1 // <max_size_type.h> -*- C++ -*-
2 
3 // Copyright (C) 2019-2021 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 bits/max_size_type.h
26  *  This is an internal header file, included by other library headers.
27  *  Do not attempt to use it directly. @headername{iterator}
28  */
29 
30 #ifndef _GLIBCXX_MAX_SIZE_TYPE_H
31 #define _GLIBCXX_MAX_SIZE_TYPE_H 1
32 
33 #pragma GCC system_header
34 
35 #if __cplusplus > 201703L && __cpp_lib_concepts
36 #include <ext/numeric_traits.h>
37 #include <numbers>
38 
39 // This header implements unsigned and signed integer-class types (as per
40 // [iterator.concept.winc]) that are one bit wider than the widest supported
41 // integer type.
42 //
43 // The set of integer types we consider includes __int128 and unsigned __int128
44 // (when they exist), even though they are really integer types only in GNU
45 // mode.  This is to obtain a consistent ABI for these integer-class types
46 // across strict mode and GNU mode.
47 
_GLIBCXX_VISIBILITY(default)48 namespace std _GLIBCXX_VISIBILITY(default)
49 {
50 _GLIBCXX_BEGIN_NAMESPACE_VERSION
51 
52 template<typename _Tp>
53   struct numeric_limits;
54 
55 namespace ranges
56 {
57   namespace __detail
58   {
59     class __max_size_type
60     {
61     public:
62       __max_size_type() = default;
63 
64       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
65 	constexpr
66 	__max_size_type(_Tp __i) noexcept
67 	  : _M_val(__i), _M_msb(__i < 0)
68 	{ }
69 
70       constexpr explicit
71       __max_size_type(const __max_diff_type& __d) noexcept;
72 
73       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
74 	constexpr explicit
75 	operator _Tp() const noexcept
76 	{ return _M_val; }
77 
78       constexpr explicit
79       operator bool() const noexcept
80       { return _M_val != 0 || _M_msb != 0; }
81 
82       constexpr __max_size_type
83       operator+() const noexcept
84       { return *this; }
85 
86       constexpr __max_size_type
87       operator~() const noexcept
88       { return __max_size_type{~_M_val, !_M_msb}; }
89 
90       constexpr __max_size_type
91       operator-() const noexcept
92       { return operator~() + 1; }
93 
94       constexpr __max_size_type&
95       operator++() noexcept
96       { return *this += 1; }
97 
98       constexpr __max_size_type
99       operator++(int) noexcept
100       {
101 	auto __tmp = *this;
102 	++*this;
103 	return __tmp;
104       }
105 
106       constexpr __max_size_type&
107       operator--() noexcept
108       { return *this -= 1; }
109 
110       constexpr __max_size_type
111       operator--(int) noexcept
112       {
113 	auto __tmp = *this;
114 	--*this;
115 	return __tmp;
116       }
117 
118       constexpr __max_size_type&
119       operator+=(const __max_size_type& __r) noexcept
120       {
121 	const auto __sum = _M_val + __r._M_val;
122 	const bool __overflow = (__sum < _M_val);
123 	_M_msb = _M_msb ^ __r._M_msb ^ __overflow;
124 	_M_val = __sum;
125 	return *this;
126       }
127 
128       constexpr __max_size_type&
129       operator-=(const __max_size_type& __r) noexcept
130       { return *this += -__r; }
131 
132       constexpr __max_size_type&
133       operator*=(__max_size_type __r) noexcept
134       {
135 	constexpr __max_size_type __threshold
136 	  = __rep(1) << (_S_rep_bits / 2 - 1);
137 	if (_M_val < __threshold && __r < __threshold)
138 	  // When both operands are below this threshold then the
139 	  // multiplication can be safely computed in the base precision.
