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[mathpart gcd_lcm Integer Utilities (Greatest Common Divisor and Least Common Multiple)]
[section Introduction]
The class and function templates in <boost/math/common_factor.hpp>
provide run-time and compile-time evaluation of the greatest common divisor
(GCD) or least common multiple (LCM) of two integers.
These facilities are useful for many numeric-oriented generic
programming problems.
[endsect]
[section Synopsis]
namespace boost
{
namespace math
{
template < typename IntegerType >
class gcd_evaluator;
template < typename IntegerType >
class lcm_evaluator;
template < typename IntegerType >
IntegerType gcd( IntegerType const &a, IntegerType const &b );
template < typename IntegerType >
IntegerType lcm( IntegerType const &a, IntegerType const &b );
typedef ``['see-below]`` static_gcd_type;
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_gcd;
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_lcm;
}
}
[endsect]
[section GCD Function Object]
[*Header: ] [@../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
template < typename IntegerType >
class boost::math::gcd_evaluator
{
public:
// Types
typedef IntegerType result_type;
typedef IntegerType first_argument_type;
typedef IntegerType second_argument_type;
// Function object interface
result_type operator ()( first_argument_type const &a,
second_argument_type const &b ) const;
};
The boost::math::gcd_evaluator class template defines a function object
class to return the greatest common divisor of two integers.
The template is parameterized by a single type, called IntegerType here.
This type should be a numeric type that represents integers.
The result of the function object is always nonnegative, even if either of
the operator arguments is negative.
This function object class template is used in the corresponding version of
the GCD function template. If a numeric type wants to customize evaluations
of its greatest common divisors, then the type should specialize on the
gcd_evaluator class template.
[endsect]
[section LCM Function Object]
[*Header: ] [@../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
template < typename IntegerType >
class boost::math::lcm_evaluator
{
public:
// Types
typedef IntegerType result_type;
typedef IntegerType first_argument_type;
typedef IntegerType second_argument_type;
// Function object interface
result_type operator ()( first_argument_type const &a,
second_argument_type const &b ) const;
};
The boost::math::lcm_evaluator class template defines a function object
class to return the least common multiple of two integers. The template
is parameterized by a single type, called IntegerType here. This type
should be a numeric type that represents integers. The result of the
function object is always nonnegative, even if either of the operator
arguments is negative. If the least common multiple is beyond the range
of the integer type, the results are undefined.
This function object class template is used in the corresponding version
of the LCM function template. If a numeric type wants to customize
evaluations of its least common multiples, then the type should
specialize on the lcm_evaluator class template.
[endsect]
[section:run_time Run-time GCD & LCM Determination]
[*Header: ] [@../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>]
template < typename IntegerType >
IntegerType boost::math::gcd( IntegerType const &a, IntegerType const &b );
template < typename IntegerType >
IntegerType boost::math::lcm( IntegerType const &a, IntegerType const &b );
The boost::math::gcd function template returns the greatest common
(nonnegative) divisor of the two integers passed to it.
The boost::math::lcm function template returns the least common
(nonnegative) multiple of the two integers passed to it.
The function templates are parameterized on the function arguments'
IntegerType, which is also the return type. Internally, these function
templates use an object of the corresponding version of the
gcd_evaluator and lcm_evaluator class templates, respectively.
[endsect]
[section:compile_time Compile time GCD and LCM determination]
[*Header: ] [@../../../../boost/math/common_factor_ct.hpp <boost/math/common_factor_ct.hpp>]
typedef ``['unspecified]`` static_gcd_type;
template < static_gcd_type Value1, static_gcd_type Value2 >
struct boost::math::static_gcd : public mpl::integral_c<static_gcd_type, implementation_defined>
{
};
template < static_gcd_type Value1, static_gcd_type Value2 >
struct boost::math::static_lcm : public mpl::integral_c<static_gcd_type, implementation_defined>
{
};
The type `static_gcd_type` is the widest unsigned-integer-type that is supported
for use in integral-constant-expressions by the compiler. Usually this
the same type as `boost::uintmax_t`, but may fall back to being `unsigned long`
for some older compilers.
The boost::math::static_gcd and boost::math::static_lcm class templates
take two value-based template parameters of the ['static_gcd_type] type
and inherit from the type `boost::mpl::integral_c`.
Inherited from the base class, they have a member /value/
that is the greatest common factor or least
common multiple, respectively, of the template arguments.
A compile-time error will occur if the least common multiple
is beyond the range of `static_gcd_type`.
[h3 Example]
#include <boost/math/common_factor.hpp>
#include <algorithm>
#include <iterator>
#include <iostream>
int main()
{
using std::cout;
using std::endl;
cout << "The GCD and LCM of 6 and 15 are "
<< boost::math::gcd(6, 15) << " and "
<< boost::math::lcm(6, 15) << ", respectively."
<< endl;
cout << "The GCD and LCM of 8 and 9 are "
<< boost::math::static_gcd<8, 9>::value
<< " and "
<< boost::math::static_lcm<8, 9>::value
<< ", respectively." << endl;
int a[] = { 4, 5, 6 }, b[] = { 7, 8, 9 }, c[3];
std::transform( a, a + 3, b, c, boost::math::gcd_evaluator<int>() );
std::copy( c, c + 3, std::ostream_iterator<int>(cout, " ") );
}
[endsect]
[section:gcd_header Header <boost/math/common_factor.hpp>]
This header simply includes the headers
[@../../../../boost/math/common_factor_ct.hpp <boost/math/common_factor_ct.hpp>]
and [@../../../../boost/math/common_factor_rt.hpp <boost/math/common_factor_rt.hpp>].
