Warning, /include/c++/v1/ratio is written in an unsupported language. File is not indexed.
0001 // -*- C++ -*-
0002 //===----------------------------------------------------------------------===//
0003 //
0004 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
0005 // See https://llvm.org/LICENSE.txt for license information.
0006 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
0007 //
0008 //===----------------------------------------------------------------------===//
0009
0010 #ifndef _LIBCPP_RATIO
0011 #define _LIBCPP_RATIO
0012
0013 /*
0014 ratio synopsis
0015
0016 namespace std
0017 {
0018
0019 template <intmax_t N, intmax_t D = 1>
0020 class ratio
0021 {
0022 public:
0023 static constexpr intmax_t num;
0024 static constexpr intmax_t den;
0025 typedef ratio<num, den> type;
0026 };
0027
0028 // ratio arithmetic
0029 template <class R1, class R2> using ratio_add = ...;
0030 template <class R1, class R2> using ratio_subtract = ...;
0031 template <class R1, class R2> using ratio_multiply = ...;
0032 template <class R1, class R2> using ratio_divide = ...;
0033
0034 // ratio comparison
0035 template <class R1, class R2> struct ratio_equal;
0036 template <class R1, class R2> struct ratio_not_equal;
0037 template <class R1, class R2> struct ratio_less;
0038 template <class R1, class R2> struct ratio_less_equal;
0039 template <class R1, class R2> struct ratio_greater;
0040 template <class R1, class R2> struct ratio_greater_equal;
0041
0042 // convenience SI typedefs
0043 using quecto = ratio <1, 1'000'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported
0044 using ronto = ratio <1, 1'000'000'000'000'000'000'000'000'000>; // Since C++26; not supported
0045 typedef ratio<1, 1000000000000000000000000> yocto; // not supported
0046 typedef ratio<1, 1000000000000000000000> zepto; // not supported
0047 typedef ratio<1, 1000000000000000000> atto;
0048 typedef ratio<1, 1000000000000000> femto;
0049 typedef ratio<1, 1000000000000> pico;
0050 typedef ratio<1, 1000000000> nano;
0051 typedef ratio<1, 1000000> micro;
0052 typedef ratio<1, 1000> milli;
0053 typedef ratio<1, 100> centi;
0054 typedef ratio<1, 10> deci;
0055 typedef ratio< 10, 1> deca;
0056 typedef ratio< 100, 1> hecto;
0057 typedef ratio< 1000, 1> kilo;
0058 typedef ratio< 1000000, 1> mega;
0059 typedef ratio< 1000000000, 1> giga;
0060 typedef ratio< 1000000000000, 1> tera;
0061 typedef ratio< 1000000000000000, 1> peta;
0062 typedef ratio< 1000000000000000000, 1> exa;
0063 typedef ratio< 1000000000000000000000, 1> zetta; // not supported
0064 typedef ratio<1000000000000000000000000, 1> yotta; // not supported
0065 using ronna = ratio <1'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported
0066 using quetta = ratio <1'000'000'000'000'000'000'000'000'000'000, 1>; // Since C++26; not supported
0067
0068 // 20.11.5, ratio comparison
0069 template <class R1, class R2> inline constexpr bool ratio_equal_v
0070 = ratio_equal<R1, R2>::value; // C++17
0071 template <class R1, class R2> inline constexpr bool ratio_not_equal_v
0072 = ratio_not_equal<R1, R2>::value; // C++17
0073 template <class R1, class R2> inline constexpr bool ratio_less_v
0074 = ratio_less<R1, R2>::value; // C++17
0075 template <class R1, class R2> inline constexpr bool ratio_less_equal_v
0076 = ratio_less_equal<R1, R2>::value; // C++17
0077 template <class R1, class R2> inline constexpr bool ratio_greater_v
0078 = ratio_greater<R1, R2>::value; // C++17
0079 template <class R1, class R2> inline constexpr bool ratio_greater_equal_v
0080 = ratio_greater_equal<R1, R2>::value; // C++17
0081 }
0082 */
0083
0084 #if __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)
0085 # include <__cxx03/ratio>
0086 #else
0087 # include <__config>
0088 # include <__type_traits/integral_constant.h>
0089 # include <climits>
0090 # include <cstdint>
0091 # include <version>
0092
0093 # if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
0094 # pragma GCC system_header
0095 # endif
0096
0097 _LIBCPP_PUSH_MACROS
0098 # include <__undef_macros>
0099
0100 _LIBCPP_BEGIN_NAMESPACE_STD
0101
0102 // __static_gcd
0103
0104 template <intmax_t _Xp, intmax_t _Yp>
0105 inline const intmax_t __static_gcd = __static_gcd<_Yp, _Xp % _Yp>;
0106
0107 template <intmax_t _Xp>
0108 inline const intmax_t __static_gcd<_Xp, 0> = _Xp;
0109
0110 template <>
0111 inline const intmax_t __static_gcd<0, 0> = 1;
0112
0113 // __static_lcm
0114
0115 template <intmax_t _Xp, intmax_t _Yp>