140 	  _M_val = _M_val * __r._M_val;
141 	else
142 	  {
143 	    // Otherwise, perform the multiplication in four steps, by
144 	    // decomposing the LHS and the RHS into 2*x+a and 2*y+b,
145 	    // respectively, and computing 4*x*y + 2*x*b + 2*y*a + a*b.
146 	    const bool __lsb = _M_val & 1;
147 	    const bool __rlsb = __r._M_val & 1;
148 	    *this >>= 1;
149 	    __r >>= 1;
150 	    _M_val = (2 * _M_val * __r._M_val
151 		      + _M_val * __rlsb + __r._M_val * __lsb);
152 	    *this <<= 1;
153 	    *this += __rlsb * __lsb;
154 	  }
155 
156 	return *this;
157       }
158 
159       constexpr __max_size_type&
160       operator/=(const __max_size_type& __r) noexcept
161       {
162 	__glibcxx_assert(__r != 0);
163 
164 	if (!_M_msb && !__r._M_msb) [[likely]]
165 	  _M_val /= __r._M_val;
166 	else if (_M_msb && __r._M_msb)
167 	  {
168 	    _M_val = (_M_val >= __r._M_val);
169 	    _M_msb = 0;
170 	  }
171 	else if (!_M_msb && __r._M_msb)
172 	  _M_val = 0;
173 	else if (_M_msb && !__r._M_msb)
174 	  {
175 	    // The non-trivial case: the dividend has its MSB set and the
176 	    // divisor doesn't.  In this case we compute ((LHS/2)/RHS)*2
177 	    // in the base precision.  This quantity is either the true
178 	    // quotient or one less than the true quotient.
179 	    const auto __orig = *this;
180 	    *this >>= 1;
181 	    _M_val /= __r._M_val;
182 	    *this <<= 1;
183 	    if (__orig - *this * __r >= __r)
184 	      ++_M_val;
185 	  }
186 	return *this;
187       }
188 
189       constexpr __max_size_type&
190       operator%=(const __max_size_type& __r) noexcept
191       {
192 	if (!_M_msb && !__r._M_msb) [[likely]]
193 	  _M_val %= __r._M_val;
194 	else
195 	  *this -= (*this / __r) * __r;
196 	return *this;
197       }
198 
199       constexpr __max_size_type&
200       operator<<=(const __max_size_type& __r) noexcept
201       {
202 	__glibcxx_assert(__r <= _S_rep_bits);
203 	if (__r != 0)
204 	  {
205 	    _M_msb = (_M_val >> (_S_rep_bits - __r._M_val)) & 1;
206 
207 	    if (__r._M_val == _S_rep_bits) [[unlikely]]
208 	      _M_val = 0;
209 	    else
210 	      _M_val <<= __r._M_val;
211 	  }
212 	return *this;
213       }
214 
215       constexpr __max_size_type&
216       operator>>=(const __max_size_type& __r) noexcept
217       {
218 	__glibcxx_assert(__r <= _S_rep_bits);
219 	if (__r != 0)
220 	  {
221 	    if (__r._M_val == _S_rep_bits) [[unlikely]]
222 	      _M_val = 0;
223 	    else
224 	      _M_val >>= __r._M_val;
225 
226 	    if (_M_msb) [[unlikely]]
227 	      {
228 		_M_val |= __rep(1) << (_S_rep_bits - __r._M_val);
229 		_M_msb = 0;
230 	      }
231 	  }
232 	return *this;
233       }
234 
235       constexpr __max_size_type&
236       operator&=(const __max_size_type& __r) noexcept
237       {
238 	_M_val &= __r._M_val;
239 	_M_msb &= __r._M_msb;
240 	return *this;
241       }
242 
243       constexpr __max_size_type&
244       operator|=(const __max_size_type& __r) noexcept
245       {
246 	_M_val |= __r._M_val;
247 	_M_msb |= __r._M_msb;
248 	return *this;
249       }
250 
251       constexpr __max_size_type&
252       operator^=(const __max_size_type& __r) noexcept
253       {
254 	_M_val ^= __r._M_val;
255 	_M_msb ^= __r._M_msb;
256 	return *this;
257       }
258 
259       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
260 	friend constexpr _Tp&
261 	operator+=(_Tp& __a, const __max_size_type& __b) noexcept
262 	{ return (__a = static_cast<_Tp>(__a + __b)); }
263 
264       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
