1 // -*- C++ -*- 2 //===---------------------------- numeric ---------------------------------===// 3 // 4 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. 5 // See https://llvm.org/LICENSE.txt for license information. 6 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception 7 // 8 //===----------------------------------------------------------------------===// 9 10 #ifndef _LIBCPP_NUMERIC 11 #define _LIBCPP_NUMERIC 12 13 /* 14 numeric synopsis 15 16 namespace std 17 { 18 19 template <class InputIterator, class T> 20 constexpr T // constexpr since C++20 21 accumulate(InputIterator first, InputIterator last, T init); 22 23 template <class InputIterator, class T, class BinaryOperation> 24 constexpr T // constexpr since C++20 25 accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); 26 27 template<class InputIterator> 28 constexpr typename iterator_traits<InputIterator>::value_type // constexpr since C++20 29 reduce(InputIterator first, InputIterator last); // C++17 30 31 template<class InputIterator, class T> 32 constexpr T // constexpr since C++20 33 reduce(InputIterator first, InputIterator last, T init); // C++17 34 35 template<class InputIterator, class T, class BinaryOperation> 36 constexpr T // constexpr since C++20 37 reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17 38 39 template <class InputIterator1, class InputIterator2, class T> 40 constexpr T // constexpr since C++20 41 inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, T init); 42 43 template <class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> 44 constexpr T // constexpr since C++20 45 inner_product(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, 46 T init, BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); 47 48 49 template<class InputIterator1, class InputIterator2, class T> 50 constexpr T // constexpr since C++20 51 transform_reduce(InputIterator1 first1, InputIterator1 last1, 52 InputIterator2 first2, T init); // C++17 53 54 template<class InputIterator1, class InputIterator2, class T, class BinaryOperation1, class BinaryOperation2> 55 constexpr T // constexpr since C++20 56 transform_reduce(InputIterator1 first1, InputIterator1 last1, 57 InputIterator2 first2, T init, 58 BinaryOperation1 binary_op1, BinaryOperation2 binary_op2); // C++17 59 60 template<class InputIterator, class T, class BinaryOperation, class UnaryOperation> 61 constexpr T // constexpr since C++20 62 transform_reduce(InputIterator first, InputIterator last, T init, 63 BinaryOperation binary_op, UnaryOperation unary_op); // C++17 64 65 template <class InputIterator, class OutputIterator> 66 constexpr OutputIterator // constexpr since C++20 67 partial_sum(InputIterator first, InputIterator last, OutputIterator result); 68 69 template <class InputIterator, class OutputIterator, class BinaryOperation> 70 constexpr OutputIterator // constexpr since C++20 71 partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); 72 73 template<class InputIterator, class OutputIterator, class T> 74 constexpr OutputIterator // constexpr since C++20 75 exclusive_scan(InputIterator first, InputIterator last, 76 OutputIterator result, T init); // C++17 77 78 template<class InputIterator, class OutputIterator, class T, class BinaryOperation> 79 constexpr OutputIterator // constexpr since C++20 80 exclusive_scan(InputIterator first, InputIterator last, 81 OutputIterator result, T init, BinaryOperation binary_op); // C++17 82 83 template<class InputIterator, class OutputIterator> 84 constexpr OutputIterator // constexpr since C++20 85 inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17 86 87 template<class InputIterator, class OutputIterator, class BinaryOperation> 88 constexpr OutputIterator // constexpr since C++20 89 inclusive_scan(InputIterator first, InputIterator last, 90 OutputIterator result, BinaryOperation binary_op); // C++17 91 92 template<class InputIterator, class OutputIterator, class BinaryOperation, class T> 93 constexpr OutputIterator // constexpr since C++20 94 inclusive_scan(InputIterator first, InputIterator last, 95 OutputIterator result, BinaryOperation binary_op, T init); // C++17 96 97 template<class InputIterator, class OutputIterator, class T, 98 class BinaryOperation, class UnaryOperation> 99 constexpr OutputIterator // constexpr since