Note this is a legacy header: it used to contain the actual implementation,
but the compile-time and run-time facilities
were moved to separate headers (since they were independent of each other).
[endsect]
[section:demo Demonstration Program]
The program [@../../../../libs/math/test/common_factor_test.cpp common_factor_test.cpp] is a demonstration of the results from
instantiating various examples of the run-time GCD and LCM function
templates and the compile-time GCD and LCM class templates.
(The run-time GCD and LCM class templates are tested indirectly through
the run-time function templates.)
[endsect]
[section Rationale]
The greatest common divisor and least common multiple functions are
greatly used in some numeric contexts, including some of the other
Boost libraries. Centralizing these functions to one header improves
code factoring and eases maintainence.
[endsect]
[section:gcd_history History]
* 13 May 2013 Moved into main Boost.Math Quickbook documentation.
* 17 Dec 2005: Converted documentation to Quickbook Format.
* 2 Jul 2002: Compile-time and run-time items separated to new headers.
* 7 Nov 2001: Initial version
[endsect]
[section:gcd_credits Credits]
The author of the Boost compilation of GCD and LCM computations is
Daryle Walker. The code was prompted by existing code hiding in the
implementations of Paul Moore's rational library and Steve Cleary's
pool library. The code had updates by Helmut Zeisel.
[endsect]
[endmathpart]
[/
Copyright 2005, 2013 Daryle Walker.
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).
]

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// Boost common_factor.hpp header file -------------------------------------//
// (C) Copyright Daryle Walker 2001-2002.
// 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 updates, documentation, and revision history.
#ifndef BOOST_MATH_COMMON_FACTOR_HPP
#define BOOST_MATH_COMMON_FACTOR_HPP
#include <boost/math/common_factor_ct.hpp>
#include <boost/math/common_factor_rt.hpp>
#endif // BOOST_MATH_COMMON_FACTOR_HPP

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// Boost common_factor_ct.hpp header file ----------------------------------//
// (C) Copyright Daryle Walker and Stephen Cleary 2001-2002.
// 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 updates, documentation, and revision history.
#ifndef BOOST_MATH_COMMON_FACTOR_CT_HPP
#define BOOST_MATH_COMMON_FACTOR_CT_HPP
#include <boost/math_fwd.hpp> // self include
#include <boost/config.hpp> // for BOOST_STATIC_CONSTANT, etc.
#include <boost/mpl/integral_c.hpp>
namespace boost
{
namespace math
{
// Implementation details --------------------------------------------------//
namespace detail
{
// Build GCD with Euclid's recursive algorithm
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_gcd_helper_t
{
private:
BOOST_STATIC_CONSTANT( static_gcd_type, new_value1 = Value2 );
BOOST_STATIC_CONSTANT( static_gcd_type, new_value2 = Value1 % Value2 );
#ifndef __BORLANDC__
#define BOOST_DETAIL_GCD_HELPER_VAL(Value) static_cast<static_gcd_type>(Value)
#else
typedef static_gcd_helper_t self_type;
#define BOOST_DETAIL_GCD_HELPER_VAL(Value) (self_type:: Value )
#endif
typedef static_gcd_helper_t< BOOST_DETAIL_GCD_HELPER_VAL(new_value1),
BOOST_DETAIL_GCD_HELPER_VAL(new_value2) > next_step_type;
#undef BOOST_DETAIL_GCD_HELPER_VAL
public:
BOOST_STATIC_CONSTANT( static_gcd_type, value = next_step_type::value );
};
// Non-recursive case
template < static_gcd_type Value1 >
struct static_gcd_helper_t< Value1, 0UL >
{
BOOST_STATIC_CONSTANT( static_gcd_type, value = Value1 );
};
// Build the LCM from the GCD
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_lcm_helper_t
{
typedef static_gcd_helper_t<Value1, Value2> gcd_type;
BOOST_STATIC_CONSTANT( static_gcd_type, value = Value1 / gcd_type::value
* Value2 );
};
// Special case for zero-GCD values
template < >
struct static_lcm_helper_t< 0UL, 0UL >
{
BOOST_STATIC_CONSTANT( static_gcd_type, value = 0UL );
};
} // namespace detail
// Compile-time greatest common divisor evaluator class declaration --------//
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_gcd : public mpl::integral_c<static_gcd_type, (detail::static_gcd_helper_t<Value1, Value2>::value) >
{
}; // boost::math::static_gcd
// Compile-time least common multiple evaluator class declaration ----------//
template < static_gcd_type Value1, static_gcd_type Value2 >
struct static_lcm : public mpl::integral_c<static_gcd_type, (detail::static_lcm_helper_t<Value1, Value2>::value) >
{
}; // boost::math::static_lcm
} // namespace math
} // namespace boost
#endif // BOOST_MATH_COMMON_FACTOR_CT_HPP

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// Boost common_factor_rt.hpp header file ----------------------------------//
// (C) Copyright Daryle Walker and Paul Moore 2001-2002. Permission to copy,
// use, modify, sell and distribute this software is granted provided this
// copyright notice appears in all copies. This software is provided "as is"
// without express or implied warranty, and with no claim as to its suitability
// for any purpose.
