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 | T |
21 | accumulate(InputIterator first, InputIterator last, T init); |
22 | |
23 | template <class InputIterator, class T, class BinaryOperation> |
24 | T |
25 | accumulate(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); |
26 | |
27 | template<class InputIterator> |
28 | typename iterator_traits<InputIterator>::value_type |
29 | reduce(InputIterator first, InputIterator last); // C++17 |
30 | |
31 | template<class InputIterator, class T> |
32 | T |
33 | reduce(InputIterator first, InputIterator last, T init); // C++17 |
34 | |
35 | template<class InputIterator, class T, class BinaryOperation> |
36 | T |
37 | reduce(InputIterator first, InputIterator last, T init, BinaryOperation binary_op); // C++17 |
38 | |
39 | template <class InputIterator1, class InputIterator2, class T> |
40 | T |
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 | T |
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 | T |
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 | T |
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 | T |
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 | OutputIterator |
67 | partial_sum(InputIterator first, InputIterator last, OutputIterator result); |
68 | |
69 | template <class InputIterator, class OutputIterator, class BinaryOperation> |
70 | OutputIterator |
71 | partial_sum(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); |
72 | |
73 | template<class InputIterator, class OutputIterator, class T> |
74 | OutputIterator |
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 | OutputIterator |
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 | OutputIterator |
85 | inclusive_scan(InputIterator first, InputIterator last, OutputIterator result); // C++17 |
86 | |
87 | template<class InputIterator, class OutputIterator, class BinaryOperation> |
88 | OutputIterator |
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 | OutputIterator |
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 | OutputIterator |
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 | OutputIterator |
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 | OutputIterator |
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 | OutputIterator |
121 | adjacent_difference(InputIterator first, InputIterator last, OutputIterator result); |
122 | |
123 | template <class InputIterator, class OutputIterator, class BinaryOperation> |
124 | OutputIterator |
125 | adjacent_difference(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); |
126 | |
127 | template <class ForwardIterator, class T> |
128 | void iota(ForwardIterator first, ForwardIterator last, T value); |
129 | |
130 | template <class M, class N> |
131 | constexpr common_type_t<M,N> gcd(M m, N n); // C++17 |
132 | |
133 | template <class M, class N> |
134 | constexpr common_type_t<M,N> lcm(M m, N n); // C++17 |
135 | |
136 | integer midpoint(integer a, integer b); // C++20 |
137 | pointer midpoint(pointer a, pointer b); // C++20 |
138 | floating_point midpoint(floating_point a, floating_point b); // C++20 |
139 | |
140 | } // std |
141 | |
142 | */ |
143 | |
144 | #include <__config> |
145 | #include <iterator> |
146 | #include <limits> // for numeric_limits |
147 | #include <functional> |
148 | #include <cmath> // for isnormal |
149 | #include <version> |
150 | |
151 | #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER) |
152 | #pragma GCC system_header |
153 | #endif |
154 | |
155 | _LIBCPP_PUSH_MACROS |
156 | #include <__undef_macros> |
157 | |
158 | _LIBCPP_BEGIN_NAMESPACE_STD |
159 | |
160 | template <class _InputIterator, class _Tp> |
161 | inline _LIBCPP_INLINE_VISIBILITY |
162 | _Tp |
163 | accumulate(_InputIterator __first, _InputIterator __last, _Tp __init) |
164 | { |
165 | for (; __first != __last; ++__first) |
166 | __init = __init + *__first; |
167 | return __init; |
