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-/* boost random/uniform_int_distribution.hpp header file
- *
- * Copyright Jens Maurer 2000-2001
- * Copyright Steven Watanabe 2011
- * 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
- * 2001-04-08 added min<max assertion (N. Becker)
- * 2001-02-18 moved to individual header files
- */
-
-#ifndef BOOST_RANDOM_UNIFORM_INT_DISTRIBUTION_HPP
-#define BOOST_RANDOM_UNIFORM_INT_DISTRIBUTION_HPP
-
-#include <iosfwd>
-#include <ios>
-#include <istream>
-#include <boost/config.hpp>
-#include <boost/limits.hpp>
-#include <boost/assert.hpp>
-#include <boost/random/detail/config.hpp>
-#include <boost/random/detail/operators.hpp>
-#include <boost/random/detail/uniform_int_float.hpp>
-#include <boost/random/detail/signed_unsigned_tools.hpp>
-#include <boost/random/traits.hpp>
-#include <boost/mpl/bool.hpp>
-#ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
-#include <boost/mpl/if.hpp>
-#endif
-
-namespace boost {
-namespace random {
-namespace detail {
-
-
-#ifdef BOOST_MSVC
-#pragma warning(push)
-// disable division by zero warning, since we can't
-// actually divide by zero.
-#pragma warning(disable:4723)
-#endif
-
-template<class Engine, class T>
-T generate_uniform_int(
- Engine& eng, T min_value, T max_value,
- boost::mpl::true_ /** is_integral<Engine::result_type> */)
-{
- typedef T result_type;
- typedef typename boost::random::traits::make_unsigned_or_unbounded<T>::type range_type;
- typedef typename Engine::result_type base_result;
- // ranges are always unsigned or unbounded
- typedef typename boost::random::traits::make_unsigned_or_unbounded<base_result>::type base_unsigned;
- const range_type range = random::detail::subtract<result_type>()(max_value, min_value);
- const base_result bmin = (eng.min)();
- const base_unsigned brange =
- random::detail::subtract<base_result>()((eng.max)(), (eng.min)());
-
- if(range == 0) {
- return min_value;
- } else if(brange == range) {
- // this will probably never happen in real life
- // basically nothing to do; just take care we don't overflow / underflow
- base_unsigned v = random::detail::subtract<base_result>()(eng(), bmin);
- return random::detail::add<base_unsigned, result_type>()(v, min_value);
- } else if(brange < range) {
- // use rejection method to handle things like 0..3 --> 0..4
- for(;;) {
- // concatenate several invocations of the base RNG
- // take extra care to avoid overflows
-
- // limit == floor((range+1)/(brange+1))
- // Therefore limit*(brange+1) <= range+1
- range_type limit;
- if(range == (std::numeric_limits<range_type>::max)()) {
- limit = range/(range_type(brange)+1);
- if(range % (range_type(brange)+1) == range_type(brange))
- ++limit;
- } else {
- limit = (range+1)/(range_type(brange)+1);
- }
-
- // We consider "result" as expressed to base (brange+1):
- // For every power of (brange+1), we determine a random factor
- range_type result = range_type(0);
- range_type mult = range_type(1);
-
- // loop invariants:
- // result < mult
- // mult <= range
- while(mult <= limit) {
- // Postcondition: result <= range, thus no overflow
- //
- // limit*(brange+1)<=range+1 def. of limit (1)
- // eng()-bmin<=brange eng() post. (2)
- // and mult<=limit. loop condition (3)
- // Therefore mult*(eng()-bmin+1)<=range+1 by (1),(2),(3) (4)
- // Therefore mult*(eng()-bmin)+mult<=range+1 rearranging (4) (5)
- // result<mult loop invariant (6)
- // Therefore result+mult*(eng()-bmin)<range+1 by (5), (6) (7)
- //
- // Postcondition: result < mult*(brange+1)
- //
- // result<mult loop invariant (1)
- // eng()-bmin<=brange eng() post. (2)
- // Therefore result+mult*(eng()-bmin) <
- // mult+mult*(eng()-bmin) by (1) (3)
- // Therefore result+(eng()-bmin)*mult <
- // mult+mult*brange by (2), (3) (4)
- // Therefore result+(eng()-bmin)*mult <
- // mult*(brange+1) by (4)
- result += static_cast<range_type>(static_cast<range_type>(random::detail::subtract<base_result>()(eng(), bmin)) * mult);
-
- // equivalent to (mult * (brange+1)) == range+1, but avoids overflow.
- if(mult * range_type(brange) == range - mult + 1) {
- // The destination range is an integer power of
- // the generator's range.
