diff options
Diffstat (limited to 'gcc-4.9/libstdc++-v3/include/std/ratio')
| -rw-r--r-- | gcc-4.9/libstdc++-v3/include/std/ratio | 538 |
1 files changed, 538 insertions, 0 deletions
diff --git a/gcc-4.9/libstdc++-v3/include/std/ratio b/gcc-4.9/libstdc++-v3/include/std/ratio new file mode 100644 index 0000000..624e198 --- /dev/null +++ b/gcc-4.9/libstdc++-v3/include/std/ratio @@ -0,0 +1,538 @@ +// ratio -*- C++ -*- + +// Copyright (C) 2008-2014 Free Software Foundation, Inc. +// +// This file is part of the GNU ISO C++ Library. This library is free +// software; you can redistribute it and/or modify it under the +// terms of the GNU General Public License as published by the +// Free Software Foundation; either version 3, or (at your option) +// any later version. + +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +// GNU General Public License for more details. + +// Under Section 7 of GPL version 3, you are granted additional +// permissions described in the GCC Runtime Library Exception, version +// 3.1, as published by the Free Software Foundation. + +// You should have received a copy of the GNU General Public License and +// a copy of the GCC Runtime Library Exception along with this program; +// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see +// <http://www.gnu.org/licenses/>. + +/** @file include/ratio + * This is a Standard C++ Library header. + */ + +#ifndef _GLIBCXX_RATIO +#define _GLIBCXX_RATIO 1 + +#pragma GCC system_header + +#if __cplusplus < 201103L +# include <bits/c++0x_warning.h> +#else + +#include <type_traits> +#include <cstdint> + +#ifdef _GLIBCXX_USE_C99_STDINT_TR1 + +namespace std _GLIBCXX_VISIBILITY(default) +{ +_GLIBCXX_BEGIN_NAMESPACE_VERSION + + /** + * @defgroup ratio Rational Arithmetic + * @ingroup utilities + * + * Compile time representation of finite rational numbers. + * @{ + */ + + template<intmax_t _Pn> + struct __static_sign + : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> + { }; + + template<intmax_t _Pn> + struct __static_abs + : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> + { }; + + template<intmax_t _Pn, intmax_t _Qn> + struct __static_gcd + : __static_gcd<_Qn, (_Pn % _Qn)> + { }; + + template<intmax_t _Pn> + struct __static_gcd<_Pn, 0> + : integral_constant<intmax_t, __static_abs<_Pn>::value> + { }; + + template<intmax_t _Qn> + struct __static_gcd<0, _Qn> + : integral_constant<intmax_t, __static_abs<_Qn>::value> + { }; + + // Let c = 2^(half # of bits in an intmax_t) + // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 + // The multiplication of N and M becomes, + // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 + // Multiplication is safe if each term and the sum of the terms + // is representable by intmax_t. + template<intmax_t _Pn, intmax_t _Qn> + struct __safe_multiply + { + private: + static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); + + static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; + static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; + static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; + static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; + + static_assert(__a1 == 0 || __b1 == 0, + "overflow in multiplication"); + static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), + "overflow in multiplication"); + static_assert(__b0 * __a0 <= __INTMAX_MAX__, + "overflow in multiplication"); + static_assert((__a0 * __b1 + __b0 * __a1) * __c + <= __INTMAX_MAX__ - __b0 * __a0, + "overflow in multiplication"); + + public: + static const intmax_t value = _Pn * _Qn; + }; + + // Some double-precision utilities, where numbers are represented as + // __hi*2^(8*sizeof(uintmax_t)) + __lo. + template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> + struct __big_less + : integral_constant<bool, (__hi1 < __hi2 + || (__hi1 == __hi2 && __lo1 < __lo2))> + { }; + + template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> + struct __big_add + { + static constexpr uintmax_t __lo = __lo1 + __lo2; + static constexpr uintmax_t __hi = (__hi1 + __hi2 + + (__lo1 + __lo2 < __lo1)); // carry + }; + + // Subtract a number from a bigger one. + template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> + struct __big_sub + { + static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, + "Internal library error"); + static constexpr uintmax_t __lo = __lo1 - __lo2; + static constexpr uintmax_t __hi = (__hi1 - __hi2 - + (__lo1 < __lo2)); // carry + }; + + // Same principle as __safe_multiply. + template<uintmax_t __x, uintmax_t __y> + struct __big_mul + { + private: + static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); + static constexpr uintmax_t __x0 = __x % __c; + static constexpr uintmax_t __x1 = __x / __c; + static constexpr uintmax_t __y0 = __y % __c; + static constexpr uintmax_t __y1 = __y / __c; + static constexpr uintmax_t __x0y0 = __x0 * __y0; + static constexpr uintmax_t __x0y1 = __x0 * __y1; + static constexpr uintmax_t __x1y0 = __x1 * __y0; + static constexpr uintmax_t __x1y1 = __x1 * __y1; + static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... + static constexpr uintmax_t __mix_lo = __mix * __c; + static constexpr uintmax_t __mix_hi + = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here + typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; + public: + static constexpr uintmax_t __hi = _Res::__hi; + static constexpr uintmax_t __lo = _Res::__lo; + }; + + // Adapted from __udiv_qrnnd_c in longlong.h + // This version assumes that the high bit of __d is 1. + template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> + struct __big_div_impl + { + private: + static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), + "Internal library error"); + static_assert(__n1 < __d, "Internal library error"); + static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); + static constexpr uintmax_t __d1 = __d / __c; + static constexpr uintmax_t __d0 = __d % __c; + + static constexpr uintmax_t __q1x = __n1 / __d1; + static constexpr uintmax_t __r1x = __n1 % __d1; + static constexpr uintmax_t __m = __q1x * __d0; + static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; + static constexpr uintmax_t __r1z = __r1y + __d; + static constexpr uintmax_t __r1 + = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) + ? (__r1z + __d) : __r1z : __r1y) - __m; + static constexpr uintmax_t __q1 + = __q1x - ((__r1y < __m) + ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); + static constexpr uintmax_t __q0x = __r1 / __d1; + static constexpr uintmax_t __r0x = __r1 % __d1; + static constexpr uintmax_t __n = __q0x * __d0; + static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; + static constexpr uintmax_t __r0z = __r0y + __d; + static constexpr uintmax_t __r0 + = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) + ? (__r0z + __d) : __r0z : __r0y) - __n; + static constexpr uintmax_t __q0 + = __q0x - ((__r0y < __n) ? ((__r0z >= __d) + && (__r0z < __n)) ? 2 : 1 : 0); + + public: + static constexpr uintmax_t __quot = __q1 * __c + __q0; + static constexpr uintmax_t __rem = __r0; + + private: + typedef __big_mul<__quot, __d> _Prod; + typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; + static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, + "Internal library error"); + }; + + template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> + struct __big_div + { + private: + static_assert(__d != 0, "Internal library error"); + static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), + "This library calls __builtin_clzll on uintmax_t, which " + "is unsafe on your platform. Please complain to " + "http://gcc.gnu.org/bugzilla/"); + static constexpr int __shift = __builtin_clzll(__d); + static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; + static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; + static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; + static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; + static constexpr uintmax_t __new_d = __d * __c1; + static constexpr uintmax_t __new_n0 = __n0 * __c1; + static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; + static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; + static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; + typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; + + public: + static constexpr uintmax_t __quot_hi = __n1 / __d; + static constexpr uintmax_t __quot_lo = _Res::__quot; + static constexpr uintmax_t __rem = _Res::__rem / __c1; + + private: + typedef __big_mul<__quot_lo, __d> _P0; + typedef __big_mul<__quot_hi, __d> _P1; + typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; + // No overflow. + static_assert(_P1::__hi == 0, "Internal library error"); + static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); + // Matches the input data. + static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, + "Internal