467 lines
16 KiB
C++
467 lines
16 KiB
C++
/* boost random/linear_congruential.hpp header file
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*
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* Copyright Jens Maurer 2000-2001
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*
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* See http://www.boost.org for most recent version including documentation.
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*
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* $Id$
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*
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* Revision history
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* 2001-02-18 moved to individual header files
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*/
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#ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
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#define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
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#include <iostream>
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#include <stdexcept>
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#include <boost/assert.hpp>
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#include <boost/config.hpp>
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#include <boost/cstdint.hpp>
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#include <boost/limits.hpp>
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#include <boost/static_assert.hpp>
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#include <boost/integer/static_log2.hpp>
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#include <boost/mpl/if.hpp>
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#include <boost/type_traits/is_arithmetic.hpp>
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#include <boost/random/detail/config.hpp>
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#include <boost/random/detail/const_mod.hpp>
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#include <boost/random/detail/seed.hpp>
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#include <boost/random/detail/seed_impl.hpp>
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#include <boost/detail/workaround.hpp>
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#include <boost/random/detail/disable_warnings.hpp>
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namespace boost {
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namespace random {
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/**
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* Instantiations of class template linear_congruential_engine model a
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* \pseudo_random_number_generator. Linear congruential pseudo-random
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* number generators are described in:
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*
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* @blockquote
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* "Mathematical methods in large-scale computing units", D. H. Lehmer,
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* Proc. 2nd Symposium on Large-Scale Digital Calculating Machines,
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* Harvard University Press, 1951, pp. 141-146
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* @endblockquote
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*
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* Let x(n) denote the sequence of numbers returned by some pseudo-random
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* number generator. Then for the linear congruential generator,
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* x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are
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* x(0), a, c, m. The template parameter IntType shall denote an integral
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* type. It must be large enough to hold values a, c, and m. The template
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* parameters a and c must be smaller than m.
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*
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* Note: The quality of the generator crucially depends on the choice of
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* the parameters. User code should use one of the sensibly parameterized
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* generators such as minstd_rand instead.
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*/
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template<class IntType, IntType a, IntType c, IntType m>
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class linear_congruential_engine
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{
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public:
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typedef IntType result_type;
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// Required for old Boost.Random concept
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BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
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BOOST_STATIC_CONSTANT(IntType, multiplier = a);
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BOOST_STATIC_CONSTANT(IntType, increment = c);
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BOOST_STATIC_CONSTANT(IntType, modulus = m);
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BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
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BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer);
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BOOST_STATIC_ASSERT(m == 0 || a < m);
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BOOST_STATIC_ASSERT(m == 0 || c < m);
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/**
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* Constructs a @c linear_congruential_engine, using the default seed
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*/
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linear_congruential_engine() { seed(); }
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/**
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* Constructs a @c linear_congruential_engine, seeding it with @c x0.
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine,
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IntType, x0)
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{ seed(x0); }
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/**
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* Constructs a @c linear_congruential_engine, seeding it with values
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* produced by a call to @c seq.generate().
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*/
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BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine,
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SeedSeq, seq)
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{ seed(seq); }
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/**
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* Constructs a @c linear_congruential_engine and seeds it
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* with values taken from the itrator range [first, last)
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* and adjusts first to point to the element after the last one
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* used. If there are not enough elements, throws @c std::invalid_argument.
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*
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* first and last must be input iterators.
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*/
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template<class It>
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linear_congruential_engine(It& first, It last)
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{
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seed(first, last);
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}
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// compiler-generated copy constructor and assignment operator are fine
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/**
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* Calls seed(default_seed)
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*/
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void seed() { seed(default_seed); }
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/**
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* If c mod m is zero and x0 mod m is zero, changes the current value of
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* the generator to 1. Otherwise, changes it to x0 mod m. If c is zero,
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* distinct seeds in the range [1,m) will leave the generator in distinct
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* states. If c is not zero, the range is [0,m).
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0)
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{
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// wrap _x if it doesn't fit in the destination
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if(modulus == 0) {
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_x = x0;
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} else {
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_x = x0 % modulus;
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}
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// handle negative seeds
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if(_x <= 0 && _x != 0) {
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_x += modulus;
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}
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// adjust to the correct range
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if(increment == 0 && _x == 0) {
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_x = 1;
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}
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BOOST_ASSERT(_x >= (min)());
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BOOST_ASSERT(_x <= (max)());
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}
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/**
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* Seeds a @c linear_congruential_engine using values from a SeedSeq.
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*/
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BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq)
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{ seed(detail::seed_one_int<IntType, m>(seq)); }
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/**
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* seeds a @c linear_congruential_engine with values taken
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* from the itrator range [first, last) and adjusts @c first to
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* point to the element after the last one used. If there are
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* not enough elements, throws @c std::invalid_argument.