- return(result);
- }
-
- // Postcondition: mult <= range
- //
- // limit*(brange+1)<=range+1 def. of limit (1)
- // mult<=limit loop condition (2)
- // Therefore mult*(brange+1)<=range+1 by (1), (2) (3)
- // mult*(brange+1)!=range+1 preceding if (4)
- // Therefore mult*(brange+1)<range+1 by (3), (4) (5)
- //
- // Postcondition: result < mult
- //
- // See the second postcondition on the change to result.
- mult *= range_type(brange)+range_type(1);
- }
- // loop postcondition: range/mult < brange+1
- //
- // mult > limit loop condition (1)
- // Suppose range/mult >= brange+1 Assumption (2)
- // range >= mult*(brange+1) by (2) (3)
- // range+1 > mult*(brange+1) by (3) (4)
- // range+1 > (limit+1)*(brange+1) by (1), (4) (5)
- // (range+1)/(brange+1) > limit+1 by (5) (6)
- // limit < floor((range+1)/(brange+1)) by (6) (7)
- // limit==floor((range+1)/(brange+1)) def. of limit (8)
- // not (2) reductio (9)
- //
- // loop postcondition: (range/mult)*mult+(mult-1) >= range
- //
- // (range/mult)*mult + range%mult == range identity (1)
- // range%mult < mult def. of % (2)
- // (range/mult)*mult+mult > range by (1), (2) (3)
- // (range/mult)*mult+(mult-1) >= range by (3) (4)
- //
- // Note that the maximum value of result at this point is (mult-1),
- // so after this final step, we generate numbers that can be
- // at least as large as range. We have to really careful to avoid
- // overflow in this final addition and in the rejection. Anything
- // that overflows is larger than range and can thus be rejected.
-
- // range/mult < brange+1 -> no endless loop
- range_type result_increment =
- generate_uniform_int(
- eng,
- static_cast<range_type>(0),
- static_cast<range_type>(range/mult),
- boost::mpl::true_());
- if(std::numeric_limits<range_type>::is_bounded && ((std::numeric_limits<range_type>::max)() / mult < result_increment)) {
- // The multiplcation would overflow. Reject immediately.
- continue;
- }
- result_increment *= mult;
- // unsigned integers are guaranteed to wrap on overflow.
- result += result_increment;
- if(result < result_increment) {
- // The addition overflowed. Reject.
- continue;
- }
- if(result > range) {
- // Too big. Reject.
- continue;
- }
- return random::detail::add<range_type, result_type>()(result, min_value);
- }
- } else { // brange > range
-#ifdef BOOST_NO_CXX11_EXPLICIT_CONVERSION_OPERATORS
- typedef typename mpl::if_c<
- std::numeric_limits<range_type>::is_specialized && std::numeric_limits<base_unsigned>::is_specialized
- && (std::numeric_limits<range_type>::digits >= std::numeric_limits<base_unsigned>::digits),
- range_type, base_unsigned>::type mixed_range_type;
-#else
- typedef base_unsigned mixed_range_type;
-#endif
-
- mixed_range_type bucket_size;
- // it's safe to add 1 to range, as long as we cast it first,
- // because we know that it is less than brange. However,
- // we do need to be careful not to cause overflow by adding 1
- // to brange. We use mixed_range_type throughout for mixed
- // arithmetic between base_unsigned and range_type - in the case
- // that range_type has more bits than base_unsigned it is always
- // safe to use range_type for this albeit it may be more effient
- // to use base_unsigned. The latter is a narrowing conversion though
- // which may be disallowed if range_type is a multiprecision type
- // and there are no explicit converison operators.
-
- if(brange == (std::numeric_limits<base_unsigned>::max)()) {
- bucket_size = static_cast<mixed_range_type>(brange) / (static_cast<mixed_range_type>(range)+1);
- if(static_cast<mixed_range_type>(brange) % (static_cast<mixed_range_type>(range)+1) == static_cast<mixed_range_type>(range)) {
- ++bucket_size;
- }
- } else {
- bucket_size = static_cast<mixed_range_type>(brange + 1) / (static_cast<mixed_range_type>(range)+1);
- }
- for(;;) {
- mixed_range_type result =
- random::detail::subtract<base_result>()(eng(), bmin);
- result /= bucket_size;
- // result and range are non-negative, and result is possibly larger
- // than range, so the cast is safe
- if(result <= static_cast<mixed_range_type>(range))
- return random::detail::add<mixed_range_type, result_type>()(result, min_value);
- }
- }
-}
-
-#ifdef BOOST_MSVC
-#pragma warning(pop)
-#endif
-
-template<class Engine, class T>
-inline T generate_uniform_int(
- Engine& eng, T min_value, T max_value,
- boost::mpl::false_ /** is_integral<Engine::result_type> */)
-{
- uniform_int_float<Engine> wrapper(eng);
- return generate_uniform_int(wrapper, min_value, max_value, boost::mpl::true_());
-}
-
-template<class Engine, class T>
-inline T generate_uniform_int(Engine& eng, T min_value, T max_value)
-{
- typedef typename Engine::result_type base_result;
- return generate_uniform_int(eng, min_value, max_value,
- boost::random::traits::is_integral<base_result>());
-}
-
-}
-
-/**
- * The class template uniform_int_distribution models a \random_distribution.