// boostinspect:nolicense (don't complain about the lack of a Boost license)
// (Paul Moore hasn't been in contact for years, so there's no way to change the
// license.)
// See http://www.boost.org for updates, documentation, and revision history.
#ifndef BOOST_MATH_COMMON_FACTOR_RT_HPP
#define BOOST_MATH_COMMON_FACTOR_RT_HPP
#include <boost/math_fwd.hpp> // self include
#include <boost/config.hpp> // for BOOST_NESTED_TEMPLATE, etc.
#include <boost/limits.hpp> // for std::numeric_limits
#include <climits> // for CHAR_MIN
#include <boost/detail/workaround.hpp>
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127 4244) // Conditional expression is constant
#endif
namespace boost
{
namespace math
{
// Forward declarations for function templates -----------------------------//
template < typename IntegerType >
IntegerType gcd( IntegerType const &a, IntegerType const &b );
template < typename IntegerType >
IntegerType lcm( IntegerType const &a, IntegerType const &b );
// Greatest common divisor evaluator class declaration ---------------------//
template < typename IntegerType >
class gcd_evaluator
{
public:
// Types
typedef IntegerType result_type, first_argument_type, second_argument_type;
// Function object interface
result_type operator ()( first_argument_type const &a,
second_argument_type const &b ) const;
}; // boost::math::gcd_evaluator
// Least common multiple evaluator class declaration -----------------------//
template < typename IntegerType >
class lcm_evaluator
{
public:
// Types
typedef IntegerType result_type, first_argument_type, second_argument_type;
// Function object interface
result_type operator ()( first_argument_type const &a,
second_argument_type const &b ) const;
}; // boost::math::lcm_evaluator
// Implementation details --------------------------------------------------//
namespace detail
{
// Greatest common divisor for rings (including unsigned integers)
template < typename RingType >
RingType
gcd_euclidean
(
RingType a,
RingType b
)
{
// Avoid repeated construction
#ifndef __BORLANDC__
RingType const zero = static_cast<RingType>( 0 );
#else
RingType zero = static_cast<RingType>( 0 );
#endif
// Reduce by GCD-remainder property [GCD(a,b) == GCD(b,a MOD b)]
while ( true )
{
if ( a == zero )
return b;
b %= a;
if ( b == zero )
return a;
a %= b;
}
}
// Greatest common divisor for (signed) integers
template < typename IntegerType >
inline
IntegerType
gcd_integer
(
IntegerType const & a,
IntegerType const & b
)
{
// Avoid repeated construction
IntegerType const zero = static_cast<IntegerType>( 0 );
IntegerType const result = gcd_euclidean( a, b );
return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
}
// Greatest common divisor for unsigned binary integers
template < typename BuiltInUnsigned >
BuiltInUnsigned
gcd_binary
(
BuiltInUnsigned u,
BuiltInUnsigned v
)
{
if ( u && v )
{
// Shift out common factors of 2
unsigned shifts = 0;
while ( !(u & 1u) && !(v & 1u) )
{
++shifts;
u >>= 1;
v >>= 1;
}
// Start with the still-even one, if any
BuiltInUnsigned r[] = { u, v };
unsigned which = static_cast<bool>( u & 1u );
// Whittle down the values via their differences
do
{
#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
while ( !(r[ which ] & 1u) )
{
r[ which ] = (r[which] >> 1);
}
#else
// Remove factors of two from the even one
while ( !(r[ which ] & 1u) )
{
r[ which ] >>= 1;
}
#endif
// Replace the larger of the two with their difference
if ( r[!which] > r[which] )
{
which ^= 1u;
}
r[ which ] -= r[ !which ];
}
while ( r[which] );
// Shift-in the common factor of 2 to the residues' GCD
return r[ !which ] << shifts;
}
else
{
// At least one input is zero, return the other
// (adding since zero is the additive identity)
// or zero if both are zero.