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*
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* @c first and @c last must be input iterators.
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*/
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template<class It>
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void seed(It& first, It last)
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{ seed(detail::get_one_int<IntType, m>(first, last)); }
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/**
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* Returns the smallest value that the @c linear_congruential_engine
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* can produce.
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*/
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static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
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{ return c == 0 ? 1 : 0; }
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/**
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* Returns the largest value that the @c linear_congruential_engine
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* can produce.
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*/
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static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
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{ return modulus-1; }
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/** Returns the next value of the @c linear_congruential_engine. */
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IntType operator()()
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{
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_x = const_mod<IntType, m>::mult_add(a, _x, c);
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return _x;
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}
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/** Fills a range with random values */
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template<class Iter>
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void generate(Iter first, Iter last)
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{ detail::generate_from_int(*this, first, last); }
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/** Advances the state of the generator by @c z. */
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void discard(boost::uintmax_t z)
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{
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typedef const_mod<IntType, m> mod_type;
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IntType b_inv = mod_type::invert(a-1);
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IntType b_gcd = mod_type::mult(a-1, b_inv);
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if(b_gcd == 1) {
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IntType a_z = mod_type::pow(a, z);
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_x = mod_type::mult_add(a_z, _x,
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mod_type::mult(mod_type::mult(c, b_inv), a_z - 1));
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} else {
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// compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd)
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// we're storing the intermediate result / b_gcd
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IntType a_zm1_over_gcd = 0;
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IntType a_km1_over_gcd = (a - 1) / b_gcd;
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boost::uintmax_t exponent = z;
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while(exponent != 0) {
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if(exponent % 2 == 1) {
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a_zm1_over_gcd =
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mod_type::mult_add(
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b_gcd,
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mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd),
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mod_type::add(a_zm1_over_gcd, a_km1_over_gcd));
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}
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a_km1_over_gcd = mod_type::mult_add(
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b_gcd,
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mod_type::mult(a_km1_over_gcd, a_km1_over_gcd),
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mod_type::add(a_km1_over_gcd, a_km1_over_gcd));
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exponent /= 2;
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}
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IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1);
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IntType num = mod_type::mult(c, a_zm1_over_gcd);
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b_inv = mod_type::invert((a-1)/b_gcd);
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_x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num));
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}
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}
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friend bool operator==(const linear_congruential_engine& x,
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const linear_congruential_engine& y)
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{ return x._x == y._x; }
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friend bool operator!=(const linear_congruential_engine& x,
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const linear_congruential_engine& y)
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{ return !(x == y); }
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#if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS)
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/** Writes a @c linear_congruential_engine to a @c std::ostream. */
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template<class CharT, class Traits>
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friend std::basic_ostream<CharT,Traits>&
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operator<<(std::basic_ostream<CharT,Traits>& os,
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const linear_congruential_engine& lcg)
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{
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return os << lcg._x;
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}
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/** Reads a @c linear_congruential_engine from a @c std::istream. */
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template<class CharT, class Traits>
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friend std::basic_istream<CharT,Traits>&
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operator>>(std::basic_istream<CharT,Traits>& is,
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linear_congruential_engine& lcg)
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{
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lcg.read(is);
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return is;
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}
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#endif
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private:
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/// \cond show_private
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template<class CharT, class Traits>
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void read(std::basic_istream<CharT, Traits>& is) {
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IntType x;
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if(is >> x) {
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if(x >= (min)() && x <= (max)()) {
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_x = x;
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} else {
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is.setstate(std::ios_base::failbit);
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}
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}
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}
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/// \endcond
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IntType _x;
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};
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#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
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// A definition is required even for integral static constants
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template<class IntType, IntType a, IntType c, IntType m>
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const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range;
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template<class IntType, IntType a, IntType c, IntType m>
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const IntType linear_congruential_engine<IntType,a,c,m>::multiplier;
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template<class IntType, IntType a, IntType c, IntType m>
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const IntType linear_congruential_engine<IntType,a,c,m>::increment;
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template<class IntType, IntType a, IntType c, IntType m>
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const IntType linear_congruential_engine<IntType,a,c,m>::modulus;
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template<class IntType, IntType a, IntType c, IntType m>
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const IntType linear_congruential_engine<IntType,a,c,m>::default_seed;
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#endif
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/// \cond show_deprecated
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// provided for backwards compatibility
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template<class IntType, IntType a, IntType c, IntType m, IntType val = 0>
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class linear_congruential : public linear_congruential_engine<IntType, a, c, m>
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{
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typedef linear_congruential_engine<IntType, a, c, m> base_type;
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public:
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linear_congruential(IntType x0 = 1) : base_type(x0) {}
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template<class It>
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linear_congruential(It& first, It last) : base_type(first, last) {}
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};
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/// \endcond
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/**
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* The specialization \minstd_rand0 was originally suggested in
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*
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* @blockquote
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* A pseudo-random number generator for the System/360, P.A. Lewis,
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* A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2,
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* 1969, pp. 136-146
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* @endblockquote
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*
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* It is examined more closely together with \minstd_rand in
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*
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* @blockquote
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* "Random Number Generators: Good ones are hard to find",
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* Stephen K. Park and Keith W. Miller, Communications of
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* the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
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* @endblockquote
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*/
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typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0;
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/** The specialization \minstd_rand was suggested in
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*
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* @blockquote
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* "Random Number Generators: Good ones are hard to find",
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* Stephen K. Park and Keith W. Miller, Communications of
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* the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
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* @endblockquote
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*/
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typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand;
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#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
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/**
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* Class @c rand48 models a \pseudo_random_number_generator. It uses
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* the linear congruential algorithm with the parameters a = 0x5DEECE66D,
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* c = 0xB, m = 2**48. It delivers identical results to the @c lrand48()
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* function available on some systems (assuming lcong48 has not been called).