- * On each invocation, it returns a random integer value uniformly
- * distributed in the set of integers {min, min+1, min+2, ..., max}.
- *
- * The template parameter IntType shall denote an integer-like value type.
- */
-template<class IntType = int>
-class uniform_int_distribution
-{
-public:
- typedef IntType input_type;
- typedef IntType result_type;
-
- class param_type
- {
- public:
-
- typedef uniform_int_distribution distribution_type;
-
- /**
- * Constructs the parameters of a uniform_int_distribution.
- *
- * Requires min <= max
- */
- explicit param_type(
- IntType min_arg = 0,
- IntType max_arg = (std::numeric_limits<IntType>::max)())
- : _min(min_arg), _max(max_arg)
- {
- BOOST_ASSERT(_min <= _max);
- }
-
- /** Returns the minimum value of the distribution. */
- IntType a() const { return _min; }
- /** Returns the maximum value of the distribution. */
- IntType b() const { return _max; }
-
- /** Writes the parameters to a @c std::ostream. */
- BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm)
- {
- os << parm._min << " " << parm._max;
- return os;
- }
-
- /** Reads the parameters from a @c std::istream. */
- BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm)
- {
- IntType min_in, max_in;
- if(is >> min_in >> std::ws >> max_in) {
- if(min_in <= max_in) {
- parm._min = min_in;
- parm._max = max_in;
- } else {
- is.setstate(std::ios_base::failbit);
- }
- }
- return is;
- }
-
- /** Returns true if the two sets of parameters are equal. */
- BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs)
- { return lhs._min == rhs._min && lhs._max == rhs._max; }
-
- /** Returns true if the two sets of parameters are different. */
- BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type)
-
- private:
-
- IntType _min;
- IntType _max;
- };
-
- /**
- * Constructs a uniform_int_distribution. @c min and @c max are
- * the parameters of the distribution.
- *
- * Requires: min <= max
- */
- explicit uniform_int_distribution(
- IntType min_arg = 0,
- IntType max_arg = (std::numeric_limits<IntType>::max)())
- : _min(min_arg), _max(max_arg)
- {
- BOOST_ASSERT(min_arg <= max_arg);
- }
- /** Constructs a uniform_int_distribution from its parameters. */
- explicit uniform_int_distribution(const param_type& parm)
- : _min(parm.a()), _max(parm.b()) {}
-
- /** Returns the minimum value of the distribution */
- IntType min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; }
- /** Returns the maximum value of the distribution */
- IntType max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; }
-
- /** Returns the minimum value of the distribution */
- IntType a() const { return _min; }
- /** Returns the maximum value of the distribution */
- IntType b() const { return _max; }
-
- /** Returns the parameters of the distribution. */
- param_type param() const { return param_type(_min, _max); }
- /** Sets the parameters of the distribution. */
- void param(const param_type& parm)
- {
- _min = parm.a();
- _max = parm.b();
- }
-
- /**
- * Effects: Subsequent uses of the distribution do not depend
- * on values produced by any engine prior to invoking reset.
- */
- void reset() { }
-
- /** Returns an integer uniformly distributed in the range [min, max]. */
- template<class Engine>
- result_type operator()(Engine& eng) const
- { return detail::generate_uniform_int(eng, _min, _max); }
-
- /**
- * Returns an integer uniformly distributed in the range
- * [param.a(), param.b()].
- */
- template<class Engine>
- result_type operator()(Engine& eng, const param_type& parm) const
- { return detail::generate_uniform_int(eng, parm.a(), parm.b()); }
-
- /** Writes the distribution to a @c std::ostream. */
- BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_int_distribution, ud)
- {
- os << ud.param();
- return os;
- }
-
- /** Reads the distribution from a @c std::istream. */
- BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_int_distribution, ud)
- {
- param_type parm;
- if(is >> parm) {
- ud.param(parm);
- }
- return is;
- }
-
- /**
- * Returns true if the two distributions will produce identical sequences
- * of values given equal generators.
- */
- BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_int_distribution, lhs, rhs)
- { return lhs._min == rhs._min && lhs._max == rhs._max; }
-
- /**
- * Returns true if the two distributions may produce different sequences
- * of values given equal generators.
- */
- BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_int_distribution)
-
-private:
- IntType _min;
- IntType _max;
-};
-
-} // namespace random
-} // namespace boost
-
-#endif // BOOST_RANDOM_UNIFORM_INT_HPP