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549 lines
16 KiB
C++
549 lines
16 KiB
C++
// Boost rational.hpp header file ------------------------------------------//
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// (C) Copyright Paul Moore 1999. Permission to copy, use, modify, sell and
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// distribute this software is granted provided this copyright notice appears
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// in all copies. This software is provided "as is" without express or
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// implied warranty, and with no claim as to its suitability for any purpose.
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// See http://www.boost.org/libs/rational for documentation.
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// Credits:
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// Thanks to the boost mailing list in general for useful comments.
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// Particular contributions included:
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// Andrew D Jewell, for reminding me to take care to avoid overflow
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// Ed Brey, for many comments, including picking up on some dreadful typos
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// Stephen Silver contributed the test suite and comments on user-defined
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// IntType
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// Nickolay Mladenov, for the implementation of operator+=
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// Revision History
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// 20 Oct 06 Fix operator bool_type for CW 8.3 (Joaquín M López Muñoz)
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// 18 Oct 06 Use EXPLICIT_TEMPLATE_TYPE helper macros from Boost.Config
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// (Joaquín M López Muñoz)
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// 27 Dec 05 Add Boolean conversion operator (Daryle Walker)
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// 28 Sep 02 Use _left versions of operators from operators.hpp
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// 05 Jul 01 Recode gcd(), avoiding std::swap (Helmut Zeisel)
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// 03 Mar 01 Workarounds for Intel C++ 5.0 (David Abrahams)
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// 05 Feb 01 Update operator>> to tighten up input syntax
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// 05 Feb 01 Final tidy up of gcd code prior to the new release
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// 27 Jan 01 Recode abs() without relying on abs(IntType)
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// 21 Jan 01 Include Nickolay Mladenov's operator+= algorithm,
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// tidy up a number of areas, use newer features of operators.hpp
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// (reduces space overhead to zero), add operator!,
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// introduce explicit mixed-mode arithmetic operations
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// 12 Jan 01 Include fixes to handle a user-defined IntType better
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// 19 Nov 00 Throw on divide by zero in operator /= (John (EBo) David)
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// 23 Jun 00 Incorporate changes from Mark Rodgers for Borland C++
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// 22 Jun 00 Change _MSC_VER to BOOST_MSVC so other compilers are not
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// affected (Beman Dawes)
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// 6 Mar 00 Fix operator-= normalization, #include <string> (Jens Maurer)
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// 14 Dec 99 Modifications based on comments from the boost list
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// 09 Dec 99 Initial Version (Paul Moore)
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#ifndef BOOST_RATIONAL_HPP
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#define BOOST_RATIONAL_HPP
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#include <iostream> // for std::istream and std::ostream
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#include <iomanip> // for std::noskipws
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#include <stdexcept> // for std::domain_error
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#include <string> // for std::string implicit constructor
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#include <boost/operators.hpp> // for boost::addable etc
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#include <cstdlib> // for std::abs
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#include <boost/call_traits.hpp> // for boost::call_traits
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#include <boost/config.hpp> // for BOOST_NO_STDC_NAMESPACE, BOOST_MSVC
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#include <boost/detail/workaround.hpp> // for BOOST_WORKAROUND
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namespace boost {
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// Note: We use n and m as temporaries in this function, so there is no value
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// in using const IntType& as we would only need to make a copy anyway...
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template <typename IntType>
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IntType gcd(IntType n, IntType m)
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{
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// Avoid repeated construction
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IntType zero(0);
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// This is abs() - given the existence of broken compilers with Koenig
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// lookup issues and other problems, I code this explicitly. (Remember,
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// IntType may be a user-defined type).
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if (n < zero)
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n = -n;
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if (m < zero)
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m = -m;
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// As n and m are now positive, we can be sure that %= returns a
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// positive value (the standard guarantees this for built-in types,
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// and we require it of user-defined types).
