--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ossrv_pub/boost_apis/boost/rational.hpp Tue Feb 02 02:01:42 2010 +0200
@@ -0,0 +1,548 @@
+// Boost rational.hpp header file ------------------------------------------//
+
+// (C) Copyright Paul Moore 1999. 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.
+
+// See http://www.boost.org/libs/rational for documentation.
+
+// Credits:
+// Thanks to the boost mailing list in general for useful comments.
+// Particular contributions included:
+// Andrew D Jewell, for reminding me to take care to avoid overflow
+// Ed Brey, for many comments, including picking up on some dreadful typos
+// Stephen Silver contributed the test suite and comments on user-defined
+// IntType
+// Nickolay Mladenov, for the implementation of operator+=
+
+// Revision History
+// 20 Oct 06 Fix operator bool_type for CW 8.3 (Joaquín M López Muñoz)
+// 18 Oct 06 Use EXPLICIT_TEMPLATE_TYPE helper macros from Boost.Config
+// (Joaquín M López Muñoz)
+// 27 Dec 05 Add Boolean conversion operator (Daryle Walker)
+// 28 Sep 02 Use _left versions of operators from operators.hpp
+// 05 Jul 01 Recode gcd(), avoiding std::swap (Helmut Zeisel)
+// 03 Mar 01 Workarounds for Intel C++ 5.0 (David Abrahams)
+// 05 Feb 01 Update operator>> to tighten up input syntax
+// 05 Feb 01 Final tidy up of gcd code prior to the new release
+// 27 Jan 01 Recode abs() without relying on abs(IntType)
+// 21 Jan 01 Include Nickolay Mladenov's operator+= algorithm,
+// tidy up a number of areas, use newer features of operators.hpp
+// (reduces space overhead to zero), add operator!,
+// introduce explicit mixed-mode arithmetic operations
+// 12 Jan 01 Include fixes to handle a user-defined IntType better
+// 19 Nov 00 Throw on divide by zero in operator /= (John (EBo) David)
+// 23 Jun 00 Incorporate changes from Mark Rodgers for Borland C++
+// 22 Jun 00 Change _MSC_VER to BOOST_MSVC so other compilers are not
+// affected (Beman Dawes)
+// 6 Mar 00 Fix operator-= normalization, #include <string> (Jens Maurer)
+// 14 Dec 99 Modifications based on comments from the boost list
+// 09 Dec 99 Initial Version (Paul Moore)
+
+#ifndef BOOST_RATIONAL_HPP
+#define BOOST_RATIONAL_HPP
+
+#include <iostream> // for std::istream and std::ostream
+#include <iomanip> // for std::noskipws
+#include <stdexcept> // for std::domain_error
+#include <string> // for std::string implicit constructor
+#include <boost/operators.hpp> // for boost::addable etc
+#include <cstdlib> // for std::abs
+#include <boost/call_traits.hpp> // for boost::call_traits
+#include <boost/config.hpp> // for BOOST_NO_STDC_NAMESPACE, BOOST_MSVC
+#include <boost/detail/workaround.hpp> // for BOOST_WORKAROUND
+
+namespace boost {
+
+// Note: We use n and m as temporaries in this function, so there is no value
+// in using const IntType& as we would only need to make a copy anyway...
+template <typename IntType>
+IntType gcd(IntType n, IntType m)
+{
+ // Avoid repeated construction
+ IntType zero(0);
+
+ // This is abs() - given the existence of broken compilers with Koenig
+ // lookup issues and other problems, I code this explicitly. (Remember,
+ // IntType may be a user-defined type).
+ if (n < zero)
+ n = -n;
+ if (m < zero)
+ m = -m;
+
+ // As n and m are now positive, we can be sure that %= returns a
+ // positive value (the standard guarantees this for built-in types,
+ // and we require it of user-defined types).
