1 // -*- C++ -*- 2 //===---------------------------- ratio -----------------------------------===// 3 // 4 // The LLVM Compiler Infrastructure 5 // 6 // This file is dual licensed under the MIT and the University of Illinois Open 7 // Source Licenses. See LICENSE.TXT for details. 8 // 9 //===----------------------------------------------------------------------===// 10 11 #ifndef _LIBCPP_RATIO 12 #define _LIBCPP_RATIO 13 14 /* 15 ratio synopsis 16 17 namespace std 18 { 19 20 template <intmax_t N, intmax_t D = 1> 21 class ratio 22 { 23 public: 24 static constexpr intmax_t num; 25 static constexpr intmax_t den; 26 typedef ratio<num, den> type; 27 }; 28 29 // ratio arithmetic 30 template <class R1, class R2> using ratio_add = ...; 31 template <class R1, class R2> using ratio_subtract = ...; 32 template <class R1, class R2> using ratio_multiply = ...; 33 template <class R1, class R2> using ratio_divide = ...; 34 35 // ratio comparison 36 template <class R1, class R2> struct ratio_equal; 37 template <class R1, class R2> struct ratio_not_equal; 38 template <class R1, class R2> struct ratio_less; 39 template <class R1, class R2> struct ratio_less_equal; 40 template <class R1, class R2> struct ratio_greater; 41 template <class R1, class R2> struct ratio_greater_equal; 42 43 // convenience SI typedefs 44 typedef ratio<1, 1000000000000000000000000> yocto; // not supported 45 typedef ratio<1, 1000000000000000000000> zepto; // not supported 46 typedef ratio<1, 1000000000000000000> atto; 47 typedef ratio<1, 1000000000000000> femto; 48 typedef ratio<1, 1000000000000> pico; 49 typedef ratio<1, 1000000000> nano; 50 typedef ratio<1, 1000000> micro; 51 typedef ratio<1, 1000> milli; 52 typedef ratio<1, 100> centi; 53 typedef ratio<1, 10> deci; 54 typedef ratio< 10, 1> deca; 55 typedef ratio< 100, 1> hecto; 56 typedef ratio< 1000, 1> kilo; 57 typedef ratio< 1000000, 1> mega; 58 typedef ratio< 1000000000, 1> giga; 59 typedef ratio< 1000000000000, 1> tera; 60 typedef ratio< 1000000000000000, 1> peta; 61 typedef ratio< 1000000000000000000, 1> exa; 62 typedef ratio< 1000000000000000000000, 1> zetta; // not supported 63 typedef ratio<1000000000000000000000000, 1> yotta; // not supported 64 65 // 20.11.5, ratio comparison 66 template <class R1, class R2> constexpr bool ratio_equal_v 67 = ratio_equal<R1, R2>::value; // C++17 68 template <class R1, class R2> constexpr bool ratio_not_equal_v 69 = ratio_not_equal<R1, R2>::value; // C++17 70 template <class R1, class R2> constexpr bool ratio_less_v 71 = ratio_less<R1, R2>::value; // C++17 72 template <class R1, class R2> constexpr bool ratio_less_equal_v 73 = ratio_less_equal<R1, R2>::value; // C++17 74 template <class R1, class R2> constexpr bool ratio_greater_v 75 = ratio_greater<R1, R2>::value; // C++17 76 template <class R1, class R2> constexpr bool ratio_greater_equal_v 77 = ratio_greater_equal<R1, R2>::value; // C++17 78 } 79 */ 80 81 #include <__config> 82 #include <cstdint> 83 #include <climits> 84 #include <type_traits> 85 86 #include <__undef_min_max> 87 88 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 89 #pragma GCC system_header 90 #endif 91 92 _LIBCPP_BEGIN_NAMESPACE_STD 93 94 // __static_gcd 95 96 template <intmax_t _Xp, intmax_t _Yp> 97 struct __static_gcd 98 { 99 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 100 }; 101 102 template <intmax_t _Xp> 103 struct __static_gcd<_Xp, 0> 104 { 105 static const intmax_t value = _Xp; 106 }; 107 108 template <> 109 struct __static_gcd<0, 0> 110 { 111 static const intmax_t value = 1; 112 }; 113 114 // __static_lcm 115 116 template <intmax_t _Xp, intmax_t _Yp> 117 struct __static_lcm 118 { 119 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 120 }; 121 122 template <intmax_t _Xp> 123 struct __static_abs 124 { 125 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 126 }; 127 128 template <intmax_t _Xp> 129 struct __static_sign 130 { 131 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 132 }; 133 134 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 135 class __ll_add; 136 137 template <intmax_t _Xp, intmax_t _Yp> 138 class __ll_add<_Xp, _Yp, 1> 139 { 140 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 141 static const intmax_t max = -min; 142 143 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 144 public: 145 static const intmax_t value = _Xp + _Yp; 146 }; 147 148 template <intmax_t _Xp, intmax_t _Yp> 149 class __ll_add<_Xp, _Yp, 0> 150 { 151 public: 152 static const intmax_t value = _Xp; 153 }; 154 155 template <intmax_t _Xp, intmax_t _Yp> 156 class __ll_add<_Xp, _Yp, -1> 157 { 158 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 159 static const intmax_t max = -min; 160 161 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 162 public: 163 static const intmax_t value = _Xp + _Yp; 164 }; 165 166 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 167 class __ll_sub; 168 169 template <intmax_t _Xp, intmax_t _Yp> 170 class __ll_sub<_Xp, _Yp, 1> 171 { 172 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 173 static const intmax_t max = -min; 174 175 