1*e4b17023SJohn Marino// ratio -*- C++ -*- 2*e4b17023SJohn Marino 3*e4b17023SJohn Marino// Copyright (C) 2008, 2009, 2010, 2011 Free Software Foundation, Inc. 4*e4b17023SJohn Marino// 5*e4b17023SJohn Marino// This file is part of the GNU ISO C++ Library. This library is free 6*e4b17023SJohn Marino// software; you can redistribute it and/or modify it under the 7*e4b17023SJohn Marino// terms of the GNU General Public License as published by the 8*e4b17023SJohn Marino// Free Software Foundation; either version 3, or (at your option) 9*e4b17023SJohn Marino// any later version. 10*e4b17023SJohn Marino 11*e4b17023SJohn Marino// This library is distributed in the hope that it will be useful, 12*e4b17023SJohn Marino// but WITHOUT ANY WARRANTY; without even the implied warranty of 13*e4b17023SJohn Marino// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14*e4b17023SJohn Marino// GNU General Public License for more details. 15*e4b17023SJohn Marino 16*e4b17023SJohn Marino// Under Section 7 of GPL version 3, you are granted additional 17*e4b17023SJohn Marino// permissions described in the GCC Runtime Library Exception, version 18*e4b17023SJohn Marino// 3.1, as published by the Free Software Foundation. 19*e4b17023SJohn Marino 20*e4b17023SJohn Marino// You should have received a copy of the GNU General Public License and 21*e4b17023SJohn Marino// a copy of the GCC Runtime Library Exception along with this program; 22*e4b17023SJohn Marino// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see 23*e4b17023SJohn Marino// <http://www.gnu.org/licenses/>. 24*e4b17023SJohn Marino 25*e4b17023SJohn Marino/** @file include/ratio 26*e4b17023SJohn Marino * This is a Standard C++ Library header. 27*e4b17023SJohn Marino */ 28*e4b17023SJohn Marino 29*e4b17023SJohn Marino#ifndef _GLIBCXX_RATIO 30*e4b17023SJohn Marino#define _GLIBCXX_RATIO 1 31*e4b17023SJohn Marino 32*e4b17023SJohn Marino#pragma GCC system_header 33*e4b17023SJohn Marino 34*e4b17023SJohn Marino#ifndef __GXX_EXPERIMENTAL_CXX0X__ 35*e4b17023SJohn Marino# include <bits/c++0x_warning.h> 36*e4b17023SJohn Marino#else 37*e4b17023SJohn Marino 38*e4b17023SJohn Marino#include <type_traits> 39*e4b17023SJohn Marino#include <cstdint> 40*e4b17023SJohn Marino 41*e4b17023SJohn Marino#ifdef _GLIBCXX_USE_C99_STDINT_TR1 42*e4b17023SJohn Marino 43*e4b17023SJohn Marinonamespace std _GLIBCXX_VISIBILITY(default) 44*e4b17023SJohn Marino{ 45*e4b17023SJohn Marino_GLIBCXX_BEGIN_NAMESPACE_VERSION 46*e4b17023SJohn Marino 47*e4b17023SJohn Marino /** 48*e4b17023SJohn Marino * @defgroup ratio Rational Arithmetic 49*e4b17023SJohn Marino * @ingroup utilities 50*e4b17023SJohn Marino * 51*e4b17023SJohn Marino * Compile time representation of finite rational numbers. 52*e4b17023SJohn Marino * @{ 53*e4b17023SJohn Marino */ 54*e4b17023SJohn Marino 55*e4b17023SJohn Marino template<intmax_t _Pn> 56*e4b17023SJohn Marino struct __static_sign 57*e4b17023SJohn Marino : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1> 58*e4b17023SJohn Marino { }; 59*e4b17023SJohn Marino 60*e4b17023SJohn Marino template<intmax_t _Pn> 61*e4b17023SJohn Marino struct __static_abs 62*e4b17023SJohn Marino : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value> 63*e4b17023SJohn Marino { }; 64*e4b17023SJohn Marino 65*e4b17023SJohn Marino template<intmax_t _Pn, intmax_t _Qn> 66*e4b17023SJohn Marino struct __static_gcd; 67*e4b17023SJohn Marino 68*e4b17023SJohn Marino template<intmax_t _Pn, intmax_t _Qn> 69*e4b17023SJohn Marino struct __static_gcd 70*e4b17023SJohn Marino : __static_gcd<_Qn, (_Pn % _Qn)> 71*e4b17023SJohn Marino { }; 72*e4b17023SJohn Marino 73*e4b17023SJohn Marino template<intmax_t _Pn> 74*e4b17023SJohn Marino struct __static_gcd<_Pn, 