return u + v;
}
}
// Least common multiple for rings (including unsigned integers)
template < typename RingType >
inline
RingType
lcm_euclidean
(
RingType const & a,
RingType const & b
)
{
RingType const zero = static_cast<RingType>( 0 );
RingType const temp = gcd_euclidean( a, b );
return ( temp != zero ) ? ( a / temp * b ) : zero;
}
// Least common multiple for (signed) integers
template < typename IntegerType >
inline
IntegerType
lcm_integer
(
IntegerType const & a,
IntegerType const & b
)
{
// Avoid repeated construction
IntegerType const zero = static_cast<IntegerType>( 0 );
IntegerType const result = lcm_euclidean( a, b );
return ( result < zero ) ? static_cast<IntegerType>(-result) : result;
}
// Function objects to find the best way of computing GCD or LCM
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
template < typename T, bool IsSpecialized, bool IsSigned >
struct gcd_optimal_evaluator_helper_t
{
T operator ()( T const &a, T const &b )
{
return gcd_euclidean( a, b );
}
};
template < typename T >
struct gcd_optimal_evaluator_helper_t< T, true, true >
{
T operator ()( T const &a, T const &b )
{
return gcd_integer( a, b );
}
};
template < typename T >
struct gcd_optimal_evaluator
{
T operator ()( T const &a, T const &b )
{
typedef ::std::numeric_limits<T> limits_type;
typedef gcd_optimal_evaluator_helper_t<T,
limits_type::is_specialized, limits_type::is_signed> helper_type;
helper_type solver;
return solver( a, b );
}
};
#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
template < typename T >
struct gcd_optimal_evaluator
{
T operator ()( T const &a, T const &b )
{
return gcd_integer( a, b );
}
};
#endif
// Specialize for the built-in integers
#define BOOST_PRIVATE_GCD_UF( Ut ) \
template < > struct gcd_optimal_evaluator<Ut> \
{ Ut operator ()( Ut a, Ut b ) const { return gcd_binary( a, b ); } }
BOOST_PRIVATE_GCD_UF( unsigned char );
BOOST_PRIVATE_GCD_UF( unsigned short );
BOOST_PRIVATE_GCD_UF( unsigned );
BOOST_PRIVATE_GCD_UF( unsigned long );
#ifdef BOOST_HAS_LONG_LONG
BOOST_PRIVATE_GCD_UF( boost::ulong_long_type );
#elif defined(BOOST_HAS_MS_INT64)
BOOST_PRIVATE_GCD_UF( unsigned __int64 );
#endif
#if CHAR_MIN == 0
BOOST_PRIVATE_GCD_UF( char ); // char is unsigned
#endif
#undef BOOST_PRIVATE_GCD_UF
#define BOOST_PRIVATE_GCD_SF( St, Ut ) \
template < > struct gcd_optimal_evaluator<St> \
{ St operator ()( St a, St b ) const { Ut const a_abs = \
static_cast<Ut>( a < 0 ? -a : +a ), b_abs = static_cast<Ut>( \
b < 0 ? -b : +b ); return static_cast<St>( \
gcd_optimal_evaluator<Ut>()(a_abs, b_abs) ); } }
BOOST_PRIVATE_GCD_SF( signed char, unsigned char );
BOOST_PRIVATE_GCD_SF( short, unsigned short );
BOOST_PRIVATE_GCD_SF( int, unsigned );
BOOST_PRIVATE_GCD_SF( long, unsigned long );
#if CHAR_MIN < 0
BOOST_PRIVATE_GCD_SF( char, unsigned char ); // char is signed
#endif
#ifdef BOOST_HAS_LONG_LONG
BOOST_PRIVATE_GCD_SF( boost::long_long_type, boost::ulong_long_type );
#elif defined(BOOST_HAS_MS_INT64)
BOOST_PRIVATE_GCD_SF( __int64, unsigned __int64 );
#endif
#undef BOOST_PRIVATE_GCD_SF
#ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
template < typename T, bool IsSpecialized, bool IsSigned >
struct lcm_optimal_evaluator_helper_t
{
T operator ()( T const &a, T const &b )
{
return lcm_euclidean( a, b );
}
};
template < typename T >
struct lcm_optimal_evaluator_helper_t< T, true, true >
{
T operator ()( T const &a, T const &b )
{
return lcm_integer( a, b );
}
};
template < typename T >
struct lcm_optimal_evaluator
{
T operator ()( T const &a, T const &b )
{
typedef ::std::numeric_limits<T> limits_type;
typedef lcm_optimal_evaluator_helper_t<T,
limits_type::is_specialized, limits_type::is_signed> helper_type;
helper_type solver;
return solver( a, b );
}
};
#else // BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS
template < typename T >
struct lcm_optimal_evaluator
{
T operator ()( T const &a, T const &b )
{
return lcm_integer( a, b );
}
};
#endif
// Functions to find the GCD or LCM in the best way
template < typename T >
inline
T
gcd_optimal
(
T const & a,
T const & b
)
{
gcd_optimal_evaluator<T> solver;
return solver( a, b );
}
template < typename T >
inline
T
lcm_optimal
(
T const & a,
T const & b
)
{
lcm_optimal_evaluator<T> solver;
return solver( a, b );
}
} // namespace detail
// Greatest common divisor evaluator member function definition ------------//
template < typename IntegerType >
inline
typename gcd_evaluator<IntegerType>::result_type
gcd_evaluator<IntegerType>::operator ()
(
first_argument_type const & a,
second_argument_type const & b
) const
{
return detail::gcd_optimal( a, b );
}
// Least common multiple evaluator member function definition --------------//
template < typename IntegerType >
inline
typename lcm_evaluator<IntegerType>::result_type
lcm_evaluator<IntegerType>::operator ()
(
first_argument_type const & a,
second_argument_type const & b
) const
{
return detail::lcm_optimal( a, b );
}
// Greatest common divisor and least common multiple function definitions --//
template < typename IntegerType >
inline
IntegerType
gcd
(
IntegerType const & a,
IntegerType const & b
)
{
gcd_evaluator<IntegerType> solver;
return solver( a, b );
}
template < typename IntegerType >
inline
IntegerType
lcm
(
IntegerType const & a,
IntegerType const & b
)
{
lcm_evaluator<IntegerType> solver;
return solver( a, b );
}
} // namespace math
} // namespace boost
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
#endif // BOOST_MATH_COMMON_FACTOR_RT_HPP

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// Boost GCD & LCM common_factor.hpp test program --------------------------//
// (C) Copyright Daryle Walker 2001, 2006.
// 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.
// Revision History
// 01 Dec 2006 Various fixes for old compilers (Joaquin M Lopez Munoz)
// 10 Nov 2006 Make long long and __int64 mutually exclusive (Daryle Walker)
// 04 Nov 2006 Use more built-in numeric types, binary-GCD (Daryle Walker)
// 03 Nov 2006 Use custom numeric types (Daryle Walker)
// 02 Nov 2006 Change to Boost.Test's unit test system (Daryle Walker)
// 07 Nov 2001 Initial version (Daryle Walker)
#define BOOST_TEST_MAIN "Boost.Math GCD & LCM unit tests"
#include <boost/config.hpp> // for BOOST_MSVC, etc.
