limits revision 249989 
1// -*- C++ -*-
2//===---------------------------- limits ----------------------------------===//
3//
4//                     The LLVM Compiler Infrastructure
5//
6// This file is dual licensed under the MIT and the University of Illinois Open
7// Source Licenses. See LICENSE.TXT for details.
8//
9//===----------------------------------------------------------------------===//
10
11#ifndef _LIBCPP_LIMITS
12#define _LIBCPP_LIMITS
13
14/*
15    limits synopsis
16
17namespace std
18{
19
20template<class T>
21class numeric_limits
22{
23public:
24    static constexpr bool is_specialized = false;
25    static constexpr T min() noexcept;
26    static constexpr T max() noexcept;
27    static constexpr T lowest() noexcept;
28
29    static constexpr int  digits = 0;
30    static constexpr int  digits10 = 0;
31    static constexpr int  max_digits10 = 0;
32    static constexpr bool is_signed = false;
33    static constexpr bool is_integer = false;
34    static constexpr bool is_exact = false;
35    static constexpr int  radix = 0;
36    static constexpr T epsilon() noexcept;
37    static constexpr T round_error() noexcept;
38
39    static constexpr int  min_exponent = 0;
40    static constexpr int  min_exponent10 = 0;
41    static constexpr int  max_exponent = 0;
42    static constexpr int  max_exponent10 = 0;
43
44    static constexpr bool has_infinity = false;
45    static constexpr bool has_quiet_NaN = false;
46    static constexpr bool has_signaling_NaN = false;
47    static constexpr float_denorm_style has_denorm = denorm_absent;
48    static constexpr bool has_denorm_loss = false;
49    static constexpr T infinity() noexcept;
50    static constexpr T quiet_NaN() noexcept;
51    static constexpr T signaling_NaN() noexcept;
52    static constexpr T denorm_min() noexcept;
53
54    static constexpr bool is_iec559 = false;
55    static constexpr bool is_bounded = false;
56    static constexpr bool is_modulo = false;
57
58    static constexpr bool traps = false;
59    static constexpr bool tinyness_before = false;
60    static constexpr float_round_style round_style = round_toward_zero;
61};
62
63enum float_round_style
64{
65    round_indeterminate       = -1,
66    round_toward_zero         =  0,
67    round_to_nearest          =  1,
68    round_toward_infinity     =  2,
69    round_toward_neg_infinity =  3
70};
71
72enum float_denorm_style
73{
74    denorm_indeterminate = -1,
75    denorm_absent = 0,
76    denorm_present = 1
77};
78
79template<> class numeric_limits<cv bool>;
80
81template<> class numeric_limits<cv char>;
82template<> class numeric_limits<cv signed char>;
83template<> class numeric_limits<cv unsigned char>;
84template<> class numeric_limits<cv wchar_t>;
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#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
106#pragma GCC system_header
107#endif
108
109#include <__config>
110#include <type_traits>
111
112#include <__undef_min_max>
113
114#if defined(_MSC_VER)
115#include "support/win32/limits_win32.h"
116#endif // _MSC_VER
117
118_LIBCPP_BEGIN_NAMESPACE_STD
119
120enum float_round_style
121{
122    round_indeterminate       = -1,
123    round_toward_zero         =  0,
124    round_to_nearest          =  1,
125    round_toward_infinity     =  2,
126    round_toward_neg_infinity =  3
127};
128
129enum float_denorm_style
130{
131    denorm_indeterminate = -1,
132    denorm_absent = 0,
133    denorm_present = 1
134};
135
136template <class _Tp, bool = is_arithmetic<_Tp>::value>
137class __libcpp_numeric_limits
138{
139protected:
140    typedef _Tp type;
141
142    static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
143    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
144    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
145    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
146
147    static _LIBCPP_CONSTEXPR const int  digits = 0;
148    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
149    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
150    static _LIBCPP_CONSTEXPR const bool is_signed = false;
151    static _LIBCPP_CONSTEXPR const bool is_integer = false;
152    static _LIBCPP_CONSTEXPR const bool is_exact = false;
153    static _LIBCPP_CONSTEXPR const int  radix = 0;
154    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
155    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
156
157    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
158    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
159    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
160    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
161
162    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
163    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
164    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
165    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
166    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
167    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
168    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
169    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
170    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
171
172    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
173    static _LIBCPP_CONSTEXPR const bool is_bounded = false;
174    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
175
176    static _LIBCPP_CONSTEXPR const bool traps = false;
177    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
178    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
179};
180
181template <class _Tp, int digits, bool is_signed>
182struct __libcpp_compute_min
183{
184    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << digits);
185};
186
187template <class _Tp, int digits>
188struct __libcpp_compute_min<_Tp, digits, false>
189{
190    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
191};
192
193template <class _Tp>
194class __libcpp_numeric_limits<_Tp, true>
195{
196protected:
197    typedef _Tp type;
198
199    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
200
201    static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
202    static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
203    static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
204    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
205    static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
206    static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
207    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
208    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
209    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
210
211    static _LIBCPP_CONSTEXPR const bool is_integer = true;
212    static _LIBCPP_CONSTEXPR const bool is_exact = true;
213    static _LIBCPP_CONSTEXPR const int  radix = 2;
214    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
215    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
216
217    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
218    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
219    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
220    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
221
222    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
223    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
224    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
225    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
226    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
227    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
228    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
229    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
230    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
231
232    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
233    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
234    static _LIBCPP_CONSTEXPR const bool is_modulo = true;
235
236#if __i386__ || __x86_64__
237    static _LIBCPP_CONSTEXPR const bool traps = true;
238#else
239    static _LIBCPP_CONSTEXPR const bool traps = false;
240#endif
241    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
242    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
243};
244
245template <>
246class __libcpp_numeric_limits<bool, true>
247{
248protected:
249    typedef bool type;
250
251    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
252
253    static _LIBCPP_CONSTEXPR const bool is_signed = false;
254    static _LIBCPP_CONSTEXPR const int  digits = 1;
255    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
256    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
257    static _LIBCPP_CONSTEXPR const type __min = false;
258    static _LIBCPP_CONSTEXPR const type __max = true;
259    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
260    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
261    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
262
263    static _LIBCPP_CONSTEXPR const bool is_integer = true;
264    static _LIBCPP_CONSTEXPR const bool is_exact = true;
265    static _LIBCPP_CONSTEXPR const int  radix = 2;
266    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
267    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
268
269    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
270    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
271    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
272    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
273
274    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
275    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
276    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
277    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
278    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
279    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
280    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
281    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
282    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
283
284    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
285    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
286    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
287
288    static _LIBCPP_CONSTEXPR const bool traps = false;
289    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
290    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
291};
292
293template <>
294class __libcpp_numeric_limits<float, true>
295{
296protected:
297    typedef float type;
298
299    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
300
301    static _LIBCPP_CONSTEXPR const bool is_signed = true;
302    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
303    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
304    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
305    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
306    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
307    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
308
309    static _LIBCPP_CONSTEXPR const bool is_integer = false;
310    static _LIBCPP_CONSTEXPR const bool is_exact = false;