168 | } |
169 | |
170 | template <class _InputIterator, class _Tp, class _BinaryOperation> |
171 | inline _LIBCPP_INLINE_VISIBILITY |
172 | _Tp |
173 | accumulate(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOperation __binary_op) |
174 | { |
175 | for (; __first != __last; ++__first) |
176 | __init = __binary_op(__init, *__first); |
177 | return __init; |
178 | } |
179 | |
180 | #if _LIBCPP_STD_VER > 14 |
181 | template <class _InputIterator, class _Tp, class _BinaryOp> |
182 | inline _LIBCPP_INLINE_VISIBILITY |
183 | _Tp |
184 | reduce(_InputIterator __first, _InputIterator __last, _Tp __init, _BinaryOp __b) |
185 | { |
186 | for (; __first != __last; ++__first) |
187 | __init = __b(__init, *__first); |
188 | return __init; |
189 | } |
190 | |
191 | template <class _InputIterator, class _Tp> |
192 | inline _LIBCPP_INLINE_VISIBILITY |
193 | _Tp |
194 | reduce(_InputIterator __first, _InputIterator __last, _Tp __init) |
195 | { |
196 | return _VSTD::reduce(__first, __last, __init, _VSTD::plus<>()); |
197 | } |
198 | |
199 | template <class _InputIterator> |
200 | inline _LIBCPP_INLINE_VISIBILITY |
201 | typename iterator_traits<_InputIterator>::value_type |
202 | reduce(_InputIterator __first, _InputIterator __last) |
203 | { |
204 | return _VSTD::reduce(__first, __last, |
205 | typename iterator_traits<_InputIterator>::value_type{}); |
206 | } |
207 | #endif |
208 | |
209 | template <class _InputIterator1, class _InputIterator2, class _Tp> |
210 | inline _LIBCPP_INLINE_VISIBILITY |
211 | _Tp |
212 | inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, _Tp __init) |
213 | { |
214 | for (; __first1 != __last1; ++__first1, (void) ++__first2) |
215 | __init = __init + *__first1 * *__first2; |
216 | return __init; |
217 | } |
218 | |
219 | template <class _InputIterator1, class _InputIterator2, class _Tp, class _BinaryOperation1, class _BinaryOperation2> |
220 | inline _LIBCPP_INLINE_VISIBILITY |
221 | _Tp |
222 | inner_product(_InputIterator1 __first1, _InputIterator1 __last1, _InputIterator2 __first2, |
223 | _Tp __init, _BinaryOperation1 __binary_op1, _BinaryOperation2 __binary_op2) |
224 | { |
225 | for (; __first1 != __last1; ++__first1, (void) ++__first2) |
226 | __init = __binary_op1(__init, __binary_op2(*__first1, *__first2)); |
227 | return __init; |
228 | } |
229 | |
230 | #if _LIBCPP_STD_VER > 14 |
231 | template <class _InputIterator, class _Tp, class _BinaryOp, class _UnaryOp> |
232 | inline _LIBCPP_INLINE_VISIBILITY |
233 | _Tp |
234 | transform_reduce(_InputIterator __first, _InputIterator __last, |
235 | _Tp __init, _BinaryOp __b, _UnaryOp __u) |
236 | { |
237 | for (; __first != __last; ++__first) |
238 | __init = __b(__init, __u(*__first)); |
239 | return __init; |
240 | } |
241 | |
242 | template <class _InputIterator1, class _InputIterator2, |
243 | class _Tp, class _BinaryOp1, class _BinaryOp2> |
244 | inline _LIBCPP_INLINE_VISIBILITY |
245 | _Tp |
246 | transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, |
247 | _InputIterator2 __first2, _Tp __init, _BinaryOp1 __b1, _BinaryOp2 __b2) |
248 | { |
249 | for (; __first1 != __last1; ++__first1, (void) ++__first2) |
250 | __init = __b1(__init, __b2(*__first1, *__first2)); |
251 | return __init; |
252 | } |
253 | |
254 | template <class _InputIterator1, class _InputIterator2, class _Tp> |
255 | inline _LIBCPP_INLINE_VISIBILITY |
256 | _Tp |
257 | transform_reduce(_InputIterator1 __first1, _InputIterator1 __last1, |
258 | _InputIterator2 __first2, _Tp __init) |
259 | { |
260 | return _VSTD::transform_reduce(__first1, __last1, __first2, _VSTD::move(__init), |
261 | _VSTD::plus<>(), _VSTD::multiplies<>()); |
262 | } |
263 | #endif |
264 | |
265 | template <class _InputIterator, class _OutputIterator> |
266 | inline _LIBCPP_INLINE_VISIBILITY |
267 | _OutputIterator |
268 | partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result) |
269 | { |
