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diff --git a/src/third_party/boost-1.60.0/boost/rational.hpp b/src/third_party/boost-1.60.0/boost/rational.hpp new file mode 100644 index 00000000000..72d11e7d06a --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/rational.hpp @@ -0,0 +1,709 @@ +// 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.Math; 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> + +// 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.Math + return integer::gcd( n, m ); +} + +template <typename IntType> +IntType lcm(IntType n, IntType m) +{ + // Defer to the version in Boost.Math + return integer::lcm( n, m ); +} +#endif // BOOST_CONTROL_RATIONAL_HAS_GCD + +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 : + 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> + > > > > > > > > > > > > > > > > +{ + // 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) {} + BOOST_CONSTEXPR + rational(param_type n) : num(n), den(1) {} + rational(param_type n, param_type d) : num(n), den(d) { normalize(); } + +#ifndef BOOST_NO_MEMBER_TEMPLATES + template < typename NewType > + BOOST_CONSTEXPR explicit + rational(rational<NewType> const &r) + : 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)){} +#endif + + // Default copy constructor and assignment are fine + + // Add assignment from IntType + rational& operator=(param_type i) { num = i; den = 1; return *this; } + + // Assign in place + rational& assign(param_type n, param_type 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); + + rational& operator+= (param_type i) { num += i * den; return *this; } + rational& operator-= (param_type i) { num -= i * den; return *this; } + rational& operator*= (param_type i); + rational& operator/= (param_type i); + + // Increment and decrement + const rational& operator++() { num += den; return *this; } + const rational& operator--() { num -= den; return *this; } + + // 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; + BOOST_CONSTEXPR + bool operator== (const rational& r) const; + + bool operator< (param_type i) const; + bool operator> (param_type i) const; + BOOST_CONSTEXPR + bool operator== (param_type i) const; + +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; + } +}; + +// Assign in place +template <typename IntType> +inline rational<IntType>& rational<IntType>::assign(param_type n, param_type d) +{ + return *this = rational( n, d ); +} + +// 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>(-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; +} + +// Mixed-mode operators +template <typename IntType> +inline rational<IntType>& +rational<IntType>::operator*= (param_type i) +{ + // Avoid overflow and preserve normalization + IntType gcd = integer::gcd(i, den); + num *= i / gcd; + den /= gcd; + + return *this; +} + +template <typename IntType> +rational<IntType>& +rational<IntType>::operator/= (param_type 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, i); + num /= gcd; + den *= i / gcd; + + if (den < zero) { + num = -num; + den = -den; + } + + return *this; +} + +// 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> +bool rational<IntType>::operator< (param_type 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 <typename IntType> +bool rational<IntType>::operator> (param_type i) const +{ + return operator==(i)? false: !operator<(i); +} + +template <typename IntType> +BOOST_CONSTEXPR +inline bool rational<IntType>::operator== (const rational<IntType>& r) const +{ + return ((num == r.num) && (den == r.den)); +} + +template <typename IntType> +BOOST_CONSTEXPR +inline bool rational<IntType>::operator== (param_type i) const +{ + return ((den == IntType(1)) && (num == i)); +} + +// 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) +{ + using namespace std; + + // The slash directly precedes the denominator, which has no prefixes. + ostringstream ss; + + ss.copyfmt( os ); + ss.tie( NULL ); + ss.exceptions( ios::goodbit ); + ss.width( 0 ); + ss << noshowpos << noshowbase << '/' << r.denominator(); + + // The numerator holds the showpos, internal, and showbase flags. + string const tail = ss.str(); + streamsize const w = os.width() - static_cast<streamsize>( tail.size() ); + + ss.clear(); + ss.str( "" ); + ss.flags( os.flags() ); + ss << setw( w < 0 || (os.flags() & ios::adjustfield) != 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 + |