0> 75*e4b17023SJohn Marino : integral_constant<intmax_t, __static_abs<_Pn>::value> 76*e4b17023SJohn Marino { }; 77*e4b17023SJohn Marino 78*e4b17023SJohn Marino template<intmax_t _Qn> 79*e4b17023SJohn Marino struct __static_gcd<0, _Qn> 80*e4b17023SJohn Marino : integral_constant<intmax_t, __static_abs<_Qn>::value> 81*e4b17023SJohn Marino { }; 82*e4b17023SJohn Marino 83*e4b17023SJohn Marino // Let c = 2^(half # of bits in an intmax_t) 84*e4b17023SJohn Marino // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0 85*e4b17023SJohn Marino // The multiplication of N and M becomes, 86*e4b17023SJohn Marino // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0 87*e4b17023SJohn Marino // Multiplication is safe if each term and the sum of the terms 88*e4b17023SJohn Marino // is representable by intmax_t. 89*e4b17023SJohn Marino template<intmax_t _Pn, intmax_t _Qn> 90*e4b17023SJohn Marino struct __safe_multiply 91*e4b17023SJohn Marino { 92*e4b17023SJohn Marino private: 93*e4b17023SJohn Marino static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 94*e4b17023SJohn Marino 95*e4b17023SJohn Marino static const uintmax_t __a0 = __static_abs<_Pn>::value % __c; 96*e4b17023SJohn Marino static const uintmax_t __a1 = __static_abs<_Pn>::value / __c; 97*e4b17023SJohn Marino static const uintmax_t __b0 = __static_abs<_Qn>::value % __c; 98*e4b17023SJohn Marino static const uintmax_t __b1 = __static_abs<_Qn>::value / __c; 99*e4b17023SJohn Marino 100*e4b17023SJohn Marino static_assert(__a1 == 0 || __b1 == 0, 101*e4b17023SJohn Marino "overflow in multiplication"); 102*e4b17023SJohn Marino static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1), 103*e4b17023SJohn Marino "overflow in multiplication"); 104*e4b17023SJohn Marino static_assert(__b0 * __a0 <= __INTMAX_MAX__, 105*e4b17023SJohn Marino "overflow in multiplication"); 106*e4b17023SJohn Marino static_assert((__a0 * __b1 + __b0 * __a1) * __c 107*e4b17023SJohn Marino <= __INTMAX_MAX__ - __b0 * __a0, 108*e4b17023SJohn Marino "overflow in multiplication"); 109*e4b17023SJohn Marino 110*e4b17023SJohn Marino public: 111*e4b17023SJohn Marino static const intmax_t value = _Pn * _Qn; 112*e4b17023SJohn Marino }; 113*e4b17023SJohn Marino 114*e4b17023SJohn Marino // Some double-precision utilities, where numbers are represented as 115*e4b17023SJohn Marino // __hi*2^(8*sizeof(uintmax_t)) + __lo. 116*e4b17023SJohn Marino template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 117*e4b17023SJohn Marino struct __big_less 118*e4b17023SJohn Marino : integral_constant<bool, (__hi1 < __hi2 119*e4b17023SJohn Marino || (__hi1 == __hi2 && __lo1 < __lo2))> 120*e4b17023SJohn Marino { }; 121*e4b17023SJohn Marino 122*e4b17023SJohn Marino template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 123*e4b17023SJohn Marino struct __big_add 124*e4b17023SJohn Marino { 125*e4b17023SJohn Marino static constexpr uintmax_t __lo = __lo1 + __lo2; 126*e4b17023SJohn Marino static constexpr uintmax_t __hi = (__hi1 + __hi2 + 127*e4b17023SJohn Marino (__lo1 + __lo2 < __lo1)); // carry 128*e4b17023SJohn Marino }; 129*e4b17023SJohn Marino 130*e4b17023SJohn Marino // Subtract a number from a bigger one. 131*e4b17023SJohn Marino template<uintmax_t __hi1, uintmax_t __lo1, uintmax_t __hi2, uintmax_t __lo2> 132*e4b17023SJohn Marino struct __big_sub 133*e4b17023SJohn Marino { 134*e4b17023SJohn Marino static_assert(!__big_less<__hi1, __lo1, __hi2, __lo2>::value, 135*e4b17023SJohn Marino "Internal library error"); 136*e4b17023SJohn Marino static constexpr uintmax_t __lo = __lo1 - __lo2; 137*e4b17023SJohn Marino static constexpr uintmax_t __hi = (__hi1 - __hi2 - 138*e4b17023SJohn Marino (__lo1 < __lo2)); // carry 139*e4b17023SJohn Marino }; 140*e4b17023SJohn Marino 141*e4b17023SJohn Marino // Same principle as __safe_multiply. 