0116 inline const intmax_t __static_lcm = _Xp / __static_gcd<_Xp, _Yp> * _Yp;
0117
0118 template <intmax_t _Xp>
0119 inline const intmax_t __static_abs = _Xp < 0 ? -_Xp : _Xp;
0120
0121 template <intmax_t _Xp>
0122 inline const intmax_t __static_sign = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1);
0123
0124 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp> >
0125 class __ll_add;
0126
0127 template <intmax_t _Xp, intmax_t _Yp>
0128 class __ll_add<_Xp, _Yp, 1> {
0129 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
0130 static const intmax_t max = -min;
0131
0132 static_assert(_Xp <= max - _Yp, "overflow in __ll_add");
0133
0134 public:
0135 static const intmax_t value = _Xp + _Yp;
0136 };
0137
0138 template <intmax_t _Xp, intmax_t _Yp>
0139 class __ll_add<_Xp, _Yp, 0> {
0140 public:
0141 static const intmax_t value = _Xp;
0142 };
0143
0144 template <intmax_t _Xp, intmax_t _Yp>
0145 class __ll_add<_Xp, _Yp, -1> {
0146 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
0147 static const intmax_t max = -min;
0148
0149 static_assert(min - _Yp <= _Xp, "overflow in __ll_add");
0150
0151 public:
0152 static const intmax_t value = _Xp + _Yp;
0153 };
0154
0155 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp> >
0156 class __ll_sub;
0157
0158 template <intmax_t _Xp, intmax_t _Yp>
0159 class __ll_sub<_Xp, _Yp, 1> {
0160 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
0161 static const intmax_t max = -min;
0162
0163 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub");
0164
0165 public:
0166 static const intmax_t value = _Xp - _Yp;
0167 };
0168
0169 template <intmax_t _Xp, intmax_t _Yp>
0170 class __ll_sub<_Xp, _Yp, 0> {
0171 public:
0172 static const intmax_t value = _Xp;
0173 };
0174
0175 template <intmax_t _Xp, intmax_t _Yp>
0176 class __ll_sub<_Xp, _Yp, -1> {
0177 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1;
0178 static const intmax_t max = -min;
0179
0180 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub");
0181
0182 public:
0183 static const intmax_t value = _Xp - _Yp;
0184 };
0185
0186 template <intmax_t _Xp, intmax_t _Yp>
0187 class __ll_mul {
0188 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
0189 static const intmax_t min = nan + 1;
0190 static const intmax_t max = -min;
0191 static const intmax_t __a_x = __static_abs<_Xp>;
0192 static const intmax_t __a_y = __static_abs<_Yp>;
0193
0194 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul");
0195
0196 public:
0197 static const intmax_t value = _Xp * _Yp;
0198 };
0199
0200 template <intmax_t _Yp>
0201 class __ll_mul<0, _Yp> {
0202 public:
0203 static const intmax_t value = 0;
0204 };
0205
0206 template <intmax_t _Xp>
0207 class __ll_mul<_Xp, 0> {
0208 public:
0209 static const intmax_t value = 0;
0210 };
0211
0212 template <>
0213 class __ll_mul<0, 0> {
0214 public:
0215 static const intmax_t value = 0;
0216 };
0217
0218 // Not actually used but left here in case needed in future maintenance
0219 template <intmax_t _Xp, intmax_t _Yp>
0220 class __ll_div {
0221 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1));
0222 static const intmax_t min = nan + 1;
0223 static const intmax_t max = -min;
0224
0225 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div");
0226
0227 public:
0228 static const intmax_t value = _Xp / _Yp;
0229 };
0230
0231 template <intmax_t _Num, intmax_t _Den = 1>
0232 class _LIBCPP_TEMPLATE_VIS ratio {
0233 static_assert(__static_abs<_Num> >= 0, "ratio numerator is out of range");
0234 static_assert(_Den != 0, "ratio divide by 0");
0235 static_assert(__static_abs<_Den> > 0, "ratio denominator is out of range");
0236 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>;
0237 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>;
0238 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num> * __static_sign<_Den>;
0239 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>;
0240
0241 public:
0242 static inline _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd;
0243 static inline _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd;
0244
0245 typedef ratio<num, den> type;
0246 };
0247
0248 template <class _Tp>
0249 inline const bool __is_ratio_v = false;
0250
0251 template <intmax_t _Num, intmax_t _Den>
0252 inline const bool __is_ratio_v<ratio<_Num, _Den> > = true;
0253
0254 typedef ratio<1LL, 1000000000000000000LL> atto;
0255 typedef ratio<1LL, 1000000000000000LL> femto;
0256 typedef ratio<1LL, 1000000000000LL> pico;