265 	friend constexpr _Tp&
266 	operator-=(_Tp& __a, const __max_size_type& __b) noexcept
267 	{ return (__a = static_cast<_Tp>(__a - __b)); }
268 
269       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
270 	friend constexpr _Tp&
271 	operator*=(_Tp& __a, const __max_size_type& __b) noexcept
272 	{ return (__a = static_cast<_Tp>(__a * __b)); }
273 
274       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
275 	friend constexpr _Tp&
276 	operator/=(_Tp& __a, const __max_size_type& __b) noexcept
277 	{ return (__a = static_cast<_Tp>(__a / __b)); }
278 
279       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
280 	friend constexpr _Tp&
281 	operator%=(_Tp& __a, const __max_size_type& __b) noexcept
282 	{ return (__a = static_cast<_Tp>(__a % __b)); }
283 
284       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
285 	friend constexpr _Tp&
286 	operator&=(_Tp& __a, const __max_size_type& __b) noexcept
287 	{ return (__a = static_cast<_Tp>(__a & __b)); }
288 
289       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
290 	friend constexpr _Tp&
291 	operator|=(_Tp& __a, const __max_size_type& __b) noexcept
292 	{ return (__a = static_cast<_Tp>(__a | __b)); }
293 
294       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
295 	friend constexpr _Tp&
296 	operator^=(_Tp& __a, const __max_size_type& __b) noexcept
297 	{ return (__a = static_cast<_Tp>(__a ^ __b)); }
298 
299       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
300 	friend constexpr _Tp&
301 	operator<<=(_Tp& __a, const __max_size_type& __b) noexcept
302 	{ return (__a = static_cast<_Tp>(__a << __b)); }
303 
304       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
305 	friend constexpr _Tp&
306 	operator>>=(_Tp& __a, const __max_size_type& __b) noexcept
307 	{ return (__a = static_cast<_Tp>(__a >> __b)); }
308 
309       friend constexpr __max_size_type
310       operator+(__max_size_type __l, const __max_size_type& __r) noexcept
311       {
312 	__l += __r;
313 	return __l;
314       }
315 
316       friend constexpr __max_size_type
317       operator-(__max_size_type __l, const __max_size_type& __r) noexcept
318       {
319 	__l -= __r;
320 	return __l;
321       }
322 
323       friend constexpr __max_size_type
324       operator*(__max_size_type __l, const __max_size_type& __r) noexcept
325       {
326 	__l *= __r;
327 	return __l;
328       }
329 
330       friend constexpr __max_size_type
331       operator/(__max_size_type __l, const __max_size_type& __r) noexcept
332       {
333 	__l /= __r;
334 	return __l;
335       }
336 
337       friend constexpr __max_size_type
338       operator%(__max_size_type __l, const __max_size_type& __r) noexcept
339       {
340 	__l %= __r;
341 	return __l;
342       }
343 
344       friend constexpr __max_size_type
345       operator<<(__max_size_type __l, const __max_size_type& __r) noexcept
346       {
347 	__l <<= __r;
348 	return __l;
349       }
350 
351       friend constexpr __max_size_type
352       operator>>(__max_size_type __l, const __max_size_type& __r) noexcept
353       {
354 	__l >>= __r;
355 	return __l;
356       }
357 
358       friend constexpr __max_size_type
359       operator&(__max_size_type __l, const __max_size_type& __r) noexcept
360       {
361 	__l &= __r;
362 	return __l;
363       }
364 
365       friend constexpr __max_size_type
366       operator|(__max_size_type __l, const __max_size_type& __r) noexcept
367       {
368 	__l |= __r;
369 	return __l;