142*e4b17023SJohn Marino template<uintmax_t __x, uintmax_t __y> 143*e4b17023SJohn Marino struct __big_mul 144*e4b17023SJohn Marino { 145*e4b17023SJohn Marino private: 146*e4b17023SJohn Marino static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 147*e4b17023SJohn Marino static constexpr uintmax_t __x0 = __x % __c; 148*e4b17023SJohn Marino static constexpr uintmax_t __x1 = __x / __c; 149*e4b17023SJohn Marino static constexpr uintmax_t __y0 = __y % __c; 150*e4b17023SJohn Marino static constexpr uintmax_t __y1 = __y / __c; 151*e4b17023SJohn Marino static constexpr uintmax_t __x0y0 = __x0 * __y0; 152*e4b17023SJohn Marino static constexpr uintmax_t __x0y1 = __x0 * __y1; 153*e4b17023SJohn Marino static constexpr uintmax_t __x1y0 = __x1 * __y0; 154*e4b17023SJohn Marino static constexpr uintmax_t __x1y1 = __x1 * __y1; 155*e4b17023SJohn Marino static constexpr uintmax_t __mix = __x0y1 + __x1y0; // possible carry... 156*e4b17023SJohn Marino static constexpr uintmax_t __mix_lo = __mix * __c; 157*e4b17023SJohn Marino static constexpr uintmax_t __mix_hi 158*e4b17023SJohn Marino = __mix / __c + ((__mix < __x0y1) ? __c : 0); // ... added here 159*e4b17023SJohn Marino typedef __big_add<__mix_hi, __mix_lo, __x1y1, __x0y0> _Res; 160*e4b17023SJohn Marino public: 161*e4b17023SJohn Marino static constexpr uintmax_t __hi = _Res::__hi; 162*e4b17023SJohn Marino static constexpr uintmax_t __lo = _Res::__lo; 163*e4b17023SJohn Marino }; 164*e4b17023SJohn Marino 165*e4b17023SJohn Marino // Adapted from __udiv_qrnnd_c in longlong.h 166*e4b17023SJohn Marino // This version assumes that the high bit of __d is 1. 167*e4b17023SJohn Marino template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 168*e4b17023SJohn Marino struct __big_div_impl 169*e4b17023SJohn Marino { 170*e4b17023SJohn Marino private: 171*e4b17023SJohn Marino static_assert(__d >= (uintmax_t(1) << (sizeof(intmax_t) * 8 - 1)), 172*e4b17023SJohn Marino "Internal library error"); 173*e4b17023SJohn Marino static_assert(__n1 < __d, "Internal library error"); 174*e4b17023SJohn Marino static constexpr uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4); 175*e4b17023SJohn Marino static constexpr uintmax_t __d1 = __d / __c; 176*e4b17023SJohn Marino static constexpr uintmax_t __d0 = __d % __c; 177*e4b17023SJohn Marino 178*e4b17023SJohn Marino static constexpr uintmax_t __q1x = __n1 / __d1; 179*e4b17023SJohn Marino static constexpr uintmax_t __r1x = __n1 % __d1; 180*e4b17023SJohn Marino static constexpr uintmax_t __m = __q1x * __d0; 181*e4b17023SJohn Marino static constexpr uintmax_t __r1y = __r1x * __c + __n0 / __c; 182*e4b17023SJohn Marino static constexpr uintmax_t __r1z = __r1y + __d; 183*e4b17023SJohn Marino static constexpr uintmax_t __r1 184*e4b17023SJohn Marino = ((__r1y < __m) ? ((__r1z >= __d) && (__r1z < __m)) 185*e4b17023SJohn Marino ? (__r1z + __d) : __r1z : __r1y) - __m; 186*e4b17023SJohn Marino static constexpr uintmax_t __q1 187*e4b17023SJohn Marino = __q1x - ((__r1y < __m) 188*e4b17023SJohn Marino ? ((__r1z >= __d) && (__r1z < __m)) ? 2 : 1 : 0); 189*e4b17023SJohn Marino static constexpr uintmax_t __q0x = __r1 / __d1; 190*e4b17023SJohn Marino static constexpr uintmax_t __r0x = __r1 % __d1; 191*e4b17023SJohn Marino static constexpr uintmax_t __n = __q0x * __d0; 192*e4b17023SJohn Marino static constexpr uintmax_t __r0y = __r0x * __c + __n0 % __c; 193*e4b17023SJohn Marino static constexpr uintmax_t __r0z = __r0y + __d; 194*e4b17023SJohn Marino static constexpr uintmax_t __r0 195*e4b17023SJohn Marino = ((__r0y < __n) ? ((__r0z >= __d) && (__r0z < __n)) 196*e4b17023SJohn Marino ? (__r0z + __d) : __r0z : __r0y) - __n; 197*e4b17023SJohn Marino static constexpr uintmax_t __q0 198*e4b17023SJohn Marino = __q0x - ((__r0y < __n) ? ((__r0z >= __d) 199*e4b17023SJohn Marino && (__r0z < __n)) ? 