270 | if (__first != __last) |
271 | { |
272 | typename iterator_traits<_InputIterator>::value_type __t(*__first); |
273 | *__result = __t; |
274 | for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) |
275 | { |
276 | __t = __t + *__first; |
277 | *__result = __t; |
278 | } |
279 | } |
280 | return __result; |
281 | } |
282 | |
283 | template <class _InputIterator, class _OutputIterator, class _BinaryOperation> |
284 | inline _LIBCPP_INLINE_VISIBILITY |
285 | _OutputIterator |
286 | partial_sum(_InputIterator __first, _InputIterator __last, _OutputIterator __result, |
287 | _BinaryOperation __binary_op) |
288 | { |
289 | if (__first != __last) |
290 | { |
291 | typename iterator_traits<_InputIterator>::value_type __t(*__first); |
292 | *__result = __t; |
293 | for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) |
294 | { |
295 | __t = __binary_op(__t, *__first); |
296 | *__result = __t; |
297 | } |
298 | } |
299 | return __result; |
300 | } |
301 | |
302 | #if _LIBCPP_STD_VER > 14 |
303 | template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp> |
304 | inline _LIBCPP_INLINE_VISIBILITY |
305 | _OutputIterator |
306 | exclusive_scan(_InputIterator __first, _InputIterator __last, |
307 | _OutputIterator __result, _Tp __init, _BinaryOp __b) |
308 | { |
309 | if (__first != __last) |
310 | { |
311 | _Tp __saved = __init; |
312 | do |
313 | { |
314 | __init = __b(__init, *__first); |
315 | *__result = __saved; |
316 | __saved = __init; |
317 | ++__result; |
318 | } while (++__first != __last); |
319 | } |
320 | return __result; |
321 | } |
322 | |
323 | template <class _InputIterator, class _OutputIterator, class _Tp> |
324 | inline _LIBCPP_INLINE_VISIBILITY |
325 | _OutputIterator |
326 | exclusive_scan(_InputIterator __first, _InputIterator __last, |
327 | _OutputIterator __result, _Tp __init) |
328 | { |
329 | return _VSTD::exclusive_scan(__first, __last, __result, __init, _VSTD::plus<>()); |
330 | } |
331 | |
332 | template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp> |
333 | _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, |
334 | _OutputIterator __result, _BinaryOp __b, _Tp __init) |
335 | { |
336 | for (; __first != __last; ++__first, (void) ++__result) { |
337 | __init = __b(__init, *__first); |
338 | *__result = __init; |
339 | } |
340 | return __result; |
341 | } |
342 | |
343 | template <class _InputIterator, class _OutputIterator, class _BinaryOp> |
344 | _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, |
345 | _OutputIterator __result, _BinaryOp __b) |
346 | { |
347 | if (__first != __last) { |
348 | typename std::iterator_traits<_InputIterator>::value_type __init = *__first; |
349 | *__result++ = __init; |
350 | if (++__first != __last) |
351 | return _VSTD::inclusive_scan(__first, __last, __result, __b, __init); |
352 | } |
353 | |
354 | return __result; |
355 | } |
356 | |
357 | template <class _InputIterator, class _OutputIterator> |
358 | _OutputIterator inclusive_scan(_InputIterator __first, _InputIterator __last, |
359 | _OutputIterator __result) |
360 | { |
361 | return _VSTD::inclusive_scan(__first, __last, __result, std::plus<>()); |
362 | } |
363 | |
364 | template <class _InputIterator, class _OutputIterator, class _Tp, |
365 | class _BinaryOp, class _UnaryOp> |
366 | inline _LIBCPP_INLINE_VISIBILITY |
367 | _OutputIterator |
368 | transform_exclusive_scan(_InputIterator __first, _InputIterator __last, |
369 | _OutputIterator __result, _Tp __init, |
370 | _BinaryOp __b, _UnaryOp __u) |
371 | { |
372 | if (__first != __last) |
373 | { |
374 | _Tp __saved = __init; |
375 | do |
376 | { |
377 | __init = __b(__init, __u(*__first)); |
378 | *__result = __saved; |
379 | __saved = __init; |
380 | ++__result; |
381 | } while (++__first != __last); |
382 | } |
383 | return __result; |
384 | } |
385 | |
386 | template <class _InputIterator, class _OutputIterator, class _Tp, class _BinaryOp, class _UnaryOp> |