#include <boost/detail/workaround.hpp>
#include <boost/math/common_factor.hpp> // for boost::math::gcd, etc.
#include <boost/mpl/list.hpp> // for boost::mpl::list
#include <boost/operators.hpp>
#include <boost/test/unit_test.hpp>
#include <istream> // for std::basic_istream
#include <limits> // for std::numeric_limits
#include <ostream> // for std::basic_ostream
namespace {
// TODO: add polynominal/non-real type; especially after any switch to the
// binary-GCD algorithm for built-in types
// Custom integer class (template)
template < typename IntType, int ID = 0 >
class my_wrapped_integer
: private ::boost::shiftable1<my_wrapped_integer<IntType, ID>,
::boost::operators<my_wrapped_integer<IntType, ID> > >
{
// Helper type-aliases
typedef my_wrapped_integer self_type;
typedef IntType self_type::* bool_type;
// Member data
IntType v_;
public:
// Template parameters
typedef IntType int_type;
BOOST_STATIC_CONSTANT(int,id = ID);
// Lifetime management (use automatic destructor and copy constructor)
my_wrapped_integer( int_type const &v = int_type() ) : v_( v ) {}
// Accessors
int_type value() const { return this->v_; }
// Operators (use automatic copy assignment)
operator bool_type() const { return this->v_ ? &self_type::v_ : 0; }
self_type & operator ++() { ++this->v_; return *this; }
self_type & operator --() { --this->v_; return *this; }
self_type operator ~() const { return self_type( ~this->v_ ); }
self_type operator !() const { return self_type( !this->v_ ); }
self_type operator +() const { return self_type( +this->v_ ); }
self_type operator -() const { return self_type( -this->v_ ); }
bool operator <( self_type const &r ) const { return this->v_ < r.v_; }
bool operator ==( self_type const &r ) const { return this->v_ == r.v_; }
self_type &operator *=(self_type const &r) {this->v_ *= r.v_; return *this;}
self_type &operator /=(self_type const &r) {this->v_ /= r.v_; return *this;}
self_type &operator %=(self_type const &r) {this->v_ %= r.v_; return *this;}
self_type &operator +=(self_type const &r) {this->v_ += r.v_; return *this;}
self_type &operator -=(self_type const &r) {this->v_ -= r.v_; return *this;}
self_type &operator<<=(self_type const &r){this->v_ <<= r.v_; return *this;}
self_type &operator>>=(self_type const &r){this->v_ >>= r.v_; return *this;}
self_type &operator &=(self_type const &r) {this->v_ &= r.v_; return *this;}
self_type &operator |=(self_type const &r) {this->v_ |= r.v_; return *this;}
self_type &operator ^=(self_type const &r) {this->v_ ^= r.v_; return *this;}
// Input & output
friend std::istream & operator >>( std::istream &i, self_type &x )
{ return i >> x.v_; }
friend std::ostream & operator <<( std::ostream &o, self_type const &x )
{ return o << x.v_; }
}; // my_wrapped_integer
template < typename IntType, int ID >
my_wrapped_integer<IntType, ID> abs( my_wrapped_integer<IntType, ID> const &x )
{ return ( x < my_wrapped_integer<IntType, ID>(0) ) ? -x : +x; }
typedef my_wrapped_integer<int> MyInt1;
typedef my_wrapped_integer<unsigned> MyUnsigned1;
typedef my_wrapped_integer<int, 1> MyInt2;
typedef my_wrapped_integer<unsigned, 1> MyUnsigned2;
// Without these explicit instantiations, MSVC++ 6.5/7.0 does not find
// some friend operators in certain contexts.