2 : 1 : 0); 200*e4b17023SJohn Marino 201*e4b17023SJohn Marino public: 202*e4b17023SJohn Marino static constexpr uintmax_t __quot = __q1 * __c + __q0; 203*e4b17023SJohn Marino static constexpr uintmax_t __rem = __r0; 204*e4b17023SJohn Marino 205*e4b17023SJohn Marino private: 206*e4b17023SJohn Marino typedef __big_mul<__quot, __d> _Prod; 207*e4b17023SJohn Marino typedef __big_add<_Prod::__hi, _Prod::__lo, 0, __rem> _Sum; 208*e4b17023SJohn Marino static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 209*e4b17023SJohn Marino "Internal library error"); 210*e4b17023SJohn Marino }; 211*e4b17023SJohn Marino 212*e4b17023SJohn Marino template<uintmax_t __n1, uintmax_t __n0, uintmax_t __d> 213*e4b17023SJohn Marino struct __big_div 214*e4b17023SJohn Marino { 215*e4b17023SJohn Marino private: 216*e4b17023SJohn Marino static_assert(__d != 0, "Internal library error"); 217*e4b17023SJohn Marino static_assert(sizeof (uintmax_t) == sizeof (unsigned long long), 218*e4b17023SJohn Marino "This library calls __builtin_clzll on uintmax_t, which " 219*e4b17023SJohn Marino "is unsafe on your platform. Please complain to " 220*e4b17023SJohn Marino "http://gcc.gnu.org/bugzilla/"); 221*e4b17023SJohn Marino static constexpr int __shift = __builtin_clzll(__d); 222*e4b17023SJohn Marino static constexpr int __coshift_ = sizeof(uintmax_t) * 8 - __shift; 223*e4b17023SJohn Marino static constexpr int __coshift = (__shift != 0) ? __coshift_ : 0; 224*e4b17023SJohn Marino static constexpr uintmax_t __c1 = uintmax_t(1) << __shift; 225*e4b17023SJohn Marino static constexpr uintmax_t __c2 = uintmax_t(1) << __coshift; 226*e4b17023SJohn Marino static constexpr uintmax_t __new_d = __d * __c1; 227*e4b17023SJohn Marino static constexpr uintmax_t __new_n0 = __n0 * __c1; 228*e4b17023SJohn Marino static constexpr uintmax_t __n1_shifted = (__n1 % __d) * __c1; 229*e4b17023SJohn Marino static constexpr uintmax_t __n0_top = (__shift != 0) ? (__n0 / __c2) : 0; 230*e4b17023SJohn Marino static constexpr uintmax_t __new_n1 = __n1_shifted + __n0_top; 231*e4b17023SJohn Marino typedef __big_div_impl<__new_n1, __new_n0, __new_d> _Res; 232*e4b17023SJohn Marino 233*e4b17023SJohn Marino public: 234*e4b17023SJohn Marino static constexpr uintmax_t __quot_hi = __n1 / __d; 235*e4b17023SJohn Marino static constexpr uintmax_t __quot_lo = _Res::__quot; 236*e4b17023SJohn Marino static constexpr uintmax_t __rem = _Res::__rem / __c1; 237*e4b17023SJohn Marino 238*e4b17023SJohn Marino private: 239*e4b17023SJohn Marino typedef __big_mul<__quot_lo, __d> _P0; 240*e4b17023SJohn Marino typedef __big_mul<__quot_hi, __d> _P1; 241*e4b17023SJohn Marino typedef __big_add<_P0::__hi, _P0::__lo, _P1::__lo, __rem> _Sum; 242*e4b17023SJohn Marino // No overflow. 243*e4b17023SJohn Marino static_assert(_P1::__hi == 0, "Internal library error"); 244*e4b17023SJohn Marino static_assert(_Sum::__hi >= _P0::__hi, "Internal library error"); 245*e4b17023SJohn Marino // Matches the input data. 246*e4b17023SJohn Marino static_assert(_Sum::__hi == __n1 && _Sum::__lo == __n0, 247*e4b17023SJohn Marino "Internal library error"); 248*e4b17023SJohn Marino static_assert(__rem < __d, "Internal library error"); 249*e4b17023SJohn Marino }; 250*e4b17023SJohn Marino 251*e4b17023SJohn Marino /** 252*e4b17023SJohn Marino * @brief Provides compile-time rational arithmetic. 