ratio

Go to the documentation of this file.
00001 // ratio -*- C++ -*-
00002 
00003 // Copyright (C) 2008, 2009 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 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 <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
00044 {
00045   /**
00046    * @defgroup ratio Rational Arithmetic
00047    * @ingroup utilities
00048    *
00049    * Compile time representation of fininte rational numbers.
00050    * @{
00051    */
00052 
00053   template<intmax_t _Pn>
00054     struct __static_sign
00055     : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
00056     { };
00057 
00058   template<intmax_t _Pn>
00059     struct __static_abs
00060     : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
00061     { };
00062 
00063   template<intmax_t _Pn, intmax_t _Qn>
00064     struct __static_gcd;
00065  
00066   template<intmax_t _Pn, intmax_t _Qn>
00067     struct __static_gcd
00068     : __static_gcd<_Qn, (_Pn % _Qn)>
00069     { };
00070 
00071   template<intmax_t _Pn>
00072     struct __static_gcd<_Pn, 0>
00073     : integral_constant<intmax_t, __static_abs<_Pn>::value>
00074     { };
00075 
00076   template<intmax_t _Qn>
00077     struct __static_gcd<0, _Qn>
00078     : integral_constant<intmax_t, __static_abs<_Qn>::value>
00079     { };
00080 
00081   // Let c = 2^(half # of bits in an intmax_t)
00082   // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
00083   // The multiplication of N and M becomes,
00084   // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
00085   // Multiplication is safe if each term and the sum of the terms
00086   // is representable by intmax_t.
00087   template<intmax_t _Pn, intmax_t _Qn>
00088     struct __safe_multiply
00089     {
00090     private:
00091       static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
00092 
00093       static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
00094       static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
00095       static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
00096       static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
00097 
00098       static_assert(__a1 == 0 || __b1 == 0, 
00099         "overflow in multiplication");
00100       static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 
00101         "overflow in multiplication");
00102       static_assert(__b0 * __a0 <= __INTMAX_MAX__, 
00103         "overflow in multiplication");
00104       static_assert((__a0 * __b1 + __b0 * __a1) * __c <= 
00105         __INTMAX_MAX__ -  __b0 * __a0, "overflow in multiplication");
00106 
00107     public:
00108       static const intmax_t value = _Pn * _Qn;
00109     };
00110 
00111   // Helpers for __safe_add
00112   template<intmax_t _Pn, intmax_t _Qn, bool>
00113     struct __add_overflow_check_impl
00114     : integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
00115     { };
00116 
00117   template<intmax_t _Pn, intmax_t _Qn>
00118     struct __add_overflow_check_impl<_Pn, _Qn, false>
00119     : integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
00120     { };
00121 
00122   template<intmax_t _Pn, intmax_t _Qn>
00123     struct __add_overflow_check
00124     : __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
00125     { };
00126 
00127   template<intmax_t _Pn, intmax_t _Qn>
00128     struct __safe_add
00129     {
00130       static_assert(__add_overflow_check<_Pn, _Qn>::value != 0, 
00131         "overflow in addition");
00132 
00133       static const intmax_t value = _Pn + _Qn;
00134     };
00135 
00136   /**
00137    *  @brief Provides compile-time rational arithmetic.
00138    *
00139    *  This class template represents any finite rational number with a
00140    *  numerator and denominator representable by compile-time constants of
00141    *  type intmax_t. The ratio is simplified when instantiated.
