boost/random/uniform_int_distribution.hpp
/* 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/type_traits/make_unsigned.hpp>
#include <boost/type_traits/is_integral.hpp>
#include <boost/mpl/bool.hpp>
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 make_unsigned<T>::type range_type;
typedef typename Engine::result_type base_result;
// ranges are always unsigned
typedef typename make_unsigned<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>(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>::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
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::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