| // 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. |
| |
| // 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/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 |
| // 12 Nov 20 Fix operators to work with C++20 rules (Glen Joseph Fernandes) |
| // 02 Sep 13 Remove unneeded forward declarations; tweak private helper |
| // function (Daryle Walker) |
| // 30 Aug 13 Improve exception safety of "assign"; start modernizing I/O code |
| // (Daryle Walker) |
| // 27 Aug 13 Add cross-version constructor template, plus some private helper |
| // functions; add constructor to exception class to take custom |
| // messages (Daryle Walker) |
| // 25 Aug 13 Add constexpr qualification wherever possible (Daryle Walker) |
| // 05 May 12 Reduced use of implicit gcd (Mario Lang) |
| // 05 Nov 06 Change rational_cast to not depend on division between different |
| // types (Daryle Walker) |
| // 04 Nov 06 Off-load GCD and LCM to Boost.Integer; add some invariant checks; |
| // add std::numeric_limits<> requirement to help GCD (Daryle Walker) |
| // 31 Oct 06 Recoded both operator< to use round-to-negative-infinity |
| // divisions; the rational-value version now uses continued fraction |
| // expansion to avoid overflows, for bug #798357 (Daryle Walker) |
| // 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 <boost/config.hpp> // for BOOST_NO_STDC_NAMESPACE, BOOST_MSVC, etc |
| #ifndef BOOST_NO_IOSTREAM |
| #include <iomanip> // for std::setw |
| #include <ios> // for std::noskipws, streamsize |
| #include <istream> // for std::istream |
| #include <ostream> // for std::ostream |
| #include <sstream> // for std::ostringstream |
| #endif |
| #include <cstddef> // for NULL |
| #include <stdexcept> // for std::domain_error |
| #include <string> // for std::string implicit constructor |
| #include <cstdlib> // for std::abs |
| #include <boost/call_traits.hpp> // for boost::call_traits |
| #include <boost/detail/workaround.hpp> // for BOOST_WORKAROUND |
| #include <boost/assert.hpp> // for BOOST_ASSERT |
| #include <boost/integer/common_factor_rt.hpp> // for boost::integer::gcd, lcm |
| #include <limits> // for std::numeric_limits |
| #include <boost/static_assert.hpp> // for BOOST_STATIC_ASSERT |
| #include <boost/throw_exception.hpp> |
| #include <boost/utility/enable_if.hpp> |
| #include <boost/type_traits/is_convertible.hpp> |
| #include <boost/type_traits/is_class.hpp> |
| #include <boost/type_traits/is_same.hpp> |
| #include <boost/type_traits/is_array.hpp> |
| |
| // Control whether depreciated GCD and LCM functions are included (default: yes) |
| #ifndef BOOST_CONTROL_RATIONAL_HAS_GCD |
| #define BOOST_CONTROL_RATIONAL_HAS_GCD 1 |
| #endif |
| |
| namespace boost { |
| |
| #if BOOST_CONTROL_RATIONAL_HAS_GCD |
| template <typename IntType> |
| IntType gcd(IntType n, IntType m) |
| { |
| // Defer to the version in Boost.Integer |
| return integer::gcd( n, m ); |
| } |
| |
| template <typename IntType> |
| IntType lcm(IntType n, IntType m) |
| { |
| // Defer to the version in Boost.Integer |
| return integer::lcm( n, m ); |
| } |
| #endif // BOOST_CONTROL_RATIONAL_HAS_GCD |
| |
| namespace rational_detail{ |
| |
| template <class FromInt, class ToInt, typename Enable = void> |
| struct is_compatible_integer; |
| |
| template <class FromInt, class ToInt> |
| struct is_compatible_integer<FromInt, ToInt, typename enable_if_c<!is_array<FromInt>::value>::type> |
| { |
| BOOST_STATIC_CONSTANT(bool, value = ((std::numeric_limits<FromInt>::is_specialized && std::numeric_limits<FromInt>::is_integer |
| && (std::numeric_limits<FromInt>::digits <= std::numeric_limits<ToInt>::digits) |
| && (std::numeric_limits<FromInt>::radix == std::numeric_limits<ToInt>::radix) |
| && ((std::numeric_limits<FromInt>::is_signed == false) || (std::numeric_limits<ToInt>::is_signed == true)) |