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*
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* It is only available on systems where @c uint64_t is provided as an
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* integral type, so that for example static in-class constants and/or
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* enum definitions with large @c uint64_t numbers work.
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*/
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class rand48
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{
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public:
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typedef boost::uint32_t result_type;
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BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
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/**
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* Returns the smallest value that the generator can produce
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*/
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static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
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/**
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* Returns the largest value that the generator can produce
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*/
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static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION ()
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{ return 0x7FFFFFFF; }
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/** Seeds the generator with the default seed. */
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rand48() : lcf(cnv(static_cast<uint32_t>(1))) {}
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/**
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* Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e.
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0)
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{ seed(x0); }
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/**
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* Seeds the generator with values produced by @c seq.generate().
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*/
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BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq)
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{ seed(seq); }
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/**
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* Seeds the generator using values from an iterator range,
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* and updates first to point one past the last value consumed.
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*/
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template<class It> rand48(It& first, It last) : lcf(first, last) { }
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// compiler-generated copy ctor and assignment operator are fine
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/** Seeds the generator with the default seed. */
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void seed() { seed(static_cast<uint32_t>(1)); }
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/**
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* Changes the current value x(n) of the generator to (x0 << 16) | 0x330e.
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*/
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BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0)
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{ lcf.seed(cnv(x0)); }
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/**
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* Seeds the generator using values from an iterator range,
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* and updates first to point one past the last value consumed.
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*/
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template<class It> void seed(It& first, It last) { lcf.seed(first,last); }
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/**
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* Seeds the generator with values produced by @c seq.generate().
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*/
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BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq)
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{ lcf.seed(seq); }
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/** Returns the next value of the generator. */
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uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); }
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/** Advances the state of the generator by @c z. */
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void discard(boost::uintmax_t z) { lcf.discard(z); }
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/** Fills a range with random values */
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template<class Iter>
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void generate(Iter first, Iter last)
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{
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for(; first != last; ++first) {
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*first = (*this)();
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}
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}
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#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
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/** Writes a @c rand48 to a @c std::ostream. */
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template<class CharT,class Traits>
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friend std::basic_ostream<CharT,Traits>&
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operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r)
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{ os << r.lcf; return os; }
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/** Reads a @c rand48 from a @c std::istream. */
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template<class CharT,class Traits>
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friend std::basic_istream<CharT,Traits>&
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operator>>(std::basic_istream<CharT,Traits>& is, rand48& r)
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{ is >> r.lcf; return is; }
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#endif
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/**
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* Returns true if the two generators will produce identical
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* sequences of values.
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*/
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friend bool operator==(const rand48& x, const rand48& y)
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{ return x.lcf == y.lcf; }
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/**
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* Returns true if the two generators will produce different
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* sequences of values.
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*/
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friend bool operator!=(const rand48& x, const rand48& y)
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{ return !(x == y); }
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private:
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/// \cond show_private
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typedef random::linear_congruential_engine<uint64_t,
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// xxxxULL is not portable
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uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32),
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0xB, uint64_t(1)<<48> lcf_t;
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lcf_t lcf;
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static boost::uint64_t cnv(boost::uint32_t x)
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{ return (static_cast<uint64_t>(x) << 16) | 0x330e; }
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/// \endcond
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};
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#endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */
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} // namespace random
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using random::minstd_rand0;
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using random::minstd_rand;
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using random::rand48;
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} // namespace boost
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#include <boost/random/detail/enable_warnings.hpp>
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#endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
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