C++20 100 transform_exclusive_scan(InputIterator first, InputIterator last, 101 OutputIterator result, T init, 102 BinaryOperation binary_op, UnaryOperation unary_op); // C++17 103 104 template<class InputIterator, class OutputIterator, 105 class BinaryOperation, class UnaryOperation> 106 constexpr OutputIterator // constexpr since C++20 107 transform_inclusive_scan(InputIterator first, InputIterator last, 108 OutputIterator result, 109 BinaryOperation binary_op, UnaryOperation unary_op); // C++17 110 111 template<class InputIterator, class OutputIterator, 112 class BinaryOperation, class UnaryOperation, class T> 113 constexpr OutputIterator // constexpr since C++20 114 transform_inclusive_scan(InputIterator first, InputIterator last, 115 OutputIterator result, 116 BinaryOperation binary_op, UnaryOperation unary_op, 117 T init); // C++17 118 119 template <class InputIterator, class OutputIterator> 120 constexpr OutputIterator // constexpr since C++20 121 adjacent_difference(InputIterator first, InputIterator last, OutputIterator result); 122 123 template <class InputIterator, class OutputIterator, class BinaryOperation> 124 constexpr OutputIterator // constexpr since C++20 125 adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); 126 127 template <class ForwardIterator, class T> 128 constexpr void // constexpr since C++20 129 iota(ForwardIterator first, ForwardIterator last, T value); 130 131 template <class M, class N> 132 constexpr common_type_t<M,N> gcd(M m, N n); // C++17 133 134 template <class M, class N> 135 constexpr common_type_t<M,N> lcm(M m, N n); // C++17 136 137 template<class T> 138 constexpr T midpoint(T a, T b) noexcept; // C++20 139 140 template<class T> 141 constexpr T* midpoint(T* a, T* b); // C++20 142 143 } // std 144 145 */ 146 147 #include <__config> 148 #include <__debug> 149 #include <cmath> // for isnormal 150 #include <functional> 151 #include <iterator> 152 #include <limits> // for numeric_limits 153 #include <version> 154 155 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) 156 #pragma GCC system_header 157 #endif 158 159 _LIBCPP_PUSH_MACROS 160 #include <__undef_macros> 161 162 _LIBCPP_BEGIN_NAMESPACE_STD 163 164 template <class _InputIterator, class _Tp> 165 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 166 _Tp 167 accumulate(_InputIterator __first, _InputIterator __last, _Tp __init) 168 { 169 for (; __first != __last; ++__first) 170 #if _LIBCPP_STD_VER > 17 171 __init = _VSTD::move(__init) + *__first; 172 #else 173 __init = __init + *__first; 174 #endif 175 return __init; 176 } 177 178 template <class _InputIterator, class _Tp, class _BinaryOperation> 179 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 180 _Tp 181 accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op) 182 { 183 for (; __first != __last; ++__first) 184 #if _LIBCPP_STD_VER > 17 185 __init = __binary_op(_VSTD::move(__init), *__first); 186 #else 187 __init = __binary_op(__init, *__first); 188 #endif 189 return __init; 190 } 191 192 #if _LIBCPP_STD_VER > 14 193 template <class _InputIterator, class _Tp, class _BinaryOp> 194 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 195 _Tp 196 reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b) 197 { 198 for (; __first != __last; ++__first) 199 __init = __b(__init, *__first); 200 return __init; 201 } 202 203 template <class _InputIterator, class _Tp> 204 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 205 _Tp 206 reduce(_InputIterator __first, _InputIterator __last, _Tp __init) 207 { 208 return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>()); 209 } 210 211 template <class _InputIterator> 212 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 213 typename iterator_traits<_InputIterator>::value_type 214 reduce(_InputIterator __first, _InputIterator __last) 215 { 216 return _VSTD::reduce(__first, __last, 217 typename iterator_traits<_InputIterator>::value_type{}); 218 } 219 #endif 220 221 template <class _InputIterator1, class _InputIterator2, class _Tp> 222 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 223 _Tp 224 inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init) 225 { 226 for (; __first1 != __last1; ++__first1, (void) ++__first2) 227 #if _LIBCPP_STD_VER > 17 228 __init = _VSTD::move(__init) + *__first1 * *__first2; 229 #else 230 __init = __init + *__first1 * *__first2; 231 #endif 232 return __init; 233 } 234 235 template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2> 236 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 237 _Tp 238 inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, 239 _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2) 240 { 241 for (; __first1 != __last1; ++__first1, (void) ++__first2) 242 #if _LIBCPP_STD_VER > 17 243 __init = __binary_op1(_VSTD::move(__init), __binary_op2(*__first1, *__first2)); 244 #else 245 __init = __binary_op1(__init, __binary_op2(*__first1, *__first2)); 246 #endif 247 return __init; 248 } 249 250 #if _LIBCPP_STD_VER > 14 251 template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp> 252 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 253 _Tp 254 transform_reduce(_InputIterator __first, _InputIterator __last, 255 _Tp __init, _BinaryOp __b, _UnaryOp __u) 256 { 257 for (; __first != __last; ++__first) 258 __init = __b(__init, __u(*__first)); 259 return __init; 260 } 261 262 template <class _InputIterator1, class _InputIterator2, 263 class _Tp, class _BinaryOp1, class _BinaryOp2> 264 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 265 _Tp 266 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 267 _InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2) 268 { 269 for (; __first1 != __last1; ++__first1, (void) ++__first2) 270 __init = __b1(__init, __b2(*__first1, *__first2)); 271 return __init; 272 } 273 274 template <class _InputIterator1, class _InputIterator2, class _Tp> 275 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 276 _Tp 277 transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, 278 _InputIterator2 __first2, _Tp __init) 279 { 280 return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init), 281 _VSTD::plus<>(), _VSTD::multiplies<>()); 282 } 283 #endif 284 285 template <class _InputIterator, class _OutputIterator> 286 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 287 _OutputIterator 288 partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result) 289 { 290 if (__first != __last) 291 { 292 typename iterator_traits<_InputIterator>::value_type __t(*__first); 293 *__result = __t; 294 for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) 295 { 296 #if _LIBCPP_STD_VER > 17 297 __t = _VSTD::move(__t) + *__first; 298 #else 299 __t = __t + *__first; 300 #endif 301 *__result = __t; 302 } 303 } 304 return __result; 305 } 306 307 template <class _InputIterator, class _OutputIterator, class _BinaryOperation> 308 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 309 _OutputIterator 310 partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result, 311 _BinaryOperation __binary_op) 312 { 313 if (__first != __last) 314 { 315 typename iterator_traits<_InputIterator>::value_type __t(*__first); 316 *__result = __t; 317 for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) 318 { 319 #if _LIBCPP_STD_VER > 17 320 __t = __binary_op(_VSTD::move(__t), *__first); 321 #else 322 __t = __binary_op(__t, *__first); 323 #endif 324 *__result = __t; 325 } 326 } 327 return __result; 328 } 329 330 #if _LIBCPP_STD_VER > 14 331 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp> 332 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 333 _OutputIterator 334 exclusive_scan(_InputIterator __first, _InputIterator __last, 335 _OutputIterator __result, _Tp __init, _BinaryOp __b) 336 { 337 if (__first != __last) 338 { 339 _Tp __tmp(__b(__init, *__first)); 340 while (true) 341 { 342 *__result = _VSTD::move(__init); 343 ++__result; 344 ++__first; 345 if (__first == __last) 346 break; 347 __init = _VSTD::move(__tmp); 348 __tmp = __b(__init, *__first); 349 } 350 } 351 return __result; 352 } 353 354 template <class _InputIterator, class _OutputIterator, class _Tp> 355 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 356 _OutputIterator 357 exclusive_scan(_InputIterator __first, _InputIterator __last, 358 _OutputIterator __result, _Tp __init) 359 { 360 return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>()); 361 } 362 363 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp> 364 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 365 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 366 _OutputIterator __result, _BinaryOp __b, _Tp __init) 