253*e4b17023SJohn Marino * 254*e4b17023SJohn Marino * This class template represents any finite rational number with a 255*e4b17023SJohn Marino * numerator and denominator representable by compile-time constants of 256*e4b17023SJohn Marino * type intmax_t. The ratio is simplified when instantiated. 257*e4b17023SJohn Marino * 258*e4b17023SJohn Marino * For example: 259*e4b17023SJohn Marino * @code 260*e4b17023SJohn Marino * std::ratio<7,-21>::num == -1; 261*e4b17023SJohn Marino * std::ratio<7,-21>::den == 3; 262*e4b17023SJohn Marino * @endcode 263*e4b17023SJohn Marino * 264*e4b17023SJohn Marino */ 265*e4b17023SJohn Marino template<intmax_t _Num, intmax_t _Den = 1> 266*e4b17023SJohn Marino struct ratio 267*e4b17023SJohn Marino { 268*e4b17023SJohn Marino static_assert(_Den != 0, "denominator cannot be zero"); 269*e4b17023SJohn Marino static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__, 270*e4b17023SJohn Marino "out of range"); 271*e4b17023SJohn Marino 272*e4b17023SJohn Marino // Note: sign(N) * abs(N) == N 273*e4b17023SJohn Marino static constexpr intmax_t num = 274*e4b17023SJohn Marino _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value; 275*e4b17023SJohn Marino 276*e4b17023SJohn Marino static constexpr intmax_t den = 277*e4b17023SJohn Marino __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value; 278*e4b17023SJohn Marino 279*e4b17023SJohn Marino typedef ratio<num, den> type; 280*e4b17023SJohn Marino }; 281*e4b17023SJohn Marino 282*e4b17023SJohn Marino template<intmax_t _Num, intmax_t _Den> 283*e4b17023SJohn Marino constexpr intmax_t ratio<_Num, _Den>::num; 284*e4b17023SJohn Marino 285*e4b17023SJohn Marino template<intmax_t _Num, intmax_t _Den> 286*e4b17023SJohn Marino constexpr intmax_t ratio<_Num, _Den>::den; 287*e4b17023SJohn Marino 288*e4b17023SJohn Marino /// ratio_multiply 289*e4b17023SJohn Marino template<typename _R1, typename _R2> 290*e4b17023SJohn Marino struct ratio_multiply 291*e4b17023SJohn Marino { 292*e4b17023SJohn Marino private: 293*e4b17023SJohn Marino static const intmax_t __gcd1 = 294*e4b17023SJohn Marino __static_gcd<_R1::num, _R2::den>::value; 295*e4b17023SJohn Marino static const intmax_t __gcd2 = 296*e4b17023SJohn Marino __static_gcd<_R2::num, _R1::den>::value; 297*e4b17023SJohn Marino 298*e4b17023SJohn Marino public: 299*e4b17023SJohn Marino typedef ratio< 300*e4b17023SJohn Marino __safe_multiply<(_R1::num / __gcd1), 301*e4b17023SJohn Marino (_R2::num / __gcd2)>::value, 302*e4b17023SJohn Marino __safe_multiply<(_R1::den / __gcd2), 303*e4b17023SJohn Marino (_R2::den / __gcd1)>::value> type; 304*e4b17023SJohn Marino 305*e4b17023SJohn Marino static constexpr intmax_t num = type::num; 306*e4b17023SJohn Marino static constexpr intmax_t den = type::den; 307*e4b17023SJohn Marino }; 308*e4b17023SJohn Marino 309*e4b17023SJohn Marino template<typename _R1, typename _R2> 310*e4b17023SJohn Marino constexpr intmax_t ratio_multiply<_R1, _R2>::num; 311*e4b17023SJohn Marino 312*e4b17023SJohn Marino template<typename _R1, typename _R2> 313*e4b17023SJohn Marino constexpr intmax_t ratio_multiply<_R1, _R2>::den; 314*e4b17023SJohn Marino 315*e4b17023SJohn Marino /// ratio_divide 316*e4b17023SJohn Marino template<typename _R1, typename _R2> 317*e4b17023SJohn Marino struct ratio_divide 318*e4b17023SJohn Marino { 319*e4b17023SJohn Marino static_assert(_R2::num != 0, "division by 0"); 320*e4b17023SJohn Marino 321*e4b17023SJohn Marino typedef typename ratio_multiply< 322*e4b17023SJohn Marino _R1, 323*e4b17023SJohn Marino ratio<_R2::den, _R2::num>>::type type; 324*e4b17023SJohn Marino 325*e4b17023SJohn Marino static constexpr intmax_t num = type::num; 326*e4b17023SJohn Marino static constexpr intmax_t den = type::den; 327*e4b17023SJohn Marino }; 328*e4b17023SJohn Marino 329*e4b17023SJohn Marino template<typename _R1, typename _R2> 330*e4b17023SJohn