MyInt1 dummy1;
MyUnsigned1 dummy2;
MyInt2 dummy3;
MyUnsigned2 dummy4;
// Various types to test with each GCD/LCM
typedef ::boost::mpl::list<signed char, short, int, long,
#ifdef BOOST_HAS_LONG_LONG
boost::long_long_type,
#elif defined(BOOST_HAS_MS_INT64)
__int64,
#endif
MyInt1> signed_test_types;
typedef ::boost::mpl::list<unsigned char, unsigned short, unsigned,
unsigned long,
#ifdef BOOST_HAS_LONG_LONG
boost::ulong_long_type,
#elif defined(BOOST_HAS_MS_INT64)
unsigned __int64,
#endif
MyUnsigned1, MyUnsigned2> unsigned_test_types;
} // namespace
#define BOOST_NO_MACRO_EXPAND /**/
// Specialize numeric_limits for _some_ of our types
namespace std
{
template < >
class numeric_limits< MyInt1 >
{
typedef MyInt1::int_type int_type;
typedef numeric_limits<int_type> limits_type;
public:
BOOST_STATIC_CONSTANT(bool, is_specialized = limits_type::is_specialized);
static MyInt1 min BOOST_NO_MACRO_EXPAND() throw() { return (limits_type::min)(); }
static MyInt1 max BOOST_NO_MACRO_EXPAND() throw() { return (limits_type::max)(); }
BOOST_STATIC_CONSTANT(int, digits = limits_type::digits);
BOOST_STATIC_CONSTANT(int, digits10 = limits_type::digits10);
#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS
BOOST_STATIC_CONSTANT(int, max_digits10 = limits_type::max_digits10);
#endif
BOOST_STATIC_CONSTANT(bool, is_signed = limits_type::is_signed);
BOOST_STATIC_CONSTANT(bool, is_integer = limits_type::is_integer);
BOOST_STATIC_CONSTANT(bool, is_exact = limits_type::is_exact);
BOOST_STATIC_CONSTANT(int, radix = limits_type::radix);
static MyInt1 epsilon() throw() { return limits_type::epsilon(); }
static MyInt1 round_error() throw() { return limits_type::round_error(); }
BOOST_STATIC_CONSTANT(int, min_exponent = limits_type::min_exponent);
BOOST_STATIC_CONSTANT(int, min_exponent10 = limits_type::min_exponent10);
BOOST_STATIC_CONSTANT(int, max_exponent = limits_type::max_exponent);
BOOST_STATIC_CONSTANT(int, max_exponent10 = limits_type::max_exponent10);
BOOST_STATIC_CONSTANT(bool, has_infinity = limits_type::has_infinity);
BOOST_STATIC_CONSTANT(bool, has_quiet_NaN = limits_type::has_quiet_NaN);
BOOST_STATIC_CONSTANT(bool, has_signaling_NaN = limits_type::has_signaling_NaN);
BOOST_STATIC_CONSTANT(float_denorm_style, has_denorm = limits_type::has_denorm);
BOOST_STATIC_CONSTANT(bool, has_denorm_loss = limits_type::has_denorm_loss);
static MyInt1 infinity() throw() { return limits_type::infinity(); }
static MyInt1 quiet_NaN() throw() { return limits_type::quiet_NaN(); }
static MyInt1 signaling_NaN() throw() {return limits_type::signaling_NaN();}
static MyInt1 denorm_min() throw() { return limits_type::denorm_min(); }
BOOST_STATIC_CONSTANT(bool, is_iec559 = limits_type::is_iec559);
BOOST_STATIC_CONSTANT(bool, is_bounded = limits_type::is_bounded);
BOOST_STATIC_CONSTANT(bool, is_modulo = limits_type::is_modulo);
BOOST_STATIC_CONSTANT(bool, traps = limits_type::traps);
BOOST_STATIC_CONSTANT(bool, tinyness_before = limits_type::tinyness_before);
BOOST_STATIC_CONSTANT(float_round_style, round_style = limits_type::round_style);
}; // std::numeric_limits<MyInt1>
template < >
class numeric_limits< MyUnsigned1 >
{
typedef MyUnsigned1::int_type int_type;
typedef numeric_limits<int_type> limits_type;
public:
BOOST_STATIC_CONSTANT(bool, is_specialized = limits_type::is_specialized);
static MyUnsigned1 min BOOST_NO_MACRO_EXPAND() throw() { return (limits_type::min)(); }
static MyUnsigned1 max BOOST_NO_MACRO_EXPAND() throw() { return (limits_type::max)(); }
BOOST_STATIC_CONSTANT(int, digits = limits_type::digits);
BOOST_STATIC_CONSTANT(int, digits10 = limits_type::digits10);
#ifndef BOOST_NO_CXX11_NUMERIC_LIMITS
BOOST_STATIC_CONSTANT(int, max_digits10 = limits_type::max_digits10);
#endif
BOOST_STATIC_CONSTANT(bool, is_signed = limits_type::is_signed);
BOOST_STATIC_CONSTANT(bool, is_integer = limits_type::is_integer);
BOOST_STATIC_CONSTANT(bool, is_exact = limits_type::is_exact);
BOOST_STATIC_CONSTANT(int, radix = limits_type::radix);
static MyUnsigned1 epsilon() throw() { return limits_type::epsilon(); }
static MyUnsigned1 round_error() throw(){return limits_type::round_error();}
BOOST_STATIC_CONSTANT(int, min_exponent = limits_type::min_exponent);
BOOST_STATIC_CONSTANT(int, min_exponent10 = limits_type::min_exponent10);
BOOST_STATIC_CONSTANT(int, max_exponent = limits_type::max_exponent);
BOOST_STATIC_CONSTANT(int, max_exponent10 = limits_type::max_exponent10);
BOOST_STATIC_CONSTANT(bool, has_infinity = limits_type::has_infinity);
BOOST_STATIC_CONSTANT(bool, has_quiet_NaN = limits_type::has_quiet_NaN);
BOOST_STATIC_CONSTANT(bool, has_signaling_NaN = limits_type::has_signaling_NaN);
BOOST_STATIC_CONSTANT(float_denorm_style, has_denorm = limits_type::has_denorm);
BOOST_STATIC_CONSTANT(bool, has_denorm_loss = limits_type::has_denorm_loss);
static MyUnsigned1 infinity() throw() { return limits_type::infinity(); }
static MyUnsigned1 quiet_NaN() throw() { return limits_type::quiet_NaN(); }
