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 } 66 */ 67 68 #include <__config> 69 #include <cstdint> 70 #include <climits> 71 #include <type_traits> 72 73 #include <__undef_min_max> 74 75 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 76 #pragma GCC system_header 77 #endif 78 79 _LIBCPP_BEGIN_NAMESPACE_STD 80 81 // __static_gcd 82 83 template <intmax_t _Xp, intmax_t _Yp> 84 struct __static_gcd 85 { 86 static const intmax_t value = __static_gcd<_Yp, _Xp % _Yp>::value; 87 }; 88 89 template <intmax_t _Xp> 90 struct __static_gcd<_Xp, 0> 91 { 92 static const intmax_t value = _Xp; 93 }; 94 95 template <> 96 struct __static_gcd<0, 0> 97 { 98 static const intmax_t value = 1; 99 }; 100 101 // __static_lcm 102 103 template <intmax_t _Xp, intmax_t _Yp> 104 struct __static_lcm 105 { 106 static const intmax_t value = _Xp / __static_gcd<_Xp, _Yp>::value * _Yp; 107 }; 108 109 template <intmax_t _Xp> 110 struct __static_abs 111 { 112 static const intmax_t value = _Xp < 0 ? -_Xp : _Xp; 113 }; 114 115 template <intmax_t _Xp> 116 struct __static_sign 117 { 118 static const intmax_t value = _Xp == 0 ? 0 : (_Xp < 0 ? -1 : 1); 119 }; 120 121 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 122 class __ll_add; 123 124 template <intmax_t _Xp, intmax_t _Yp> 125 class __ll_add<_Xp, _Yp, 1> 126 { 127 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 128 static const intmax_t max = -min; 129 130 static_assert(_Xp <= max - _Yp, "overflow in __ll_add"); 131 public: 132 static const intmax_t value = _Xp + _Yp; 133 }; 134 135 template <intmax_t _Xp, intmax_t _Yp> 136 class __ll_add<_Xp, _Yp, 0> 137 { 138 public: 139 static const intmax_t value = _Xp; 140 }; 141 142 template <intmax_t _Xp, intmax_t _Yp> 143 class __ll_add<_Xp, _Yp, -1> 144 { 145 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 146 static const intmax_t max = -min; 147 148 static_assert(min - _Yp <= _Xp, "overflow in __ll_add"); 149 public: 150 static const intmax_t value = _Xp + _Yp; 151 }; 152 153 template <intmax_t _Xp, intmax_t _Yp, intmax_t = __static_sign<_Yp>::value> 154 class __ll_sub; 155 156 template <intmax_t _Xp, intmax_t _Yp> 157 class __ll_sub<_Xp, _Yp, 1> 158 { 159 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 160 static const intmax_t max = -min; 161 162 static_assert(min + _Yp <= _Xp, "overflow in __ll_sub"); 163 public: 164 static const intmax_t value = _Xp - _Yp; 165 }; 166 167 template <intmax_t _Xp, intmax_t _Yp> 168 class __ll_sub<_Xp, _Yp, 0> 169 { 170 public: 171 static const intmax_t value = _Xp; 172 }; 173 174 template <intmax_t _Xp, intmax_t _Yp> 175 class __ll_sub<_Xp, _Yp, -1> 176 { 177 static const intmax_t min = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)) + 1; 178 static const intmax_t max = -min; 179 180 static_assert(_Xp <= max + _Yp, "overflow in __ll_sub"); 181 public: 182 static const intmax_t value = _Xp - _Yp; 183 }; 184 185 template <intmax_t _Xp, intmax_t _Yp> 186 class __ll_mul 187 { 188 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 189 static const intmax_t min = nan + 1; 190 static const intmax_t max = -min; 191 static const intmax_t __a_x = __static_abs<_Xp>::value; 192 static const intmax_t __a_y = __static_abs<_Yp>::value; 193 194 static_assert(_Xp != nan && _Yp != nan && __a_x <= max / __a_y, "overflow in __ll_mul"); 195 public: 196 static const intmax_t value = _Xp * _Yp; 197 }; 198 199 template <intmax_t _Yp> 200 class __ll_mul<0, _Yp> 201 { 202 public: 203 static const intmax_t value = 0; 204 }; 205 206 template <intmax_t _Xp> 207 class __ll_mul<_Xp, 0> 208 { 209 public: 210 static const intmax_t value = 0; 211 }; 212 213 template <> 214 class __ll_mul<0, 0> 215 { 216 public: 217 static const intmax_t value = 0; 218 }; 219 220 // Not actually used but left here in case needed in future maintenance 221 template <intmax_t _Xp, intmax_t _Yp> 222 class __ll_div 223 { 224 static const intmax_t nan = (1LL << (sizeof(intmax_t) * CHAR_BIT - 1)); 225 static const intmax_t min = nan + 1; 226 static const intmax_t max = -min; 227 228 static_assert(_Xp != nan && _Yp != nan && _Yp != 0, "overflow in __ll_div"); 229 public: 230 static const