1// <bit> -*- C++ -*-
2
3// Copyright (C) 2018-2025 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library. This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file include/bit
26 * This is a Standard C++ Library header.
27 */
28
29#ifndef _GLIBCXX_BIT
30#define _GLIBCXX_BIT 1
31
32#ifdef _GLIBCXX_SYSHDR
33#pragma GCC system_header
34#endif
35
36#if __cplusplus >= 201402L
37
38#include <concepts> // for std::integral
39#include <type_traits>
40
41#if _GLIBCXX_HOSTED || __has_include(<ext/numeric_traits.h>)
42# include <ext/numeric_traits.h>
43#else
44# include <limits>
45/// @cond undocumented
46namespace __gnu_cxx
47{
48 template<typename _Tp>
49 struct __int_traits
50 {
51 static constexpr int __digits = std::numeric_limits<_Tp>::digits;
52 static constexpr _Tp __max = std::numeric_limits<_Tp>::max();
53 };
54}
55/// @endcond
56#endif
57
58#define __glibcxx_want_bit_cast
59#define __glibcxx_want_byteswap
60#define __glibcxx_want_bitops
61#define __glibcxx_want_int_pow2
62#define __glibcxx_want_endian
63#include <bits/version.h>
64
65namespace std _GLIBCXX_VISIBILITY(default)
66{
67_GLIBCXX_BEGIN_NAMESPACE_VERSION
68
69 /**
70 * @defgroup bit_manip Bit manipulation
71 * @ingroup numerics
72 *
73 * Utilities for examining and manipulating individual bits.
74 *
75 * @{
76 */
77
78#ifdef __cpp_lib_bit_cast // C++ >= 20
79
80 /// Create a value of type `To` from the bits of `from`.
81 /**
82 * @tparam _To A trivially-copyable type.
83 * @param __from A trivially-copyable object of the same size as `_To`.
84 * @return An object of type `_To`.
85 * @since C++20
86 */
87 template<typename _To, typename _From>
88 [[nodiscard]]
89 constexpr _To
90 bit_cast(const _From& __from) noexcept
91#ifdef __cpp_concepts
92 requires (sizeof(_To) == sizeof(_From))
93 && is_trivially_copyable_v<_To> && is_trivially_copyable_v<_From>
94#endif
95 {
96 return __builtin_bit_cast(_To, __from);
97 }
98#endif // __cpp_lib_bit_cast
99
100#ifdef __cpp_lib_byteswap // C++ >= 23
101
102 /// Reverse order of bytes in the object representation of `value`.
103 /**
104 * @tparam _Tp An integral type.
105 * @param __value An object of integer type.
106 * @return An object of the same type, with the bytes reversed.
107 * @since C++23
108 */
109 template<integral _Tp>
110 [[nodiscard]]
111 constexpr _Tp
112 byteswap(_Tp __value) noexcept
113 {
114 if constexpr (sizeof(_Tp) == 1)
115 return __value;
116#if __cpp_if_consteval >= 202106L && __CHAR_BIT__ == 8
117 if !consteval
118 {
119 if constexpr (sizeof(_Tp) == 2)
120 return __builtin_bswap16(__value);
121 if constexpr (sizeof(_Tp) == 4)
122 return __builtin_bswap32(__value);
123 if constexpr (sizeof(_Tp) == 8)
124 return __builtin_bswap64(__value);
125 if constexpr (sizeof(_Tp) == 16)
126#if __has_builtin(__builtin_bswap128)
127 return __builtin_bswap128(__value);
128#else
129 return (__builtin_bswap64(__value >> 64)
130 | (static_cast<_Tp>(__builtin_bswap64(__value)) << 64));
131#endif
132 }
133#endif
134
135 // Fallback implementation that handles even __int24 etc.
