xref: /freebsd/contrib/llvm-project/libcxx/include/limits (revision 525fe93dc7487a1e63a90f6a2b956abc601963c1) 
1// -*- C++ -*-
2//===----------------------------------------------------------------------===//
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_LIMITS
11#define _LIBCPP_LIMITS
12
13/*
14    limits synopsis
15
16namespace std
17{
18
19template<class T>
20class numeric_limits
21{
22public:
23    static constexpr bool is_specialized = false;
24    static constexpr T min() noexcept;
25    static constexpr T max() noexcept;
26    static constexpr T lowest() noexcept;
27
28    static constexpr int  digits = 0;
29    static constexpr int  digits10 = 0;
30    static constexpr int  max_digits10 = 0;
31    static constexpr bool is_signed = false;
32    static constexpr bool is_integer = false;
33    static constexpr bool is_exact = false;
34    static constexpr int  radix = 0;
35    static constexpr T epsilon() noexcept;
36    static constexpr T round_error() noexcept;
37
38    static constexpr int  min_exponent = 0;
39    static constexpr int  min_exponent10 = 0;
40    static constexpr int  max_exponent = 0;
41    static constexpr int  max_exponent10 = 0;
42
43    static constexpr bool has_infinity = false;
44    static constexpr bool has_quiet_NaN = false;
45    static constexpr bool has_signaling_NaN = false;
46    static constexpr float_denorm_style has_denorm = denorm_absent;
47    static constexpr bool has_denorm_loss = false;
48    static constexpr T infinity() noexcept;
49    static constexpr T quiet_NaN() noexcept;
50    static constexpr T signaling_NaN() noexcept;
51    static constexpr T denorm_min() noexcept;
52
53    static constexpr bool is_iec559 = false;
54    static constexpr bool is_bounded = false;
55    static constexpr bool is_modulo = false;
56
57    static constexpr bool traps = false;
58    static constexpr bool tinyness_before = false;
59    static constexpr float_round_style round_style = round_toward_zero;
60};
61
62enum float_round_style
63{
64    round_indeterminate       = -1,
65    round_toward_zero         =  0,
66    round_to_nearest          =  1,
67    round_toward_infinity     =  2,
68    round_toward_neg_infinity =  3
69};
70
71enum float_denorm_style
72{
73    denorm_indeterminate = -1,
74    denorm_absent = 0,
75    denorm_present = 1
76};
77
78template<> class numeric_limits<cv bool>;
79
80template<> class numeric_limits<cv char>;
81template<> class numeric_limits<cv signed char>;
82template<> class numeric_limits<cv unsigned char>;
83template<> class numeric_limits<cv wchar_t>;
84template<> class numeric_limits<cv char8_t>; // C++20
85template<> class numeric_limits<cv char16_t>;
86template<> class numeric_limits<cv char32_t>;
87
88template<> class numeric_limits<cv short>;
89template<> class numeric_limits<cv int>;
90template<> class numeric_limits<cv long>;
91template<> class numeric_limits<cv long long>;
92template<> class numeric_limits<cv unsigned short>;
93template<> class numeric_limits<cv unsigned int>;
94template<> class numeric_limits<cv unsigned long>;
95template<> class numeric_limits<cv unsigned long long>;
96
97template<> class numeric_limits<cv float>;
98template<> class numeric_limits<cv double>;
99template<> class numeric_limits<cv long double>;
100
101}  // std
102
103*/
104
105#include <__assert> // all public C++ headers provide the assertion handler
106#include <__config>
107#include <__type_traits/is_arithmetic.h>
108#include <__type_traits/is_signed.h>
109#include <__type_traits/remove_cv.h>
110
111#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
112#  pragma GCC system_header
113#endif
114
115_LIBCPP_PUSH_MACROS
116#include <__undef_macros>
117#include <version>
118
119
120_LIBCPP_BEGIN_NAMESPACE_STD
121
122enum float_round_style
123{
124    round_indeterminate       = -1,
125    round_toward_zero         =  0,
126    round_to_nearest          =  1,
127    round_toward_infinity     =  2,
128    round_toward_neg_infinity =  3
129};
130
131enum float_denorm_style
132{
133    denorm_indeterminate = -1,
134    denorm_absent = 0,
135    denorm_present = 1
136};
137
138template <class _Tp, bool = is_arithmetic<_Tp>::value>
139class __libcpp_numeric_limits
140{
141protected:
142    typedef _Tp type;
143
144    static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
145    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
146    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
147    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
148
149    static _LIBCPP_CONSTEXPR const int  digits = 0;
150    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
151    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
152    static _LIBCPP_CONSTEXPR const bool is_signed = false;
153    static _LIBCPP_CONSTEXPR const bool is_integer = false;
154    static _LIBCPP_CONSTEXPR const bool is_exact = false;
155    static _LIBCPP_CONSTEXPR const int  radix = 0;
156    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
157    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
158
159    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
160    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
161    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
162    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
163
164    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
165    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
166    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
167    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
168    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
169    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
170    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
171    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
172    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
173
174    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
175    static _LIBCPP_CONSTEXPR const bool is_bounded = false;
176    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
177
178    static _LIBCPP_CONSTEXPR const bool traps = false;
179    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
180    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
181};
182
183template <class _Tp, int __digits, bool _IsSigned>
184struct __libcpp_compute_min
185{
186    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << __digits);
187};
188
189template <class _Tp, int __digits>
190struct __libcpp_compute_min<_Tp, __digits, false>
191{
192    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
193};
194
195template <class _Tp>
196class __libcpp_numeric_limits<_Tp, true>
197{
198protected:
199    typedef _Tp type;
200
201    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
202
203    static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
204    static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
205    static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
206    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
207    static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
208    static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
209    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
210    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
211    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
212
213    static _LIBCPP_CONSTEXPR const bool is_integer = true;
214    static _LIBCPP_CONSTEXPR const bool is_exact = true;
215    static _LIBCPP_CONSTEXPR const int  radix = 2;
216    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
217    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
218
219    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
220    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
221    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
222    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
223
224    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
225    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
226    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
227    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
228    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
229    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
230    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
231    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
232    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
233
234    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
235    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
236    static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value;
237
238#if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__) || \
239    defined(__wasm__)