311    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
312    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
313    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
314
315    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
316    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
317    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
318    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
319
320    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
321    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
322    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
323    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
324    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
325    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
326    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
327    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
328    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
329
330    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
331    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
332    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
333
334    static _LIBCPP_CONSTEXPR const bool traps = false;
335    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
336    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
337};
338
339template <>
340class __libcpp_numeric_limits<double, true>
341{
342protected:
343    typedef double type;
344
345    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
346
347    static _LIBCPP_CONSTEXPR const bool is_signed = true;
348    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
349    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
350    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
351    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
352    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
353    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
354
355    static _LIBCPP_CONSTEXPR const bool is_integer = false;
356    static _LIBCPP_CONSTEXPR const bool is_exact = false;
357    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
358    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
359    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
360
361    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
362    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
363    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
364    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
365
366    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
367    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
368    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
369    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
370    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
371    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
372    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
373    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
374    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
375
376    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
377    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
378    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
379
380    static _LIBCPP_CONSTEXPR const bool traps = false;
381    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
382    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
383};
384
385template <>
386class __libcpp_numeric_limits<long double, true>
387{
388protected:
389    typedef long double type;
390
391    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
392
393    static _LIBCPP_CONSTEXPR const bool is_signed = true;
394    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
395    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
396    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
397    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
398    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
399    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
400
401    static _LIBCPP_CONSTEXPR const bool is_integer = false;
402    static _LIBCPP_CONSTEXPR const bool is_exact = false;
403    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
404    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
405    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
406
407    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
408    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
409    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
410    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
411
412    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
413    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
414    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
415    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
416    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
417    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
418    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
419    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
420    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
421
422#if (defined(__ppc__) || defined(__ppc64__))
423    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
424#else
425    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
426#endif
427    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
428    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
429
430    static _LIBCPP_CONSTEXPR const bool traps = false;
431    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
432    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
433};
434
435template <class _Tp>
436class _LIBCPP_TYPE_VIS numeric_limits
437    : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
438{
439    typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
440    typedef typename __base::type type;
441public:
442    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
443    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
444    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
445    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
446
447    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
448    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
449    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
450    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
451    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
452    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
453    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
454    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
455    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
456
457    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
458    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
459    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
460    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
461
462    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
463    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
464    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
465    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
466    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
467    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
468    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
469    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
470    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
471
472    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
473    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
474    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
475
476    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
477    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
478    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
479};
480
481template <class _Tp>
482    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
483template <class _Tp>
484    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
485template <class _Tp>
486    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
487template <class _Tp>
488    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
489template <class _Tp>
490    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
491template <class _Tp>
492    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
493template <class _Tp>
494    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
495template <class _Tp>
496    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
497template <class _Tp>
498    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
499template <class _Tp>
500    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
501template <class _Tp>
502    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
503template <class _Tp>
504    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
505template <class _Tp>
506    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
507template <class _Tp>
508    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
509template <class _Tp>
510    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
511template <class _Tp>
512    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
513template <class _Tp>
514    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
515template <class _Tp>
516    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
517template <class _Tp>
518    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
519template <class _Tp>
520    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
521template <class _Tp>
522    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
523template <class _Tp>
524    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
525template <class _Tp>
526    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
527
528template <class _Tp>
529class _LIBCPP_TYPE_VIS numeric_limits<const _Tp>
530    : private numeric_limits<_Tp>
531{
532    typedef numeric_limits<_Tp> __base;
533    typedef _Tp type;
534public:
535    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
536    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
537    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
538    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
539
540    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
541    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
542    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
543    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
544    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
545    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
546    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
547    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
548    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
549
550    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
551    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
552    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
553    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
554
555    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