136 using _Up = typename __make_unsigned<__remove_cv_t<_Tp>>::__type;
137 size_t __diff = __CHAR_BIT__ * (sizeof(_Tp) - 1);
138 _Up __mask1 = static_cast<unsigned char>(~0);
139 _Up __mask2 = __mask1 << __diff;
140 _Up __val = __value;
141 for (size_t __i = 0; __i < sizeof(_Tp) / 2; ++__i)
142 {
143 _Up __byte1 = __val & __mask1;
144 _Up __byte2 = __val & __mask2;
145 __val = (__val ^ __byte1 ^ __byte2
146 ^ (__byte1 << __diff) ^ (__byte2 >> __diff));
147 __mask1 <<= __CHAR_BIT__;
148 __mask2 >>= __CHAR_BIT__;
149 __diff -= 2 * __CHAR_BIT__;
150 }
151 return __val;
152 }
153#endif // __cpp_lib_byteswap
154
155 /// @cond undocumented
156
157 template<typename _Tp>
158 constexpr _Tp
159 __rotl(_Tp __x, int __s) noexcept
160 {
161 constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
162 if _GLIBCXX17_CONSTEXPR ((_Nd & (_Nd - 1)) == 0)
163 {
164 // Variant for power of two _Nd which the compiler can
165 // easily pattern match.
166 constexpr unsigned __uNd = _Nd;
167 const unsigned __r = __s;
168 return (__x << (__r % __uNd)) | (__x >> ((-__r) % __uNd));
169 }
170 const int __r = __s % _Nd;
171 if (__r == 0)
172 return __x;
173 else if (__r > 0)
174 return (__x << __r) | (__x >> ((_Nd - __r) % _Nd));
175 else
176 return (__x >> -__r) | (__x << ((_Nd + __r) % _Nd)); // rotr(x, -r)
177 }
178
179 template<typename _Tp>
180 constexpr _Tp
181 __rotr(_Tp __x, int __s) noexcept
182 {
183 constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
184 if _GLIBCXX17_CONSTEXPR ((_Nd & (_Nd - 1)) == 0)
185 {
186 // Variant for power of two _Nd which the compiler can
187 // easily pattern match.
188 constexpr unsigned __uNd = _Nd;
189 const unsigned __r = __s;
190 return (__x >> (__r % __uNd)) | (__x << ((-__r) % __uNd));
191 }
192 const int __r = __s % _Nd;
193 if (__r == 0)
194 return __x;
195 else if (__r > 0)
196 return (__x >> __r) | (__x << ((_Nd - __r) % _Nd));
197 else
198 return (__x << -__r) | (__x >> ((_Nd + __r) % _Nd)); // rotl(x, -r)
199 }
200
201 template<typename _Tp>
202 constexpr int
203 __countl_zero(_Tp __x) noexcept
204 {
205 using __gnu_cxx::__int_traits;
206 constexpr auto _Nd = __int_traits<_Tp>::__digits;
207
208#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_clzg)
209 return __builtin_clzg(__x, _Nd);
210#else
211 if (__x == 0)
212 return _Nd;
213
214 constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
215 constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
216 constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
217
218 if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
219 {
220 constexpr int __diff = _Nd_u - _Nd;
221 return __builtin_clz(__x) - __diff;
222 }
223 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
224 {
225 constexpr int __diff = _Nd_ul - _Nd;
226 return __builtin_clzl(__x) - __diff;
227 }
228 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
229 {
230 constexpr int __diff = _Nd_ull - _Nd;
231 return __builtin_clzll(__x) - __diff;
232 }
233 else // (_Nd > _Nd_ull)
234 {
235 static_assert(_Nd <= (2 * _Nd_ull),
236 "Maximum supported integer size is 128-bit");
237
238 unsigned long long __high = __x >> _Nd_ull;
239 if (__high != 0)
240 {
241 constexpr int __diff = (2 * _Nd_ull) - _Nd;
242 return __builtin_clzll(__high) - __diff;
243 }
244 constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
245 unsigned long long __low = __x & __max_ull;
246 return (_Nd - _Nd_ull) + __builtin_clzll(__low);
247 }
248#endif
249 }
250
251 template<typename _Tp>
252 constexpr int
253 __countl_one(_Tp __x) noexcept
254 {
255 return std::__countl_zero<_Tp>((_Tp)~__x);
256 }
257
258 template<typename _Tp>
259 constexpr int
260 __countr_zero(_Tp __x) noexcept