387 | _OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last, |
388 | _OutputIterator __result, _BinaryOp __b, _UnaryOp __u, _Tp __init) |
389 | { |
390 | for (; __first != __last; ++__first, (void) ++__result) { |
391 | __init = __b(__init, __u(*__first)); |
392 | *__result = __init; |
393 | } |
394 | |
395 | return __result; |
396 | } |
397 | |
398 | template <class _InputIterator, class _OutputIterator, class _BinaryOp, class _UnaryOp> |
399 | _OutputIterator transform_inclusive_scan(_InputIterator __first, _InputIterator __last, |
400 | _OutputIterator __result, _BinaryOp __b, _UnaryOp __u) |
401 | { |
402 | if (__first != __last) { |
403 | typename std::iterator_traits<_InputIterator>::value_type __init = __u(*__first); |
404 | *__result++ = __init; |
405 | if (++__first != __last) |
406 | return _VSTD::transform_inclusive_scan(__first, __last, __result, __b, __u, __init); |
407 | } |
408 | |
409 | return __result; |
410 | } |
411 | #endif |
412 | |
413 | template <class _InputIterator, class _OutputIterator> |
414 | inline _LIBCPP_INLINE_VISIBILITY |
415 | _OutputIterator |
416 | adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result) |
417 | { |
418 | if (__first != __last) |
419 | { |
420 | typename iterator_traits<_InputIterator>::value_type __t1(*__first); |
421 | *__result = __t1; |
422 | for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) |
423 | { |
424 | typename iterator_traits<_InputIterator>::value_type __t2(*__first); |
425 | *__result = __t2 - __t1; |
426 | __t1 = _VSTD::move(__t2); |
427 | } |
428 | } |
429 | return __result; |
430 | } |
431 | |
432 | template <class _InputIterator, class _OutputIterator, class _BinaryOperation> |
433 | inline _LIBCPP_INLINE_VISIBILITY |
434 | _OutputIterator |
435 | adjacent_difference(_InputIterator __first, _InputIterator __last, _OutputIterator __result, |
436 | _BinaryOperation __binary_op) |
437 | { |
438 | if (__first != __last) |
439 | { |
440 | typename iterator_traits<_InputIterator>::value_type __t1(*__first); |
441 | *__result = __t1; |
442 | for (++__first, (void) ++__result; __first != __last; ++__first, (void) ++__result) |
443 | { |
444 | typename iterator_traits<_InputIterator>::value_type __t2(*__first); |
445 | *__result = __binary_op(__t2, __t1); |
446 | __t1 = _VSTD::move(__t2); |
447 | } |
448 | } |
449 | return __result; |
450 | } |
451 | |
452 | template <class _ForwardIterator, class _Tp> |
453 | inline _LIBCPP_INLINE_VISIBILITY |
454 | void |
455 | iota(_ForwardIterator __first, _ForwardIterator __last, _Tp __value_) |
456 | { |
457 | for (; __first != __last; ++__first, (void) ++__value_) |
458 | *__first = __value_; |
459 | } |
460 | |
461 | |
462 | #if _LIBCPP_STD_VER > 14 |
463 | template <typename _Result, typename _Source, bool _IsSigned = is_signed<_Source>::value> struct __ct_abs; |
464 | |
465 | template <typename _Result, typename _Source> |
466 | struct __ct_abs<_Result, _Source, true> { |
467 | _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
468 | _Result operator()(_Source __t) const noexcept |
469 | { |
470 | if (__t >= 0) return __t; |
471 | if (__t == numeric_limits<_Source>::min()) return -static_cast<_Result>(__t); |
472 | return -__t; |
473 | } |
474 | }; |
475 | |
476 | template <typename _Result, typename _Source> |
477 | struct __ct_abs<_Result, _Source, false> { |
478 | _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
479 | _Result operator()(_Source __t) const noexcept { return __t; } |
480 | }; |
481 | |
482 | |
483 | template<class _Tp> |
484 | _LIBCPP_CONSTEXPR _LIBCPP_HIDDEN |
485 | _Tp __gcd(_Tp __m, _Tp __n) |
486 | { |
487 | static_assert((!is_signed<_Tp>::value), "" ); |
488 | return __n == 0 ? __m : _VSTD::__gcd<_Tp>(__n, __m % __n); |
489 | } |
490 | |
491 | |
492 | template<class _Tp, class _Up> |
493 | _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