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for(;;) {
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if(m == zero)
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return n;
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n %= m;
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if(n == zero)
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return m;
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m %= n;
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}
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}
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template <typename IntType>
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IntType lcm(IntType n, IntType m)
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{
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// Avoid repeated construction
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IntType zero(0);
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if (n == zero || m == zero)
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return zero;
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n /= gcd(n, m);
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n *= m;
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if (n < zero)
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n = -n;
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return n;
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}
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class bad_rational : public std::domain_error
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{
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public:
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explicit bad_rational() : std::domain_error("bad rational: zero denominator") {}
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};
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template <typename IntType>
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class rational;
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template <typename IntType>
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rational<IntType> abs(const rational<IntType>& r);
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template <typename IntType>
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class rational :
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less_than_comparable < rational<IntType>,
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equality_comparable < rational<IntType>,
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less_than_comparable2 < rational<IntType>, IntType,
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equality_comparable2 < rational<IntType>, IntType,
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addable < rational<IntType>,
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subtractable < rational<IntType>,
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multipliable < rational<IntType>,
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dividable < rational<IntType>,
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addable2 < rational<IntType>, IntType,
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subtractable2 < rational<IntType>, IntType,
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subtractable2_left < rational<IntType>, IntType,
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multipliable2 < rational<IntType>, IntType,
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dividable2 < rational<IntType>, IntType,
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dividable2_left < rational<IntType>, IntType,
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incrementable < rational<IntType>,
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decrementable < rational<IntType>
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> > > > > > > > > > > > > > > >
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{
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typedef typename boost::call_traits<IntType>::param_type param_type;
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struct helper { IntType parts[2]; };
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typedef IntType (helper::* bool_type)[2];
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public:
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typedef IntType int_type;
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rational() : num(0), den(1) {}
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rational(param_type n) : num(n), den(1) {}
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rational(param_type n, param_type d) : num(n), den(d) { normalize(); }
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// Default copy constructor and assignment are fine
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// Add assignment from IntType
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rational& operator=(param_type n) { return assign(n, 1); }
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// Assign in place
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rational& assign(param_type n, param_type d);
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// Access to representation
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IntType numerator() const { return num; }
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IntType denominator() const { return den; }
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// Arithmetic assignment operators
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rational& operator+= (const rational& r);
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rational& operator-= (const rational& r);
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rational& operator*= (const rational& r);
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rational& operator/= (const rational& r);
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rational& operator+= (param_type i);
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rational& operator-= (param_type i);
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rational& operator*= (param_type i);
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rational& operator/= (param_type i);
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// Increment and decrement
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const rational& operator++();
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const rational& operator--();
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// Operator not
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bool operator!() const { return !num; }
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// Boolean conversion
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#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
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// The "ISO C++ Template Parser" option in CW 8.3 chokes on the
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// following, hence we selectively disable that option for the
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// offending memfun.
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#pragma parse_mfunc_templ off
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#endif
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operator bool_type() const { return operator !() ? 0 : &helper::parts; }
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#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
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#pragma parse_mfunc_templ reset
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#endif
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// Comparison operators
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bool operator< (const rational& r) const;
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bool operator== (const rational& r) const;
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bool operator< (param_type i) const;
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bool operator> (param_type i) const;
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bool operator== (param_type i) const;
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private:
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// Implementation - numerator and denominator (normalized).
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// Other possibilities - separate whole-part, or sign, fields?
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IntType num;
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IntType den;
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// Representation note: Fractions are kept in normalized form at all
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// times. normalized form is defined as gcd(num,den) == 1 and den > 0.
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// In particular, note that the implementation of abs() below relies
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// on den always being positive.
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void normalize();
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};
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// Assign in place
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template <typename IntType>
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inline rational<IntType>& rational<IntType>::assign(param_type n, param_type d)
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{
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num = n;
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den = d;
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normalize();
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return *this;
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}
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// Unary plus and minus
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template <typename IntType>
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inline rational<IntType> operator+ (const rational<IntType>& r)
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{
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return r;
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}
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template <typename IntType>
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inline rational<IntType> operator- (const rational<IntType>& r)
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{
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return rational<IntType>(-r.numerator(), r.denominator());
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}
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// Arithmetic assignment operators
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template <typename IntType>
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rational<IntType>& rational<IntType>::operator+= (const rational<IntType>& r)
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{
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// This calculation avoids overflow, and minimises the number of expensive
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// calculations. Thanks to Nickolay Mladenov for this algorithm.
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//
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// Proof:
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// We have to compute a/b + c/d, where gcd(a,b)=1 and gcd(b,c)=1.
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// Let g = gcd(b,d), and b = b1*g, d=d1*g. Then gcd(b1,d1)=1
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//
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// The result is (a*d1 + c*b1) / (b1*d1*g).
