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 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 87 #pragma GCC system_header 88 #endif 89 90 _LIBCPP_PUSH_MACROS 91 #include <__undef_macros> 92 93 94 _LIBCPP_BEGIN_NAMESPACE_STD 95 96 // __static_gcd 97 98 template <intmax_t _Xp, intmax_t _Yp> 99 struct __static_gcd 100 { 101 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 102 }; 103 104 template <intmax_t _Xp> 105 struct __static_gcd<_Xp, 0> 106 { 107 static const intmax_t value = _Xp; 108 }; 109 110 template <> 111 struct __static_gcd<0, 0> 112 { 113 static const intmax_t value = 1; 114 }; 115 116 // __static_lcm 117 118 template <intmax_t _Xp, intmax_t _Yp> 119 struct __static_lcm 120 { 121 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 122 }; 123 124 template <intmax_t _Xp> 125 struct __static_abs 126 { 127 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 128 }; 129 130 template <intmax_t _Xp> 131 struct __static_sign 132 { 133 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 134 }; 135 136 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 137 class __ll_add; 138 139 template <intmax_t _Xp, intmax_t _Yp> 140 class __ll_add<_Xp, _Yp, 1> 141 { 142 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 143 static const intmax_t max = -min; 144 145 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 146 public: 147 static const intmax_t value = _Xp + _Yp; 148 }; 149 150 template <intmax_t _Xp, intmax_t _Yp> 151 class __ll_add<_Xp, _Yp, 0> 152 { 153 public: 154 static const intmax_t value = _Xp; 155 }; 156 157 template <intmax_t _Xp, intmax_t _Yp> 158 class __ll_add<_Xp, _Yp, -1> 159 { 160 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 161 static const intmax_t max = -min; 162 163 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 164 public: 165 static const intmax_t value = _Xp + _Yp; 166 }; 167 168 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 169 class __ll_sub; 170 171 template <intmax_t _Xp, intmax_t _Yp> 172 class __ll_sub<_Xp, _Yp, 1> 173 { 174 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 175 static const intmax_t max = -min; 176 177 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 178 public: 179 static const intmax_t value = _Xp - _Yp; 180 }; 181 182 template <intmax_t _Xp, intmax_t _Yp> 183 class __ll_sub<_Xp, _Yp, 0> 184 { 185 public: 186 static const intmax_t value = _Xp; 187 }; 188 189 template <intmax_t _Xp, intmax_t _Yp> 190 class __ll_sub<_Xp, _Yp, -1> 191 { 192 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 193 static const intmax_t max = -min; 194 195 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 196 public: 197 static const intmax_t value = _Xp - _Yp; 198 }; 199 200 template <intmax_t _Xp, intmax_t _Yp> 201 class __ll_mul 202 { 203 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 204 static const intmax_t min = nan + 1; 205 static const intmax_t max = -min; 206 static const intmax_t __a_x = __static_abs<_Xp>::value; 207 static const intmax_t __a_y = __static_abs<_Yp>::value; 208 209 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 210 public: 211 static const intmax_t value = _Xp * _Yp; 212 }; 213 214 template <intmax_t _Yp> 215 class __ll_mul<0, _Yp> 216 { 217 public: 218 static const intmax_t value = 0; 219 }; 220 221 template <intmax_t _Xp> 222 class __ll_mul<_Xp, 0> 223 { 224 public: 225 static const intmax_t value = 0; 226 }; 227 228 template <> 229 class __ll_mul<0, 0> 230 { 231 public: 232 static const intmax_t value = 0; 233 }; 234 235 // Not actually used but left here in case needed in future maintenance 236 template <intmax_t _Xp, intmax_t _Yp> 237 class __ll_div 238 { 239 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 240 static const intmax_t min = nan + 1; 241 static const intmax_t max = -min; 242 243 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 244 public: 245 static const intmax_t value = _Xp / _Yp; 246 }; 247 248 template <intmax_t _Num, intmax_t _Den = 1> 249 class _LIBCPP_TEMPLATE_VIS ratio 250 { 251 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 252 static_assert(_Den != 0, "ratio