370       }
371 
372       friend constexpr __max_size_type
373       operator^(__max_size_type __l, const __max_size_type& __r) noexcept
374       {
375 	__l ^= __r;
376 	return __l;
377       }
378 
379       friend constexpr bool
380       operator==(const __max_size_type& __l, const __max_size_type& __r) noexcept
381       { return __l._M_val == __r._M_val && __l._M_msb == __r._M_msb; }
382 
383 #if __cpp_lib_three_way_comparison
384       friend constexpr strong_ordering
385       operator<=>(const __max_size_type& __l, const __max_size_type& __r) noexcept
386       {
387 	if (__l._M_msb ^ __r._M_msb)
388 	  return __l._M_msb ? strong_ordering::greater : strong_ordering::less;
389 	else
390 	  return __l._M_val <=> __r._M_val;
391       }
392 #else
393       friend constexpr bool
394       operator!=(const __max_size_type& __l, const __max_size_type& __r) noexcept
395       { return !(__l == __r); }
396 
397       friend constexpr bool
398       operator<(const __max_size_type& __l, const __max_size_type& __r) noexcept
399       {
400 	if (__l._M_msb == __r._M_msb)
401 	  return __l._M_val < __r._M_val;
402 	else
403 	  return __r._M_msb;
404       }
405 
406       friend constexpr bool
407       operator>(const __max_size_type& __l, const __max_size_type& __r) noexcept
408       { return __r < __l; }
409 
410       friend constexpr bool
411       operator<=(const __max_size_type& __l, const __max_size_type& __r) noexcept
412       { return !(__l > __r); }
413 
414       friend constexpr bool
415       operator>=(const __max_size_type& __l, const __max_size_type& __r) noexcept
416       { return __r <= __l; }
417 #endif
418 
419 #if __SIZEOF_INT128__
420       using __rep = unsigned __int128;
421 #else
422       using __rep = unsigned long long;
423 #endif
424       static constexpr size_t _S_rep_bits = sizeof(__rep) * __CHAR_BIT__;
425     private:
426       __rep _M_val = 0;
427       unsigned _M_msb:1 = 0;
428 
429       constexpr explicit
430       __max_size_type(__rep __val, int __msb) noexcept
431 	: _M_val(__val), _M_msb(__msb)
432       { }
433 
434       friend __max_diff_type;
435       friend std::numeric_limits<__max_size_type>;
436       friend std::numeric_limits<__max_diff_type>;
437     };
438 
439     class __max_diff_type
440     {
441     public:
442       __max_diff_type() = default;
443 
444       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
445 	constexpr
446 	__max_diff_type(_Tp __i) noexcept
447 	  : _M_rep(__i)
448 	{ }
449 
450       constexpr explicit
451       __max_diff_type(const __max_size_type& __d) noexcept
452 	: _M_rep(__d)
453       { }
454 
455       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
456 	constexpr explicit
457 	operator _Tp() const noexcept
458 	{ return static_cast<_Tp>(_M_rep); }
459 
460       constexpr explicit
461       operator bool() const noexcept
462       { return _M_rep != 0; }
463 
464       constexpr __max_diff_type
465       operator+() const noexcept
466       { return *this; }
467 
468       constexpr __max_diff_type
469       operator-() const noexcept
470       { return __max_diff_type(-_M_rep); }
471 
472       constexpr __max_diff_type
473       operator~() const noexcept
474       { return __max_diff_type(~_M_rep); }
475 
476       constexpr __max_diff_type&
477       operator++() noexcept
478       { return *this += 1; }
479 
480       constexpr __max_diff_type
481       operator++(int) noexcept
482       {
483 	auto __tmp = *this;
484 	++*this;