+ for(;;) {
+ if(m == zero)
+ return n;
+ n %= m;
+ if(n == zero)
+ return m;
+ m %= n;
+ }
+}
+
+template <typename IntType>
+IntType lcm(IntType n, IntType m)
+{
+ // Avoid repeated construction
+ IntType zero(0);
+
+ if (n == zero || m == zero)
+ return zero;
+
+ n /= gcd(n, m);
+ n *= m;
+
+ if (n < zero)
+ n = -n;
+ return n;
+}
+
+class bad_rational : public std::domain_error
+{
+public:
+ explicit bad_rational() : std::domain_error("bad rational: zero denominator") {}
+};
+
+template <typename IntType>
+class rational;
+
+template <typename IntType>
+rational<IntType> abs(const rational<IntType>& r);
+
+template <typename IntType>
+class rational :
+ less_than_comparable < rational<IntType>,
+ equality_comparable < rational<IntType>,
+ less_than_comparable2 < rational<IntType>, IntType,
+ equality_comparable2 < rational<IntType>, IntType,
+ addable < rational<IntType>,
+ subtractable < rational<IntType>,
+ multipliable < rational<IntType>,
+ dividable < rational<IntType>,
+ addable2 < rational<IntType>, IntType,
+ subtractable2 < rational<IntType>, IntType,
+ subtractable2_left < rational<IntType>, IntType,
+ multipliable2 < rational<IntType>, IntType,
+ dividable2 < rational<IntType>, IntType,
+ dividable2_left < rational<IntType>, IntType,
+ incrementable < rational<IntType>,
+ decrementable < rational<IntType>
+ > > > > > > > > > > > > > > > >
+{
+ typedef typename boost::call_traits<IntType>::param_type param_type;
+
+ struct helper { IntType parts[2]; };
+ typedef IntType (helper::* bool_type)[2];
+
+public:
+ typedef IntType int_type;
+ rational() : num(0), den(1) {}
+ rational(param_type n) : num(n), den(1) {}
+ rational(param_type n, param_type d) : num(n), den(d) { normalize(); }
+
+ // Default copy constructor and assignment are fine
+
+ // Add assignment from IntType
+ rational& operator=(param_type n) { return assign(n, 1); }
+
+ // Assign in place
+ rational& assign(param_type n, param_type d);
+
+ // Access to representation
+ IntType numerator() const { return num; }
+ IntType denominator() const { return den; }
+
+ // Arithmetic assignment operators
+ rational& operator+= (const rational& r);
+ rational& operator-= (const rational& r);
+ rational& operator*= (const rational& r);
+ rational& operator/= (const rational& r);
+
+ rational& operator+= (param_type i);
+ rational& operator-= (param_type i);
+ rational& operator*= (param_type i);
+ rational& operator/= (param_type i);
+
+ // Increment and decrement
+ const rational& operator++();
+ const rational& operator--();
+
+ // Operator not
+ bool operator!() const { return !num; }
+
+ // Boolean conversion
+
+#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
+ // The "ISO C++ Template Parser" option in CW 8.3 chokes on the
+ // following, hence we selectively disable that option for the
+ // offending memfun.
+#pragma parse_mfunc_templ off
+#endif
+
+ operator bool_type() const { return operator !() ? 0 : &helper::parts; }
+
+#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
+#pragma parse_mfunc_templ reset
+#endif
+
+ // Comparison operators
+ bool operator< (const rational& r) const;
+ bool operator== (const rational& r) const;
+
+ bool operator< (param_type i) const;
+ bool operator> (param_type i) const;
+ bool operator== (param_type i) const;
+
+private:
+ // Implementation - numerator and denominator (normalized).
+ // Other possibilities - separate whole-part, or sign, fields?
+ IntType num;
+ IntType den;
+
+ // Representation note: Fractions are kept in normalized form at all
+ // times. normalized form is defined as gcd(num,den) == 1 and den > 0.
+ // In particular, note that the implementation of abs() below relies
+ // on den always being positive.
+ void normalize();
+};
+
+// Assign in place
+template <typename IntType>
+inline rational<IntType>& rational<IntType>::assign(param_type n, param_type d)
+{
+ num = n;
+ den = d;
+ normalize();
+ return *this;
+}
+
+// Unary plus and minus
+template <typename IntType>
+inline rational<IntType> operator+ (const rational<IntType>& r)
+{
+ return r;
+}
+
+template <typename IntType>
+inline rational<IntType> operator- (const rational<IntType>& r)
+{
+ return rational<IntType>(-r.numerator(), r.denominator());
+}
+
+// Arithmetic assignment operators
+template <typename IntType>
+rational<IntType>& rational<IntType>::operator+= (const rational<IntType>& r)
+{
+ // This calculation avoids overflow, and minimises the number of expensive
+ // calculations. Thanks to Nickolay Mladenov for this algorithm.
+ //
+ // Proof:
+ // We have to compute a/b + c/d, where gcd(a,b)=1 and gcd(b,c)=1.
+ // Let g = gcd(b,d), and b = b1*g, d=d1*g. Then gcd(b1,d1)=1
+ //
+ // The result is (a*d1 + c*b1) / (b1*d1*g).
+ // Now we have to normalize this ratio.
