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Diffstat (limited to 'inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/rational.hpp')
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diff --git a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/rational.hpp b/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/rational.hpp deleted file mode 100644 index 4fc06c9ed..000000000 --- a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/rational.hpp +++ /dev/null @@ -1,1002 +0,0 @@ -// 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 -// 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 <boost/operators.hpp> // for boost::addable etc -#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> - -// 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> - struct is_compatible_integer - { - 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)); - }; - -} - -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> - 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> - 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> - 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> - 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> - rational(const T& n, 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 - >::type const* = 0) - { - assign(n, static_cast<T>(1)); - } - template <class T, class U> - 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> - 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> - 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 - rational& operator+= (const rational& r); - rational& operator-= (const rational& r); - rational& operator*= (const rational& r); - rational& operator/= (const rational& r); - - template <class T> - 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> - 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> - 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> - 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 - const rational& operator++() { num += den; return *this; } - const rational& operator--() { num -= den; return *this; } - - rational operator++(int) - { - rational t(*this); - ++(*this); - return t; - } - 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 - bool operator< (const rational& r) const; - bool operator> (const rational& r) const { return r < *this; } - BOOST_CONSTEXPR - bool operator== (const rational& r) const; - - template <class T> - 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> - 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. - bool test_invariant() const; - 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> -inline rational<IntType> operator- (const rational<IntType>& r) -{ - return rational<IntType>(static_cast<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 = 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> -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> -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> -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> -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> -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> -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> -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> -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> -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> -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> -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> -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 > b); -} -template <class Arg, class IntType> -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> -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 < b); -} -template <class Arg, class IntType> -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> -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 == b); -} -template <class Arg, class IntType> -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> -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 Arg, class IntType> -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 Arg, class IntType> -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; -} - -// Comparison operators -template <typename IntType> -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> -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> -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; - - // Ensure that the denominator is positive - if (den < zero) { - num = -num; - den = -den; - } - - // ...But acknowledge that the previous step doesn't always work. - // (Nominally, this should be done before the mutating steps, but this - // member function is only called during the constructor, so we never have - // to worry about zombie objects.) - if (den < zero) - BOOST_THROW_EXCEPTION(bad_rational("bad rational: non-zero singular denominator")); - - 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> -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 |