485 	return __tmp;
486       }
487 
488       constexpr __max_diff_type&
489       operator--() noexcept
490       { return *this -= 1; }
491 
492       constexpr __max_diff_type
493       operator--(int) noexcept
494       {
495 	auto __tmp = *this;
496 	--*this;
497 	return __tmp;
498       }
499 
500       constexpr __max_diff_type&
501       operator+=(const __max_diff_type& __r) noexcept
502       {
503 	_M_rep += __r._M_rep;
504 	return *this;
505       }
506 
507       constexpr __max_diff_type&
508       operator-=(const __max_diff_type& __r) noexcept
509       {
510 	_M_rep -= __r._M_rep;
511 	return *this;
512       }
513 
514       constexpr __max_diff_type&
515       operator*=(const __max_diff_type& __r) noexcept
516       {
517 	_M_rep *= __r._M_rep;
518 	return *this;
519       }
520 
521       constexpr __max_diff_type&
522       operator/=(const __max_diff_type& __r) noexcept
523       {
524 	__glibcxx_assert (__r != 0);
525 	const bool __neg = *this < 0;
526 	const bool __rneg = __r < 0;
527 	if (!__neg && !__rneg)
528 	  _M_rep = _M_rep / __r._M_rep;
529 	else if (__neg && __rneg)
530 	  _M_rep = -_M_rep / -__r._M_rep;
531 	else if (__neg && !__rneg)
532 	  _M_rep = -(-_M_rep / __r._M_rep);
533 	else
534 	  _M_rep = -(_M_rep / -__r._M_rep);
535 	return *this ;
536       }
537 
538       constexpr __max_diff_type&
539       operator%=(const __max_diff_type& __r) noexcept
540       {
541 	__glibcxx_assert (__r != 0);
542 	if (*this >= 0 && __r > 0)
543 	  _M_rep %= __r._M_rep;
544 	else
545 	  *this -= (*this / __r) * __r;
546 	return *this;
547       }
548 
549       constexpr __max_diff_type&
550       operator<<=(const __max_diff_type& __r) noexcept
551       {
552 	_M_rep.operator<<=(__r._M_rep);
553 	return *this;
554       }
555 
556       constexpr __max_diff_type&
557       operator>>=(const __max_diff_type& __r) noexcept
558       {
559 	// Arithmetic right shift.
560 	const auto __msb = _M_rep._M_msb;
561 	_M_rep >>= __r._M_rep;
562 	_M_rep._M_msb |= __msb;
563 	return *this;
564       }
565 
566       constexpr __max_diff_type&
567       operator&=(const __max_diff_type& __r) noexcept
568       {
569 	_M_rep &= __r._M_rep;
570 	return *this;
571       }
572 
573       constexpr __max_diff_type&
574       operator|=(const __max_diff_type& __r) noexcept
575       {
576 	_M_rep |= __r._M_rep;
577 	return *this;
578       }
579 
580       constexpr __max_diff_type&
581       operator^=(const __max_diff_type& __r) noexcept
582       {
583 	_M_rep ^= __r._M_rep;
584 	return *this;
585       }
586 
587       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
588 	friend constexpr _Tp&
589 	operator+=(_Tp& __a, const __max_diff_type& __b) noexcept
590 	{ return (__a = static_cast<_Tp>(__a + __b)); }
591 
592       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
593 	friend constexpr _Tp&
594 	operator-=(_Tp& __a, const __max_diff_type& __b) noexcept
595 	{ return (__a = static_cast<_Tp>(__a - __b)); }
596 
597       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
598 	friend constexpr _Tp&
599 	operator*=(_Tp& __a, const __max_diff_type& __b) noexcept
600 	{ return (__a = static_cast<_Tp>(__a * __b)); }
601 
602       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
603 	friend constexpr _Tp&
604 	operator/=(_Tp& __a, const __max_diff_type& __b) noexcept
605 	{ return (__a = static_cast<_Tp>(__a / __b)); }
606 
607       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
608 	friend constexpr _Tp&