0257 typedef ratio<1LL, 1000000000LL> nano;
0258 typedef ratio<1LL, 1000000LL> micro;
0259 typedef ratio<1LL, 1000LL> milli;
0260 typedef ratio<1LL, 100LL> centi;
0261 typedef ratio<1LL, 10LL> deci;
0262 typedef ratio< 10LL, 1LL> deca;
0263 typedef ratio< 100LL, 1LL> hecto;
0264 typedef ratio< 1000LL, 1LL> kilo;
0265 typedef ratio< 1000000LL, 1LL> mega;
0266 typedef ratio< 1000000000LL, 1LL> giga;
0267 typedef ratio< 1000000000000LL, 1LL> tera;
0268 typedef ratio< 1000000000000000LL, 1LL> peta;
0269 typedef ratio<1000000000000000000LL, 1LL> exa;
0270
0271 template <class _R1, class _R2>
0272 struct __ratio_multiply {
0273 private:
0274 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>;
0275 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>;
0276
0277 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0278 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0279
0280 public:
0281 typedef typename ratio< __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value,
0282 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value >::type type;
0283 };
0284
0285 # ifndef _LIBCPP_CXX03_LANG
0286
0287 template <class _R1, class _R2>
0288 using ratio_multiply = typename __ratio_multiply<_R1, _R2>::type;
0289
0290 # else // _LIBCPP_CXX03_LANG
0291
0292 template <class _R1, class _R2>
0293 struct _LIBCPP_TEMPLATE_VIS ratio_multiply : public __ratio_multiply<_R1, _R2>::type {};
0294
0295 # endif // _LIBCPP_CXX03_LANG
0296
0297 template <class _R1, class _R2>
0298 struct __ratio_divide {
0299 private:
0300 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;
0301 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;
0302
0303 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0304 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0305
0306 public:
0307 typedef typename ratio< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
0308 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::type type;
0309 };
0310
0311 # ifndef _LIBCPP_CXX03_LANG
0312
0313 template <class _R1, class _R2>
0314 using ratio_divide = typename __ratio_divide<_R1, _R2>::type;
0315
0316 # else // _LIBCPP_CXX03_LANG
0317
0318 template <class _R1, class _R2>
0319 struct _LIBCPP_TEMPLATE_VIS ratio_divide : public __ratio_divide<_R1, _R2>::type {};
0320
0321 # endif // _LIBCPP_CXX03_LANG
0322
0323 template <class _R1, class _R2>
0324 struct __ratio_add {
0325 private:
0326 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;
0327 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;
0328
0329 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0330 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0331
0332 public:
0333 typedef typename ratio_multiply<
0334 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
0335 ratio< __ll_add< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
0336 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::value,
0337 _R2::den > >::type type;
0338 };
0339
0340 # ifndef _LIBCPP_CXX03_LANG
0341
0342 template <class _R1, class _R2>
0343 using ratio_add = typename __ratio_add<_R1, _R2>::type;
0344
0345 # else // _LIBCPP_CXX03_LANG
0346
0347 template <class _R1, class _R2>
0348 struct _LIBCPP_TEMPLATE_VIS ratio_add : public __ratio_add<_R1, _R2>::type {};
0349
0350 # endif // _LIBCPP_CXX03_LANG
0351
0352 template <class _R1, class _R2>
0353 struct __ratio_subtract {
0354 private:
0355 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>;
0356 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>;
0357
0358 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0359 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0360
0361 public:
0362 typedef typename ratio_multiply<
0363 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>,
0364 ratio< __ll_sub< __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value,
0365 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value >::value,
0366 _R2::den > >::type type;
0367 };
0368
0369 # ifndef _LIBCPP_CXX03_LANG
0370
0371 template <class _R1, class _R2>
0372 using ratio_subtract = typename __ratio_subtract<_R1, _R2>::type;
0373
0374 # else // _LIBCPP_CXX03_LANG
0375
0376 template <class _R1, class _R2>
0377 struct _LIBCPP_TEMPLATE_VIS ratio_subtract : public __ratio_subtract<_R1, _R2>::type {};
0378
0379 # endif // _LIBCPP_CXX03_LANG
0380
0381 // ratio_equal
0382
0383 template <class _R1, class _R2>
0384 struct _LIBCPP_TEMPLATE_VIS ratio_equal : _BoolConstant<(_R1::num == _R2::num && _R1::den == _R2::den)> {