494 | common_type_t<_Tp,_Up> |
495 | gcd(_Tp __m, _Up __n) |
496 | { |
497 | static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to gcd must be integer types" ); |
498 | static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to gcd cannot be bool" ); |
499 | static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to gcd cannot be bool" ); |
500 | using _Rp = common_type_t<_Tp,_Up>; |
501 | using _Wp = make_unsigned_t<_Rp>; |
502 | return static_cast<_Rp>(_VSTD::__gcd( |
503 | static_cast<_Wp>(__ct_abs<_Rp, _Tp>()(__m)), |
504 | static_cast<_Wp>(__ct_abs<_Rp, _Up>()(__n)))); |
505 | } |
506 | |
507 | template<class _Tp, class _Up> |
508 | _LIBCPP_CONSTEXPR _LIBCPP_INLINE_VISIBILITY |
509 | common_type_t<_Tp,_Up> |
510 | lcm(_Tp __m, _Up __n) |
511 | { |
512 | static_assert((is_integral<_Tp>::value && is_integral<_Up>::value), "Arguments to lcm must be integer types" ); |
513 | static_assert((!is_same<typename remove_cv<_Tp>::type, bool>::value), "First argument to lcm cannot be bool" ); |
514 | static_assert((!is_same<typename remove_cv<_Up>::type, bool>::value), "Second argument to lcm cannot be bool" ); |
515 | if (__m == 0 || __n == 0) |
516 | return 0; |
517 | |
518 | using _Rp = common_type_t<_Tp,_Up>; |
519 | _Rp __val1 = __ct_abs<_Rp, _Tp>()(__m) / _VSTD::gcd(__m, __n); |
520 | _Rp __val2 = __ct_abs<_Rp, _Up>()(__n); |
521 | _LIBCPP_ASSERT((numeric_limits<_Rp>::max() / __val1 > __val2), "Overflow in lcm" ); |
522 | return __val1 * __val2; |
523 | } |
524 | |
525 | #endif /* _LIBCPP_STD_VER > 14 */ |
526 | |
527 | #if _LIBCPP_STD_VER > 17 |
528 | template <class _Tp> |
529 | _LIBCPP_INLINE_VISIBILITY constexpr |
530 | enable_if_t<is_integral_v<_Tp> && !is_same_v<bool, _Tp> && !is_null_pointer_v<_Tp>, _Tp> |
531 | midpoint(_Tp __a, _Tp __b) noexcept |
532 | _LIBCPP_DISABLE_UBSAN_UNSIGNED_INTEGER_CHECK |
533 | { |
534 | using _Up = std::make_unsigned_t<_Tp>; |
535 | constexpr _Up __bitshift = std::numeric_limits<_Up>::digits - 1; |
536 | |
537 | _Up __diff = _Up(__b) - _Up(__a); |
538 | _Up __sign_bit = __b < __a; |
539 | |
540 | _Up __half_diff = (__diff / 2) + (__sign_bit << __bitshift) + (__sign_bit & __diff); |
541 | |
542 | return __a + __half_diff; |
543 | } |
544 | |
545 | |
546 | template <class _TPtr> |
547 | _LIBCPP_INLINE_VISIBILITY constexpr |
548 | enable_if_t<is_pointer_v<_TPtr> |
549 | && is_object_v<remove_pointer_t<_TPtr>> |
550 | && ! is_void_v<remove_pointer_t<_TPtr>> |
551 | && (sizeof(remove_pointer_t<_TPtr>) > 0), _TPtr> |
552 | midpoint(_TPtr __a, _TPtr __b) noexcept |
553 | { |
554 | return __a + _VSTD::midpoint(ptrdiff_t(0), __b - __a); |
555 | } |
556 | |
557 | |
558 | template <typename _Tp> |
559 | constexpr int __sign(_Tp __val) { |
560 | return (_Tp(0) < __val) - (__val < _Tp(0)); |
561 | } |
562 | |
563 | template <typename _Fp> |
564 | constexpr _Fp __fp_abs(_Fp __f) { return __f >= 0 ? __f : -__f; } |
565 | |
566 | template <class _Fp> |
567 | _LIBCPP_INLINE_VISIBILITY constexpr |
568 | enable_if_t<is_floating_point_v<_Fp>, _Fp> |
569 | midpoint(_Fp __a, _Fp __b) noexcept |
570 | { |
571 | constexpr _Fp __lo = numeric_limits<_Fp>::min()*2; |
572 | constexpr _Fp __hi = numeric_limits<_Fp>::max()/2; |
573 | return __fp_abs(__a) <= __hi && __fp_abs(__b) <= __hi ? // typical case: overflow is impossible |
574 | (__a + __b)/2 : // always correctly rounded |
575 | __fp_abs(__a) < __lo ? __a + __b/2 : // not safe to halve a |
576 | __fp_abs(__a) < __lo ? __a/2 + __b : // not safe to halve b |
577 | __a/2 + __b/2; // otherwise correctly rounded |
578 | } |
579 | |
580 | #endif // _LIBCPP_STD_VER > 17 |
581 | |
582 | _LIBCPP_END_NAMESPACE_STD |
583 | |
584 | _LIBCPP_POP_MACROS |
585 | |
586 | #if defined(_LIBCPP_HAS_PARALLEL_ALGORITHMS) && _LIBCPP_STD_VER >= 17 |
587 | # include <__pstl_numeric> |
588 | #endif |
589 | |
590 | #endif // _LIBCPP_NUMERIC |
591 | |