609 	operator%=(_Tp& __a, const __max_diff_type& __b) noexcept
610 	{ return (__a = static_cast<_Tp>(__a % __b)); }
611 
612       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
613 	friend constexpr _Tp&
614 	operator&=(_Tp& __a, const __max_diff_type& __b) noexcept
615 	{ return (__a = static_cast<_Tp>(__a & __b)); }
616 
617       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
618 	friend constexpr _Tp&
619 	operator|=(_Tp& __a, const __max_diff_type& __b) noexcept
620 	{ return (__a = static_cast<_Tp>(__a | __b)); }
621 
622       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
623 	friend constexpr _Tp&
624 	operator^=(_Tp& __a, const __max_diff_type& __b) noexcept
625 	{ return (__a = static_cast<_Tp>(__a ^ __b)); }
626 
627       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
628 	friend constexpr _Tp&
629 	operator<<=(_Tp& __a, const __max_diff_type& __b) noexcept
630 	{ return (__a = static_cast<_Tp>(__a << __b)); }
631 
632       template<typename _Tp> requires integral<_Tp> || __is_int128<_Tp>
633 	friend constexpr _Tp&
634 	operator>>=(_Tp& __a, const __max_diff_type& __b) noexcept
635 	{ return (__a = static_cast<_Tp>(__a >> __b)); }
636 
637       friend constexpr __max_diff_type
638       operator+(__max_diff_type __l, const __max_diff_type& __r) noexcept
639       {
640 	__l += __r;
641 	return __l;
642       }
643 
644       friend constexpr __max_diff_type
645       operator-(__max_diff_type __l, const __max_diff_type& __r) noexcept
646       {
647 	__l -= __r;
648 	return __l;
649       }
650 
651       friend constexpr __max_diff_type
652       operator*(__max_diff_type __l, const __max_diff_type& __r) noexcept
653       {
654 	__l *= __r;
655 	return __l;
656       }
657 
658       friend constexpr __max_diff_type
659       operator/(__max_diff_type __l, const __max_diff_type& __r) noexcept
660       {
661 	__l /= __r;
662 	return __l;
663       }
664 
665       friend constexpr __max_diff_type
666       operator%(__max_diff_type __l, const __max_diff_type& __r) noexcept
667       {
668 	__l %= __r;
669 	return __l;
670       }
671 
672       friend constexpr __max_diff_type
673       operator<<(__max_diff_type __l, const __max_diff_type& __r) noexcept
674       {
675 	__l <<= __r;
676 	return __l;
677       }
678 
679       friend constexpr __max_diff_type
680       operator>>(__max_diff_type __l, const __max_diff_type& __r) noexcept
681       {
682 	__l >>= __r;
683 	return __l;
684       }
685 
686       friend constexpr __max_diff_type
687       operator&(__max_diff_type __l, const __max_diff_type& __r) noexcept
688       {
689 	__l &= __r;
690 	return __l;
691       }
692 
693       friend constexpr __max_diff_type
694       operator|(__max_diff_type __l, const __max_diff_type& __r) noexcept
695       {
696 	__l |= __r;
697 	return __l;
698       }
699 
700       friend constexpr __max_diff_type
701       operator^(__max_diff_type __l, const __max_diff_type& __r) noexcept
702       {
703 	__l ^= __r;
704 	return __l;
705       }
706 
707       friend constexpr bool
708       operator==(const __max_diff_type& __l, const __max_diff_type& __r) noexcept
709       { return __l._M_rep == __r._M_rep; }
710 
711 #if __cpp_lib_three_way_comparison
712       constexpr strong_ordering
713       operator<=>(const __max_diff_type& __r) const noexcept
714       {
715 	const auto __lsign = _M_rep._M_msb;
716 	const auto __rsign = __r._M_rep._M_msb;
717 	if (__lsign ^ __rsign)
718 	  return __lsign ? strong_ordering::less : strong_ordering::greater;