| && is_convertible<FromInt, ToInt>::value) |
| || is_same<FromInt, ToInt>::value) |
| || (is_class<ToInt>::value && is_class<FromInt>::value && is_convertible<FromInt, ToInt>::value)); |
| }; |
| |
| template <class FromInt, class ToInt> |
| struct is_compatible_integer<FromInt, ToInt, typename enable_if_c<is_array<FromInt>::value>::type> |
| { |
| BOOST_STATIC_CONSTANT(bool, value = false); |
| }; |
| |
| template <class FromInt, class ToInt, typename Enable = void> |
| struct is_backward_compatible_integer; |
| |
| template <class FromInt, class ToInt> |
| struct is_backward_compatible_integer<FromInt, ToInt, typename enable_if_c<!is_array<FromInt>::value>::type> |
| { |
| BOOST_STATIC_CONSTANT(bool, value = (std::numeric_limits<FromInt>::is_specialized && std::numeric_limits<FromInt>::is_integer |
| && !is_compatible_integer<FromInt, ToInt>::value |
| && (std::numeric_limits<FromInt>::radix == std::numeric_limits<ToInt>::radix) |
| && is_convertible<FromInt, ToInt>::value)); |
| }; |
| |
| template <class FromInt, class ToInt> |
| struct is_backward_compatible_integer<FromInt, ToInt, typename enable_if_c<is_array<FromInt>::value>::type> |
| { |
| BOOST_STATIC_CONSTANT(bool, value = false); |
| }; |
| } |
| |
| class bad_rational : public std::domain_error |
| { |
| public: |
| explicit bad_rational() : std::domain_error("bad rational: zero denominator") {} |
| explicit bad_rational( char const *what ) : std::domain_error( what ) {} |
| }; |
| |
| template <typename IntType> |
| class rational |
| { |
| // Class-wide pre-conditions |
| BOOST_STATIC_ASSERT( ::std::numeric_limits<IntType>::is_specialized ); |
| |
| // Helper types |
| typedef typename boost::call_traits<IntType>::param_type param_type; |
| |
| struct helper { IntType parts[2]; }; |
| typedef IntType (helper::* bool_type)[2]; |
| |
| public: |
| // Component type |
| typedef IntType int_type; |
| |
| BOOST_CONSTEXPR |
| rational() : num(0), den(1) {} |
| |
| template <class T>//, typename enable_if_c<!is_array<T>::value>::type> |
| BOOST_CONSTEXPR rational(const T& n, typename enable_if_c< |
| rational_detail::is_compatible_integer<T, IntType>::value |
| >::type const* = 0) : num(n), den(1) {} |
| |
| template <class T, class U> |
| BOOST_CXX14_CONSTEXPR rational(const T& n, const U& d, typename enable_if_c< |
| rational_detail::is_compatible_integer<T, IntType>::value && rational_detail::is_compatible_integer<U, IntType>::value |
| >::type const* = 0) : num(n), den(d) { |
| normalize(); |
| } |
| |
| template < typename NewType > |
| BOOST_CONSTEXPR explicit |
| rational(rational<NewType> const &r, typename enable_if_c<rational_detail::is_compatible_integer<NewType, IntType>::value>::type const* = 0) |
| : num(r.numerator()), den(is_normalized(int_type(r.numerator()), |
| int_type(r.denominator())) ? r.denominator() : |
| (BOOST_THROW_EXCEPTION(bad_rational("bad rational: denormalized conversion")), 0)){} |
| |
| template < typename NewType > |
| BOOST_CONSTEXPR explicit |
| rational(rational<NewType> const &r, typename disable_if_c<rational_detail::is_compatible_integer<NewType, IntType>::value>::type const* = 0) |
| : num(r.numerator()), den(is_normalized(int_type(r.numerator()), |
| int_type(r.denominator())) && is_safe_narrowing_conversion(r.denominator()) && is_safe_narrowing_conversion(r.numerator()) ? r.denominator() : |
| (BOOST_THROW_EXCEPTION(bad_rational("bad rational: denormalized conversion")), 0)){} |
| // Default copy constructor and assignment are fine |
| |
| // Add assignment from IntType |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename enable_if_c< |
| rational_detail::is_compatible_integer<T, IntType>::value, rational & |
| >::type operator=(const T& n) { return assign(static_cast<IntType>(n), static_cast<IntType>(1)); } |