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// Now we have to normalize this ratio.
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// Let's assume h | gcd((a*d1 + c*b1), (b1*d1*g)), and h > 1
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// If h | b1 then gcd(h,d1)=1 and hence h|(a*d1+c*b1) => h|a.
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// But since gcd(a,b1)=1 we have h=1.
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// Similarly h|d1 leads to h=1.
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// So we have that h | gcd((a*d1 + c*b1) , (b1*d1*g)) => h|g
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// Finally we have gcd((a*d1 + c*b1), (b1*d1*g)) = gcd((a*d1 + c*b1), g)
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// Which proves that instead of normalizing the result, it is better to
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// divide num and den by gcd((a*d1 + c*b1), g)
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// Protect against self-modification
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IntType r_num = r.num;
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IntType r_den = r.den;
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IntType g = gcd(den, r_den);
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den /= g; // = b1 from the calculations above
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num = num * (r_den / g) + r_num * den;
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g = gcd(num, g);
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num /= g;
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den *= r_den/g;
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return *this;
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}
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template <typename IntType>
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rational<IntType>& rational<IntType>::operator-= (const rational<IntType>& r)
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{
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// Protect against self-modification
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IntType r_num = r.num;
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IntType r_den = r.den;
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// This calculation avoids overflow, and minimises the number of expensive
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// calculations. It corresponds exactly to the += case above
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IntType g = gcd(den, r_den);
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den /= g;
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num = num * (r_den / g) - r_num * den;
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g = gcd(num, g);
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num /= g;
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den *= r_den/g;
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return *this;
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}
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template <typename IntType>
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rational<IntType>& rational<IntType>::operator*= (const rational<IntType>& r)
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{
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// Protect against self-modification
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IntType r_num = r.num;
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IntType r_den = r.den;
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// Avoid overflow and preserve normalization
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IntType gcd1 = gcd<IntType>(num, r_den);
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IntType gcd2 = gcd<IntType>(r_num, den);
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num = (num/gcd1) * (r_num/gcd2);
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den = (den/gcd2) * (r_den/gcd1);
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return *this;
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}
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template <typename IntType>
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rational<IntType>& rational<IntType>::operator/= (const rational<IntType>& r)
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{
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// Protect against self-modification
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IntType r_num = r.num;
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IntType r_den = r.den;
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// Avoid repeated construction
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IntType zero(0);
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// Trap division by zero
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if (r_num == zero)
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throw bad_rational();
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if (num == zero)
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return *this;
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// Avoid overflow and preserve normalization
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IntType gcd1 = gcd<IntType>(num, r_num);
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IntType gcd2 = gcd<IntType>(r_den, den);
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num = (num/gcd1) * (r_den/gcd2);
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den = (den/gcd2) * (r_num/gcd1);
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if (den < zero) {
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num = -num;
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den = -den;
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}
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return *this;
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}
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// Mixed-mode operators
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template <typename IntType>
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inline rational<IntType>&
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rational<IntType>::operator+= (param_type i)
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{
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return operator+= (rational<IntType>(i));
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}
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template <typename IntType>
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inline rational<IntType>&
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rational<IntType>::operator-= (param_type i)
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{
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return operator-= (rational<IntType>(i));
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}
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template <typename IntType>
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inline rational<IntType>&
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rational<IntType>::operator*= (param_type i)
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{
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return operator*= (rational<IntType>(i));
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}
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template <typename IntType>
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inline rational<IntType>&
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rational<IntType>::operator/= (param_type i)
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{
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return operator/= (rational<IntType>(i));
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}
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// Increment and decrement
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template <typename IntType>
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inline const rational<IntType>& rational<IntType>::operator++()
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{
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// This can never denormalise the fraction
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num += den;
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return *this;
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}
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template <typename IntType>
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inline const rational<IntType>& rational<IntType>::operator--()
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{
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// This can never denormalise the fraction
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num -= den;
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return *this;
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}
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// Comparison operators
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template <typename IntType>
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bool rational<IntType>::operator< (const rational<IntType>& r) const
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{
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// Avoid repeated construction
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IntType zero(0);
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// If the two values have different signs, we don't need to do the
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// expensive calculations below. We take advantage here of the fact
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// that the denominator is always positive.
