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    defined(__wasm__)
242    static _LIBCPP_CONSTEXPR const bool traps = true;
243#else
244    static _LIBCPP_CONSTEXPR const bool traps = false;
245#endif
246    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
247    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
248};
249
250template <>
251class __libcpp_numeric_limits<bool, true>
252{
253protected:
254    typedef bool type;
255
256    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
257
258    static _LIBCPP_CONSTEXPR const bool is_signed = false;
259    static _LIBCPP_CONSTEXPR const int  digits = 1;
260    static _LIBCPP_CONSTEXPR const int  digits10 = 0;
261    static _LIBCPP_CONSTEXPR const int  max_digits10 = 0;
262    static _LIBCPP_CONSTEXPR const type __min = false;
263    static _LIBCPP_CONSTEXPR const type __max = true;
264    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __min;}
265    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __max;}
266    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return min();}
267
268    static _LIBCPP_CONSTEXPR const bool is_integer = true;
269    static _LIBCPP_CONSTEXPR const bool is_exact = true;
270    static _LIBCPP_CONSTEXPR const int  radix = 2;
271    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return type(0);}
272    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return type(0);}
273
274    static _LIBCPP_CONSTEXPR const int  min_exponent = 0;
275    static _LIBCPP_CONSTEXPR const int  min_exponent10 = 0;
276    static _LIBCPP_CONSTEXPR const int  max_exponent = 0;
277    static _LIBCPP_CONSTEXPR const int  max_exponent10 = 0;
278
279    static _LIBCPP_CONSTEXPR const bool has_infinity = false;
280    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = false;
281    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = false;
282    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_absent;
283    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
284    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return type(0);}
285    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return type(0);}
286    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return type(0);}
287    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return type(0);}
288
289    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
290    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
291    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
292
293    static _LIBCPP_CONSTEXPR const bool traps = false;
294    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
295    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_toward_zero;
296};
297
298template <>
299class __libcpp_numeric_limits<float, true>
300{
301protected:
302    typedef float type;
303
304    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
305
306    static _LIBCPP_CONSTEXPR const bool is_signed = true;
307    static _LIBCPP_CONSTEXPR const int  digits = __FLT_MANT_DIG__;
308    static _LIBCPP_CONSTEXPR const int  digits10 = __FLT_DIG__;
309    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
310    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __FLT_MIN__;}
311    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __FLT_MAX__;}
312    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
313
314    static _LIBCPP_CONSTEXPR const bool is_integer = false;
315    static _LIBCPP_CONSTEXPR const bool is_exact = false;
316    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
317    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __FLT_EPSILON__;}
318    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5F;}
319
320    static _LIBCPP_CONSTEXPR const int  min_exponent = __FLT_MIN_EXP__;
321    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __FLT_MIN_10_EXP__;
322    static _LIBCPP_CONSTEXPR const int  max_exponent = __FLT_MAX_EXP__;
323    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __FLT_MAX_10_EXP__;
324
325    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
326    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
327    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
328    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
329    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
330    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_valf();}
331    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanf("");}
332    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansf("");}
333    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __FLT_DENORM_MIN__;}
334
335    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
336    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
337    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
338
339    static _LIBCPP_CONSTEXPR const bool traps = false;
340    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
341    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
342};
343
344template <>
345class __libcpp_numeric_limits<double, true>
346{
347protected:
348    typedef double type;
349
350    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
351
352    static _LIBCPP_CONSTEXPR const bool is_signed = true;
353    static _LIBCPP_CONSTEXPR const int  digits = __DBL_MANT_DIG__;
354    static _LIBCPP_CONSTEXPR const int  digits10 = __DBL_DIG__;
355    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
356    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __DBL_MIN__;}
357    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __DBL_MAX__;}
358    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
359
360    static _LIBCPP_CONSTEXPR const bool is_integer = false;
361    static _LIBCPP_CONSTEXPR const bool is_exact = false;
362    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
363    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __DBL_EPSILON__;}
364    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
365
366    static _LIBCPP_CONSTEXPR const int  min_exponent = __DBL_MIN_EXP__;
367    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __DBL_MIN_10_EXP__;
368    static _LIBCPP_CONSTEXPR const int  max_exponent = __DBL_MAX_EXP__;
369    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __DBL_MAX_10_EXP__;
370
371    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
372    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
373    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
374    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
375    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
376    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_val();}
377    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nan("");}
378    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nans("");}
379    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __DBL_DENORM_MIN__;}
380
381    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
382    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
383    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
384
385    static _LIBCPP_CONSTEXPR const bool traps = false;
386    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