| |
| // Assign in place |
| template <class T, class U> |
| BOOST_CXX14_CONSTEXPR typename enable_if_c< |
| rational_detail::is_compatible_integer<T, IntType>::value && rational_detail::is_compatible_integer<U, IntType>::value, rational & |
| >::type assign(const T& n, const U& d) |
| { |
| return *this = rational<IntType>(static_cast<IntType>(n), static_cast<IntType>(d)); |
| } |
| // |
| // The following overloads should probably *not* be provided - |
| // but are provided for backwards compatibity reasons only. |
| // These allow for construction/assignment from types that |
| // are wider than IntType only if there is an implicit |
| // conversion from T to IntType, they will throw a bad_rational |
| // if the conversion results in loss of precision or undefined behaviour. |
| // |
| template <class T>//, typename enable_if_c<!is_array<T>::value>::type> |
| BOOST_CXX14_CONSTEXPR rational(const T& n, typename enable_if_c< |
| rational_detail::is_backward_compatible_integer<T, IntType>::value |
| >::type const* = 0) |
| { |
| assign(n, static_cast<T>(1)); |
| } |
| template <class T, class U> |
| BOOST_CXX14_CONSTEXPR rational(const T& n, const U& d, typename enable_if_c< |
| (!rational_detail::is_compatible_integer<T, IntType>::value |
| || !rational_detail::is_compatible_integer<U, IntType>::value) |
| && std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer |
| && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix) |
| && is_convertible<T, IntType>::value && |
| std::numeric_limits<U>::is_specialized && std::numeric_limits<U>::is_integer |
| && (std::numeric_limits<U>::radix == std::numeric_limits<IntType>::radix) |
| && is_convertible<U, IntType>::value |
| >::type const* = 0) |
| { |
| assign(n, d); |
| } |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename enable_if_c< |
| std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer |
| && !rational_detail::is_compatible_integer<T, IntType>::value |
| && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix) |
| && is_convertible<T, IntType>::value, |
| rational & |
| >::type operator=(const T& n) { return assign(n, static_cast<T>(1)); } |
| |
| template <class T, class U> |
| BOOST_CXX14_CONSTEXPR typename enable_if_c< |
| (!rational_detail::is_compatible_integer<T, IntType>::value |
| || !rational_detail::is_compatible_integer<U, IntType>::value) |
| && std::numeric_limits<T>::is_specialized && std::numeric_limits<T>::is_integer |
| && (std::numeric_limits<T>::radix == std::numeric_limits<IntType>::radix) |
| && is_convertible<T, IntType>::value && |
| std::numeric_limits<U>::is_specialized && std::numeric_limits<U>::is_integer |
| && (std::numeric_limits<U>::radix == std::numeric_limits<IntType>::radix) |
| && is_convertible<U, IntType>::value, |
| rational & |
| >::type assign(const T& n, const U& d) |
| { |
| if(!is_safe_narrowing_conversion(n) || !is_safe_narrowing_conversion(d)) |
| BOOST_THROW_EXCEPTION(bad_rational()); |
| return *this = rational<IntType>(static_cast<IntType>(n), static_cast<IntType>(d)); |
| } |
| |
| // Access to representation |
| BOOST_CONSTEXPR |
| const IntType& numerator() const { return num; } |
| BOOST_CONSTEXPR |
| const IntType& denominator() const { return den; } |
| |
| // Arithmetic assignment operators |
| BOOST_CXX14_CONSTEXPR rational& operator+= (const rational& r); |
| BOOST_CXX14_CONSTEXPR rational& operator-= (const rational& r); |
| BOOST_CXX14_CONSTEXPR rational& operator*= (const rational& r); |
| BOOST_CXX14_CONSTEXPR rational& operator/= (const rational& r); |
| |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator+= (const T& i) |
| { |
| num += i * den; |
| return *this; |
| } |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator-= (const T& i) |
| { |
| num -= i * den; |