719 	else
720 	  return _M_rep <=> __r._M_rep;
721       }
722 #else
723       friend constexpr bool
724       operator!=(const __max_diff_type& __l, const __max_diff_type& __r) noexcept
725       { return !(__l == __r); }
726 
727       constexpr bool
728       operator<(const __max_diff_type& __r) const noexcept
729       {
730 	const auto __lsign = _M_rep._M_msb;
731 	const auto __rsign = __r._M_rep._M_msb;
732 	if (__lsign ^ __rsign)
733 	  return __lsign;
734 	else
735 	  return _M_rep < __r._M_rep;
736       }
737 
738       friend constexpr bool
739       operator>(const __max_diff_type& __l, const __max_diff_type& __r) noexcept
740       { return __r < __l; }
741 
742       friend constexpr bool
743       operator<=(const __max_diff_type& __l, const __max_diff_type& __r) noexcept
744       { return !(__r < __l); }
745 
746       friend constexpr bool
747       operator>=(const __max_diff_type& __l, const __max_diff_type& __r) noexcept
748       { return !(__l < __r); }
749 #endif
750 
751     private:
752       __max_size_type _M_rep = 0;
753 
754       friend class __max_size_type;
755     };
756 
757     constexpr
758     __max_size_type::__max_size_type(const __max_diff_type& __d) noexcept
759       : __max_size_type(__d._M_rep)
760     { }
761 
762   } // namespace __detail
763 } // namespace ranges
764 
765   template<>
766     struct numeric_limits<ranges::__detail::__max_size_type>
767     {
768       using _Sp = ranges::__detail::__max_size_type;
769       static constexpr bool is_specialized = true;
770       static constexpr bool is_signed = false;
771       static constexpr bool is_integer = true;
772       static constexpr bool is_exact = true;
773 #if __SIZEOF_INT128__
774       static_assert(same_as<_Sp::__rep, unsigned __int128>);
775       static constexpr int digits = 129;
776 #else
777       static_assert(same_as<_Sp::__rep, unsigned long long>);
778       static constexpr int digits
779 	= __gnu_cxx::__int_traits<unsigned long long>::__digits + 1;
780 #endif
781       static constexpr int digits10
782 	= static_cast<int>(digits * numbers::ln2 / numbers::ln10);
783 
784       static constexpr _Sp
785       min() noexcept
786       { return 0; }
787 
788       static constexpr _Sp
789       max() noexcept
790       { return _Sp(static_cast<_Sp::__rep>(-1), 1); }
791 
792       static constexpr _Sp
793       lowest() noexcept
794       { return min(); }
795     };
796 
797   template<>
798     struct numeric_limits<ranges::__detail::__max_diff_type>
799     {
800       using _Dp = ranges::__detail::__max_diff_type;
801       using _Sp = ranges::__detail::__max_size_type;
802       static constexpr bool is_specialized = true;
803       static constexpr bool is_signed = true;
804       static constexpr bool is_integer = true;
805       static constexpr bool is_exact = true;
806       static constexpr int digits = numeric_limits<_Sp>::digits - 1;
807       static constexpr int digits10
808 	= static_cast<int>(digits * numbers::ln2 / numbers::ln10);
809 
810       static constexpr _Dp
811       min() noexcept
812       { return _Dp(_Sp(0, 1)); }
813 
814       static constexpr _Dp
815       max() noexcept
816       { return _Dp(_Sp(static_cast<_Sp::__rep>(-1), 0)); }
817 
818       static constexpr _Dp
819       lowest() noexcept
820       { return min(); }
821     };
822 
823 _GLIBCXX_END_NAMESPACE_VERSION
824 } // namespace
825 
826 #endif // C++20 && library concepts
827 #endif // _GLIBCXX_MAX_SIZE_TYPE_H
828