240    static _LIBCPP_CONSTEXPR const bool traps = true;
241#else
242    static _LIBCPP_CONSTEXPR const bool traps = false;
243#endif
244    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
245    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
246};
247
248template <>
249class __libcpp_numeric_limits<bool, true>
250{
251protected:
252    typedef bool type;
253
254    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
255
256    static _LIBCPP_CONSTEXPR const bool is_signed = false;
257    static _LIBCPP_CONSTEXPR const int  digits = 1;
258    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
259    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
260    static _LIBCPP_CONSTEXPR const type __min = false;
261    static _LIBCPP_CONSTEXPR const type __max = true;
262    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
263    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
264    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
265
266    static _LIBCPP_CONSTEXPR const bool is_integer = true;
267    static _LIBCPP_CONSTEXPR const bool is_exact = true;
268    static _LIBCPP_CONSTEXPR const int  radix = 2;
269    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
270    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
271
272    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
273    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
274    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
275    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
276
277    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
278    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
279    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
280    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
281    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
282    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
283    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
284    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
285    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
286
287    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
288    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
289    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
290
291    static _LIBCPP_CONSTEXPR const bool traps = false;
292    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
293    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
294};
295
296template <>
297class __libcpp_numeric_limits<float, true>
298{
299protected:
300    typedef float type;
301
302    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
303
304    static _LIBCPP_CONSTEXPR const bool is_signed = true;
305    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
306    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
307    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
308    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
309    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
310    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
311
312    static _LIBCPP_CONSTEXPR const bool is_integer = false;
313    static _LIBCPP_CONSTEXPR const bool is_exact = false;
314    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
315    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
316    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
317
318    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
319    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
320    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
321    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
322
323    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
324    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
325    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
326    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
327    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
328    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
329    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
330    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
331    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
332
333    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
334    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
335    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
336
337    static _LIBCPP_CONSTEXPR const bool traps = false;
338#if (defined(__arm__) || defined(__aarch64__))
339    static _LIBCPP_CONSTEXPR const bool tinyness_before = true;
340#else
341    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
342#endif
343    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
344};
345
346template <>
347class __libcpp_numeric_limits<double, true>
348{
349protected:
350    typedef double type;
351
352    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
353
354    static _LIBCPP_CONSTEXPR const bool is_signed = true;
355    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
356    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
357    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
358    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
359    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
360    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
361
362    static _LIBCPP_CONSTEXPR const bool is_integer = false;
363    static _LIBCPP_CONSTEXPR const bool is_exact = false;
364    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
365    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
366    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
367
368    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
369    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
370    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
371    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
372
373    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
374    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
375    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
376    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
377    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
378    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
379    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
380    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
381    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
382
383    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
384    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
385    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
386
387    static _LIBCPP_CONSTEXPR const bool traps = false;
388#if (defined(__arm__) || defined(__aarch64__))
389    static _LIBCPP_CONSTEXPR const bool tinyness_before = true;
390#else
391    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
392#endif
393    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
394};
395
396template <>
397class __libcpp_numeric_limits<long double, true>
398{
399protected:
400    typedef long double type;
401
402    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
403
404    static _LIBCPP_CONSTEXPR const bool is_signed = true;
405    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
406    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
407    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103l)/100000l;
408    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
409    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
410    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
411
412    static _LIBCPP_CONSTEXPR const bool is_integer = false;
413    static _LIBCPP_CONSTEXPR const bool is_exact = false;
414    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
415    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
416    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5L;}
417
418    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
419    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
420    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
421    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
422
423    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
424    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
425    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
426    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
427    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
428    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
429    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
430    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
431    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
432
433#if defined(__powerpc__) && defined(__LONG_DOUBLE_IBM128__)