| return *this; |
| } |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator*= (const T& i) |
| { |
| // Avoid overflow and preserve normalization |
| IntType gcd = integer::gcd(static_cast<IntType>(i), den); |
| num *= i / gcd; |
| den /= gcd; |
| return *this; |
| } |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, rational&>::type operator/= (const T& i) |
| { |
| // Avoid repeated construction |
| IntType const zero(0); |
| |
| if(i == zero) BOOST_THROW_EXCEPTION(bad_rational()); |
| if(num == zero) return *this; |
| |
| // Avoid overflow and preserve normalization |
| IntType const gcd = integer::gcd(num, static_cast<IntType>(i)); |
| num /= gcd; |
| den *= i / gcd; |
| |
| if(den < zero) { |
| num = -num; |
| den = -den; |
| } |
| |
| return *this; |
| } |
| |
| // Increment and decrement |
| BOOST_CXX14_CONSTEXPR const rational& operator++() { num += den; return *this; } |
| BOOST_CXX14_CONSTEXPR const rational& operator--() { num -= den; return *this; } |
| |
| BOOST_CXX14_CONSTEXPR rational operator++(int) |
| { |
| rational t(*this); |
| ++(*this); |
| return t; |
| } |
| BOOST_CXX14_CONSTEXPR rational operator--(int) |
| { |
| rational t(*this); |
| --(*this); |
| return t; |
| } |
| |
| // Operator not |
| BOOST_CONSTEXPR |
| 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 |
| |
| BOOST_CONSTEXPR |
| operator bool_type() const { return operator !() ? 0 : &helper::parts; } |
| |
| #if BOOST_WORKAROUND(__MWERKS__,<=0x3003) |
| #pragma parse_mfunc_templ reset |
| #endif |
| |
| // Comparison operators |
| BOOST_CXX14_CONSTEXPR bool operator< (const rational& r) const; |
| BOOST_CXX14_CONSTEXPR bool operator> (const rational& r) const { return r < *this; } |
| BOOST_CONSTEXPR |
| bool operator== (const rational& r) const; |
| |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator< (const T& i) const |
| { |
| // Avoid repeated construction |
| int_type const zero(0); |
| |
| // Break value into mixed-fraction form, w/ always-nonnegative remainder |
| BOOST_ASSERT(this->den > zero); |
| int_type q = this->num / this->den, r = this->num % this->den; |
| while(r < zero) { r += this->den; --q; } |
| |
| // Compare with just the quotient, since the remainder always bumps the |
| // value up. [Since q = floor(n/d), and if n/d < i then q < i, if n/d == i |
| // then q == i, if n/d == i + r/d then q == i, and if n/d >= i + 1 then |
| // q >= i + 1 > i; therefore n/d < i iff q < i.] |
| return q < i; |
| } |
| template <class T> |
| BOOST_CXX14_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator>(const T& i) const |
| { |
| return operator==(i) ? false : !operator<(i); |
| } |
| template <class T> |
| BOOST_CONSTEXPR typename boost::enable_if_c<rational_detail::is_compatible_integer<T, IntType>::value, bool>::type operator== (const T& i) const |
| { |
| return ((den == IntType(1)) && (num == i)); |
| } |
| |
| private: |
| // Implementation - numerator and denominator (normalized). |
| // Other possibilities - separate whole-part, or sign, fields? |
| IntType num; |
| IntType den; |
| |
| // Helper functions |
| static BOOST_CONSTEXPR |
| int_type inner_gcd( param_type a, param_type b, int_type const &zero = |
| int_type(0) ) |
| { return b == zero ? a : inner_gcd(b, a % b, zero); } |
| |
| static BOOST_CONSTEXPR |
| int_type inner_abs( param_type x, int_type const &zero = int_type(0) ) |
| { return x < zero ? -x : +x; } |
| |
| // 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. |
| BOOST_CXX14_CONSTEXPR bool test_invariant() const; |
| BOOST_CXX14_CONSTEXPR void normalize(); |
| |
| static BOOST_CONSTEXPR |
| bool is_normalized( param_type n, param_type d, int_type const &zero = |
| int_type(0), int_type const &one = int_type(1) ) |
| { |
| return d > zero && ( n != zero || d == one ) && inner_abs( inner_gcd(n, |
