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