387    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
388};
389
390template <>
391class __libcpp_numeric_limits<long double, true>
392{
393protected:
394    typedef long double type;
395
396    static _LIBCPP_CONSTEXPR const bool is_specialized = true;
397
398    static _LIBCPP_CONSTEXPR const bool is_signed = true;
399    static _LIBCPP_CONSTEXPR const int  digits = __LDBL_MANT_DIG__;
400    static _LIBCPP_CONSTEXPR const int  digits10 = __LDBL_DIG__;
401    static _LIBCPP_CONSTEXPR const int  max_digits10 = 2+(digits * 30103)/100000;
402    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __LDBL_MIN__;}
403    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __LDBL_MAX__;}
404    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return -max();}
405
406    static _LIBCPP_CONSTEXPR const bool is_integer = false;
407    static _LIBCPP_CONSTEXPR const bool is_exact = false;
408    static _LIBCPP_CONSTEXPR const int  radix = __FLT_RADIX__;
409    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __LDBL_EPSILON__;}
410    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return 0.5;}
411
412    static _LIBCPP_CONSTEXPR const int  min_exponent = __LDBL_MIN_EXP__;
413    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __LDBL_MIN_10_EXP__;
414    static _LIBCPP_CONSTEXPR const int  max_exponent = __LDBL_MAX_EXP__;
415    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __LDBL_MAX_10_EXP__;
416
417    static _LIBCPP_CONSTEXPR const bool has_infinity = true;
418    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = true;
419    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = true;
420    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = denorm_present;
421    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = false;
422    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __builtin_huge_vall();}
423    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __builtin_nanl("");}
424    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __builtin_nansl("");}
425    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __LDBL_DENORM_MIN__;}
426
427#if (defined(__ppc__) || defined(__ppc64__))
428    static _LIBCPP_CONSTEXPR const bool is_iec559 = false;
429#else
430    static _LIBCPP_CONSTEXPR const bool is_iec559 = true;
431#endif
432    static _LIBCPP_CONSTEXPR const bool is_bounded = true;
433    static _LIBCPP_CONSTEXPR const bool is_modulo = false;
434
435    static _LIBCPP_CONSTEXPR const bool traps = false;
436    static _LIBCPP_CONSTEXPR const bool tinyness_before = false;
437    static _LIBCPP_CONSTEXPR const float_round_style round_style = round_to_nearest;
438};
439
440template <class _Tp>
441class _LIBCPP_TYPE_VIS_ONLY numeric_limits
442    : private __libcpp_numeric_limits<typename remove_cv<_Tp>::type>
443{
444    typedef __libcpp_numeric_limits<typename remove_cv<_Tp>::type> __base;
445    typedef typename __base::type type;
446public:
447    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
448    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
449    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
450    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
451
452    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
453    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
454    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
455    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
456    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
457    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
458    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
459    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
460    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
461
462    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
463    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
464    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
465    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
466
467    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
468    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
469    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
470    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
471    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
472    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
473    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
474    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
475    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
476
477    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
478    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
479    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
480
481    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
482    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
483    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
484};
485
486template <class _Tp>
487    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_specialized;
488template <class _Tp>
489    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits;
490template <class _Tp>
491    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::digits10;
492template <class _Tp>
493    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_digits10;
494template <class _Tp>
495    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_signed;
496template <class _Tp>
497    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_integer;
498template <class _Tp>
499    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_exact;
500template <class _Tp>
501    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::radix;
502template <class _Tp>
503    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent;
504template <class _Tp>
505    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::min_exponent10;
506template <class _Tp>
507    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent;
508template <class _Tp>
509    _LIBCPP_CONSTEXPR const int numeric_limits<_Tp>::max_exponent10;
510template <class _Tp>
511    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_infinity;
512template <class _Tp>
513    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_quiet_NaN;
514template <class _Tp>
515    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_signaling_NaN;
516template <class _Tp>
517    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<_Tp>::has_denorm;
518template <class _Tp>
519    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::has_denorm_loss;
520template <class _Tp>
521    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_iec559;
522template <class _Tp>
523    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_bounded;
524template <class _Tp>
525    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::is_modulo;
526template <class _Tp>
527    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::traps;
528template <class _Tp>
529    _LIBCPP_CONSTEXPR const bool numeric_limits<_Tp>::tinyness_before;
530template <class _Tp>
531    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<_Tp>::round_style;