+ // Let's assume h | gcd((a*d1 + c*b1), (b1*d1*g)), and h > 1
+ // If h | b1 then gcd(h,d1)=1 and hence h|(a*d1+c*b1) => h|a.
+ // But since gcd(a,b1)=1 we have h=1.
+ // Similarly h|d1 leads to h=1.
+ // So we have that h | gcd((a*d1 + c*b1) , (b1*d1*g)) => h|g
+ // Finally we have gcd((a*d1 + c*b1), (b1*d1*g)) = gcd((a*d1 + c*b1), g)
+ // Which proves that instead of normalizing the result, it is better to
+ // divide num and den by gcd((a*d1 + c*b1), g)
+
+ // Protect against self-modification
+ IntType r_num = r.num;
+ IntType r_den = r.den;
+
+ IntType g = gcd(den, r_den);
+ den /= g; // = b1 from the calculations above
+ num = num * (r_den / g) + r_num * den;
+ g = gcd(num, g);
+ num /= g;
+ den *= r_den/g;
+
+ return *this;
+}
+
+template <typename IntType>
+rational<IntType>& rational<IntType>::operator-= (const rational<IntType>& r)
+{
+ // Protect against self-modification
+ IntType r_num = r.num;
+ IntType r_den = r.den;
+
+ // This calculation avoids overflow, and minimises the number of expensive
+ // calculations. It corresponds exactly to the += case above
+ IntType g = gcd(den, r_den);
+ den /= g;
+ num = num * (r_den / g) - r_num * den;
+ g = gcd(num, g);
+ num /= g;
+ den *= r_den/g;
+
+ return *this;
+}
+
+template <typename IntType>
+rational<IntType>& rational<IntType>::operator*= (const rational<IntType>& r)
+{
+ // Protect against self-modification
+ IntType r_num = r.num;
+ IntType r_den = r.den;
+
+ // Avoid overflow and preserve normalization
+ IntType gcd1 = gcd<IntType>(num, r_den);
+ IntType gcd2 = gcd<IntType>(r_num, den);
+ num = (num/gcd1) * (r_num/gcd2);
+ den = (den/gcd2) * (r_den/gcd1);
+ return *this;
+}
+
+template <typename IntType>
+rational<IntType>& rational<IntType>::operator/= (const rational<IntType>& r)
+{
+ // Protect against self-modification
+ IntType r_num = r.num;
+ IntType r_den = r.den;
+
+ // Avoid repeated construction
+ IntType zero(0);
+
+ // Trap division by zero
+ if (r_num == zero)
+ throw bad_rational();
+ if (num == zero)
+ return *this;
+
+ // Avoid overflow and preserve normalization
+ IntType gcd1 = gcd<IntType>(num, r_num);
+ IntType gcd2 = gcd<IntType>(r_den, den);
+ num = (num/gcd1) * (r_den/gcd2);
+ den = (den/gcd2) * (r_num/gcd1);
+
+ if (den < zero) {
+ num = -num;
+ den = -den;
+ }
+ return *this;
+}
+
+// Mixed-mode operators
+template <typename IntType>
+inline rational<IntType>&
+rational<IntType>::operator+= (param_type i)
+{
+ return operator+= (rational<IntType>(i));
+}
+
+template <typename IntType>
+inline rational<IntType>&
+rational<IntType>::operator-= (param_type i)
+{
+ return operator-= (rational<IntType>(i));
+}
+
+template <typename IntType>
+inline rational<IntType>&
+rational<IntType>::operator*= (param_type i)
+{
+ return operator*= (rational<IntType>(i));
+}
+
+template <typename IntType>
+inline rational<IntType>&
+rational<IntType>::operator/= (param_type i)
+{
+ return operator/= (rational<IntType>(i));
+}
+
+// Increment and decrement
+template <typename IntType>
+inline const rational<IntType>& rational<IntType>::operator++()
+{
+ // This can never denormalise the fraction
+ num += den;
+ return *this;
+}
+
+template <typename IntType>
+inline const rational<IntType>& rational<IntType>::operator--()
+{
+ // This can never denormalise the fraction
+ num -= den;
+ return *this;
+}
+
+// Comparison operators
+template <typename IntType>
+bool rational<IntType>::operator< (const rational<IntType>& r) const
+{
+ // Avoid repeated construction
+ IntType zero(0);
+
+ // If the two values have different signs, we don't need to do the
+ // expensive calculations below. We take advantage here of the fact
+ // that the denominator is always positive.