00142    *
00143    *  For example:
00144    *  @code
00145    *    std::ratio<7,-21>::num == -1;
00146    *    std::ratio<7,-21>::den == 3;
00147    *  @endcode
00148    *  
00149   */
00150   template<intmax_t _Num, intmax_t _Den = 1>
00151     struct ratio
00152     {
00153       static_assert(_Den != 0, "denominator cannot be zero");
00154       static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
00155             "out of range");
00156 
00157       // Note: sign(N) * abs(N) == N
00158       static const intmax_t num =
00159         _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
00160 
00161       static const intmax_t den =
00162         __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
00163     };
00164 
00165   template<intmax_t _Num, intmax_t _Den>
00166     const intmax_t ratio<_Num, _Den>::num;
00167 
00168   template<intmax_t _Num, intmax_t _Den>
00169     const intmax_t ratio<_Num, _Den>::den;
00170 
00171   /// ratio_add
00172   template<typename _R1, typename _R2>
00173     struct ratio_add
00174     {
00175     private:
00176       static const intmax_t __gcd =
00177         __static_gcd<_R1::den, _R2::den>::value;
00178       
00179     public:
00180       typedef ratio<
00181         __safe_add<
00182           __safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
00183           __safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
00184         __safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
00185     };
00186 
00187   /// ratio_subtract
00188   template<typename _R1, typename _R2>
00189     struct ratio_subtract
00190     {
00191       typedef typename ratio_add<
00192         _R1,
00193         ratio<-_R2::num, _R2::den>>::type type;
00194     };
00195 
00196   /// ratio_multiply
00197   template<typename _R1, typename _R2>
00198     struct ratio_multiply
00199     {
00200     private:
00201       static const intmax_t __gcd1 =
00202         __static_gcd<_R1::num, _R2::den>::value;
00203       static const intmax_t __gcd2 =
00204         __static_gcd<_R2::num, _R1::den>::value;
00205 
00206     public:
00207       typedef ratio<
00208         __safe_multiply<(_R1::num / __gcd1),
00209                         (_R2::num / __gcd2)>::value,
00210         __safe_multiply<(_R1::den / __gcd2),
00211                         (_R2::den / __gcd1)>::value> type;
00212     };
00213 
00214   /// ratio_divide
00215   template<typename _R1, typename _R2>
00216     struct ratio_divide
00217     {
00218       static_assert(_R2::num != 0, "division by 0");
00219 
00220       typedef typename ratio_multiply<
00221         _R1,
00222         ratio<_R2::den, _R2::num>>::type type;
00223     };
00224 
00225   /// ratio_equal
00226   template<typename _R1, typename _R2>
00227     struct ratio_equal
00228     : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
00229     { };
00230   
00231   /// ratio_not_equal
00232   template<typename _R1, typename _R2>
00233     struct ratio_not_equal
00234     : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
00235     { };
00236   
00237   template<typename _R1, typename _R2>
00238     struct __ratio_less_simple_impl
00239     : integral_constant<bool,
00240             (__safe_multiply<_R1::num, _R2::den>::value
00241              < __safe_multiply<_R2::num, _R1::den>::value)>
00242     { };
00243 
00244   // If the denominators are equal or the signs differ, we can just compare
00245   // numerators, otherwise fallback to the simple cross-multiply method.
00246   template<typename _R1, typename _R2>
00247     struct __ratio_less_impl
00248     : conditional<(_R1::den == _R2::den
00249            || (__static_sign<_R1::num>::value
00250                != __static_sign<_R2::num>::value)),
00251       integral_constant<bool, (_R1::num < _R2::num)>,
00252       __ratio_less_simple_impl<_R1, _R2>>::type
00253     { };
00254 
00255   /// ratio_less
00256   template<typename _R1, typename _R2>
00257     struct ratio_less
00258     : __ratio_less_impl<_R1, _R2>::type
00259     { };
00260     
00261   /// ratio_less_equal
00262   template<typename _R1, typename _R2>
00263     struct ratio_less_equal
00264     : integral_constant<bool, !ratio_less<_R2, _R1>::value>
00265     { };
00266   
00267   /// ratio_greater
00268   template<typename _R1, typename _R2>
00269     struct ratio_greater
00270     : integral_constant<bool, ratio_less<_R2, _R1>::value>
00271     { };
00272 
00273   /// ratio_greater_equal
00274   template<typename _R1, typename _R2>
00275     struct ratio_greater_equal
00276     : integral_constant<bool, !ratio_less<_R1, _R2>::value>
00277     { };
00278 
00279   typedef ratio<1,       1000000000000000000> atto;
00280   typedef ratio<1,          1000000000000000> femto;
00281   typedef ratio<1,             1000000000000> pico;
00282   typedef ratio<1,                1000000000> nano;
00283   typedef ratio<1,                   1000000> micro;
00284   typedef ratio<1,                      1000> milli;
00285   typedef ratio<1,                       100> centi;
00286   typedef ratio<1,                        10> deci;
00287   typedef ratio<                       10, 1> deca;
00288   typedef ratio<                      100, 1> hecto;
00289   typedef ratio<                     1000, 1> kilo;
00290   typedef ratio<                  1000000, 1> mega;
00291   typedef ratio<               1000000000, 1> giga;
00292   typedef ratio<            1000000000000, 1> tera;
00293   typedef ratio<         1000000000000000, 1> peta;
00294   typedef ratio<      1000000000000000000, 1> exa;
00295 
00296   // @} group ratio
00297 }
00298 
00299 #endif //_GLIBCXX_USE_C99_STDINT_TR1
00300 
00301 #endif //__GXX_EXPERIMENTAL_CXX0X__
00302 
00303 #endif //_GLIBCXX_RATIO

Generated on Thu Jul 23 21:16:13 2009 for libstdc++ by  doxygen 1.5.8