Marino constexpr intmax_t ratio_divide<_R1, _R2>::num; 331*e4b17023SJohn Marino 332*e4b17023SJohn Marino template<typename _R1, typename _R2> 333*e4b17023SJohn Marino constexpr intmax_t ratio_divide<_R1, _R2>::den; 334*e4b17023SJohn Marino 335*e4b17023SJohn Marino /// ratio_equal 336*e4b17023SJohn Marino template<typename _R1, typename _R2> 337*e4b17023SJohn Marino struct ratio_equal 338*e4b17023SJohn Marino : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> 339*e4b17023SJohn Marino { }; 340*e4b17023SJohn Marino 341*e4b17023SJohn Marino /// ratio_not_equal 342*e4b17023SJohn Marino template<typename _R1, typename _R2> 343*e4b17023SJohn Marino struct ratio_not_equal 344*e4b17023SJohn Marino : integral_constant<bool, !ratio_equal<_R1, _R2>::value> 345*e4b17023SJohn Marino { }; 346*e4b17023SJohn Marino 347*e4b17023SJohn Marino // Both numbers are positive. 348*e4b17023SJohn Marino template<typename _R1, typename _R2, 349*e4b17023SJohn Marino typename _Left = __big_mul<_R1::num,_R2::den>, 350*e4b17023SJohn Marino typename _Right = __big_mul<_R2::num,_R1::den> > 351*e4b17023SJohn Marino struct __ratio_less_impl_1 352*e4b17023SJohn Marino : integral_constant<bool, __big_less<_Left::__hi, _Left::__lo, 353*e4b17023SJohn Marino _Right::__hi, _Right::__lo>::value> 354*e4b17023SJohn Marino { }; 355*e4b17023SJohn Marino 356*e4b17023SJohn Marino template<typename _R1, typename _R2, 357*e4b17023SJohn Marino bool = (_R1::num == 0 || _R2::num == 0 358*e4b17023SJohn Marino || (__static_sign<_R1::num>::value 359*e4b17023SJohn Marino != __static_sign<_R2::num>::value)), 360*e4b17023SJohn Marino bool = (__static_sign<_R1::num>::value == -1 361*e4b17023SJohn Marino && __static_sign<_R2::num>::value == -1)> 362*e4b17023SJohn Marino struct __ratio_less_impl 363*e4b17023SJohn Marino : __ratio_less_impl_1<_R1, _R2>::type 364*e4b17023SJohn Marino { }; 365*e4b17023SJohn Marino 366*e4b17023SJohn Marino template<typename _R1, typename _R2> 367*e4b17023SJohn Marino struct __ratio_less_impl<_R1, _R2, true, false> 368*e4b17023SJohn Marino : integral_constant<bool, _R1::num < _R2::num> 369*e4b17023SJohn Marino { }; 370*e4b17023SJohn Marino 371*e4b17023SJohn Marino template<typename _R1, typename _R2> 372*e4b17023SJohn Marino struct __ratio_less_impl<_R1, _R2, false, true> 373*e4b17023SJohn Marino : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>, 374*e4b17023SJohn Marino ratio<-_R1::num, _R1::den> >::type 375*e4b17023SJohn Marino { }; 376*e4b17023SJohn Marino 377*e4b17023SJohn Marino /// ratio_less 378*e4b17023SJohn Marino template<typename _R1, typename _R2> 379*e4b17023SJohn Marino struct ratio_less 380*e4b17023SJohn Marino : __ratio_less_impl<_R1, _R2>::type 381*e4b17023SJohn Marino { }; 382*e4b17023SJohn Marino 383*e4b17023SJohn Marino /// ratio_less_equal 384*e4b17023SJohn Marino template<typename _R1, typename _R2> 385*e4b17023SJohn Marino struct ratio_less_equal 386*e4b17023SJohn Marino : integral_constant<bool, !ratio_less<_R2, _R1>::value> 387*e4b17023SJohn Marino { }; 388*e4b17023SJohn Marino 389*e4b17023SJohn Marino /// ratio_greater 390*e4b17023SJohn Marino template<typename _R1, typename _R2> 391*e4b17023SJohn Marino struct ratio_greater 392*e4b17023SJohn Marino : integral_constant<bool, ratio_less<_R2, _R1>::value> 393*e4b17023SJohn Marino { }; 394*e4b17023SJohn Marino 395*e4b17023SJohn Marino /// ratio_greater_equal 396*e4b17023SJohn Marino template<typename _R1, typename _R2> 397*e4b17023SJohn Marino struct ratio_greater_equal 398*e4b17023SJohn Marino : integral_constant<bool, !ratio_less<_R1, _R2>::value> 399*e4b17023SJohn Marino { }; 400*e4b17023SJohn Marino 401*e4b17023SJohn Marino template<typename _R1, typename _R2, 