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 176 public: 177 static const intmax_t value = _Xp - _Yp; 178 }; 179 180 template <intmax_t _Xp, intmax_t _Yp> 181 class __ll_sub<_Xp, _Yp, 0> 182 { 183 public: 184 static const intmax_t value = _Xp; 185 }; 186 187 template <intmax_t _Xp, intmax_t _Yp> 188 class __ll_sub<_Xp, _Yp, -1> 189 { 190 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 191 static const intmax_t max = -min; 192 193 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 194 public: 195 static const intmax_t value = _Xp - _Yp; 196 }; 197 198 template <intmax_t _Xp, intmax_t _Yp> 199 class __ll_mul 200 { 201 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 202 static const intmax_t min = nan + 1; 203 static const intmax_t max = -min; 204 static const intmax_t __a_x = __static_abs<_Xp>::value; 205 static const intmax_t __a_y = __static_abs<_Yp>::value; 206 207 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 208 public: 209 static const intmax_t value = _Xp * _Yp; 210 }; 211 212 template <intmax_t _Yp> 213 class __ll_mul<0, _Yp> 214 { 215 public: 216 static const intmax_t value = 0; 217 }; 218 219 template <intmax_t _Xp> 220 class __ll_mul<_Xp, 0> 221 { 222 public: 223 static const intmax_t value = 0; 224 }; 225 226 template <> 227 class __ll_mul<0, 0> 228 { 229 public: 230 static const intmax_t value = 0; 231 }; 232 233 // Not actually used but left here in case needed in future maintenance 234 template <intmax_t _Xp, intmax_t _Yp> 235 class __ll_div 236 { 237 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 238 static const intmax_t min = nan + 1; 239 static const intmax_t max = -min; 240 241 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 242 public: 243 static const intmax_t value = _Xp / _Yp; 244 }; 245 246 template <intmax_t _Num, intmax_t _Den = 1> 247 class _LIBCPP_TEMPLATE_VIS ratio 248 { 249 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 250 static_assert(_Den != 0, "ratio divide by 0"); 251 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 252 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 253 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 254 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 255 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 256 public: 257 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 258 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 259 260 typedef ratio<num, den> type; 261 }; 262 263 template <intmax_t _Num, intmax_t _Den> 264 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 265 266 template <intmax_t _Num, intmax_t _Den> 267 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 268 269 template <class _Tp> struct __is_ratio : false_type {}; 270 template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 271 272 typedef ratio<1LL, 1000000000000000000LL> atto; 273 typedef ratio<1LL, 1000000000000000LL> femto; 274 typedef ratio<1LL, 1000000000000LL> pico; 275 typedef ratio<1LL, 1000000000LL> nano; 276 typedef ratio<1LL, 1000000LL> micro; 277 typedef ratio<1LL, 1000LL> milli; 278 typedef ratio<1LL, 100LL> centi; 279 typedef ratio<1LL, 10LL> deci; 280 typedef ratio< 10LL, 1LL> deca; 281 typedef ratio< 100LL, 1LL> hecto; 282 typedef ratio< 1000LL, 1LL> kilo; 283 typedef ratio< 1000000LL, 1LL> mega; 284 typedef ratio< 1000000000LL, 1LL> giga; 285 typedef ratio< 1000000000000LL, 1LL> tera; 286 typedef ratio< 1000000000000000LL, 1LL> peta; 287 typedef ratio<1000000000000000000LL, 1LL> exa; 288 289 template <class _R1, class _R2> 290 struct __ratio_multiply 291 { 292 private: 293 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 294 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 295 public: 296 typedef typename ratio 297 < 298 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 299 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 300 >::type type; 301 }; 302 303 #ifndef _LIBCPP_CXX03_LANG 304 305 template <class _R1, class _R2> using ratio_multiply 306 = typename __ratio_multiply<_R1, _R2>::type; 307 308 #else // _LIBCPP_CXX03_LANG 309 310 template <class _R1, class _R2> 311 struct _LIBCPP_TEMPLATE_VIS ratio_multiply 312 : public __ratio_multiply<_R1, _R2>::type {}; 313 314 #endif // _LIBCPP_CXX03_LANG 315 316 template <class _R1, class _R2> 317 struct __ratio_divide 318 { 319 private: 320 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 321 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 322 public: 323 typedef typename ratio 324 < 325 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 326 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 327 >::type type; 328 }; 329 330 #ifndef _LIBCPP_CXX03_LANG 331 332 template <class _R1, class _R2> using ratio_divide 333 = typename __ratio_divide<_R1, _R2>::type; 334 335 #else // _LIBCPP_CXX03_LANG 336 337 template <class _R1, class _R2> 338 struct _LIBCPP_TEMPLATE_VIS ratio_divide 339 : public __ratio_divide<_R1, _R2>::type {}; 340 341 #endif // _LIBCPP_CXX03_LANG 342 343 template <class _R1, class _R2> 344 struct __ratio_add 345 { 346 private: 347 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 