434    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
435#else
436    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
437#endif
438    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
439    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
440
441    static _LIBCPP_CONSTEXPR const bool traps = false;
442#if (defined(__arm__) || defined(__aarch64__))
443    static _LIBCPP_CONSTEXPR const bool tinyness_before = true;
444#else
445    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
446#endif
447    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
448};
449
450template <class _Tp>
451class _LIBCPP_TEMPLATE_VIS numeric_limits
452    : private __libcpp_numeric_limits<__remove_cv_t<_Tp> >
453{
454    typedef __libcpp_numeric_limits<__remove_cv_t<_Tp> > __base;
455    typedef typename __base::type type;
456public:
457    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
458    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
459    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
460    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
461
462    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
463    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
464    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
465    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
466    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
467    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
468    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
469    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
470    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
471
472    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
473    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
474    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
475    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
476
477    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
478    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
479    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
480    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
481    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
482    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
483    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
484    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
485    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
486
487    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
488    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
489    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
490
491    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
492    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
493    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
494};
495
496template <class _Tp>
497    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
498template <class _Tp>
499    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
500template <class _Tp>
501    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
502template <class _Tp>
503    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
504template <class _Tp>
505    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
506template <class _Tp>
507    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
508template <class _Tp>
509    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
510template <class _Tp>
511    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
512template <class _Tp>
513    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
514template <class _Tp>
515    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
516template <class _Tp>
517    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
518template <class _Tp>
519    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
520template <class _Tp>
521    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
522template <class _Tp>
523    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
524template <class _Tp>
525    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
526template <class _Tp>
527    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
528template <class _Tp>
529    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
530template <class _Tp>
531    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
532template <class _Tp>
533    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
534template <class _Tp>
535    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
536template <class _Tp>
537    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
538template <class _Tp>
539    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
540template <class _Tp>
541    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
542
543template <class _Tp>
544class _LIBCPP_TEMPLATE_VIS numeric_limits<const _Tp>
545    : private numeric_limits<_Tp>
546{
547    typedef numeric_limits<_Tp> __base;
548    typedef _Tp type;
549public:
550    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
551    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
552    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
553    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
554
555    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
556    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
557    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
558    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
559    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
560    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
561    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
562    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
563    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
564
565    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
566    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
567    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
568    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
569
570    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
571    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
572    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
573    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
574    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
575    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
576    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
577    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
578    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
579
580    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
581    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
582    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
583
584    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
585    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
586    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
587};
588
589template <class _Tp>
590    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
591template <class _Tp>
592    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
593template <class _Tp>
594    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
595template <class _Tp>
596    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
597template <class _Tp>
598    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
599template <class _Tp>
600    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
601template <class _Tp>
602    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
603template <class _Tp>
604    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
605template <class _Tp>
606    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
607template <class _Tp>
608    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
609template <class _Tp>
610    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
611template <class _Tp>
612    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
613template <class _Tp>
614    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
615template <class _Tp>
616    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
617template <class _Tp>
618    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
619template <class _Tp>
620    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
621template <class _Tp>
622    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
623template <class _Tp>
624    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
625template <class _Tp>
626    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
627template <class _Tp>
628    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
629template <class _Tp>