| d, zero), zero ) == one; |
| } |
| // |
| // Conversion checks: |
| // |
| // (1) From an unsigned type with more digits than IntType: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val) |
| { |
| return val < (T(1) << std::numeric_limits<IntType>::digits); |
| } |
| // |
| // (2) From a signed type with more digits than IntType, and IntType also signed: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T& val) |
| { |
| // Note that this check assumes IntType has a 2's complement representation, |
| // we don't want to try to convert a std::numeric_limits<IntType>::min() to |
| // a T because that conversion may not be allowed (this happens when IntType |
| // is from Boost.Multiprecision). |
| return (val < (T(1) << std::numeric_limits<IntType>::digits)) && (val >= -(T(1) << std::numeric_limits<IntType>::digits)); |
| } |
| // |
| // (3) From a signed type with more digits than IntType, and IntType unsigned: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits > std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val) |
| { |
| return (val < (T(1) << std::numeric_limits<IntType>::digits)) && (val >= 0); |
| } |
| // |
| // (4) From a signed type with fewer digits than IntType, and IntType unsigned: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T& val) |
| { |
| return val >= 0; |
| } |
| // |
| // (5) From an unsigned type with fewer digits than IntType, and IntType signed: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T&) |
| { |
| return true; |
| } |
| // |
| // (6) From an unsigned type with fewer digits than IntType, and IntType unsigned: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == false) && (std::numeric_limits<IntType>::is_signed == false), bool>::type is_safe_narrowing_conversion(const T&) |
| { |
| return true; |
| } |
| // |
| // (7) From an signed type with fewer digits than IntType, and IntType signed: |
| // |
| template <class T> |
| BOOST_CONSTEXPR static typename boost::enable_if_c<(std::numeric_limits<T>::digits <= std::numeric_limits<IntType>::digits) && (std::numeric_limits<T>::is_signed == true) && (std::numeric_limits<IntType>::is_signed == true), bool>::type is_safe_narrowing_conversion(const T&) |
| { |
| return true; |
| } |
| }; |
| |
| // Unary plus and minus |
| template <typename IntType> |
| BOOST_CONSTEXPR |
| inline rational<IntType> operator+ (const rational<IntType>& r) |
| { |
| return r; |
| } |
| |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline rational<IntType> operator- (const rational<IntType>& r) |
| { |
| return rational<IntType>(static_cast<IntType>(-r.numerator()), r.denominator()); |
| } |
| |
| // Arithmetic assignment operators |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR 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 = integer::gcd(den, r_den); |
| den /= g; // = b1 from the calculations above |
| num = num * (r_den / g) + r_num * den; |
| g = integer::gcd(num, g); |
| num /= g; |
| den *= r_den/g; |
| |
| return *this; |
| } |
| |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR 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 = integer::gcd(den, r_den); |
| den /= g; |
| num = num * (r_den / g) - r_num * den; |
| g = integer::gcd(num, g); |
| num /= g; |
| den *= r_den/g; |
| |
| return *this; |
| } |
| |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR 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 = integer::gcd(num, r_den); |
| IntType gcd2 = integer::gcd(r_num, den); |
| num = (num/gcd1) * (r_num/gcd2); |
| den = (den/gcd2) * (r_den/gcd1); |
| return *this; |
| } |
| |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR 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) |
| BOOST_THROW_EXCEPTION(bad_rational()); |
| if (num == zero) |
| return *this; |
| |
| // Avoid overflow and preserve normalization |
