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 const intmax_t num; 25 static const 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 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 const intmax_t __na = __static_abs<_Num>::value; 240 static const intmax_t __da = __static_abs<_Den>::value; 241 static const intmax_t __s = __static_sign<_Num>::value * __static_sign<_Den>::value; 242 static const intmax_t __gcd = __static_gcd<__na, __da>::value; 243 public: 244 static const intmax_t num = __s * __na / __gcd; 245 static const intmax_t den = __da / __gcd; 246 247 typedef ratio<num, den> type; 248 }; 249 250 template <intmax_t _Num, intmax_t _Den> const intmax_t ratio<_Num, _Den>::num; 251 template <intmax_t _Num, intmax_t _Den> const intmax_t ratio<_Num, _Den>::den; 252 253 template <class _Tp> struct __is_ratio : false_type {}; 254 template <intmax_t _Num, intmax_t _Den> struct __is_ratio<ratio<_Num, _Den> > : true_type {}; 255 256 typedef ratio<1LL, 1000000000000000000LL> atto; 257 typedef ratio<1LL, 1000000000000000LL> femto; 258 typedef ratio<1LL, 1000000000000LL> pico; 259 typedef ratio<1LL, 1000000000LL> nano; 260 typedef ratio<1LL, 1000000LL> micro; 261 typedef ratio<1LL, 1000LL> milli; 262 typedef ratio<1LL, 100LL> centi; 263 typedef ratio<1LL, 10LL> deci; 264 typedef ratio< 10LL, 1LL> deca; 265 typedef ratio< 100LL, 1LL> hecto; 266 typedef ratio< 1000LL, 1LL> kilo; 267 typedef ratio< 1000000LL, 1LL> mega; 268 typedef ratio< 1000000000LL, 1LL> giga; 269 typedef ratio< 1000000000000LL, 1LL> tera; 270 typedef ratio< 1000000000000000LL, 1LL> peta; 271 typedef ratio<1000000000000000000LL, 1LL> exa; 272 273 template <class _R1, class _R2> 274 struct __ratio_multiply 275 { 276 private: 277 static const intmax_t __gcd_n1_d2 = __static_gcd<_R1::num, _R2::den>::value; 278 static const intmax_t __gcd_d1_n2 = __static_gcd<_R1::den, _R2::num>::value; 279 public: 280 typedef typename ratio 281 < 282 __ll_mul<_R1::num / __gcd_n1_d2, _R2::num / __gcd_d1_n2>::value, 283 __ll_mul<_R2::den / __gcd_n1_d2, _R1::den / __gcd_d1_n2>::value 284 >::type type; 285 }; 286 287 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 288 289 template <class _R1, class _R2> using ratio_multiply 290 = typename __ratio_multiply<_R1, _R2>::type; 291 292 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 293 294 template <class _R1, class _R2> 295 struct _LIBCPP_TYPE_VIS ratio_multiply 296 : public __ratio_multiply<_R1, _R2>::type {}; 297 298 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 299 300 template <class _R1, class _R2> 301 struct __ratio_divide 302 { 303 private: 304 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 305 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 306 public: 307 typedef typename ratio 308 < 309 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 310 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 311 >::type type; 312 }; 313 314 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 315 316 template <class _R1, class _R2> using ratio_divide 317 = typename __ratio_divide<_R1, _R2>::type; 318 319 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 320 321 template <class _R1, class _R2> 322 struct _LIBCPP_TYPE_VIS ratio_divide 323 : public __ratio_divide<_R1, _R2>::type {}; 324 325 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 326 327 template <class _R1, class _R2> 328 struct __ratio_add 329 { 330 private: 331 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 332 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 333 public: 334 typedef typename ratio_multiply 335 < 336 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 337 ratio 338 < 339 __ll_add 340 < 341 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 342 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 343 >::value, 344 _R2::den 345 > 346 >::type type; 347 }; 348 349 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 350 351 template <class _R1, class _R2> using ratio_add 352 = typename __ratio_add<_R1, _R2>::type; 353 354 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 355 356 template <class _R1, class _R2> 357 struct _LIBCPP_TYPE_VIS ratio_add 358 : public __ratio_add<_R1, _R2>::type {}; 359 360 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 361 362 template <class _R1, class _R2> 363 struct __ratio_subtract 364 { 365 private: 366 static const intmax_t __gcd_n1_n2 = __static_gcd<_R1::num, _R2::num>::value; 367 static const intmax_t __gcd_d1_d2 = __static_gcd<_R1::den, _R2::den>::value; 368 public: 369 typedef typename ratio_multiply 370 < 371 ratio<__gcd_n1_n2, _R1::den / __gcd_d1_d2>, 372 ratio 373 < 374 __ll_sub 375 < 376 __ll_mul<_R1::num / __gcd_n1_n2, _R2::den / __gcd_d1_d2>::value, 377 __ll_mul<_R2::num / __gcd_n1_n2, _R1::den / __gcd_d1_d2>::value 378 >::value, 379 _R2::den 380 > 381 >::type type; 382 }; 383 384 #ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES 385 386 template <class _R1, class _R2> using ratio_subtract 387 = typename __ratio_subtract<_R1, _R2>::type; 388 389 #else // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 390 391 template <class _R1, class _R2> 392 struct _LIBCPP_TYPE_VIS ratio_subtract 393 : public __ratio_subtract<_R1, _R2>::type {}; 394 395 #endif // _LIBCPP_HAS_NO_TEMPLATE_ALIASES 396 397 // ratio_equal 398 399 template <class _R1, class _R2> 400 struct _LIBCPP_TYPE_VIS ratio_equal 401 : public integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den> {}; 402 403 template <class _R1, class _R2> 404 struct _LIBCPP_TYPE_VIS ratio_not_equal 405 : public integral_constant<bool, !ratio_equal<_R1, _R2>::value> {}; 406 407 // ratio_less 408 409 template <class _R1, class _R2, bool _Odd = false, 410 intmax_t _Q1 = _R1::num / _R1::den, intmax_t _M1 = _R1::num % _R1::den, 411 intmax_t _Q2 = _R2::num / _R2::den, intmax_t _M2 = _R2::num % _R2::den> 412 struct __ratio_less1 413 { 414 static const bool value = _Odd ? _Q2 < _Q1 : _Q1 < _Q2; 415 }; 416 417 template <class _R1, class _R2, bool _Odd, intmax_t _Qp> 418 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, 0> 419 { 420 static const bool value = false; 421 }; 422 423 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M2> 424 struct __ratio_less1<_R1, _R2, _Odd, _Qp, 0, _Qp, _M2> 425 { 426 static const bool value = !_Odd; 427 }; 428 429 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1> 430 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, 0> 431 { 432 static const bool value = _Odd; 433 }; 434 435 template <class _R1, class _R2, bool _Odd, intmax_t _Qp, intmax_t _M1, 436 intmax_t _M2> 437 struct __ratio_less1<_R1, _R2, _Odd, _Qp, _M1, _Qp, _M2> 438 { 439 static const bool value = __ratio_less1<ratio<_R1::den, _M1>, 440 ratio<_R2::den, _M2>, !_Odd>::value; 441 }; 442 443 template <class _R1, class _R2, intmax_t _S1 = __static_sign<_R1::num>::value, 444 intmax_t _S2 = __static_sign<_R2::num>::value> 445 struct __ratio_less 446 { 447 static const bool value = _S1 < _S2; 448 }; 449 450 template <class _R1, class _R2> 451 struct __ratio_less<_R1, _R2, 1LL, 1LL> 452 { 453 static const bool value = __ratio_less1<_R1, _R2>::value; 454 }; 455 456 template <class _R1, class _R2> 457 struct __ratio_less<_R1, _R2, -1LL, -1LL> 458 { 459 static const bool value = __ratio_less1<ratio<-_R2::num, _R2::den>, ratio<-_R1::num, _R1::den> >::value; 460 }; 461 462 template <class _R1, class _R2> 463 struct _LIBCPP_TYPE_VIS ratio_less 464 : public integral_constant<bool, __ratio_less<_R1, _R2>::value> {}; 465 466 template <class _R1, class _R2> 467 struct _LIBCPP_TYPE_VIS ratio_less_equal 468 : public integral_constant<bool, !ratio_less<_R2, _R1>::value> {}; 469 470 template <class _R1, class _R2> 471 struct _LIBCPP_TYPE_VIS ratio_greater 472 : public integral_constant<bool, ratio_less<_R2, _R1>::value> {}; 473 474 template <class _R1, class _R2> 475 struct _LIBCPP_TYPE_VIS ratio_greater_equal 476 : public integral_constant<bool, !ratio_less<_R1, _R2>::value> {}; 477 478 template <class _R1, class _R2> 479 struct __ratio_gcd 480 { 481 typedef ratio<__static_gcd<_R1::num, _R2::num>::value, 482 __static_lcm<_R1::den, _R2::den>::value> type; 483 }; 484 485 _LIBCPP_END_NAMESPACE_STD 486 487 #endif // _LIBCPP_RATIO 488