630    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
631template <class _Tp>
632    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
633template <class _Tp>
634    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
635
636template <class _Tp>
637class _LIBCPP_TEMPLATE_VIS numeric_limits<volatile _Tp>
638    : private numeric_limits<_Tp>
639{
640    typedef numeric_limits<_Tp> __base;
641    typedef _Tp type;
642public:
643    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
644    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
645    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
646    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
647
648    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
649    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
650    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
651    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
652    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
653    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
654    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
655    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
656    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
657
658    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
659    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
660    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
661    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
662
663    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
664    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
665    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
666    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
667    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
668    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
669    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
670    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
671    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
672
673    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
674    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
675    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
676
677    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
678    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
679    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
680};
681
682template <class _Tp>
683    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
684template <class _Tp>
685    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
686template <class _Tp>
687    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
688template <class _Tp>
689    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
690template <class _Tp>
691    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
692template <class _Tp>
693    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
694template <class _Tp>
695    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
696template <class _Tp>
697    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
698template <class _Tp>
699    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
700template <class _Tp>
701    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
702template <class _Tp>
703    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
704template <class _Tp>
705    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
706template <class _Tp>
707    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
708template <class _Tp>
709    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
710template <class _Tp>
711    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
712template <class _Tp>
713    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
714template <class _Tp>
715    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
716template <class _Tp>
717    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
718template <class _Tp>
719    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
720template <class _Tp>
721    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
722template <class _Tp>
723    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
724template <class _Tp>
725    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
726template <class _Tp>
727    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
728
729template <class _Tp>
730class _LIBCPP_TEMPLATE_VIS numeric_limits<const volatile _Tp>
731    : private numeric_limits<_Tp>
732{
733    typedef numeric_limits<_Tp> __base;
734    typedef _Tp type;
735public:
736    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
737    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
738    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
739    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
740
741    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
742    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
743    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
744    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
745    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
746    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
747    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
748    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
749    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
750
751    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
752    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
753    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
754    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
755
756    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
757    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
758    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
759    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
760    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
761    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
762    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
763    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
764    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
765
766    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
767    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
768    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
769
770    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
771    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
772    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
773};
774
775template <class _Tp>
776    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
777template <class _Tp>
778    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
779template <class _Tp>
780    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
781template <class _Tp>
782    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
783template <class _Tp>
784    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
785template <class _Tp>
786    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
787template <class _Tp>
788    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
789template <class _Tp>
790    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
791template <class _Tp>
792    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
793template <class _Tp>
794    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
795template <class _Tp>
796    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
797template <class _Tp>
798    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
799template <class _Tp>
800    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
801template <class _Tp>
802    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
803template <class _Tp>
804    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
805template <class _Tp>
806    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
807template <class _Tp>
808    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
809template <class _Tp>
810    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
811template <class _Tp>
812    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
813template <class _Tp>
814    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
815template <class _Tp>
816    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
817template <class _Tp>
818    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
819template <class _Tp>
820    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
821
822_LIBCPP_END_NAMESPACE_STD
823
824_LIBCPP_POP_MACROS
825
826#if !defined(_LIBCPP_REMOVE_TRANSITIVE_INCLUDES) && _LIBCPP_STD_VER <= 20
827#  include <type_traits>
828#endif
829
830#endif // _LIBCPP_LIMITS
831