402*e4b17023SJohn Marino bool = (_R1::num >= 0), 403*e4b17023SJohn Marino bool = (_R2::num >= 0), 404*e4b17023SJohn Marino bool = ratio_less<ratio<__static_abs<_R1::num>::value, _R1::den>, 405*e4b17023SJohn Marino ratio<__static_abs<_R2::num>::value, _R2::den> >::value> 406*e4b17023SJohn Marino struct __ratio_add_impl 407*e4b17023SJohn Marino { 408*e4b17023SJohn Marino private: 409*e4b17023SJohn Marino typedef typename __ratio_add_impl< 410*e4b17023SJohn Marino ratio<-_R1::num, _R1::den>, 411*e4b17023SJohn Marino ratio<-_R2::num, _R2::den> >::type __t; 412*e4b17023SJohn Marino public: 413*e4b17023SJohn Marino typedef ratio<-__t::num, __t::den> type; 414*e4b17023SJohn Marino }; 415*e4b17023SJohn Marino 416*e4b17023SJohn Marino // True addition of nonnegative numbers. 417*e4b17023SJohn Marino template<typename _R1, typename _R2, bool __b> 418*e4b17023SJohn Marino struct __ratio_add_impl<_R1, _R2, true, true, __b> 419*e4b17023SJohn Marino { 420*e4b17023SJohn Marino private: 421*e4b17023SJohn Marino static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 422*e4b17023SJohn Marino static constexpr uintmax_t __d2 = _R2::den / __g; 423*e4b17023SJohn Marino typedef __big_mul<_R1::den, __d2> __d; 424*e4b17023SJohn Marino typedef __big_mul<_R1::num, _R2::den / __g> __x; 425*e4b17023SJohn Marino typedef __big_mul<_R2::num, _R1::den / __g> __y; 426*e4b17023SJohn Marino typedef __big_add<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 427*e4b17023SJohn Marino static_assert(__n::__hi >= __x::__hi, "Internal library error"); 428*e4b17023SJohn Marino typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 429*e4b17023SJohn Marino static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 430*e4b17023SJohn Marino typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 431*e4b17023SJohn Marino static_assert(__n_final::__rem == 0, "Internal library error"); 432*e4b17023SJohn Marino static_assert(__n_final::__quot_hi == 0 && 433*e4b17023SJohn Marino __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 434*e4b17023SJohn Marino typedef __big_mul<_R1::den / __g2, __d2> __d_final; 435*e4b17023SJohn Marino static_assert(__d_final::__hi == 0 && 436*e4b17023SJohn Marino __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 437*e4b17023SJohn Marino public: 438*e4b17023SJohn Marino typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 439*e4b17023SJohn Marino }; 440*e4b17023SJohn Marino 441*e4b17023SJohn Marino template<typename _R1, typename _R2> 442*e4b17023SJohn Marino struct __ratio_add_impl<_R1, _R2, false, true, true> 443*e4b17023SJohn Marino : __ratio_add_impl<_R2, _R1> 444*e4b17023SJohn Marino { }; 445*e4b17023SJohn Marino 446*e4b17023SJohn Marino // True subtraction of nonnegative numbers yielding a nonnegative result. 447*e4b17023SJohn Marino template<typename _R1, typename _R2> 448*e4b17023SJohn Marino struct __ratio_add_impl<_R1, _R2, true, false, false> 449*e4b17023SJohn Marino { 450*e4b17023SJohn Marino private: 451*e4b17023SJohn Marino static constexpr uintmax_t __g = __static_gcd<_R1::den, _R2::den>::value; 452*e4b17023SJohn Marino static constexpr uintmax_t __d2 = _R2::den / __g; 453*e4b17023SJohn Marino typedef __big_mul<_R1::den, __d2> __d; 454*e4b17023SJohn Marino typedef __big_mul<_R1::num, _R2::den / __g> __x; 455*e4b17023SJohn Marino typedef __big_mul<-_R2::num, _R1::den / __g> __y; 456*e4b17023SJohn Marino typedef __big_sub<__x::__hi, __x::__lo, __y::__hi, __y::__lo> __n; 457*e4b17023SJohn Marino typedef __big_div<__n::__hi, __n::__lo, __g> __ng; 458*e4b17023SJohn Marino static constexpr uintmax_t __g2 = __static_gcd<__ng::__rem, __g>::value; 459*e4b17023SJohn Marino typedef __big_div<__n::__hi, __n::__lo, __g2> __n_final; 