| IntType gcd1 = integer::gcd(num, r_num); |
| IntType gcd2 = integer::gcd(r_den, den); |
| num = (num/gcd1) * (r_den/gcd2); |
| den = (den/gcd2) * (r_num/gcd1); |
| |
| if (den < zero) { |
| num = -num; |
| den = -den; |
| } |
| return *this; |
| } |
| |
| |
| // |
| // Non-member operators: previously these were provided by Boost.Operator, but these had a number of |
| // drawbacks, most notably, that in order to allow inter-operability with IntType code such as this: |
| // |
| // rational<int> r(3); |
| // assert(r == 3.5); // compiles and passes!! |
| // |
| // Happens to be allowed as well :-( |
| // |
| // There are three possible cases for each operator: |
| // 1) rational op rational. |
| // 2) rational op integer |
| // 3) integer op rational |
| // Cases (1) and (2) are folded into the one function. |
| // |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type |
| operator + (const rational<IntType>& a, const Arg& b) |
| { |
| rational<IntType> t(a); |
| return t += b; |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type |
| operator + (const Arg& b, const rational<IntType>& a) |
| { |
| rational<IntType> t(a); |
| return t += b; |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type |
| operator - (const rational<IntType>& a, const Arg& b) |
| { |
| rational<IntType> t(a); |
| return t -= b; |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type |
| operator - (const Arg& b, const rational<IntType>& a) |
| { |
| rational<IntType> t(a); |
| return -(t -= b); |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type |
| operator * (const rational<IntType>& a, const Arg& b) |
| { |
| rational<IntType> t(a); |
| return t *= b; |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type |
| operator * (const Arg& b, const rational<IntType>& a) |
| { |
| rational<IntType> t(a); |
| return t *= b; |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, rational<IntType> >::type |
| operator / (const rational<IntType>& a, const Arg& b) |
| { |
| rational<IntType> t(a); |
| return t /= b; |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, rational<IntType> >::type |
| operator / (const Arg& b, const rational<IntType>& a) |
| { |
| rational<IntType> t(b); |
| return t /= a; |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type |
| operator <= (const rational<IntType>& a, const Arg& b) |
| { |
| return !a.operator>(b); |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator <= (const Arg& b, const rational<IntType>& a) |
| { |
| return a >= b; |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type |
| operator >= (const rational<IntType>& a, const Arg& b) |
| { |
| return !a.operator<(b); |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator >= (const Arg& b, const rational<IntType>& a) |
| { |
| return a <= b; |
| } |
| |
| template <class IntType, class Arg> |
| BOOST_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value || is_same<rational<IntType>, Arg>::value, bool>::type |
| operator != (const rational<IntType>& a, const Arg& b) |
| { |
| return !a.operator==(b); |
| } |
| template <class Arg, class IntType> |
| BOOST_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator != (const Arg& b, const rational<IntType>& a) |
| { |
| return !(b == a); |
| } |
| |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator < (const Arg& b, const rational<IntType>& a) |
| { |
| return a.operator>(b); |
| } |
| template <class Arg, class IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator > (const Arg& b, const rational<IntType>& a) |
| { |
| return a.operator<(b); |
| } |
| template <class Arg, class IntType> |
| BOOST_CONSTEXPR |
| inline typename boost::enable_if_c < |
| rational_detail::is_compatible_integer<Arg, IntType>::value, bool>::type |
