limits revision 278724 
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(_LIBCPP_MSVCRT)
115#include "support/win32/limits_win32.h"
116#endif // _LIBCPP_MSVCRT
117
118#if defined(__IBMCPP__)
119#include "support/ibm/limits.h"
120#endif // __IBMCPP__
121
122_LIBCPP_BEGIN_NAMESPACE_STD
123
124enum float_round_style
125{
126    round_indeterminate       = -1,
127    round_toward_zero         =  0,
128    round_to_nearest          =  1,
129    round_toward_infinity     =  2,
130    round_toward_neg_infinity =  3
131};
132
133enum float_denorm_style
134{
135    denorm_indeterminate = -1,
136    denorm_absent = 0,
137    denorm_present = 1
138};
139
140template <class _Tp, bool = is_arithmetic<_Tp>::value>
141class __libcpp_numeric_limits
142{
143protected:
144    typedef _Tp type;
145
146    static _LIBCPP_CONSTEXPR const  bool is_specialized = false;
147    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return type();}
148    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return type();}
149    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return type();}
150
151    static _LIBCPP_CONSTEXPR const int  digits = 0;
152    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
153    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
154    static _LIBCPP_CONSTEXPR const bool is_signed = false;
155    static _LIBCPP_CONSTEXPR const bool is_integer = false;
156    static _LIBCPP_CONSTEXPR const bool is_exact = false;
157    static _LIBCPP_CONSTEXPR const int  radix = 0;
158    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type();}
159    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type();}
160
161    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
162    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
163    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
164    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
165
166    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
167    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
168    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
169    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
170    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
171    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type();}
172    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type();}
173    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type();}
174    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type();}
175
176    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
177    static _LIBCPP_CONSTEXPR const bool is_bounded = false;
178    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
179
180    static _LIBCPP_CONSTEXPR const bool traps = false;
181    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
182    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
183};
184
185template <class _Tp, int digits, bool is_signed>
186struct __libcpp_compute_min
187{
188    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(_Tp(1) << digits);
189};
190
191template <class _Tp, int digits>
192struct __libcpp_compute_min<_Tp, digits, false>
193{
194    static _LIBCPP_CONSTEXPR const _Tp value = _Tp(0);
195};
196
197template <class _Tp>
198class __libcpp_numeric_limits<_Tp, true>
199{
200protected:
201    typedef _Tp type;
202
203    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
204
205    static _LIBCPP_CONSTEXPR const bool is_signed = type(-1) < type(0);
206    static _LIBCPP_CONSTEXPR const int  digits = static_cast<int>(sizeof(type) * __CHAR_BIT__ - is_signed);
207    static _LIBCPP_CONSTEXPR const int  digits10 = digits * 3 / 10;
208    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
209    static _LIBCPP_CONSTEXPR const type __min = __libcpp_compute_min<type, digits, is_signed>::value;
210    static _LIBCPP_CONSTEXPR const type __max = is_signed ? type(type(~0) ^ __min) : type(~0);
211    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
212    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
213    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
214
215    static _LIBCPP_CONSTEXPR const bool is_integer = true;
216    static _LIBCPP_CONSTEXPR const bool is_exact = true;
217    static _LIBCPP_CONSTEXPR const int  radix = 2;
218    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
219    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
220
221    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
222    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
223    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
224    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
225
226    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
227    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
228    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
229    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
230    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
231    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
232    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
233    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
234    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
235
236    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
237    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
238    static _LIBCPP_CONSTEXPR const bool is_modulo = !_VSTD::is_signed<_Tp>::value;
239
240#if defined(__i386__) || defined(__x86_64__) || defined(__pnacl__)
241    static _LIBCPP_CONSTEXPR const bool traps = true;
242#else
243    static _LIBCPP_CONSTEXPR const bool traps = false;
244#endif
245    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
246    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
247};
248
249template <>
250class __libcpp_numeric_limits<bool, true>
251{
252protected:
253    typedef bool type;
254
255    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
256
257    static _LIBCPP_CONSTEXPR const bool is_signed = false;
258    static _LIBCPP_CONSTEXPR const int  digits = 1;
259    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
260    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
261    static _LIBCPP_CONSTEXPR const type __min = false;
262    static _LIBCPP_CONSTEXPR const type __max = true;
263    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
264    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
265    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
266
267    static _LIBCPP_CONSTEXPR const bool is_integer = true;
268    static _LIBCPP_CONSTEXPR const bool is_exact = true;
269    static _LIBCPP_CONSTEXPR const int  radix = 2;
270    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
271    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
272
273    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
274    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
275    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
276    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
277
278    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
279    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
280    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
281    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
282    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
283    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
284    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
285    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
286    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
287
288    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
289    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
290    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
291
292    static _LIBCPP_CONSTEXPR const bool traps = false;
293    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
294    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
295};
296
297template <>
298class __libcpp_numeric_limits<float, true>
299{
300protected:
301    typedef float type;
302
303    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
304
305    static _LIBCPP_CONSTEXPR const bool is_signed = true;
306    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
307    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
308    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
309    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
310    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
311    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
312
313    static _LIBCPP_CONSTEXPR const bool is_integer = false;
314    static _LIBCPP_CONSTEXPR const bool is_exact = false;
315    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
316    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
317    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
318
319    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
320    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
321    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
322    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
323
324    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
325    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
326    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
327    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
328    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
329    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
330    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
331    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
332    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
333
334    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
335    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
336    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
337
338    static _LIBCPP_CONSTEXPR const bool traps = false;
339    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
340    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
341};
342
343template <>
344class __libcpp_numeric_limits<double, true>
345{
346protected:
347    typedef double type;
348
349    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
350
351    static _LIBCPP_CONSTEXPR const bool is_signed = true;
352    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
353    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