261 {
262 using __gnu_cxx::__int_traits;
263 constexpr auto _Nd = __int_traits<_Tp>::__digits;
264
265#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_ctzg)
266 return __builtin_ctzg(__x, _Nd);
267#else
268 if (__x == 0)
269 return _Nd;
270
271 constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
272 constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
273 constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
274
275 if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
276 return __builtin_ctz(__x);
277 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
278 return __builtin_ctzl(__x);
279 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
280 return __builtin_ctzll(__x);
281 else // (_Nd > _Nd_ull)
282 {
283 static_assert(_Nd <= (2 * _Nd_ull),
284 "Maximum supported integer size is 128-bit");
285
286 constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
287 unsigned long long __low = __x & __max_ull;
288 if (__low != 0)
289 return __builtin_ctzll(__low);
290 unsigned long long __high = __x >> _Nd_ull;
291 return __builtin_ctzll(__high) + _Nd_ull;
292 }
293#endif
294 }
295
296 template<typename _Tp>
297 constexpr int
298 __countr_one(_Tp __x) noexcept
299 {
300 return std::__countr_zero((_Tp)~__x);
301 }
302
303 template<typename _Tp>
304 constexpr int
305 __popcount(_Tp __x) noexcept
306 {
307#if _GLIBCXX_USE_BUILTIN_TRAIT(__builtin_popcountg)
308 return __builtin_popcountg(__x);
309#else
310 using __gnu_cxx::__int_traits;
311 constexpr auto _Nd = __int_traits<_Tp>::__digits;
312
313 constexpr auto _Nd_ull = __int_traits<unsigned long long>::__digits;
314 constexpr auto _Nd_ul = __int_traits<unsigned long>::__digits;
315 constexpr auto _Nd_u = __int_traits<unsigned>::__digits;
316
317 if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_u)
318 return __builtin_popcount(__x);
319 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ul)
320 return __builtin_popcountl(__x);
321 else if _GLIBCXX17_CONSTEXPR (_Nd <= _Nd_ull)
322 return __builtin_popcountll(__x);
323 else // (_Nd > _Nd_ull)
324 {
325 static_assert(_Nd <= (2 * _Nd_ull),
326 "Maximum supported integer size is 128-bit");
327
328 constexpr auto __max_ull = __int_traits<unsigned long long>::__max;
329 unsigned long long __low = __x & __max_ull;
330 unsigned long long __high = __x >> _Nd_ull;
331 return __builtin_popcountll(__low) + __builtin_popcountll(__high);
332 }
333#endif
334 }
335
336 template<typename _Tp>
337 constexpr bool
338 __has_single_bit(_Tp __x) noexcept
339 { return std::__popcount(__x) == 1; }
340
341 template<typename _Tp>
342 constexpr _Tp
343 __bit_ceil(_Tp __x) noexcept
344 {
345 using __gnu_cxx::__int_traits;
346 constexpr auto _Nd = __int_traits<_Tp>::__digits;
347 if (__x == 0 || __x == 1)
348 return 1;
349 auto __shift_exponent = _Nd - std::__countl_zero((_Tp)(__x - 1u));
350 // If the shift exponent equals _Nd then the correct result is not
351 // representable as a value of _Tp, and so the result is undefined.
352 // Want that undefined behaviour to be detected in constant expressions,
353 // by UBSan, and by debug assertions.
354 if (!std::__is_constant_evaluated())
355 {
356 __glibcxx_assert( __shift_exponent != __int_traits<_Tp>::__digits );
357 }
358
359 using __promoted_type = decltype(__x << 1);
360 if _GLIBCXX17_CONSTEXPR (!is_same<__promoted_type, _Tp>::value)
361 {
362 // If __x undergoes integral promotion then shifting by _Nd is
363 // not undefined. In order to make the shift undefined, so that
364 // it is diagnosed in constant expressions and by UBsan, we also
365 // need to "promote" the shift exponent to be too large for the
366 // promoted type.