460*e4b17023SJohn Marino static_assert(__n_final::__rem == 0, "Internal library error"); 461*e4b17023SJohn Marino static_assert(__n_final::__quot_hi == 0 && 462*e4b17023SJohn Marino __n_final::__quot_lo <= __INTMAX_MAX__, "overflow in addition"); 463*e4b17023SJohn Marino typedef __big_mul<_R1::den / __g2, __d2> __d_final; 464*e4b17023SJohn Marino static_assert(__d_final::__hi == 0 && 465*e4b17023SJohn Marino __d_final::__lo <= __INTMAX_MAX__, "overflow in addition"); 466*e4b17023SJohn Marino public: 467*e4b17023SJohn Marino typedef ratio<__n_final::__quot_lo, __d_final::__lo> type; 468*e4b17023SJohn Marino }; 469*e4b17023SJohn Marino 470*e4b17023SJohn Marino /// ratio_add 471*e4b17023SJohn Marino template<typename _R1, typename _R2> 472*e4b17023SJohn Marino struct ratio_add 473*e4b17023SJohn Marino { 474*e4b17023SJohn Marino typedef typename __ratio_add_impl<_R1, _R2>::type type; 475*e4b17023SJohn Marino static constexpr intmax_t num = type::num; 476*e4b17023SJohn Marino static constexpr intmax_t den = type::den; 477*e4b17023SJohn Marino }; 478*e4b17023SJohn Marino 479*e4b17023SJohn Marino template<typename _R1, typename _R2> 480*e4b17023SJohn Marino constexpr intmax_t ratio_add<_R1, _R2>::num; 481*e4b17023SJohn Marino 482*e4b17023SJohn Marino template<typename _R1, typename _R2> 483*e4b17023SJohn Marino constexpr intmax_t ratio_add<_R1, _R2>::den; 484*e4b17023SJohn Marino 485*e4b17023SJohn Marino /// ratio_subtract 486*e4b17023SJohn Marino template<typename _R1, typename _R2> 487*e4b17023SJohn Marino struct ratio_subtract 488*e4b17023SJohn Marino { 489*e4b17023SJohn Marino typedef typename ratio_add< 490*e4b17023SJohn Marino _R1, 491*e4b17023SJohn Marino ratio<-_R2::num, _R2::den>>::type type; 492*e4b17023SJohn Marino 493*e4b17023SJohn Marino static constexpr intmax_t num = type::num; 494*e4b17023SJohn Marino static constexpr intmax_t den = type::den; 495*e4b17023SJohn Marino }; 496*e4b17023SJohn Marino 497*e4b17023SJohn Marino template<typename _R1, typename _R2> 498*e4b17023SJohn Marino constexpr intmax_t ratio_subtract<_R1, _R2>::num; 499*e4b17023SJohn Marino 500*e4b17023SJohn Marino template<typename _R1, typename _R2> 501*e4b17023SJohn Marino constexpr intmax_t ratio_subtract<_R1, _R2>::den; 502*e4b17023SJohn Marino 503*e4b17023SJohn Marino 504*e4b17023SJohn Marino 505*e4b17023SJohn Marino typedef ratio<1, 1000000000000000000> atto; 506*e4b17023SJohn Marino typedef ratio<1, 1000000000000000> femto; 507*e4b17023SJohn Marino typedef ratio<1, 1000000000000> pico; 508*e4b17023SJohn Marino typedef ratio<1, 1000000000> nano; 509*e4b17023SJohn Marino typedef ratio<1, 1000000> micro; 510*e4b17023SJohn Marino typedef ratio<1, 1000> milli; 511*e4b17023SJohn Marino typedef ratio<1, 100> centi; 512*e4b17023SJohn Marino typedef ratio<1, 10> deci; 513*e4b17023SJohn Marino typedef ratio< 10, 1> deca; 514*e4b17023SJohn Marino typedef ratio< 100, 1> hecto; 515*e4b17023SJohn Marino typedef ratio< 1000, 1> kilo; 516*e4b17023SJohn Marino typedef ratio< 1000000, 1> mega; 517*e4b17023SJohn Marino typedef ratio< 1000000000, 1> giga; 518*e4b17023SJohn Marino typedef ratio< 1000000000000, 1> tera; 519*e4b17023SJohn Marino typedef ratio< 1000000000000000, 1> peta; 520*e4b17023SJohn Marino typedef ratio< 1000000000000000000, 1> exa; 521*e4b17023SJohn Marino 522*e4b17023SJohn Marino // @} group ratio 523*e4b17023SJohn Marino_GLIBCXX_END_NAMESPACE_VERSION 524*e4b17023SJohn Marino} // namespace 525*e4b17023SJohn Marino 526*e4b17023SJohn Marino#endif //_GLIBCXX_USE_C99_STDINT_TR1 527*e4b17023SJohn Marino 528*e4b17023SJohn Marino#endif //__GXX_EXPERIMENTAL_CXX0X__ 529*e4b17023SJohn Marino 530*e4b17023SJohn Marino#endif //_GLIBCXX_RATIO 531