532
533template <class _Tp>
534class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const _Tp>
535    : private numeric_limits<_Tp>
536{
537    typedef numeric_limits<_Tp> __base;
538    typedef _Tp type;
539public:
540    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
541    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
542    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
543    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
544
545    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
546    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
547    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
548    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
549    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
550    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
551    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
552    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
553    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
554
555    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
556    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
557    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
558    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
559
560    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
561    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
562    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
563    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
564    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
565    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
566    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
567    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
568    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
569
570    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
571    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
572    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
573
574    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
575    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
576    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
577};
578
579template <class _Tp>
580    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_specialized;
581template <class _Tp>
582    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits;
583template <class _Tp>
584    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::digits10;
585template <class _Tp>
586    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_digits10;
587template <class _Tp>
588    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_signed;
589template <class _Tp>
590    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_integer;
591template <class _Tp>
592    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_exact;
593template <class _Tp>
594    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::radix;
595template <class _Tp>
596    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent;
597template <class _Tp>
598    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::min_exponent10;
599template <class _Tp>
600    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent;
601template <class _Tp>
602    _LIBCPP_CONSTEXPR const int numeric_limits<const _Tp>::max_exponent10;
603template <class _Tp>
604    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_infinity;
605template <class _Tp>
606    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_quiet_NaN;
607template <class _Tp>
608    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_signaling_NaN;
609template <class _Tp>
610    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const _Tp>::has_denorm;
611template <class _Tp>
612    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::has_denorm_loss;
613template <class _Tp>
614    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_iec559;
615template <class _Tp>
616    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_bounded;
617template <class _Tp>
618    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::is_modulo;
619template <class _Tp>
620    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::traps;
621template <class _Tp>
622    _LIBCPP_CONSTEXPR const bool numeric_limits<const _Tp>::tinyness_before;
623template <class _Tp>
624    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const _Tp>::round_style;
625
626template <class _Tp>
627class _LIBCPP_TYPE_VIS_ONLY numeric_limits<volatile _Tp>
628    : private numeric_limits<_Tp>
629{
630    typedef numeric_limits<_Tp> __base;
631    typedef _Tp type;
632public:
633    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
634    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
635    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
636    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
637
638    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
639    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
640    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
641    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
642    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
643    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
644    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
645    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
646    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
647
648    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
649    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
650    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
651    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
652
653    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
654    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
655    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
656    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
657    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
658    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
659    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
660    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
661    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
662
663    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
664    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
665    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
666
667    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
668    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
669    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
670};
671
672template <class _Tp>
673    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_specialized;
674template <class _Tp>
675    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits;
676template <class _Tp>
677    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::digits10;
678template <class _Tp>
679    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_digits10;
680template <class _Tp>
681    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_signed;
682template <class _Tp>