library error"); + static_assert(__rem < __d, "Internal library error"); + }; + + /** + * @brief Provides compile-time rational arithmetic. + * + * This class template represents any finite rational number with a + * numerator and denominator representable by compile-time constants of + * type intmax_t. The ratio is simplified when instantiated. + * + * For example: + * @code + * std::ratio<7,-21>::num == -1; + * std::ratio<7,-21>::den == 3; + * @endcode + * + */ + template<intmax_t _Num, intmax_t _Den = 1> + struct ratio + { + static_assert(_Den != 0, "denominator cannot be zero"); + static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, + "out of range"); + + // Note: sign(N) * abs(N) == N + static constexpr intmax_t num = + _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; + + static constexpr intmax_t den = + __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; + + typedef ratio<num, den> type; + }; + + template<intmax_t _Num, intmax_t _Den> + constexpr intmax_t ratio<_Num, _Den>::num; + + template<intmax_t _Num, intmax_t _Den> + constexpr intmax_t ratio<_Num, _Den>::den; + + template<typename _R1, typename _R2> + struct __ratio_multiply + { + private: + static const intmax_t __gcd1 = + __static_gcd<_R1::num, _R2::den>::value; + static const intmax_t __gcd2 = + __static_gcd<_R2::num, _R1::den>::value; + + public: + typedef ratio< + __safe_multiply<(_R1::num / __gcd1), + (_R2::num / __gcd2)>::value, + __safe_multiply<(_R1::den / __gcd2), + (_R2::den / __gcd1)>::value> type; + + static constexpr intmax_t num = type::num; + static constexpr intmax_t den = type::den; + }; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_multiply<_R1, _R2>::num; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_multiply<_R1, _R2>::den; + + /// ratio_multiply + template<typename _R1, typename _R2> + using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type; + + template<typename _R1, typename _R2> + struct __ratio_divide + { + static_assert(_R2::num != 0, "division by 0"); + + typedef typename __ratio_multiply< + _R1, + ratio<_R2::den, _R2::num>>::type type; + + static constexpr intmax_t num = type::num; + static constexpr intmax_t den = type::den; + }; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_divide<_R1, _R2>::num; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_divide<_R1, _R2>::den; + + /// ratio_divide + template<typename _R1, typename _R2> + using ratio_divide = typename __ratio_divide<_R1, _R2>::type; + + /// ratio_equal + template<typename _R1, typename _R2> + struct ratio_equal + : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> + { }; + + /// ratio_not_equal + template<typename _R1, typename _R2> + struct ratio_not_equal + : integral_constant<bool, !ratio_equal<_R1, _R2>::value> + { }; + + // Both numbers are positive. + template<typename _R1, typename _R2, + typename _Left = __big_mul<_R1::num,_R2::den>, + typename _Right = __big_mul<_R2::num,_R1::den> > + struct __ratio_less_impl_1 + : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, + _Right::__hi, _Right::__lo>::value> + { }; + + template<typename _R1, typename _R2, + bool = (_R1::num == 0 || _R2::num == 0 + || (__static_sign<_R1::num>::value + != __static_sign<_R2::num>::value)), + bool = (__static_sign<_R1::num>::value == -1 + && __static_sign<_R2::num>::value == -1)> + struct __ratio_less_impl + : __ratio_less_impl_1<_R1, _R2>::type + { }; + + template<typename _R1, typename _R2> + struct __ratio_less_impl<_R1, _R2, true, false> + : integral_constant<bool, _R1::num < _R2::num> + { }; + + template<typename _R1, typename _R2> + struct __ratio_less_impl<_R1, _R2, false, true> + : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, + ratio<-_R1::num, _R1::den> >::type + { }; + + /// ratio_less + template<typename _R1, typename _R2> + struct ratio_less + : __ratio_less_impl<_R1, _R2>::type + { }; + + /// ratio_less_equal + template<typename _R1, typename _R2> + struct ratio_less_equal + : integral_constant<bool, !ratio_less<_R2, _R1>::value> + { }; + + /// ratio_greater + template<typename _R1, typename _R2> + struct ratio_greater + : integral_constant<bool, ratio_less<_R2, _R1>::value> + { }; + + /// ratio_greater_equal + template<typename _R1, typename _R2> + struct ratio_greater_equal + : integral_constant<bool, !ratio_less<_R1, _R2>::value> + { }; + + template<typename _R1, typename _R2, + bool = (_R1::num >= 0), + bool = (_R2::num >= 0), + bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, + ratio<__static_abs<_R2::num>::value, _R2::den> >::value> + struct __ratio_add_impl + { + private: + typedef typename __ratio_add_impl< + ratio<-_R1::num, _R1::den>, + ratio<-_R2::num, _R2::den> >::type __t; + public: + typedef ratio<-__t::num, __t::den> type; + }; + + // True addition of nonnegative numbers. + template<typename _R1, typename _R2, bool __b> + struct __ratio_add_impl<_R1, _R2, true, true, __b> + { + private: + static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; + static constexpr uintmax_t __d2 = _R2::den / __g; + typedef __big_mul<_R1::den, __d2> __d; + typedef __big_mul<_R1::num, _R2::den / __g> __x; + typedef __big_mul<_R2::num, _R1::den / __g> __y; + typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; + static_assert(__n::__hi >= __x::__hi, "Internal library error"); + typedef __big_div<__n::__hi, __n::__lo, __g> __ng; + static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; + typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; + static_assert(__n_final::__rem == 0, "Internal library error"); + static_assert(__n_final::__quot_hi == 0 && + __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); + typedef __big_mul<_R1::den / __g2, __d2> __d_final; + static_assert(__d_final::__hi == 0 && + __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); + public: + typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; + }; + + template<typename _R1, typename _R2> + struct __ratio_add_impl<_R1, _R2, false, true, true> + : __ratio_add_impl<_R2, _R1> + { }; + + // True subtraction of nonnegative numbers yielding a nonnegative result. + template<typename _R1, typename _R2> + struct __ratio_add_impl<_R1, _R2, true, false, false> + { + private: + static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; + static constexpr uintmax_t __d2 = _R2::den / __g; + typedef __big_mul<_R1::den, __d2> __d; + typedef __big_mul<_R1::num, _R2::den / __g> __x; + typedef __big_mul<-_R2::num, _R1::den / __g> __y; + typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; + typedef __big_div<__n::__hi, __n::__lo, __g> __ng; + static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; + typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; + static_assert(__n_final::__rem == 0, "Internal library error"); + static_assert(__n_final::__quot_hi == 0 && + __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); + typedef __big_mul<_R1::den / __g2, __d2> __d_final; + static_assert(__d_final::__hi == 0 && + __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); + public: + typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; + }; + + template<typename _R1, typename _R2> + struct __ratio_add + { + typedef typename __ratio_add_impl<_R1, _R2>::type type; + static constexpr intmax_t num = type::num; + static constexpr intmax_t den = type::den; + }; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_add<_R1, _R2>::num; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_add<_R1, _R2>::den; + + /// ratio_add + template<typename _R1, typename _R2> + using ratio_add = typename __ratio_add<_R1, _R2>::type; + + template<typename _R1, typename _R2> + struct __ratio_subtract + { + typedef typename __ratio_add< + _R1, + ratio<-_R2::num, _R2::den>>::type type; + + static constexpr intmax_t num = type::num; + static constexpr intmax_t den = type::den; + }; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_subtract<_R1, _R2>::num; + + template<typename _R1, typename _R2> + constexpr intmax_t __ratio_subtract<_R1, _R2>::den; + + /// ratio_subtract + template<typename _R1, typename _R2> + using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type; + + + typedef ratio<1, 1000000000000000000> atto; + typedef ratio<1, 1000000000000000> femto; + typedef ratio<1, 1000000000000> pico; + typedef ratio<1, 1000000000> nano; + typedef ratio<1, 1000000> micro; + typedef ratio<1, 1000> milli; + typedef ratio<1, 100> centi; + typedef ratio<1, 10> deci; + typedef ratio< 10, 1> deca; + typedef ratio< 100, 1> hecto; + typedef ratio< 1000, 1> kilo; + typedef ratio< 1000000, 1> mega; + typedef ratio< 1000000000, 1> giga; + typedef ratio< 1000000000000, 1> tera; + typedef ratio< 1000000000000000, 1> peta; + typedef ratio< 1000000000000000000, 1> exa; + + // @} group ratio +_GLIBCXX_END_NAMESPACE_VERSION +} // namespace + +#endif //_GLIBCXX_USE_C99_STDINT_TR1 + +#endif // C++11 + +#endif //_GLIBCXX_RATIO |