348 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 349 public: 350 typedef typename ratio_multiply 351 < 352 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 353 ratio 354 < 355 __ll_add 356 < 357 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 358 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 359 >::value, 360 _R2::den 361 > 362 >::type type; 363 }; 364 365 #ifndef _LIBCPP_CXX03_LANG 366 367 template <class _R1, class _R2> using ratio_add 368 = typename __ratio_add<_R1, _R2>::type; 369 370 #else // _LIBCPP_CXX03_LANG 371 372 template <class _R1, class _R2> 373 struct _LIBCPP_TEMPLATE_VIS ratio_add 374 : public __ratio_add<_R1, _R2>::type {}; 375 376 #endif // _LIBCPP_CXX03_LANG 377 378 template <class _R1, class _R2> 379 struct __ratio_subtract 380 { 381 private: 382 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 383 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 384 public: 385 typedef typename ratio_multiply 386 < 387 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 388 ratio 389 < 390 __ll_sub 391 < 392 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 393 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 394 >::value, 395 _R2::den 396 > 397 >::type type; 398 }; 399 400 #ifndef _LIBCPP_CXX03_LANG 401 402 template <class _R1, class _R2> using ratio_subtract 403 = typename __ratio_subtract<_R1, _R2>::type; 404 405 #else // _LIBCPP_CXX03_LANG 406 407 template <class _R1, class _R2> 408 struct _LIBCPP_TEMPLATE_VIS ratio_subtract 409 : public __ratio_subtract<_R1, _R2>::type {}; 410 411 #endif // _LIBCPP_CXX03_LANG 412 413 // ratio_equal 414 415 template <class _R1, class _R2> 416 struct _LIBCPP_TEMPLATE_VIS ratio_equal 417 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 418 419 template <class _R1, class _R2> 420 struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 421 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 422 423 // ratio_less 424 425 template <class _R1, class _R2, bool _Odd = false, 426 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 427 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 428 struct __ratio_less1 429 { 430 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 431 }; 432 433 template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 434 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 435 { 436 static const bool value = false; 437 }; 438 439 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 440 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 441 { 442 static const bool value = !_Odd; 443 }; 444 445 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 446 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 447 { 448 static const bool value = _Odd; 449 }; 450 451 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 452 intmax_t _M2> 453 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 454 { 455 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 456 ratio<_R2::den, _M2>, !_Odd>::value; 457 }; 458 459 template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 460 intmax_t _S2 = __static_sign<_R2::num>::value> 461 struct __ratio_less 462 { 463 static const bool value = _S1 < _S2; 464 }; 465 466 template <class _R1, class _R2> 467 struct __ratio_less<_R1, _R2, 1LL, 1LL> 468 { 469 static const bool value = __ratio_less1<_R1, _R2>::value; 470 }; 471 472 template <class _R1, class _R2> 473 struct __ratio_less<_R1, _R2, -1LL, -1LL> 474 { 475 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 476 }; 477 478 template <class _R1, class _R2> 479 struct _LIBCPP_TEMPLATE_VIS ratio_less 480 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 481 482 template <class _R1, class _R2> 483 struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 484 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 485 486 template <class _R1, class _R2> 487 struct _LIBCPP_TEMPLATE_VIS ratio_greater 488 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 489 490 template <class _R1, class _R2> 491 struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 492 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 493 494 template <class _R1, class _R2> 495 struct __ratio_gcd 496 { 497 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 498 __static_lcm<_R1::den, _R2::den>::value> type; 499 }; 500 501 #if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES) 502 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_equal_v 503 = ratio_equal<_R1, _R2>::value; 504 505 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_not_equal_v 506 = ratio_not_equal<_R1, _R2>::value; 507 508 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_v 509 = ratio_less<_R1, _R2>::value; 510 511 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_equal_v 512 = ratio_less_equal<_R1, _R2>::value; 513 514 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_v 515 = ratio_greater<_R1, _R2>::value; 516 517 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_equal_v 518 = ratio_greater_equal<_R1, _R2>::value; 519 #endif 520 521 _LIBCPP_END_NAMESPACE_STD 522 523 #endif // _LIBCPP_RATIO 524
