c linear_congruential_engine. */
IntType operator()()
{
_x = const_mod<IntType, m>::mult_add(a, _x, c);
return _x;
}
/** 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)
{
typedef const_mod<IntType, m> mod_type;
IntType b_inv = mod_type::invert(a-1);
IntType b_gcd = mod_type::mult(a-1, b_inv);
if(b_gcd == 1) {
IntType a_z = mod_type::pow(a, z);
_x = mod_type::mult_add(a_z, _x,
mod_type::mult(mod_type::mult(c, b_inv), a_z - 1));
} else {
// compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd)
// we're storing the intermediate result / b_gcd
IntType a_zm1_over_gcd = 0;
IntType a_km1_over_gcd = (a - 1) / b_gcd;
boost::uintmax_t exponent = z;
while(exponent != 0) {
if(exponent % 2 == 1) {
a_zm1_over_gcd =
mod_type::mult_add(
b_gcd,
mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd),
mod_type::add(a_zm1_over_gcd, a_km1_over_gcd));
}
a_km1_over_gcd = mod_type::mult_add(
b_gcd,
mod_type::mult(a_km1_over_gcd, a_km1_over_gcd),
mod_type::add(a_km1_over_gcd, a_km1_over_gcd));
exponent /= 2;
}
IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1);
IntType num = mod_type::mult(c, a_zm1_over_gcd);
b_inv = mod_type::invert((a-1)/b_gcd);
_x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num));
}
}
friend bool operator==(const linear_congruential_engine& x,
const linear_congruential_engine& y)
{ return x._x == y._x; }
friend bool operator!=(const linear_congruential_engine& x,
const linear_congruential_engine& y)
{ return !(x == y); }
#if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS)
/** Writes a @c linear_congruential_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 linear_congruential_engine& lcg)
{
return os << lcg._x;
}
/** Reads a @c linear_congruential_engine from a @c std::istream. */
template<class CharT, class Traits>
friend std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& is,
linear_congruential_engine& lcg)
{
lcg.read(is);
return is;
}
#endif
private:
/// \cond show_private
template<class CharT, class Traits>
void read(std::basic_istream<CharT, Traits>& is) {
IntType x;
if(is >> x) {
if(x >= (min)() && x <= (max)()) {
_x = x;
} else {
is.setstate(std::ios_base::failbit);
}
}
}
/// \endcond
IntType _x;
};
#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
// A definition is required even for integral static constants
template<class IntType, IntType a, IntType c, IntType m>
const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range;
template<class IntType, IntType a, IntType c, IntType m>
const IntType linear_congruential_engine<IntType,a,c,m>::multiplier;
template<class IntType, IntType a, IntType c, IntType m>
const IntType linear_congruential_engine<IntType,a,c,m>::increment;
template<class IntType, IntType a, IntType c, IntType m>
const IntType linear_congruential_engine<IntType,a,c,m>::modulus;
template<class IntType, IntType a, IntType c, IntType m>
const IntType linear_congruential_engine<IntType,a,c,m>::default_seed;
#endif
/// \cond show_deprecated
// provided for backwards compatibility
template<class IntType, IntType a, IntType c, IntType m, IntType val = 0>
class linear_congruential : public linear_congruential_engine<IntType, a, c, m>
{
typedef linear_congruential_engine<IntType, a, c, m> base_type;
public:
linear_congruential(IntType x0 = 1) : base_type(x0) {}
template<class It>
linear_congruential(It& first, It last) : base_type(first, last) {}
};
/// \endcond
/**
* The specialization \minstd_rand0 was originally suggested in
*
* @blockquote
* A pseudo-random number generator for the System/360, P.A. Lewis,
* A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2,
* 1969, pp. 136-146
* @endblockquote
*
* It is examined more closely together with \minstd_rand in
*
* @blockquote
* "Random Number Generators: Good ones are hard to find",
* Stephen K. Park and Keith W. Miller, Communications of
* the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
* @endblockquote
*/
typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0;
/** The specialization \minstd_rand was suggested in
*
* @blockquote
* "Random Number Generators: Good ones are hard to find",
* Stephen K. Park and Keith W. Miller, Communications of
* the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
* @endblockquote
*/
typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand;
#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
/**
* Class @c rand48 models a \pseudo_random_number_generator. It uses
* the linear congruential algorithm with the parameters a = 0x5DEECE66D,
* c = 0xB, m = 2**48. It delivers identical results to the @c lrand48()
* function available on some systems (assuming lcong48 has not been called).
*
* It is only available on systems where @c uint64_t is provided as an
* integral type, so that for example static in-class constants and/or
* enum definitions with large @c uint64_t numbers work.
*/
class rand48
{
public:
typedef boost::uint32_t result_type;
BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
/**
* Returns the smallest value that the generator can produce
*/
static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
/**
* Returns the largest value that the generator can produce
*/
static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{ return 0x7FFFFFFF; }
/** Seeds the generator with the default seed. */
rand48() : lcf(cnv(static_cast<uint32_t>(1))) {}
/**
* Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e.
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0)
{ seed(x0); }
/**
* Seeds the generator with values produced by @c seq.generate().
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq)
{ seed(seq); }
/**
* Seeds the generator using values from an iterator range,
* and updates first to point one past the last value consumed.
*/
template<class It> rand48(It& first, It last) : lcf(first, last) { }
// compiler-generated copy ctor and assignment operator are fine
/** Seeds the generator with the default seed. */
void seed() { seed(static_cast<uint32_t>(1)); }
/**
* Changes the current value x(n) of the generator to (x0 << 16) | 0x330e.
*/
BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0)
{ lcf.seed(cnv(x0)); }
/**
* Seeds the generator using values from an iterator range,
* and updates first to point one past the last value consumed.
*/
template<class It> void seed(It& first, It last) { lcf.seed(first,last); }
/**
* Seeds the generator with values produced by @c seq.generate().
*/
BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq)
{ lcf.seed(seq); }
/** Returns the next value of the generator. */
uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); }
/** Advances the state of the generator by @c z. */
void discard(boost::uintmax_t z) { lcf.discard(z); }
/** Fills a range with random values */
template<class Iter>
void generate(Iter first, Iter last)
{
for(; first != last; ++first) {
*first = (*this)();
}
}
#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
/** Writes a @c rand48 to a @c std::ostream. */
template<class CharT,class Traits>
friend std::basic_ostream<CharT,Traits>&
operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r)
{ os << r.lcf; return os; }
/** Reads a @c rand48 from a @c std::istream. */
template<class CharT,class Traits>
friend std::basic_istream<CharT,Traits>&
operator>>(std::basic_istream<CharT,Traits>& is, rand48& r)
{ is >> r.lcf; return is; }
#endif
/**
* Returns true if the two generators will produce identical
* sequences of values.
*/
friend bool operator==(const rand48& x, const rand48& y)
{ return x.lcf == y.lcf; }
/**
* Returns true if the two generators will produce different
* sequences of values.
*/
friend bool operator!=(const rand48& x, const rand48& y)
{ return !(x == y); }
private:
/// \cond show_private
typedef random::linear_congruential_engine<uint64_t,
// xxxxULL is not portable
uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32),
0xB, uint64_t(1)<<48> lcf_t;
lcf_t lcf;
static boost::uint64_t cnv(boost::uint32_t x)
{ return (static_cast<uint64_t>(x) << 16) | 0x330e; }
/// \endcond
};
#endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */
} // namespace random
using random::minstd_rand0;
using random::minstd_rand;
using random::rand48;
} // namespace boost
#include <boost/random/detail/enable_warnings.hpp>
#endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP