libstdc++
ratio
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00001 // ratio -*- C++ -*-
00002 
00003 // Copyright (C) 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
00004 //
00005 // This file is part of the GNU ISO C++ Library.  This library is free
00006 // software; you can redistribute it and/or modify it under the 
00007 // terms of the GNU General Public License as published by the 
00008 // Free Software Foundation; either version 3, or (at your option)
00009 // any later version.
00010 
00011 // This library is distributed in the hope that it will be useful,
00012 // but WITHOUT ANY WARRANTY; without even the implied warranty of
00013 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 
00014 // GNU General Public License for more details.
00015 
00016 // Under Section 7 of GPL version 3, you are granted additional
00017 // permissions described in the GCC Runtime Library Exception, version
00018 // 3.1, as published by the Free Software Foundation.
00019 
00020 // You should have received a copy of the GNU General Public License and
00021 // a copy of the GCC Runtime Library Exception along with this program;
00022 // see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
00023 // <http://www.gnu.org/licenses/>.
00024 
00025 /** @file include/ratio
00026  *  This is a Standard C++ Library header.
00027  */
00028 
00029 #ifndef _GLIBCXX_RATIO
00030 #define _GLIBCXX_RATIO 1
00031 
00032 #pragma GCC system_header
00033 
00034 #ifndef __GXX_EXPERIMENTAL_CXX0X__
00035 # include <bits/c++0x_warning.h>
00036 #else
00037 
00038 #include <type_traits>
00039 #include <cstdint>
00040 
00041 #ifdef _GLIBCXX_USE_C99_STDINT_TR1
00042 
00043 namespace std _GLIBCXX_VISIBILITY(default)
00044 {
00045 _GLIBCXX_BEGIN_NAMESPACE_VERSION
00046 
00047   /**
00048    * @defgroup ratio Rational Arithmetic
00049    * @ingroup utilities
00050    *
00051    * Compile time representation of finite rational numbers.
00052    * @{
00053    */
00054 
00055   template<intmax_t _Pn>
00056     struct __static_sign
00057     : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
00058     { };
00059 
00060   template<intmax_t _Pn>
00061     struct __static_abs
00062     : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
00063     { };
00064 
00065   template<intmax_t _Pn, intmax_t _Qn>
00066     struct __static_gcd;
00067  
00068   template<intmax_t _Pn, intmax_t _Qn>
00069     struct __static_gcd
00070     : __static_gcd<_Qn, (_Pn % _Qn)>
00071     { };
00072 
00073   template<intmax_t _Pn>
00074     struct __static_gcd<_Pn, 0>
00075     : integral_constant<intmax_t, __static_abs<_Pn>::value>
00076     { };
00077 
00078   template<intmax_t _Qn>
00079     struct __static_gcd<0, _Qn>
00080     : integral_constant<intmax_t, __static_abs<_Qn>::value>
00081     { };
00082 
00083   // Let c = 2^(half # of bits in an intmax_t)
00084   // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
00085   // The multiplication of N and M becomes,
00086   // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
00087   // Multiplication is safe if each term and the sum of the terms
00088   // is representable by intmax_t.
00089   template<intmax_t _Pn, intmax_t _Qn>
00090     struct __safe_multiply
00091     {
00092     private:
00093       static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
00094 
00095       static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
00096       static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
00097       static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
00098       static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
00099 
00100       static_assert(__a1 == 0 || __b1 == 0, 
00101         "overflow in multiplication");
00102       static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 
00103         "overflow in multiplication");
00104       static_assert(__b0 * __a0 <= __INTMAX_MAX__, 
00105         "overflow in multiplication");
00106       static_assert((__a0 * __b1 + __b0 * __a1) * __c <= 
00107         __INTMAX_MAX__ -  __b0 * __a0, "overflow in multiplication");
00108 
00109     public:
00110       static const intmax_t value = _Pn * _Qn;
00111     };
00112 
00113   // Helpers for __safe_add
00114   template<intmax_t _Pn, intmax_t _Qn, bool>
00115     struct __add_overflow_check_impl
00116     : integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
00117     { };
00118 
00119   template<intmax_t _Pn, intmax_t _Qn>
00120     struct __add_overflow_check_impl<_Pn, _Qn, false>
00121     : integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
00122     { };
00123 
00124   template<intmax_t _Pn, intmax_t _Qn>
00125     struct __add_overflow_check
00126     : __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
00127     { };
00128 
00129   template<intmax_t _Pn, intmax_t _Qn>
00130     struct __safe_add
00131     {
00132       static_assert(__add_overflow_check<_Pn, _Qn>::value != 0, 
00133         "overflow in addition");
00134 
00135       static const intmax_t value = _Pn + _Qn;
00136     };
00137 
00138   /**
00139    *  @brief Provides compile-time rational arithmetic.
00140    *
00141    *  This class template represents any finite rational number with a
00142    *  numerator and denominator representable by compile-time constants of
00143    *  type intmax_t. The ratio is simplified when instantiated.
00144    *
00145    *  For example:
00146    *  @code
00147    *    std::ratio<7,-21>::num == -1;
00148    *    std::ratio<7,-21>::den == 3;
00149    *  @endcode
00150    *  
00151   */
00152   template<intmax_t _Num, intmax_t _Den = 1>
00153     struct ratio
00154     {
00155       static_assert(_Den != 0, "denominator cannot be zero");
00156       static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
00157             "out of range");
00158 
00159       // Note: sign(N) * abs(N) == N
00160       static constexpr intmax_t num =
00161         _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
00162 
00163       static constexpr intmax_t den =
00164         __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
00165 
00166       typedef ratio<num, den> type;
00167     };
00168 
00169   template<intmax_t _Num, intmax_t _Den>
00170     constexpr intmax_t ratio<_Num, _Den>::num;
00171 
00172   template<intmax_t _Num, intmax_t _Den>
00173     constexpr intmax_t ratio<_Num, _Den>::den;
00174 
00175   /// ratio_add
00176   template<typename _R1, typename _R2>
00177     struct ratio_add
00178     {
00179     private:
00180       static constexpr intmax_t __gcd =
00181         __static_gcd<_R1::den, _R2::den>::value;
00182       static constexpr intmax_t __n = __safe_add<
00183         __safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
00184         __safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value;
00185 
00186       // The new numerator may have common factors with the denominator,
00187       // but they have to also be factors of __gcd.
00188       static constexpr intmax_t __gcd2 = __static_gcd<__n, __gcd>::value;
00189       
00190     public:
00191       typedef ratio<__n / __gcd2,
00192         __safe_multiply<_R1::den / __gcd2, _R2::den / __gcd>::value> type;
00193 
00194       static constexpr intmax_t num = type::num;
00195       static constexpr intmax_t den = type::den;
00196     };
00197 
00198   template<typename _R1, typename _R2>
00199     constexpr intmax_t ratio_add<_R1, _R2>::num;
00200 
00201   template<typename _R1, typename _R2>
00202     constexpr intmax_t ratio_add<_R1, _R2>::den;
00203 
00204   /// ratio_subtract
00205   template<typename _R1, typename _R2>
00206     struct ratio_subtract
00207     {
00208       typedef typename ratio_add<
00209         _R1,
00210         ratio<-_R2::num, _R2::den>>::type type;
00211 
00212       static constexpr intmax_t num = type::num;
00213       static constexpr intmax_t den = type::den;
00214     };
00215 
00216   template<typename _R1, typename _R2>
00217     constexpr intmax_t ratio_subtract<_R1, _R2>::num;
00218 
00219   template<typename _R1, typename _R2>
00220     constexpr intmax_t ratio_subtract<_R1, _R2>::den;
00221 
00222   /// ratio_multiply
00223   template<typename _R1, typename _R2>
00224     struct ratio_multiply
00225     {
00226     private:
00227       static const intmax_t __gcd1 =
00228         __static_gcd<_R1::num, _R2::den>::value;
00229       static const intmax_t __gcd2 =
00230         __static_gcd<_R2::num, _R1::den>::value;
00231 
00232     public:
00233       typedef ratio<
00234         __safe_multiply<(_R1::num / __gcd1),
00235                         (_R2::num / __gcd2)>::value,
00236         __safe_multiply<(_R1::den / __gcd2),
00237                         (_R2::den / __gcd1)>::value> type;
00238 
00239       static constexpr intmax_t num = type::num;
00240       static constexpr intmax_t den = type::den;
00241     };
00242 
00243   template<typename _R1, typename _R2>
00244     constexpr intmax_t ratio_multiply<_R1, _R2>::num;
00245 
00246   template<typename _R1, typename _R2>
00247     constexpr intmax_t ratio_multiply<_R1, _R2>::den;
00248 
00249   /// ratio_divide
00250   template<typename _R1, typename _R2>
00251     struct ratio_divide
00252     {
00253       static_assert(_R2::num != 0, "division by 0");
00254 
00255       typedef typename ratio_multiply<
00256         _R1,
00257         ratio<_R2::den, _R2::num>>::type type;
00258 
00259       static constexpr intmax_t num = type::num;
00260       static constexpr intmax_t den = type::den;
00261     };
00262 
00263   template<typename _R1, typename _R2>
00264     constexpr intmax_t ratio_divide<_R1, _R2>::num;
00265 
00266   template<typename _R1, typename _R2>
00267     constexpr intmax_t ratio_divide<_R1, _R2>::den;
00268 
00269   /// ratio_equal
00270   template<typename _R1, typename _R2>
00271     struct ratio_equal
00272     : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
00273     { };
00274   