static MyUnsigned1 signaling_NaN() throw()
{ return limits_type::signaling_NaN(); }
static MyUnsigned1 denorm_min() throw(){ return limits_type::denorm_min(); }
BOOST_STATIC_CONSTANT(bool, is_iec559 = limits_type::is_iec559);
BOOST_STATIC_CONSTANT(bool, is_bounded = limits_type::is_bounded);
BOOST_STATIC_CONSTANT(bool, is_modulo = limits_type::is_modulo);
BOOST_STATIC_CONSTANT(bool, traps = limits_type::traps);
BOOST_STATIC_CONSTANT(bool, tinyness_before = limits_type::tinyness_before);
BOOST_STATIC_CONSTANT(float_round_style, round_style = limits_type::round_style);
}; // std::numeric_limits<MyUnsigned1>
#if BOOST_WORKAROUND(BOOST_MSVC,<1300)
// MSVC 6.0 lacks operator<< for __int64, see
// http://support.microsoft.com/default.aspx?scid=kb;en-us;168440
inline ostream& operator<<(ostream& os, __int64 i)
{
char buf[20];
sprintf(buf,"%I64d", i);
os << buf;
return os;
}
inline ostream& operator<<(ostream& os, unsigned __int64 i)
{
char buf[20];
sprintf(buf,"%I64u", i);
os << buf;
return os;
}
#endif
} // namespace std
// GCD tests
BOOST_AUTO_TEST_SUITE( gcd_test_suite )
// GCD on signed integer types
BOOST_AUTO_TEST_CASE_TEMPLATE( gcd_int_test, T, signed_test_types )
{
#ifndef BOOST_MSVC
using boost::math::gcd;
#else
using namespace boost::math;
#endif
// Originally from Boost.Rational tests
BOOST_CHECK_EQUAL( gcd<T>( 1, -1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( -1, 1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( 1, 1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( -1, -1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( 0, 0), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( gcd<T>( 7, 0), static_cast<T>( 7) );
BOOST_CHECK_EQUAL( gcd<T>( 0, 9), static_cast<T>( 9) );
BOOST_CHECK_EQUAL( gcd<T>( -7, 0), static_cast<T>( 7) );
BOOST_CHECK_EQUAL( gcd<T>( 0, -9), static_cast<T>( 9) );
BOOST_CHECK_EQUAL( gcd<T>( 42, 30), static_cast<T>( 6) );
BOOST_CHECK_EQUAL( gcd<T>( 6, -9), static_cast<T>( 3) );
BOOST_CHECK_EQUAL( gcd<T>(-10, -10), static_cast<T>(10) );
BOOST_CHECK_EQUAL( gcd<T>(-25, -10), static_cast<T>( 5) );
BOOST_CHECK_EQUAL( gcd<T>( 3, 7), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( 8, 9), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( gcd<T>( 7, 49), static_cast<T>( 7) );
}
// GCD on unmarked signed integer type
BOOST_AUTO_TEST_CASE( gcd_unmarked_int_test )
{
#ifndef BOOST_MSVC
using boost::math::gcd;
#else
using namespace boost::math;
#endif
// The regular signed-integer GCD function performs the unsigned version,
// then does an absolute-value on the result. Signed types that are not
// marked as such (due to no std::numeric_limits specialization) may be off
// by a sign.
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 1, -1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( -1, 1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 1, 1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( -1, -1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 0, 0 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 7, 0 )), MyInt2( 7) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 0, 9 )), MyInt2( 9) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( -7, 0 )), MyInt2( 7) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 0, -9 )), MyInt2( 9) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 42, 30 )), MyInt2( 6) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 6, -9 )), MyInt2( 3) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( -10, -10 )), MyInt2(10) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( -25, -10 )), MyInt2( 5) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 3, 7 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 8, 9 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(gcd<MyInt2>( 7, 49 )), MyInt2( 7) );
}
// GCD on unsigned integer types
BOOST_AUTO_TEST_CASE_TEMPLATE( gcd_unsigned_test, T, unsigned_test_types )
{
#ifndef BOOST_MSVC
using boost::math::gcd;
#else
using namespace boost::math;
#endif
// Note that unmarked types (i.e. have no std::numeric_limits
// specialization) are treated like non/unsigned types
BOOST_CHECK_EQUAL( gcd<T>( 1u, 1u), static_cast<T>( 1u) );
BOOST_CHECK_EQUAL( gcd<T>( 0u, 0u), static_cast<T>( 0u) );
BOOST_CHECK_EQUAL( gcd<T>( 7u, 0u), static_cast<T>( 7u) );
BOOST_CHECK_EQUAL( gcd<T>( 0u, 9u), static_cast<T>( 9u) );
BOOST_CHECK_EQUAL( gcd<T>(42u, 30u), static_cast<T>( 6u) );
BOOST_CHECK_EQUAL( gcd<T>( 3u, 7u), static_cast<T>( 1u) );
BOOST_CHECK_EQUAL( gcd<T>( 8u, 9u), static_cast<T>( 1u) );
BOOST_CHECK_EQUAL( gcd<T>( 7u, 49u), static_cast<T>( 7u) );
}
// GCD at compile-time
BOOST_AUTO_TEST_CASE( gcd_static_test )
{
#ifndef BOOST_MSVC
using boost::math::static_gcd;
#else
using namespace boost::math;
#endif
// Can't use "BOOST_CHECK_EQUAL", otherwise the "value" member will be
// disqualified as compile-time-only constant, needing explicit definition