0385 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0386 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0387 };
0388
0389 template <class _R1, class _R2>
0390 struct _LIBCPP_TEMPLATE_VIS ratio_not_equal : _BoolConstant<!ratio_equal<_R1, _R2>::value> {
0391 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0392 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0393 };
0394
0395 // ratio_less
0396
0397 template <class _R1,
0398 class _R2,
0399 bool _Odd = false,
0400 intmax_t _Q1 = _R1::num / _R1::den,
0401 intmax_t _M1 = _R1::num % _R1::den,
0402 intmax_t _Q2 = _R2::num / _R2::den,
0403 intmax_t _M2 = _R2::num % _R2::den>
0404 struct __ratio_less1 {
0405 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2;
0406 };
0407
0408 template <class _R1, class _R2, bool _Odd, intmax_t _Qp>
0409 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> {
0410 static const bool value = false;
0411 };
0412
0413 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2>
0414 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> {
0415 static const bool value = !_Odd;
0416 };
0417
0418 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1>
0419 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> {
0420 static const bool value = _Odd;
0421 };
0422
0423 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, intmax_t _M2>
0424 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> {
0425 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, ratio<_R2::den, _M2>, !_Odd>::value;
0426 };
0427
0428 template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>, intmax_t _S2 = __static_sign<_R2::num> >
0429 struct __ratio_less {
0430 static const bool value = _S1 < _S2;
0431 };
0432
0433 template <class _R1, class _R2>
0434 struct __ratio_less<_R1, _R2, 1LL, 1LL> {
0435 static const bool value = __ratio_less1<_R1, _R2>::value;
0436 };
0437
0438 template <class _R1, class _R2>
0439 struct __ratio_less<_R1, _R2, -1LL, -1LL> {
0440 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value;
0441 };
0442
0443 template <class _R1, class _R2>
0444 struct _LIBCPP_TEMPLATE_VIS ratio_less : _BoolConstant<__ratio_less<_R1, _R2>::value> {
0445 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0446 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0447 };
0448
0449 template <class _R1, class _R2>
0450 struct _LIBCPP_TEMPLATE_VIS ratio_less_equal : _BoolConstant<!ratio_less<_R2, _R1>::value> {
0451 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0452 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0453 };
0454
0455 template <class _R1, class _R2>
0456 struct _LIBCPP_TEMPLATE_VIS ratio_greater : _BoolConstant<ratio_less<_R2, _R1>::value> {
0457 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0458 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0459 };
0460
0461 template <class _R1, class _R2>
0462 struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal : _BoolConstant<!ratio_less<_R1, _R2>::value> {
0463 static_assert(__is_ratio_v<_R1>, "[ratio.general]/2 requires R1 to be a specialisation of the ratio template");
0464 static_assert(__is_ratio_v<_R2>, "[ratio.general]/2 requires R2 to be a specialisation of the ratio template");
0465 };
0466
0467 template <class _R1, class _R2>
0468 using __ratio_gcd _LIBCPP_NODEBUG = ratio<__static_gcd<_R1::num, _R2::num>, __static_lcm<_R1::den, _R2::den> >;
0469
0470 # if _LIBCPP_STD_VER >= 17
0471 template <class _R1, class _R2>
0472 inline constexpr bool ratio_equal_v = ratio_equal<_R1, _R2>::value;
0473
0474 template <class _R1, class _R2>
0475 inline constexpr bool ratio_not_equal_v = ratio_not_equal<_R1, _R2>::value;
0476
0477 template <class _R1, class _R2>
0478 inline constexpr bool ratio_less_v = ratio_less<_R1, _R2>::value;
0479
0480 template <class _R1, class _R2>
0481 inline constexpr bool ratio_less_equal_v = ratio_less_equal<_R1, _R2>::value;
0482
0483 template <class _R1, class _R2>
0484 inline constexpr bool ratio_greater_v = ratio_greater<_R1, _R2>::value;
0485
0486 template <class _R1, class _R2>
0487 inline constexpr bool ratio_greater_equal_v = ratio_greater_equal<_R1, _R2>::value;
0488 # endif
0489
0490 _LIBCPP_END_NAMESPACE_STD
0491
0492 _LIBCPP_POP_MACROS
0493
0494 # if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
0495 # include <type_traits>
0496 # endif
0497 #endif // __cplusplus < 201103L && defined(_LIBCPP_USE_FROZEN_CXX03_HEADERS)
0498
0499 #endif // _LIBCPP_RATIO