00275   /// ratio_not_equal
00276   template<typename _R1, typename _R2>
00277     struct ratio_not_equal
00278     : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
00279     { };
00280 
00281   // 0 <= _Ri < 1
00282   // If one is 0, conclude
00283   // Otherwise, x < y iff 1/y < 1/x
00284   template<typename _R1, typename _R2>
00285     struct __ratio_less_impl_2;
00286 
00287   // _Ri > 0
00288   // Compare the integral parts, and remove them if they are equal
00289   template<typename _R1, typename _R2, intmax_t __q1 = _R1::num / _R1::den,
00290            intmax_t __q2 = _R2::num / _R2::den, bool __eq = (__q1 == __q2)>
00291     struct __ratio_less_impl_1
00292     : __ratio_less_impl_2<ratio<_R1::num % _R1::den, _R1::den>,
00293            ratio<_R2::num % _R2::den, _R2::den> >::type
00294     { }; 
00295 
00296   template<typename _R1, typename _R2, intmax_t __q1, intmax_t __q2>
00297     struct __ratio_less_impl_1<_R1, _R2, __q1, __q2, false>
00298     : integral_constant<bool, (__q1 < __q2) >
00299     { };
00300 
00301   template<typename _R1, typename _R2>
00302     struct __ratio_less_impl_2
00303     : __ratio_less_impl_1<ratio<_R2::den, _R2::num>,
00304            ratio<_R1::den, _R1::num> >::type
00305     { }; 
00306 
00307   template<intmax_t __d1, typename _R2>
00308     struct __ratio_less_impl_2<ratio<0, __d1>, _R2>
00309     : integral_constant<bool, true>
00310     { }; 
00311 
00312   template<typename _R1, intmax_t __d2>
00313     struct __ratio_less_impl_2<_R1, ratio<0, __d2> >
00314     : integral_constant<bool, false>
00315     { }; 
00316 
00317   template<intmax_t __d1, intmax_t __d2>
00318     struct __ratio_less_impl_2<ratio<0, __d1>, ratio<0, __d2> >
00319     : integral_constant<bool, false>
00320     { }; 
00321 
00322   template<typename _R1, typename _R2,
00323        bool = (_R1::num == 0 || _R2::num == 0
00324            || (__static_sign<_R1::num>::value
00325                != __static_sign<_R2::num>::value)),
00326        bool = (__static_sign<_R1::num>::value == -1
00327            && __static_sign<_R2::num>::value == -1)>
00328     struct __ratio_less_impl
00329     : __ratio_less_impl_1<_R1, _R2>::type
00330     { };
00331 
00332   template<typename _R1, typename _R2>
00333     struct __ratio_less_impl<_R1, _R2, true, false>
00334     : integral_constant<bool, _R1::num < _R2::num>
00335     { };
00336 
00337   template<typename _R1, typename _R2>
00338     struct __ratio_less_impl<_R1, _R2, false, true>
00339     : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
00340            ratio<-_R1::num, _R1::den> >::type
00341     { };
00342 
00343   /// ratio_less
00344   // using a continued fraction expansion
00345   template<typename _R1, typename _R2>
00346     struct ratio_less
00347     : __ratio_less_impl<_R1, _R2>::type
00348     { };
00349     
00350   /// ratio_less_equal
00351   template<typename _R1, typename _R2>
00352     struct ratio_less_equal
00353     : integral_constant<bool, !ratio_less<_R2, _R1>::value>
00354     { };
00355   
00356   /// ratio_greater
00357   template<typename _R1, typename _R2>
00358     struct ratio_greater
00359     : integral_constant<bool, ratio_less<_R2, _R1>::value>
00360     { };
00361 
00362   /// ratio_greater_equal
00363   template<typename _R1, typename _R2>
00364     struct ratio_greater_equal
00365     : integral_constant<bool, !ratio_less<_R1, _R2>::value>
00366     { };
00367 
00368   typedef ratio<1,       1000000000000000000> atto;
00369   typedef ratio<1,          1000000000000000> femto;
00370   typedef ratio<1,             1000000000000> pico;
00371   typedef ratio<1,                1000000000> nano;
00372   typedef ratio<1,                   1000000> micro;
00373   typedef ratio<1,                      1000> milli;
00374   typedef ratio<1,                       100> centi;
00375   typedef ratio<1,                        10> deci;
00376   typedef ratio<                       10, 1> deca;
00377   typedef ratio<                      100, 1> hecto;
00378   typedef ratio<                     1000, 1> kilo;
00379   typedef ratio<                  1000000, 1> mega;
00380   typedef ratio<               1000000000, 1> giga;
00381   typedef ratio<            1000000000000, 1> tera;
00382   typedef ratio<         1000000000000000, 1> peta;
00383   typedef ratio<      1000000000000000000, 1> exa;
00384 
00385   // @} group ratio
00386 _GLIBCXX_END_NAMESPACE_VERSION
00387 } // namespace
00388 
00389 #endif //_GLIBCXX_USE_C99_STDINT_TR1
00390 
00391 #endif //__GXX_EXPERIMENTAL_CXX0X__
00392 
00393 #endif //_GLIBCXX_RATIO