intmax_t value = _Xp / _Yp; 231 }; 232 233 template <intmax_t _Num, intmax_t _Den = 1> 234 class _LIBCPP_TYPE_VIS_ONLY ratio 235 { 236 static_assert(__static_abs<_Num>::value >= 0, "ratio numerator is out of range"); 237 static_assert(_Den != 0, "ratio divide by 0"); 238 static_assert(__static_abs<_Den>::value > 0, "ratio denominator is out of range"); 239 static _LIBCPP_CONSTEXPR const intmax_t __na = __static_abs<_Num>::value; 240 static _LIBCPP_CONSTEXPR const intmax_t __da = __static_abs<_Den>::value; 241 static _LIBCPP_CONSTEXPR const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 242 static _LIBCPP_CONSTEXPR const intmax_t __gcd = __static_gcd<__na, __da>::value; 243 public: 244 static _LIBCPP_CONSTEXPR const intmax_t num = __s * __na / __gcd; 245 static _LIBCPP_CONSTEXPR const intmax_t den = __da / __gcd; 246 247 typedef ratio<num, den> type; 248 }; 249 250 template <intmax_t _Num, intmax_t _Den> 251 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::num; 252 253 template <intmax_t _Num, intmax_t _Den> 254 _LIBCPP_CONSTEXPR const intmax_t ratio<_Num, _Den>::den; 255 256 template <class _Tp> struct __is_ratio : false_type {}; 257 template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 258 259 typedef ratio<1LL, 1000000000000000000LL> atto; 260 typedef ratio<1LL, 1000000000000000LL> femto; 261 typedef ratio<1LL, 1000000000000LL> pico; 262 typedef ratio<1LL, 1000000000LL> nano; 263 typedef ratio<1LL, 1000000LL> micro; 264 typedef ratio<1LL, 1000LL> milli; 265 typedef ratio<1LL, 100LL> centi; 266 typedef ratio<1LL, 10LL> deci; 267 typedef ratio< 10LL, 1LL> deca; 268 typedef ratio< 100LL, 1LL> hecto; 269 typedef ratio< 1000LL, 1LL> kilo; 270 typedef ratio< 1000000LL, 1LL> mega; 271 typedef ratio< 1000000000LL, 1LL> giga; 272 typedef ratio< 1000000000000LL, 1LL> tera; 273 typedef ratio< 1000000000000000LL, 1LL> peta; 274 typedef ratio<1000000000000000000LL, 1LL> exa; 275 276 template <class _R1, class _R2> 277 struct __ratio_multiply 278 { 279 private: 280 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 281 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 282 public: 283 typedef typename ratio 284 < 285 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 286 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 287 >::type type; 288 }; 289 290 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 291 292 template <class _R1, class _R2> using ratio_multiply 293 = typename __ratio_multiply<_R1, _R2>::type; 294 295 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 296 297 template <class _R1, class _R2> 298 struct _LIBCPP_TYPE_VIS_ONLY ratio_multiply 299 : public __ratio_multiply<_R1, _R2>::type {}; 300 301 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 302 303 template <class _R1, class _R2> 304 struct __ratio_divide 305 { 306 private: 307 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 308 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 309 public: 310 typedef typename ratio 311 < 312 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 313 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 314 >::type type; 315 }; 316 317 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 318 319 template <class _R1, class _R2> using ratio_divide 320 = typename __ratio_divide<_R1, _R2>::type; 321 322 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 323 324 template <class _R1, class _R2> 325 struct _LIBCPP_TYPE_VIS_ONLY ratio_divide 326 : public __ratio_divide<_R1, _R2>::type {}; 327 328 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 329 330 template <class _R1, class _R2> 331 struct __ratio_add 332 { 333 private: 334 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 335 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 336 public: 337 typedef typename ratio_multiply 338 < 339 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 340 ratio 341 < 342 __ll_add 343 < 344 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 345 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 346 >::value, 347 _R2::den 348 > 349 >::type type; 350 }; 351 352 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 353 