BOOST_CHECK( (static_gcd< 1, 1>::value) == 1 );
BOOST_CHECK( (static_gcd< 0, 0>::value) == 0 );
BOOST_CHECK( (static_gcd< 7, 0>::value) == 7 );
BOOST_CHECK( (static_gcd< 0, 9>::value) == 9 );
BOOST_CHECK( (static_gcd<42, 30>::value) == 6 );
BOOST_CHECK( (static_gcd< 3, 7>::value) == 1 );
BOOST_CHECK( (static_gcd< 8, 9>::value) == 1 );
BOOST_CHECK( (static_gcd< 7, 49>::value) == 7 );
}
// TODO: non-built-in signed and unsigned integer tests, with and without
// numeric_limits specialization; polynominal tests; note any changes if
// built-ins switch to binary-GCD algorithm
BOOST_AUTO_TEST_SUITE_END()
// LCM tests
BOOST_AUTO_TEST_SUITE( lcm_test_suite )
// LCM on signed integer types
BOOST_AUTO_TEST_CASE_TEMPLATE( lcm_int_test, T, signed_test_types )
{
#ifndef BOOST_MSVC
using boost::math::lcm;
#else
using namespace boost::math;
#endif
// Originally from Boost.Rational tests
BOOST_CHECK_EQUAL( lcm<T>( 1, -1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( lcm<T>( -1, 1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( lcm<T>( 1, 1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( lcm<T>( -1, -1), static_cast<T>( 1) );
BOOST_CHECK_EQUAL( lcm<T>( 0, 0), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( lcm<T>( 6, 0), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( lcm<T>( 0, 7), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( lcm<T>( -5, 0), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( lcm<T>( 0, -4), static_cast<T>( 0) );
BOOST_CHECK_EQUAL( lcm<T>( 18, 30), static_cast<T>(90) );
BOOST_CHECK_EQUAL( lcm<T>( -6, 9), static_cast<T>(18) );
BOOST_CHECK_EQUAL( lcm<T>(-10, -10), static_cast<T>(10) );
BOOST_CHECK_EQUAL( lcm<T>( 25, -10), static_cast<T>(50) );
BOOST_CHECK_EQUAL( lcm<T>( 3, 7), static_cast<T>(21) );
BOOST_CHECK_EQUAL( lcm<T>( 8, 9), static_cast<T>(72) );
BOOST_CHECK_EQUAL( lcm<T>( 7, 49), static_cast<T>(49) );
}
// LCM on unmarked signed integer type
BOOST_AUTO_TEST_CASE( lcm_unmarked_int_test )
{
#ifndef BOOST_MSVC
using boost::math::lcm;
#else
using namespace boost::math;
#endif
// The regular signed-integer LCM function performs the unsigned version,
// then does an absolute-value on the result. Signed types that are not
// marked as such (due to no std::numeric_limits specialization) may be off
// by a sign.
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 1, -1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( -1, 1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 1, 1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( -1, -1 )), MyInt2( 1) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 0, 0 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 6, 0 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 0, 7 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( -5, 0 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 0, -4 )), MyInt2( 0) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 18, 30 )), MyInt2(90) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( -6, 9 )), MyInt2(18) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( -10, -10 )), MyInt2(10) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 25, -10 )), MyInt2(50) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 3, 7 )), MyInt2(21) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 8, 9 )), MyInt2(72) );
BOOST_CHECK_EQUAL( abs(lcm<MyInt2>( 7, 49 )), MyInt2(49) );
}
// LCM on unsigned integer types
BOOST_AUTO_TEST_CASE_TEMPLATE( lcm_unsigned_test, T, unsigned_test_types )
{
#ifndef BOOST_MSVC
using boost::math::lcm;
#else
using namespace boost::math;
#endif
// Note that unmarked types (i.e. have no std::numeric_limits
// specialization) are treated like non/unsigned types
BOOST_CHECK_EQUAL( lcm<T>( 1u, 1u), static_cast<T>( 1u) );
BOOST_CHECK_EQUAL( lcm<T>( 0u, 0u), static_cast<T>( 0u) );
BOOST_CHECK_EQUAL( lcm<T>( 6u, 0u), static_cast<T>( 0u) );
BOOST_CHECK_EQUAL( lcm<T>( 0u, 7u), static_cast<T>( 0u) );
BOOST_CHECK_EQUAL( lcm<T>(18u, 30u), static_cast<T>(90u) );
BOOST_CHECK_EQUAL( lcm<T>( 3u, 7u), static_cast<T>(21u) );
BOOST_CHECK_EQUAL( lcm<T>( 8u, 9u), static_cast<T>(72u) );
BOOST_CHECK_EQUAL( lcm<T>( 7u, 49u), static_cast<T>(49u) );
}
// LCM at compile-time
BOOST_AUTO_TEST_CASE( lcm_static_test )
{
#ifndef BOOST_MSVC
using boost::math::static_lcm;
#else
using namespace boost::math;
#endif
// Can't use "BOOST_CHECK_EQUAL", otherwise the "value" member will be
// disqualified as compile-time-only constant, needing explicit definition
BOOST_CHECK( (static_lcm< 1, 1>::value) == 1 );
BOOST_CHECK( (static_lcm< 0, 0>::value) == 0 );
BOOST_CHECK( (static_lcm< 6, 0>::value) == 0 );
BOOST_CHECK( (static_lcm< 0, 7>::value) == 0 );
BOOST_CHECK( (static_lcm<18, 30>::value) == 90 );
BOOST_CHECK( (static_lcm< 3, 7>::value) == 21 );
BOOST_CHECK( (static_lcm< 8, 9>::value) == 72 );
BOOST_CHECK( (static_lcm< 7, 49>::value) == 49 );
}
// TODO: see GCD to-do
BOOST_AUTO_TEST_SUITE_END()