367 { 368 for (; __first != __last; ++__first, (void) ++__result) { 369 __init = __b(__init, *__first); 370 *__result = __init; 371 } 372 return __result; 373 } 374 375 template <class _InputIterator, class _OutputIterator, class _BinaryOp> 376 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 377 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 378 _OutputIterator __result, _BinaryOp __b) 379 { 380 if (__first != __last) { 381 typename iterator_traits<_InputIterator>::value_type __init = *__first; 382 *__result++ = __init; 383 if (++__first != __last) 384 return _VSTD::inclusive_scan(__first, __last, __result, __b, __init); 385 } 386 387 return __result; 388 } 389 390 template <class _InputIterator, class _OutputIterator> 391 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 392 _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, 393 _OutputIterator __result) 394 { 395 return _VSTD::inclusive_scan(__first, __last, __result, _VSTD::plus<>()); 396 } 397 398 template <class _InputIterator, class _OutputIterator, class _Tp, 399 class _BinaryOp, class _UnaryOp> 400 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 401 _OutputIterator 402 transform_exclusive_scan(_InputIterator __first, _InputIterator __last, 403 _OutputIterator __result, _Tp __init, 404 _BinaryOp __b, _UnaryOp __u) 405 { 406 if (__first != __last) 407 { 408 _Tp __saved = __init; 409 do 410 { 411 __init = __b(__init, __u(*__first)); 412 *__result = __saved; 413 __saved = __init; 414 ++__result; 415 } while (++__first != __last); 416 } 417 return __result; 418 } 419 420 template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp> 421 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 422 _OutputIterator 423 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 424 _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init) 425 { 426 for (; __first != __last; ++__first, (void) ++__result) { 427 __init = __b(__init, __u(*__first)); 428 *__result = __init; 429 } 430 431 return __result; 432 } 433 434 template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp> 435 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 436 _OutputIterator 437 transform_inclusive_scan(_InputIterator __first, _InputIterator __last, 438 _OutputIterator __result, _BinaryOp __b, _UnaryOp __u) 439 { 440 if (__first != __last) { 441 typename iterator_traits<_InputIterator>::value_type __init = __u(*__first); 442 *__result++ = __init; 443 if (++__first != __last) 444 return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init); 445 } 446 447 return __result; 448 } 449 #endif 450 451 template <class _InputIterator, class _OutputIterator> 452 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 453 _OutputIterator 454 adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result) 455 { 456 if (__first != __last) 457 { 458 typename iterator_traits<_InputIterator>::value_type __acc(*__first); 459 *__result = __acc; 460 for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) 461 { 462 typename iterator_traits<_InputIterator>::value_type __val(*__first); 463 #if _LIBCPP_STD_VER > 17 464 *__result = __val - _VSTD::move(__acc); 465 #else 466 *__result = __val - __acc; 467 #endif 468 __acc = _VSTD::move(__val); 469 } 470 } 471 return __result; 472 } 473 474 template <class _InputIterator, class _OutputIterator, class _BinaryOperation> 475 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 476 _OutputIterator 477 adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result, 478 _BinaryOperation __binary_op) 479 { 480 if (__first != __last) 481 { 482 typename iterator_traits<_InputIterator>::value_type __acc(*__first); 483 *__result = __acc; 484 for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) 485 { 486 typename iterator_traits<_InputIterator>::value_type __val(*__first); 487 #if _LIBCPP_STD_VER > 17 488 *__result = __binary_op(__val, _VSTD::move(__acc)); 489 #else 490 *__result = __binary_op(__val, __acc); 491 #endif 492 __acc = _VSTD::move(__val); 493 } 494 } 495 return __result; 496 } 497 498 template <class _ForwardIterator, class _Tp> 499 _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_AFTER_CXX17 500 void 501 iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_) 502 { 503 for (; __first != __last; ++__first, (void) ++__value_) 504 *__first = __value_; 505 } 506 507 508 #if _LIBCPP_STD_VER > 14 509 template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs; 510 511 template <typename _Result, typename _Source> 512 struct __ct_abs<_Result, _Source, true> { 513 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY 514 _Result operator()(_Source __t) const noexcept 515 { 516 if (__t >= 0) return __t; 517 if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t); 518 return -__t; 519 } 520 }; 521 522 template <typename _Result, typename _Source> 523 struct __ct_abs<_Result, _Source, false> { 524 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY 525 _Result operator()(_Source __t) const noexcept { return __t; } 526 }; 527 528 529 template<class _Tp> 530 _LIBCPP_CONSTEXPR _LIBCPP_HIDDEN 531 _Tp __gcd(_Tp __m, _Tp __n) 532 { 533 static_assert((!is_signed<_Tp>::value), ""); 534 return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n); 535 } 536 537 538 template<class _Tp, class _Up> 539 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY 540 common_type_t<_Tp,_Up> 541 gcd(_Tp __m, _Up __n) 542 { 543 static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types"); 544 static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" ); 545 static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" ); 546 using _Rp = common_type_t<_Tp,_Up>; 547 using _Wp = make_unsigned_t<_Rp>; 548 return static_cast<_Rp>(_VSTD::__gcd( 549 static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), 550 static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n)))); 551 } 552 553 template<class _Tp, class _Up> 554 _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY 555 common_type_t<_Tp,_Up> 556 lcm(_Tp __m, _Up __n) 557 { 558 static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types"); 559 static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" ); 560 static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" ); 561 if (__m == 0 || __n == 0) 562 return 0; 563 564 using _Rp = common_type_t<_Tp,_Up>; 565 _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n); 566 _Rp __val2 = __ct_abs<_Rp, _Up>()(__n); 567 _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm"); 568 return __val1 * __val2; 569 } 570 571 #endif /* _LIBCPP_STD_VER > 14 */ 572 573 #if _LIBCPP_STD_VER > 17 574 template <class _Tp> 575 _LIBCPP_INLINE_VISIBILITY constexpr 576 enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp> 577 midpoint(_Tp __a, _Tp __b) noexcept 578 _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK 579 { 580 using _Up = make_unsigned_t<_Tp>; 581 constexpr _Up __bitshift = numeric_limits<_Up>::digits - 1; 582 583 _Up __diff = _Up(__b) - _Up(__a); 584 _Up __sign_bit = __b < __a; 585 586 _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff); 587 588 return __a + __half_diff; 589 } 590 591 592 template <class _TPtr> 593 _LIBCPP_INLINE_VISIBILITY constexpr 594 enable_if_t<is_pointer_v<_TPtr> 595 && is_object_v<remove_pointer_t<_TPtr>> 596 && ! is_void_v<remove_pointer_t<_TPtr>> 597 && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr> 598 midpoint(_TPtr __a, _TPtr __b) noexcept 599 { 600 return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a); 601 } 602 603 604 template <typename _Tp> 605 constexpr int __sign(_Tp __val) { 606 return (_Tp(0) < __val) - (__val < _Tp(0)); 607 } 608 609 template <typename _Fp> 610 constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; } 611 612 template <class _Fp> 613 _LIBCPP_INLINE_VISIBILITY constexpr 614 enable_if_t<is_floating_point_v<_Fp>, _Fp> 615 midpoint(_Fp __a, _Fp __b) noexcept 616 { 617 constexpr _Fp __lo = numeric_limits<_Fp>::min()*2; 618 constexpr _Fp __hi = numeric_limits<_Fp>::max()/2; 619 return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ? // typical case: overflow is impossible 620 (__a + __b)/2 : // always correctly rounded 621 __fp_abs(__a) < __lo ? __a + __b/2 : // not safe to halve a 622 __fp_abs(__b) < __lo ? __a/2 + __b : // not safe to halve b 623 __a/2 + __b/2; // otherwise correctly rounded 624 } 625 626 #endif // _LIBCPP_STD_VER > 17 627 628 _LIBCPP_END_NAMESPACE_STD 629 630 _LIBCPP_POP_MACROS 631 632 #if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17 633 # include <__pstl_numeric> 634 #endif 635 636 #endif // _LIBCPP_NUMERIC 637
Indexes created Wed May 06 00:24:28 UTC 2026