| operator == (const Arg& b, const rational<IntType>& a) |
| { |
| return a.operator==(b); |
| } |
| |
| // Comparison operators |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR |
| bool rational<IntType>::operator< (const rational<IntType>& r) const |
| { |
| // Avoid repeated construction |
| int_type const zero( 0 ); |
| |
| // This should really be a class-wide invariant. The reason for these |
| // checks is that for 2's complement systems, INT_MIN has no corresponding |
| // positive, so negating it during normalization keeps it INT_MIN, which |
| // is bad for later calculations that assume a positive denominator. |
| BOOST_ASSERT( this->den > zero ); |
| BOOST_ASSERT( r.den > zero ); |
| |
| // Determine relative order by expanding each value to its simple continued |
| // fraction representation using the Euclidian GCD algorithm. |
| struct { int_type n, d, q, r; } |
| ts = { this->num, this->den, static_cast<int_type>(this->num / this->den), |
| static_cast<int_type>(this->num % this->den) }, |
| rs = { r.num, r.den, static_cast<int_type>(r.num / r.den), |
| static_cast<int_type>(r.num % r.den) }; |
| unsigned reverse = 0u; |
| |
| // Normalize negative moduli by repeatedly adding the (positive) denominator |
| // and decrementing the quotient. Later cycles should have all positive |
| // values, so this only has to be done for the first cycle. (The rules of |
| // C++ require a nonnegative quotient & remainder for a nonnegative dividend |
| // & positive divisor.) |
| while ( ts.r < zero ) { ts.r += ts.d; --ts.q; } |
| while ( rs.r < zero ) { rs.r += rs.d; --rs.q; } |
| |
| // Loop through and compare each variable's continued-fraction components |
| for ( ;; ) |
| { |
| // The quotients of the current cycle are the continued-fraction |
| // components. Comparing two c.f. is comparing their sequences, |
| // stopping at the first difference. |
| if ( ts.q != rs.q ) |
| { |
| // Since reciprocation changes the relative order of two variables, |
| // and c.f. use reciprocals, the less/greater-than test reverses |
| // after each index. (Start w/ non-reversed @ whole-number place.) |
| return reverse ? ts.q > rs.q : ts.q < rs.q; |
| } |
| |
| // Prepare the next cycle |
| reverse ^= 1u; |
| |
| if ( (ts.r == zero) || (rs.r == zero) ) |
| { |
| // At least one variable's c.f. expansion has ended |
| break; |
| } |
| |
| ts.n = ts.d; ts.d = ts.r; |
| ts.q = ts.n / ts.d; ts.r = ts.n % ts.d; |
| rs.n = rs.d; rs.d = rs.r; |
| rs.q = rs.n / rs.d; rs.r = rs.n % rs.d; |
| } |
| |
| // Compare infinity-valued components for otherwise equal sequences |
| if ( ts.r == rs.r ) |
| { |
| // Both remainders are zero, so the next (and subsequent) c.f. |
| // components for both sequences are infinity. Therefore, the sequences |
| // and their corresponding values are equal. |
| return false; |
| } |
| else |
| { |
| #ifdef BOOST_MSVC |
| #pragma warning(push) |
| #pragma warning(disable:4800) |
| #endif |
| // Exactly one of the remainders is zero, so all following c.f. |
| // components of that variable are infinity, while the other variable |
| // has a finite next c.f. component. So that other variable has the |
| // lesser value (modulo the reversal flag!). |
| return ( ts.r != zero ) != static_cast<bool>( reverse ); |
| #ifdef BOOST_MSVC |
| #pragma warning(pop) |
| #endif |
| } |
| } |
| |
| template <typename IntType> |
| BOOST_CONSTEXPR |
| inline bool rational<IntType>::operator== (const rational<IntType>& r) const |
| { |
| return ((num == r.num) && (den == r.den)); |
| } |
| |
| // Invariant check |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR |
| inline bool rational<IntType>::test_invariant() const |
| { |
| return ( this->den > int_type(0) ) && ( integer::gcd(this->num, this->den) == |
| int_type(1) ); |
| } |
| |
| // Normalisation |