683    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_integer;
684template <class _Tp>
685    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_exact;
686template <class _Tp>
687    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::radix;
688template <class _Tp>
689    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent;
690template <class _Tp>
691    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::min_exponent10;
692template <class _Tp>
693    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent;
694template <class _Tp>
695    _LIBCPP_CONSTEXPR const int numeric_limits<volatile _Tp>::max_exponent10;
696template <class _Tp>
697    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_infinity;
698template <class _Tp>
699    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_quiet_NaN;
700template <class _Tp>
701    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_signaling_NaN;
702template <class _Tp>
703    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<volatile _Tp>::has_denorm;
704template <class _Tp>
705    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::has_denorm_loss;
706template <class _Tp>
707    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_iec559;
708template <class _Tp>
709    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_bounded;
710template <class _Tp>
711    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::is_modulo;
712template <class _Tp>
713    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::traps;
714template <class _Tp>
715    _LIBCPP_CONSTEXPR const bool numeric_limits<volatile _Tp>::tinyness_before;
716template <class _Tp>
717    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<volatile _Tp>::round_style;
718
719template <class _Tp>
720class _LIBCPP_TYPE_VIS_ONLY numeric_limits<const volatile _Tp>
721    : private numeric_limits<_Tp>
722{
723    typedef numeric_limits<_Tp> __base;
724    typedef _Tp type;
725public:
726    static _LIBCPP_CONSTEXPR const bool is_specialized = __base::is_specialized;
727    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type min() _NOEXCEPT {return __base::min();}
728    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type max() _NOEXCEPT {return __base::max();}
729    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type lowest() _NOEXCEPT {return __base::lowest();}
730
731    static _LIBCPP_CONSTEXPR const int  digits = __base::digits;
732    static _LIBCPP_CONSTEXPR const int  digits10 = __base::digits10;
733    static _LIBCPP_CONSTEXPR const int  max_digits10 = __base::max_digits10;
734    static _LIBCPP_CONSTEXPR const bool is_signed = __base::is_signed;
735    static _LIBCPP_CONSTEXPR const bool is_integer = __base::is_integer;
736    static _LIBCPP_CONSTEXPR const bool is_exact = __base::is_exact;
737    static _LIBCPP_CONSTEXPR const int  radix = __base::radix;
738    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type epsilon() _NOEXCEPT {return __base::epsilon();}
739    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type round_error() _NOEXCEPT {return __base::round_error();}
740
741    static _LIBCPP_CONSTEXPR const int  min_exponent = __base::min_exponent;
742    static _LIBCPP_CONSTEXPR const int  min_exponent10 = __base::min_exponent10;
743    static _LIBCPP_CONSTEXPR const int  max_exponent = __base::max_exponent;
744    static _LIBCPP_CONSTEXPR const int  max_exponent10 = __base::max_exponent10;
745
746    static _LIBCPP_CONSTEXPR const bool has_infinity = __base::has_infinity;
747    static _LIBCPP_CONSTEXPR const bool has_quiet_NaN = __base::has_quiet_NaN;
748    static _LIBCPP_CONSTEXPR const bool has_signaling_NaN = __base::has_signaling_NaN;
749    static _LIBCPP_CONSTEXPR const float_denorm_style has_denorm = __base::has_denorm;
750    static _LIBCPP_CONSTEXPR const bool has_denorm_loss = __base::has_denorm_loss;
751    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type infinity() _NOEXCEPT {return __base::infinity();}
752    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type quiet_NaN() _NOEXCEPT {return __base::quiet_NaN();}
753    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type signaling_NaN() _NOEXCEPT {return __base::signaling_NaN();}
754    _LIBCPP_INLINE_VISIBILITY static _LIBCPP_CONSTEXPR type denorm_min() _NOEXCEPT {return __base::denorm_min();}
755
756    static _LIBCPP_CONSTEXPR const bool is_iec559 = __base::is_iec559;
757    static _LIBCPP_CONSTEXPR const bool is_bounded = __base::is_bounded;
758    static _LIBCPP_CONSTEXPR const bool is_modulo = __base::is_modulo;
759
760    static _LIBCPP_CONSTEXPR const bool traps = __base::traps;
761    static _LIBCPP_CONSTEXPR const bool tinyness_before = __base::tinyness_before;
762    static _LIBCPP_CONSTEXPR const float_round_style round_style = __base::round_style;
763};
764
765template <class _Tp>
766    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_specialized;
767template <class _Tp>
768    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits;
769template <class _Tp>
770    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::digits10;
771template <class _Tp>
772    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_digits10;
773template <class _Tp>
774    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_signed;
775template <class _Tp>
776    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_integer;
777template <class _Tp>
778    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_exact;
779template <class _Tp>
780    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::radix;
781template <class _Tp>
782    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent;
783template <class _Tp>
784    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::min_exponent10;
785template <class _Tp>
786    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent;
787template <class _Tp>
788    _LIBCPP_CONSTEXPR const int numeric_limits<const volatile _Tp>::max_exponent10;
789template <class _Tp>
790    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_infinity;
791template <class _Tp>
792    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_quiet_NaN;
793template <class _Tp>
794    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_signaling_NaN;
795template <class _Tp>
796    _LIBCPP_CONSTEXPR const float_denorm_style numeric_limits<const volatile _Tp>::has_denorm;
797template <class _Tp>
798    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::has_denorm_loss;
799template <class _Tp>
800    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_iec559;
801template <class _Tp>
802    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_bounded;
803template <class _Tp>
804    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::is_modulo;
805template <class _Tp>
806    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::traps;
807template <class _Tp>
808    _LIBCPP_CONSTEXPR const bool numeric_limits<const volatile _Tp>::tinyness_before;
809template <class _Tp>
810    _LIBCPP_CONSTEXPR const float_round_style numeric_limits<const volatile _Tp>::round_style;
811
812_LIBCPP_END_NAMESPACE_STD
813
814#endif  // _LIBCPP_LIMITS
815