354    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
355    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
356    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
357    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
358
359    static _LIBCPP_CONSTEXPR const bool is_integer = false;
360    static _LIBCPP_CONSTEXPR const bool is_exact = false;
361    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
362    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
363    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
364
365    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
366    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
367    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
368    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
369
370    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
371    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
372    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
373    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
374    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
375    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
376    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
377    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
378    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
379
380    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
381    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
382    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
383
384    static _LIBCPP_CONSTEXPR const bool traps = false;
385    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
386    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
387};
388
389template <>
390class __libcpp_numeric_limits<long double, true>
391{
392protected:
393    typedef long double type;
394
395    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
396
397    static _LIBCPP_CONSTEXPR const bool is_signed = true;
398    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
399    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
400    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
401    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
402    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
403    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
404
405    static _LIBCPP_CONSTEXPR const bool is_integer = false;
406    static _LIBCPP_CONSTEXPR const bool is_exact = false;
407    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
408    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
409    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
410
411    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
412    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
413    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
414    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
415
416    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
417    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
418    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
419    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
420    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
421    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
422    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
423    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
424    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
425
426#if (defined(__ppc__) || defined(__ppc64__))
427    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
428#else
429    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
430#endif
431    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
432    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
433
434    static _LIBCPP_CONSTEXPR const bool traps = false;
435    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
436    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
437};
438
439template <class _Tp>
440class _LIBCPP_TYPE_VIS_ONLY numeric_limits
441    : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
442{
443    typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
444    typedef typename __base::type type;
445public:
446    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
447    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
448    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
449    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
450
451    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
452    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
453    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
454    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
455    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
456    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
457    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
458    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
459    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
460
461    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
462    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
463    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
464    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
465
466    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
467    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
468    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
469    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
470    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
471    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
472    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
473    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
474    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
475
476    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
477    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
478    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
479
480    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
481    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
482    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
483};
484
485template <class _Tp>
486    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
487template <class _Tp>
488    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
489template <class _Tp>
490    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
491template <class _Tp>
492    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
493template <class _Tp>
494    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
495template <class _Tp>
496    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
497template <class _Tp>
498    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
499template <class _Tp>
500    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
501template <class _Tp>
502    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
503template <class _Tp>
504    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
505template <class _Tp>
506    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
507template <class _Tp>
508    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
509template <class _Tp>
510    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
511template <class _Tp>
512    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
513template <class _Tp>
514    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
515template <class _Tp>
516    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
517template <class _Tp>
518    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
519template <class _Tp>
520    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
521template <class _Tp>
522    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
523template <class _Tp>
524    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
525template <class _Tp>
526    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
527template <class _Tp>
528    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
529template <class _Tp>
530    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
531
532template <class _Tp>
533class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const _Tp>
534    : private numeric_limits<_Tp>
535{
536    typedef numeric_limits<_Tp> __base;
537    typedef _Tp type;
538public:
539    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
540    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
541    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
542    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
543
544    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
545    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
546    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
547    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
548    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
549    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
550    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
551    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
552    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
553
554    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
555    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
556    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
557    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
558
559    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
560    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
561    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
562    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
563    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
564    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
565    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
566    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
567    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
568
569    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
570    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
571    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
572
573    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
574    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
575    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