| template <typename IntType> |
| BOOST_CXX14_CONSTEXPR void rational<IntType>::normalize() |
| { |
| // Avoid repeated construction |
| IntType zero(0); |
| |
| if (den == zero) |
| BOOST_THROW_EXCEPTION(bad_rational()); |
| |
| // Handle the case of zero separately, to avoid division by zero |
| if (num == zero) { |
| den = IntType(1); |
| return; |
| } |
| |
| IntType g = integer::gcd(num, den); |
| |
| num /= g; |
| den /= g; |
| |
| if (den < -(std::numeric_limits<IntType>::max)()) { |
| BOOST_THROW_EXCEPTION(bad_rational("bad rational: non-zero singular denominator")); |
| } |
| |
| // Ensure that the denominator is positive |
| if (den < zero) { |
| num = -num; |
| den = -den; |
| } |
| |
| BOOST_ASSERT( this->test_invariant() ); |
| } |
| |
| #ifndef BOOST_NO_IOSTREAM |
| 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) |
| { |
| using std::ios; |
| |
| IntType n = IntType(0), d = IntType(1); |
| char c = 0; |
| detail::resetter sentry(is); |
| |
| if ( is >> n ) |
| { |
| if ( is.get(c) ) |
| { |
| if ( c == '/' ) |
| { |
| if ( is >> std::noskipws >> d ) |
| try { |
| r.assign( n, d ); |
| } catch ( bad_rational & ) { // normalization fail |
| try { is.setstate(ios::failbit); } |
| catch ( ... ) {} // don't throw ios_base::failure... |
| if ( is.exceptions() & ios::failbit ) |
| throw; // ...but the original exception instead |
| // ELSE: suppress the exception, use just error flags |
| } |
| } |
| else |
| is.setstate( ios::failbit ); |
| } |
| } |
| |
| return is; |
| } |
| |
| // Add manipulators for output format? |
| template <typename IntType> |
| std::ostream& operator<< (std::ostream& os, const rational<IntType>& r) |
| { |
| // The slash directly precedes the denominator, which has no prefixes. |
| std::ostringstream ss; |
| |
| ss.copyfmt( os ); |
| ss.tie( NULL ); |
| ss.exceptions( std::ios::goodbit ); |
| ss.width( 0 ); |
| ss << std::noshowpos << std::noshowbase << '/' << r.denominator(); |
| |
| // The numerator holds the showpos, internal, and showbase flags. |
| std::string const tail = ss.str(); |
| std::streamsize const w = |
| os.width() - static_cast<std::streamsize>( tail.size() ); |
| |
| ss.clear(); |
| ss.str( "" ); |
| ss.flags( os.flags() ); |
| ss << std::setw( w < 0 || (os.flags() & std::ios::adjustfield) != |
| std::ios::internal ? 0 : w ) << r.numerator(); |
| return os << ss.str() + tail; |
| } |
| #endif // BOOST_NO_IOSTREAM |
| |
| // Type conversion |
| template <typename T, typename IntType> |
| BOOST_CONSTEXPR |
| inline T rational_cast(const rational<IntType>& src) |
| { |
| return static_cast<T>(src.numerator())/static_cast<T>(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> |
| BOOST_CXX14_CONSTEXPR |
| inline rational<IntType> abs(const rational<IntType>& r) |
| { |
| return r.numerator() >= IntType(0)? r: -r; |
| } |
| |
| namespace integer { |
| |
| template <typename IntType> |
| struct gcd_evaluator< rational<IntType> > |
| { |
| typedef rational<IntType> result_type, |
| first_argument_type, second_argument_type; |
| result_type operator() ( first_argument_type const &a |
| , second_argument_type const &b |
| ) const |
| { |
| return result_type(integer::gcd(a.numerator(), b.numerator()), |
| integer::lcm(a.denominator(), b.denominator())); |
| } |
| }; |
| |
| template <typename IntType> |
| struct lcm_evaluator< rational<IntType> > |
| { |
| typedef rational<IntType> result_type, |
| first_argument_type, second_argument_type; |
| result_type operator() ( first_argument_type const &a |
| , second_argument_type const &b |
| ) const |
| { |
| return result_type(integer::lcm(a.numerator(), b.numerator()), |
| integer::gcd(a.denominator(), b.denominator())); |
| } |
| }; |
| |
| } // namespace integer |
| |
| } // namespace boost |
| |
| #endif // BOOST_RATIONAL_HPP |