354 template <class _R1, class _R2> using ratio_add 355 = typename __ratio_add<_R1, _R2>::type; 356 357 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 358 359 template <class _R1, class _R2> 360 struct _LIBCPP_TYPE_VIS_ONLY ratio_add 361 : public __ratio_add<_R1, _R2>::type {}; 362 363 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 364 365 template <class _R1, class _R2> 366 struct __ratio_subtract 367 { 368 private: 369 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 370 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 371 public: 372 typedef typename ratio_multiply 373 < 374 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 375 ratio 376 < 377 __ll_sub 378 < 379 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 380 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 381 >::value, 382 _R2::den 383 > 384 >::type type; 385 }; 386 387 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 388 389 template <class _R1, class _R2> using ratio_subtract 390 = typename __ratio_subtract<_R1, _R2>::type; 391 392 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 393 394 template <class _R1, class _R2> 395 struct _LIBCPP_TYPE_VIS_ONLY ratio_subtract 396 : public __ratio_subtract<_R1, _R2>::type {}; 397 398 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 399 400 // ratio_equal 401 402 template <class _R1, class _R2> 403 struct _LIBCPP_TYPE_VIS_ONLY ratio_equal 404 : public _LIBCPP_BOOL_CONSTANT((_R1::num == _R2::num && _R1::den == _R2::den)) {}; 405 406 template <class _R1, class _R2> 407 struct _LIBCPP_TYPE_VIS_ONLY ratio_not_equal 408 : public _LIBCPP_BOOL_CONSTANT((!ratio_equal<_R1, _R2>::value)) {}; 409 410 // ratio_less 411 412 template <class _R1, class _R2, bool _Odd = false, 413 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 414 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 415 struct __ratio_less1 416 { 417 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 418 }; 419 420 template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 421 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 422 { 423 static const bool value = false; 424 }; 425 426 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 427 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 428 { 429 static const bool value = !_Odd; 430 }; 431 432 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 433 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 434 { 435 static const bool value = _Odd; 436 }; 437 438 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 439 intmax_t _M2> 440 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 441 { 442 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 443 ratio<_R2::den, _M2>, !_Odd>::value; 444 }; 445 446 template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 447 intmax_t _S2 = __static_sign<_R2::num>::value> 448 struct __ratio_less 449 { 450 static const bool value = _S1 < _S2; 451 }; 452 453 template <class _R1, class _R2> 454 struct __ratio_less<_R1, _R2, 1LL, 1LL> 455 { 456 static const bool value = __ratio_less1<_R1, _R2>::value; 457 }; 458 459 template <class _R1, class _R2> 460 struct __ratio_less<_R1, _R2, -1LL, -1LL> 461 { 462 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 463 }; 464 465 template <class _R1, class _R2> 466 struct _LIBCPP_TYPE_VIS_ONLY ratio_less 467 : public _LIBCPP_BOOL_CONSTANT((__ratio_less<_R1, _R2>::value)) {}; 468 469 template <class _R1, class _R2> 470 struct _LIBCPP_TYPE_VIS_ONLY ratio_less_equal 471 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R2, _R1>::value)) {}; 472 473 template <class _R1, class _R2> 474 struct _LIBCPP_TYPE_VIS_ONLY ratio_greater 475 : public _LIBCPP_BOOL_CONSTANT((ratio_less<_R2, _R1>::value)) {}; 476 477 template <class _R1, class _R2> 478 struct _LIBCPP_TYPE_VIS_ONLY ratio_greater_equal 479 : public _LIBCPP_BOOL_CONSTANT((!ratio_less<_R1, _R2>::value)) {}; 480 481 template <class _R1, class _R2> 482 struct __ratio_gcd 483 { 484 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 485 __static_lcm<_R1::den, _R2::den>::value> type; 486 }; 487 488 _LIBCPP_END_NAMESPACE_STD 489 490 #endif // _LIBCPP_RATIO 491