576};
577
578template <class _Tp>
579    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
580template <class _Tp>
581    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
582template <class _Tp>
583    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
584template <class _Tp>
585    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
586template <class _Tp>
587    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
588template <class _Tp>
589    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
590template <class _Tp>
591    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
592template <class _Tp>
593    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
594template <class _Tp>
595    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
596template <class _Tp>
597    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
598template <class _Tp>
599    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
600template <class _Tp>
601    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
602template <class _Tp>
603    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
604template <class _Tp>
605    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
606template <class _Tp>
607    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
608template <class _Tp>
609    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
610template <class _Tp>
611    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
612template <class _Tp>
613    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
614template <class _Tp>
615    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
616template <class _Tp>
617    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
618template <class _Tp>
619    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
620template <class _Tp>
621    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
622template <class _Tp>
623    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
624
625template <class _Tp>
626class _LIBCPP_TYPE_VIS_ONLY numeric_limits<volatile _Tp>
627    : private numeric_limits<_Tp>
628{
629    typedef numeric_limits<_Tp> __base;
630    typedef _Tp type;
631public:
632    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
633    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
634    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
635    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
636
637    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
638    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
639    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
640    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
641    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
642    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
643    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
644    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
645    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
646
647    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
648    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
649    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
650    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
651
652    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
653    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
654    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
655    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
656    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
657    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
658    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
659    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
660    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
661
662    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
663    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
664    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
665
666    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
667    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
668    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
669};
670
671template <class _Tp>
672    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
673template <class _Tp>
674    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
675template <class _Tp>
676    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
677template <class _Tp>
678    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
679template <class _Tp>
680    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
681template <class _Tp>
682    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
683template <class _Tp>
684    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
685template <class _Tp>
686    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
687template <class _Tp>
688    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
689template <class _Tp>
690    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
691template <class _Tp>
692    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
693template <class _Tp>
694    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
695template <class _Tp>
696    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
697template <class _Tp>
698    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
699template <class _Tp>
700    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
701template <class _Tp>
702    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
703template <class _Tp>
704    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
705template <class _Tp>
706    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
707template <class _Tp>
708    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
709template <class _Tp>
710    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
711template <class _Tp>
712    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
713template <class _Tp>
714    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
715template <class _Tp>
716    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
717
718template <class _Tp>
719class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const volatile _Tp>
720    : private numeric_limits<_Tp>
721{
722    typedef numeric_limits<_Tp> __base;
723    typedef _Tp type;
724public:
725    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
726    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
727    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
728    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
729
730    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
731    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
732    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
733    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
734    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
735    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
736    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
737    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
738    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
739
740    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
741    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
742    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
743    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
744
745    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
746    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
747    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
748    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
749    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
750    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
751    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
752    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
753    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
754
755    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
756    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
757    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
758
759    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
760    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
761    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
762};
763
764template <class _Tp>
765    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
766template <class _Tp>
767    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
768template <class _Tp>
769    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
770template <class _Tp>
771    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
772template <class _Tp>
773    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
774template <class _Tp>
775    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
776template <class _Tp>
777    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
778template <class _Tp>
779    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
780template <class _Tp>
781    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
782template <class _Tp>
783    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
784template <class _Tp>
785    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
786template <class _Tp>
787    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
788template <class _Tp>
789    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
790template <class _Tp>
791    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
792template <class _Tp>
793    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
794template <class _Tp>
795    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
796template <class _Tp>
797    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
798template <class _Tp>
799    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
800template <class _Tp>
801    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
802template <class _Tp>
803    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
804template <class _Tp>
805    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
806template <class _Tp>
807    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
808template <class _Tp>
809    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
810
811_LIBCPP_END_NAMESPACE_STD
812
813#endif  // _LIBCPP_LIMITS
814