divide by 0"); 253 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 254 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 255 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 256 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 257 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 258 public: 259 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 260 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 261 262 typedef ratio<num, den> type; 263 }; 264 265 template <intmax_t _Num, intmax_t _Den> 266 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 267 268 template <intmax_t _Num, intmax_t _Den> 269 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 270 271 template <class _Tp> struct __is_ratio : false_type {}; 272 template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 273 274 typedef ratio<1LL, 1000000000000000000LL> atto; 275 typedef ratio<1LL, 1000000000000000LL> femto; 276 typedef ratio<1LL, 1000000000000LL> pico; 277 typedef ratio<1LL, 1000000000LL> nano; 278 typedef ratio<1LL, 1000000LL> micro; 279 typedef ratio<1LL, 1000LL> milli; 280 typedef ratio<1LL, 100LL> centi; 281 typedef ratio<1LL, 10LL> deci; 282 typedef ratio< 10LL, 1LL> deca; 283 typedef ratio< 100LL, 1LL> hecto; 284 typedef ratio< 1000LL, 1LL> kilo; 285 typedef ratio< 1000000LL, 1LL> mega; 286 typedef ratio< 1000000000LL, 1LL> giga; 287 typedef ratio< 1000000000000LL, 1LL> tera; 288 typedef ratio< 1000000000000000LL, 1LL> peta; 289 typedef ratio<1000000000000000000LL, 1LL> exa; 290 291 template <class _R1, class _R2> 292 struct __ratio_multiply 293 { 294 private: 295 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 296 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 297 public: 298 typedef typename ratio 299 < 300 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 301 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 302 >::type type; 303 }; 304 305 #ifndef _LIBCPP_CXX03_LANG 306 307 template <class _R1, class _R2> using ratio_multiply 308 = typename __ratio_multiply<_R1, _R2>::type; 309 310 #else // _LIBCPP_CXX03_LANG 311 312 template <class _R1, class _R2> 313 struct _LIBCPP_TEMPLATE_VIS ratio_multiply 314 : public __ratio_multiply<_R1, _R2>::type {}; 315 316 #endif // _LIBCPP_CXX03_LANG 317 318 template <class _R1, class _R2> 319 struct __ratio_divide 320 { 321 private: 322 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 323 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 324 public: 325 typedef typename ratio 326 < 327 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 328 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 329 >::type type; 330 }; 331 332 #ifndef _LIBCPP_CXX03_LANG 333 334 template <class _R1, class _R2> using ratio_divide 335 = typename __ratio_divide<_R1, _R2>::type; 336 337 #else // _LIBCPP_CXX03_LANG 338 339 template <class _R1, class _R2> 340 struct _LIBCPP_TEMPLATE_VIS ratio_divide 341 : public __ratio_divide<_R1, _R2>::type {}; 342 343 #endif // _LIBCPP_CXX03_LANG 344 345 template <class _R1, class _R2> 346 struct __ratio_add 347 { 348 private: 349 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 350 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 351 public: 352 typedef typename ratio_multiply 353 < 354 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 355 ratio 356 < 357 __ll_add 358 < 359 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 360 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 361 >::value, 362 _R2::den 363 > 364 >::type type; 365 }; 366 367 #ifndef _LIBCPP_CXX03_LANG 368 369 template <class _R1, class _R2> using ratio_add 370 = typename __ratio_add<_R1, _R2>::type; 371 372 #else // _LIBCPP_CXX03_LANG 373 374 template <class _R1, class _R2> 375 struct _LIBCPP_TEMPLATE_VIS ratio_add 376 : public __ratio_add<_R1, _R2>::type {}; 377 378 #endif // _LIBCPP_CXX03_LANG 379 380 template <class _R1, class _R2> 381 struct __ratio_subtract 382 { 383 private: 384 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 385 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 386 public: 387 typedef typename ratio_multiply 388 < 389 