556    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
557    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
558    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
559    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
560    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
561    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
562    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
563    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
564
565    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
566    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
567    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
568
569    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
570    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
571    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
572};
573
574template <class _Tp>
575    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
576template <class _Tp>
577    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
578template <class _Tp>
579    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
580template <class _Tp>
581    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
582template <class _Tp>
583    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
584template <class _Tp>
585    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
586template <class _Tp>
587    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
588template <class _Tp>
589    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
590template <class _Tp>
591    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
592template <class _Tp>
593    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
594template <class _Tp>
595    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
596template <class _Tp>
597    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
598template <class _Tp>
599    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
600template <class _Tp>
601    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
602template <class _Tp>
603    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
604template <class _Tp>
605    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
606template <class _Tp>
607    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
608template <class _Tp>
609    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
610template <class _Tp>
611    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
612template <class _Tp>
613    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
614template <class _Tp>
615    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
616template <class _Tp>
617    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
618template <class _Tp>
619    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
620
621template <class _Tp>
622class _LIBCPP_TYPE_VIS numeric_limits<volatile _Tp>
623    : private numeric_limits<_Tp>
624{
625    typedef numeric_limits<_Tp> __base;
626    typedef _Tp type;
627public:
628    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
629    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
630    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
631    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
632
633    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
634    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
635    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
636    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
637    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
638    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
639    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
640    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
641    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
642
643    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
644    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
645    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
646    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
647
648    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
649    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
650    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
651    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
652    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
653    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
654    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
655    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
656    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
657
658    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
659    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
660    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
661
662    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
663    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
664    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
665};
666
667template <class _Tp>
668    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
669template <class _Tp>
670    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
671template <class _Tp>
672    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
673template <class _Tp>
674    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
675template <class _Tp>
676    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
677template <class _Tp>
678    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
679template <class _Tp>
680    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
681template <class _Tp>
682    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
683template <class _Tp>
684    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
685template <class _Tp>
686    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
687template <class _Tp>
688    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
689template <class _Tp>
690    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
691template <class _Tp>
692    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
693template <class _Tp>
694    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
695template <class _Tp>
696    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
697template <class _Tp>
698    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
699template <class _Tp>
700    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
701template <class _Tp>
702    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
703template <class _Tp>
704    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
705template <class _Tp>
706    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
707template <class _Tp>
708    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
709template <class _Tp>
710    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
711template <class _Tp>
712    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
713
714template <class _Tp>
715class _LIBCPP_TYPE_VIS numeric_limits<const volatile _Tp>
716    : private numeric_limits<_Tp>
717{
718    typedef numeric_limits<_Tp> __base;
719    typedef _Tp type;
720public:
721    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
722    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
723    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
724    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
725
726    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
727    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
728    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
729    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
730    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
731    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
732    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
733    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
734    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
735
736    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
737    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
738    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
739    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
740
741    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
742    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
743    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
744    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
745    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
746    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
747    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
748    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
749    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
750
751    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
752    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
753    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
754
755    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
756    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
757    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
758};
759
760template <class _Tp>
761    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
762template <class _Tp>
763    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
764template <class _Tp>
765    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
766template <class _Tp>
767    const int numeric_limits<const volatile _Tp>::max_digits10;
768template <class _Tp>
769    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
770template <class _Tp>
771    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
772template <class _Tp>
773    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
774template <class _Tp>
775    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
776template <class _Tp>
777    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
778template <class _Tp>
779    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
780template <class _Tp>
781    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
782template <class _Tp>
783    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
784template <class _Tp>
785    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
786template <class _Tp>
787    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
788template <class _Tp>
789    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
790template <class _Tp>
791    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
792template <class _Tp>
793    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
794template <class _Tp>
795    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
796template <class _Tp>
797    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
798template <class _Tp>
799    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
800template <class _Tp>
801    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
802template <class _Tp>
803    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
804template <class _Tp>
805    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
806
807_LIBCPP_END_NAMESPACE_STD
808
809#endif  // _LIBCPP_LIMITS
810