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if (num < zero && r.num >= zero) // -ve < +ve
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return true;
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if (num >= zero && r.num <= zero) // +ve or zero is not < -ve or zero
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return false;
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// Avoid overflow
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IntType gcd1 = gcd<IntType>(num, r.num);
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IntType gcd2 = gcd<IntType>(r.den, den);
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return (num/gcd1) * (r.den/gcd2) < (den/gcd2) * (r.num/gcd1);
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}
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template <typename IntType>
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bool rational<IntType>::operator< (param_type i) const
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{
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// Avoid repeated construction
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IntType zero(0);
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// If the two values have different signs, we don't need to do the
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// expensive calculations below. We take advantage here of the fact
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// that the denominator is always positive.
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if (num < zero && i >= zero) // -ve < +ve
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return true;
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if (num >= zero && i <= zero) // +ve or zero is not < -ve or zero
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return false;
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// Now, use the fact that n/d truncates towards zero as long as n and d
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// are both positive.
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// Divide instead of multiplying to avoid overflow issues. Of course,
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// division may be slower, but accuracy is more important than speed...
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if (num > zero)
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return (num/den) < i;
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else
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return -i < (-num/den);
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}
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template <typename IntType>
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bool rational<IntType>::operator> (param_type i) const
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{
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// Trap equality first
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if (num == i && den == IntType(1))
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return false;
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// Otherwise, we can use operator<
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return !operator<(i);
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}
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template <typename IntType>
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inline bool rational<IntType>::operator== (const rational<IntType>& r) const
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{
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return ((num == r.num) && (den == r.den));
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}
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template <typename IntType>
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inline bool rational<IntType>::operator== (param_type i) const
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{
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return ((den == IntType(1)) && (num == i));
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}
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// Normalisation
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template <typename IntType>
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void rational<IntType>::normalize()
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{
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// Avoid repeated construction
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IntType zero(0);
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if (den == zero)
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throw bad_rational();
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// Handle the case of zero separately, to avoid division by zero
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if (num == zero) {
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den = IntType(1);
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return;
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}
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IntType g = gcd<IntType>(num, den);
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num /= g;
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den /= g;
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// Ensure that the denominator is positive
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if (den < zero) {
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num = -num;
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den = -den;
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}
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}
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namespace detail {
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// A utility class to reset the format flags for an istream at end
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// of scope, even in case of exceptions
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struct resetter {
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resetter(std::istream& is) : is_(is), f_(is.flags()) {}
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~resetter() { is_.flags(f_); }
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std::istream& is_;
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std::istream::fmtflags f_; // old GNU c++ lib has no ios_base
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};
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}
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// Input and output
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template <typename IntType>
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std::istream& operator>> (std::istream& is, rational<IntType>& r)
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{
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IntType n = IntType(0), d = IntType(1);
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char c = 0;
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detail::resetter sentry(is);
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is >> n;
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c = is.get();
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if (c != '/')
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is.clear(std::istream::badbit); // old GNU c++ lib has no ios_base
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#if !defined(__GNUC__) || (defined(__GNUC__) && (__GNUC__ >= 3)) || defined __SGI_STL_PORT
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is >> std::noskipws;
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#else
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is.unsetf(ios::skipws); // compiles, but seems to have no effect.
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#endif
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is >> d;
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if (is)
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r.assign(n, d);
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return is;
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}
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// Add manipulators for output format?
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template <typename IntType>
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std::ostream& operator<< (std::ostream& os, const rational<IntType>& r)
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{
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os << r.numerator() << '/' << r.denominator();
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return os;
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}
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// Type conversion
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template <typename T, typename IntType>
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inline T rational_cast(
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const rational<IntType>& src BOOST_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
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|
{
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|
return static_cast<T>(src.numerator())/src.denominator();
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|
}
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|
// Do not use any abs() defined on IntType - it isn't worth it, given the
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|
// difficulties involved (Koenig lookup required, there may not *be* an abs()
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|
// defined, etc etc).
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|
template <typename IntType>
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|
inline rational<IntType> abs(const rational<IntType>& r)
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|
{
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|
if (r.numerator() >= IntType(0))
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|
return r;
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|
|
|
return rational<IntType>(-r.numerator(), r.denominator());
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|
}
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|
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|
} // namespace boost
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|
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|
#endif // BOOST_RATIONAL_HPP
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|
|