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 390 ratio 391 < 392 __ll_sub 393 < 394 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 395 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 396 >::value, 397 _R2::den 398 > 399 >::type type; 400 }; 401 402 #ifndef _LIBCPP_CXX03_LANG 403 404 template <class _R1, class _R2> using ratio_subtract 405 = typename __ratio_subtract<_R1, _R2>::type; 406 407 #else // _LIBCPP_CXX03_LANG 408 409 template <class _R1, class _R2> 410 struct _LIBCPP_TEMPLATE_VIS ratio_subtract 411 : public __ratio_subtract<_R1, _R2>::type {}; 412 413 #endif // _LIBCPP_CXX03_LANG 414 415 // ratio_equal 416 417 template <class _R1, class _R2> 418 struct _LIBCPP_TEMPLATE_VIS ratio_equal 419 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 420 421 template <class _R1, class _R2> 422 struct _LIBCPP_TEMPLATE_VIS ratio_not_equal 423 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 424 425 // ratio_less 426 427 template <class _R1, class _R2, bool _Odd = false, 428 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 429 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 430 struct __ratio_less1 431 { 432 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 433 }; 434 435 template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 436 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 437 { 438 static const bool value = false; 439 }; 440 441 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 442 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 443 { 444 static const bool value = !_Odd; 445 }; 446 447 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 448 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 449 { 450 static const bool value = _Odd; 451 }; 452 453 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 454 intmax_t _M2> 455 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 456 { 457 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 458 ratio<_R2::den, _M2>, !_Odd>::value; 459 }; 460 461 template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 462 intmax_t _S2 = __static_sign<_R2::num>::value> 463 struct __ratio_less 464 { 465 static const bool value = _S1 < _S2; 466 }; 467 468 template <class _R1, class _R2> 469 struct __ratio_less<_R1, _R2, 1LL, 1LL> 470 { 471 static const bool value = __ratio_less1<_R1, _R2>::value; 472 }; 473 474 template <class _R1, class _R2> 475 struct __ratio_less<_R1, _R2, -1LL, -1LL> 476 { 477 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 478 }; 479 480 template <class _R1, class _R2> 481 struct _LIBCPP_TEMPLATE_VIS ratio_less 482 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 483 484 template <class _R1, class _R2> 485 struct _LIBCPP_TEMPLATE_VIS ratio_less_equal 486 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 487 488 template <class _R1, class _R2> 489 struct _LIBCPP_TEMPLATE_VIS ratio_greater 490 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 491 492 template <class _R1, class _R2> 493 struct _LIBCPP_TEMPLATE_VIS ratio_greater_equal 494 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 495 496 template <class _R1, class _R2> 497 struct __ratio_gcd 498 { 499 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 500 __static_lcm<_R1::den, _R2::den>::value> type; 501 }; 502 503 #if _LIBCPP_STD_VER > 14 && !defined(_LIBCPP_HAS_NO_VARIABLE_TEMPLATES) 504 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_equal_v 505 = ratio_equal<_R1, _R2>::value; 506 507 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_not_equal_v 508 = ratio_not_equal<_R1, _R2>::value; 509 510 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_v 511 = ratio_less<_R1, _R2>::value; 512 513 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_less_equal_v 514 = ratio_less_equal<_R1, _R2>::value; 515 516 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_v 517 = ratio_greater<_R1, _R2>::value; 518 519 template <class _R1, class _R2> _LIBCPP_CONSTEXPR bool ratio_greater_equal_v 520 = ratio_greater_equal<_R1, _R2>::value; 521 #endif 522 523 _LIBCPP_END_NAMESPACE_STD 524 525 _LIBCPP_POP_MACROS 526 527 #endif // _LIBCPP_RATIO 528