+ if (num < zero && r.num >= zero) // -ve < +ve
+ return true;
+ if (num >= zero && r.num <= zero) // +ve or zero is not < -ve or zero
+ return false;
+
+ // Avoid overflow
+ IntType gcd1 = gcd<IntType>(num, r.num);
+ IntType gcd2 = gcd<IntType>(r.den, den);
+ return (num/gcd1) * (r.den/gcd2) < (den/gcd2) * (r.num/gcd1);
+}
+
+template <typename IntType>
+bool rational<IntType>::operator< (param_type i) const
+{
+ // Avoid repeated construction
+ IntType zero(0);
+
+ // If the two values have different signs, we don't need to do the
+ // expensive calculations below. We take advantage here of the fact
+ // that the denominator is always positive.
+ if (num < zero && i >= zero) // -ve < +ve
+ return true;
+ if (num >= zero && i <= zero) // +ve or zero is not < -ve or zero
+ return false;
+
+ // Now, use the fact that n/d truncates towards zero as long as n and d
+ // are both positive.
+ // Divide instead of multiplying to avoid overflow issues. Of course,
+ // division may be slower, but accuracy is more important than speed...
+ if (num > zero)
+ return (num/den) < i;
+ else
+ return -i < (-num/den);
+}
+
+template <typename IntType>
+bool rational<IntType>::operator> (param_type i) const
+{
+ // Trap equality first
+ if (num == i && den == IntType(1))
+ return false;
+
+ // Otherwise, we can use operator<
+ return !operator<(i);
+}
+
+template <typename IntType>
+inline bool rational<IntType>::operator== (const rational<IntType>& r) const
+{
+ return ((num == r.num) && (den == r.den));
+}
+
+template <typename IntType>
+inline bool rational<IntType>::operator== (param_type i) const
+{
+ return ((den == IntType(1)) && (num == i));
+}
+
+// Normalisation
+template <typename IntType>
+void rational<IntType>::normalize()
+{
+ // Avoid repeated construction
+ IntType zero(0);
+
+ if (den == zero)
+ throw bad_rational();
+
+ // Handle the case of zero separately, to avoid division by zero
+ if (num == zero) {
+ den = IntType(1);
+ return;
+ }
+
+ IntType g = gcd<IntType>(num, den);
+
+ num /= g;
+ den /= g;
+
+ // Ensure that the denominator is positive
+ if (den < zero) {
+ num = -num;
+ den = -den;
+ }
+}
+
+namespace detail {
+
+ // A utility class to reset the format flags for an istream at end
+ // of scope, even in case of exceptions
+ struct resetter {
+ resetter(std::istream& is) : is_(is), f_(is.flags()) {}
+ ~resetter() { is_.flags(f_); }
+ std::istream& is_;
+ std::istream::fmtflags f_; // old GNU c++ lib has no ios_base
+ };
+
+}
+
+// Input and output
+template <typename IntType>
+std::istream& operator>> (std::istream& is, rational<IntType>& r)
+{
+ IntType n = IntType(0), d = IntType(1);
+ char c = 0;
+ detail::resetter sentry(is);
+
+ is >> n;
+ c = is.get();
+
+ if (c != '/')
+ is.clear(std::istream::badbit); // old GNU c++ lib has no ios_base
+
+#if !defined(__GNUC__) || (defined(__GNUC__) && (__GNUC__ >= 3)) || defined __SGI_STL_PORT
+ is >> std::noskipws;
+#else
+ is.unsetf(ios::skipws); // compiles, but seems to have no effect.
+#endif
+ is >> d;
+
+ if (is)
+ r.assign(n, d);
+
+ return is;
+}
+
+// Add manipulators for output format?
+template <typename IntType>
+std::ostream& operator<< (std::ostream& os, const rational<IntType>& r)
+{
+ os << r.numerator() << '/' << r.denominator();
+ return os;
+}
+
+// Type conversion
+template <typename T, typename IntType>
+inline T rational_cast(
+ const rational<IntType>& src BOOST_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
+{
+ return static_cast<T>(src.numerator())/src.denominator();
+}
+
+// Do not use any abs() defined on IntType - it isn't worth it, given the
+// difficulties involved (Koenig lookup required, there may not *be* an abs()
+// defined, etc etc).
+template <typename IntType>
+inline rational<IntType> abs(const rational<IntType>& r)
+{
+ if (r.numerator() >= IntType(0))
+ return r;
+
+ return rational<IntType>(-r.numerator(), r.denominator());
+}
+
+} // namespace boost
+
+#endif // BOOST_RATIONAL_HPP
+