367 const int __extra_exp = sizeof(__promoted_type) / sizeof(_Tp) / 2;
368 __shift_exponent |= (__shift_exponent & _Nd) << __extra_exp;
369 }
370 return (_Tp)1u << __shift_exponent;
371 }
372
373 template<typename _Tp>
374 constexpr _Tp
375 __bit_floor(_Tp __x) noexcept
376 {
377 constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
378 if (__x == 0)
379 return 0;
380 return (_Tp)1u << (_Nd - std::__countl_zero((_Tp)(__x >> 1)));
381 }
382
383 template<typename _Tp>
384 constexpr int
385 __bit_width(_Tp __x) noexcept
386 {
387 constexpr auto _Nd = __gnu_cxx::__int_traits<_Tp>::__digits;
388 return _Nd - std::__countl_zero(__x);
389 }
390
391 /// @endcond
392
393#ifdef __cpp_lib_bitops // C++ >= 20
394
395 /// @cond undocumented
396 template<typename _Tp>
397 concept __unsigned_integer = __is_unsigned_integer<_Tp>::value;
398 /// @endcond
399
400 // [bit.rot], rotating
401
402 /// Rotate `x` to the left by `s` bits.
403 template<__unsigned_integer _Tp>
404 [[nodiscard]] constexpr _Tp
405 rotl(_Tp __x, int __s) noexcept
406 { return std::__rotl(__x, __s); }
407
408 /// Rotate `x` to the right by `s` bits.
409 template<__unsigned_integer _Tp>
410 [[nodiscard]] constexpr _Tp
411 rotr(_Tp __x, int __s) noexcept
412 { return std::__rotr(__x, __s); }
413
414 // [bit.count], counting
415
416 /// The number of contiguous zero bits, starting from the highest bit.
417 template<__unsigned_integer _Tp>
418 constexpr int
419 countl_zero(_Tp __x) noexcept
420 { return std::__countl_zero(__x); }
421
422 /// The number of contiguous one bits, starting from the highest bit.
423 template<__unsigned_integer _Tp>
424 constexpr int
425 countl_one(_Tp __x) noexcept
426 { return std::__countl_one(__x); }
427
428 /// The number of contiguous zero bits, starting from the lowest bit.
429 template<__unsigned_integer _Tp>
430 constexpr int
431 countr_zero(_Tp __x) noexcept
432 { return std::__countr_zero(__x); }
433
434 /// The number of contiguous one bits, starting from the lowest bit.
435 template<__unsigned_integer _Tp>
436 constexpr int
437 countr_one(_Tp __x) noexcept
438 { return std::__countr_one(__x); }
439
440 /// The number of bits set in `x`.
441 template<__unsigned_integer _Tp>
442 constexpr int
443 popcount(_Tp __x) noexcept
444 { return std::__popcount(__x); }
445#endif // __cpp_lib_bitops
446
447#ifdef __cpp_lib_int_pow2 // C++ >= 20
448 // [bit.pow.two], integral powers of 2
449
450 /// True if `x` is a power of two, false otherwise.
451 template<__unsigned_integer _Tp>
452 constexpr bool
453 has_single_bit(_Tp __x) noexcept
454 { return std::__has_single_bit(__x); }
455
456 /// The smallest power-of-two not less than `x`.
457 template<__unsigned_integer _Tp>
458 constexpr _Tp
459 bit_ceil(_Tp __x) noexcept
460 { return std::__bit_ceil(__x); }
461
462 /// The largest power-of-two not greater than `x`.
463 template<__unsigned_integer _Tp>
464 constexpr _Tp
465 bit_floor(_Tp __x) noexcept
466 { return std::__bit_floor(__x); }
467
468 // _GLIBCXX_RESOLVE_LIB_DEFECTS
469 // 3656. Inconsistent bit operations returning a count
470 /// The smallest integer greater than the base-2 logarithm of `x`.
471 template<__unsigned_integer _Tp>
472 constexpr int
473 bit_width(_Tp __x) noexcept
474 { return std::__bit_width(__x); }
475#endif // defined (__cpp_lib_int_pow2)
476
477#ifdef __cpp_lib_endian // C++ >= 20
478
479 /// Byte order constants
480 /**
481 * The platform endianness can be checked by comparing `std::endian::native`
482 * to one of `std::endian::big` or `std::endian::little`.
483 *
484 * @since C++20
485 */
486 enum class endian
487 {
488 little = __ORDER_LITTLE_ENDIAN__,
489 big = __ORDER_BIG_ENDIAN__,
490 native = __BYTE_ORDER__
491 };
492#endif // __cpp_lib_endian
493
494 /// @}
495
496_GLIBCXX_END_NAMESPACE_VERSION
497} // namespace std
498
499#endif // C++14
500#endif // _GLIBCXX_BIT
501