boost/random/uniform_int.hpp
/* boost random/uniform_int.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: uniform_int.hpp 60755 2010-03-22 00:45:06Z steven_watanabe $ * * Revision history * 2001-04-08 added min<max assertion (N. Becker) * 2001-02-18 moved to individual header files */ #ifndef BOOST_RANDOM_UNIFORM_INT_HPP #define BOOST_RANDOM_UNIFORM_INT_HPP #include <cassert> #include <iostream> #include <boost/config.hpp> #include <boost/limits.hpp> #include <boost/static_assert.hpp> #include <boost/detail/workaround.hpp> #include <boost/random/detail/config.hpp> #include <boost/random/detail/signed_unsigned_tools.hpp> #include <boost/type_traits/make_unsigned.hpp> namespace boost { /** * The distribution function uniform_int models a \random_distribution. * On each invocation, it returns a random integer value uniformly * distributed in the set of integer numbers {min, min+1, min+2, ..., max}. * * The template parameter IntType shall denote an integer-like value type. */ template<class IntType = int> class uniform_int { public: typedef IntType input_type; typedef IntType result_type; /// \cond hide_private_members typedef typename make_unsigned<result_type>::type range_type; /// \endcond /** * Constructs a uniform_int object. @c min and @c max are * the parameters of the distribution. * * Requires: min <= max */ explicit uniform_int(IntType min_arg = 0, IntType max_arg = 9) : _min(min_arg), _max(max_arg) { #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS // MSVC fails BOOST_STATIC_ASSERT with std::numeric_limits at class scope BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer); #endif assert(min_arg <= max_arg); init(); } /** * Returns: The "min" parameter of the distribution */ result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; } /** * Returns: The "max" parameter of the distribution */ result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; } void reset() { } // can't have member function templates out-of-line due to MSVC bugs template<class Engine> result_type operator()(Engine& eng) { return generate(eng, _min, _max, _range); } template<class Engine> result_type operator()(Engine& eng, result_type n) { assert(n > 0); if (n == 1) { return 0; } return generate(eng, 0, n - 1, n - 1); } #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS template<class CharT, class Traits> friend std::basic_ostream<CharT,Traits>& operator<<(std::basic_ostream<CharT,Traits>& os, const uniform_int& ud) { os << ud._min << " " << ud._max; return os; } template<class CharT, class Traits> friend std::basic_istream<CharT,Traits>& operator>>(std::basic_istream<CharT,Traits>& is, uniform_int& ud) { is >> std::ws >> ud._min >> std::ws >> ud._max; ud.init(); return is; } #endif private: #ifdef BOOST_MSVC #pragma warning(push) // disable division by zero warning, since we can't // actually divide by zero. #pragma warning(disable:4723) #endif /// \cond hide_private_members template<class Engine> static result_type generate(Engine& eng, result_type min_value, result_type /*max_value*/, range_type range) { typedef typename Engine::result_type base_result; // ranges are always unsigned typedef typename make_unsigned<base_result>::type base_unsigned; 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>(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 = uniform_int<range_type>(0, range/mult)(eng); if((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 base_unsigned 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. if(brange == (std::numeric_limits<base_unsigned>::max)()) { bucket_size = brange / (static_cast<base_unsigned>(range)+1); if(brange % (static_cast<base_unsigned>(range)+1) == static_cast<base_unsigned>(range)) { ++bucket_size; } } else { bucket_size = (brange+1) / (static_cast<base_unsigned>(range)+1); } for(;;) { base_unsigned 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<base_unsigned>(range)) return random::detail::add<base_unsigned, result_type>()(result, min_value); } } } #ifdef BOOST_MSVC #pragma warning(pop) #endif void init() { _range = random::detail::subtract<result_type>()(_max, _min); } /// \endcond // The result_type may be signed or unsigned, but the _range is always // unsigned. result_type _min, _max; range_type _range; }; } // namespace boost #endif // BOOST_RANDOM_UNIFORM_INT_HPP