1// The template and inlines for the numeric_limits classes. -*- C++ -*-
2
3// Copyright (C) 1999-2014 Free Software Foundation, Inc.
4//
5// This file is part of the GNU ISO C++ Library.  This library is free
6// software; you can redistribute it and/or modify it under the
7// terms of the GNU General Public License as published by the
8// Free Software Foundation; either version 3, or (at your option)
9// any later version.
10
11// This library is distributed in the hope that it will be useful,
12// but WITHOUT ANY WARRANTY; without even the implied warranty of
13// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
14// GNU General Public License for more details.
15
16// Under Section 7 of GPL version 3, you are granted additional
17// permissions described in the GCC Runtime Library Exception, version
18// 3.1, as published by the Free Software Foundation.
19
20// You should have received a copy of the GNU General Public License and
21// a copy of the GCC Runtime Library Exception along with this program;
22// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
23// <http://www.gnu.org/licenses/>.
24
25/** @file include/limits
26 *  This is a Standard C++ Library header.
27 */
28
29// Note: this is not a conforming implementation.
30// Written by Gabriel Dos Reis <gdr@codesourcery.com>
31
32//
33// ISO 14882:1998
34// 18.2.1
35//
36
37#ifndef _GLIBCXX_NUMERIC_LIMITS
38#define _GLIBCXX_NUMERIC_LIMITS 1
39
40#pragma GCC system_header
41
42#include <bits/c++config.h>
43
44//
45// The numeric_limits<> traits document implementation-defined aspects
46// of fundamental arithmetic data types (integers and floating points).
47// From Standard C++ point of view, there are 14 such types:
48//   * integers
49//         bool							(1)
50//         char, signed char, unsigned char, wchar_t            (4)
51//         short, unsigned short				(2)
52//         int, unsigned					(2)
53//         long, unsigned long					(2)
54//
55//   * floating points
56//         float						(1)
57//         double						(1)
58//         long double						(1)
59//
60// GNU C++ understands (where supported by the host C-library)
61//   * integer
62//         long long, unsigned long long			(2)
63//
64// which brings us to 16 fundamental arithmetic data types in GNU C++.
65//
66//
67// Since a numeric_limits<> is a bit tricky to get right, we rely on
68// an interface composed of macros which should be defined in config/os
69// or config/cpu when they differ from the generic (read arbitrary)
70// definitions given here.
71//
72
73// These values can be overridden in the target configuration file.
74// The default values are appropriate for many 32-bit targets.
75
76// GCC only intrinsically supports modulo integral types.  The only remaining
77// integral exceptional values is division by zero.  Only targets that do not
78// signal division by zero in some "hard to ignore" way should use false.
79#ifndef __glibcxx_integral_traps
80# define __glibcxx_integral_traps true
81#endif
82
83// float
84//
85
86// Default values.  Should be overridden in configuration files if necessary.
87
88#ifndef __glibcxx_float_has_denorm_loss
89#  define __glibcxx_float_has_denorm_loss false
90#endif
91#ifndef __glibcxx_float_traps
92#  define __glibcxx_float_traps false
93#endif
94#ifndef __glibcxx_float_tinyness_before
95#  define __glibcxx_float_tinyness_before false
96#endif
97
98// double
99
100// Default values.  Should be overridden in configuration files if necessary.
101
102#ifndef __glibcxx_double_has_denorm_loss
103#  define __glibcxx_double_has_denorm_loss false
104#endif
105#ifndef __glibcxx_double_traps
106#  define __glibcxx_double_traps false
107#endif
108#ifndef __glibcxx_double_tinyness_before
109#  define __glibcxx_double_tinyness_before false
110#endif
111
112// long double
113
114// Default values.  Should be overridden in configuration files if necessary.
115
116#ifndef __glibcxx_long_double_has_denorm_loss
117#  define __glibcxx_long_double_has_denorm_loss false
118#endif
119#ifndef __glibcxx_long_double_traps
120#  define __glibcxx_long_double_traps false
121#endif
122#ifndef __glibcxx_long_double_tinyness_before
123#  define __glibcxx_long_double_tinyness_before false
124#endif
125
126// You should not need to define any macros below this point.
127
128#define __glibcxx_signed(T)	((T)(-1) < 0)
129
130#define __glibcxx_min(T) \
131  (__glibcxx_signed (T) ? -__glibcxx_max (T) - 1 : (T)0)
132
133#define __glibcxx_max(T) \
134  (__glibcxx_signed (T) ? \
135   (((((T)1 << (__glibcxx_digits (T) - 1)) - 1) << 1) + 1) : ~(T)0)
136
137#define __glibcxx_digits(T) \
138  (sizeof(T) * __CHAR_BIT__ - __glibcxx_signed (T))
139
140// The fraction 643/2136 approximates log10(2) to 7 significant digits.
141#define __glibcxx_digits10(T) \
142  (__glibcxx_digits (T) * 643L / 2136)
143
144#define __glibcxx_max_digits10(T) \
145  (2 + (T) * 643L / 2136)
146
147namespace std _GLIBCXX_VISIBILITY(default)
148{
149_GLIBCXX_BEGIN_NAMESPACE_VERSION
150
151  /**
152   *  @brief Describes the rounding style for floating-point types.
153   *
154   *  This is used in the std::numeric_limits class.
155  */
156  enum float_round_style
157  {
158    round_indeterminate       = -1,    /// Intermediate.
159    round_toward_zero         = 0,     /// To zero.
160    round_to_nearest          = 1,     /// To the nearest representable value.
161    round_toward_infinity     = 2,     /// To infinity.
162    round_toward_neg_infinity = 3      /// To negative infinity.
163  };
164
165  /**
166   *  @brief Describes the denormalization for floating-point types.
167   *
168   *  These values represent the presence or absence of a variable number
169   *  of exponent bits.  This type is used in the std::numeric_limits class.
170  */
171  enum float_denorm_style
172  {
173    /// Indeterminate at compile time whether denormalized values are allowed.
174    denorm_indeterminate = -1,
175    /// The type does not allow denormalized values.
176    denorm_absent        = 0,
177    /// The type allows denormalized values.
178    denorm_present       = 1
179  };
180
181  /**
182   *  @brief Part of std::numeric_limits.
183   *
184   *  The @c static @c const members are usable as integral constant
185   *  expressions.
186   *
187   *  @note This is a separate class for purposes of efficiency; you
188   *        should only access these members as part of an instantiation
189   *        of the std::numeric_limits class.
190  */
191  struct __numeric_limits_base
192  {
193    /** This will be true for all fundamental types (which have
194	specializations), and false for everything else.  */
195    static _GLIBCXX_USE_CONSTEXPR bool is_specialized = false;
196
197    /** The number of @c radix digits that be represented without change:  for
198	integer types, the number of non-sign bits in the mantissa; for
199	floating types, the number of @c radix digits in the mantissa.  */
200    static _GLIBCXX_USE_CONSTEXPR int digits = 0;
201
202    /** The number of base 10 digits that can be represented without change. */
203    static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
204
205#if __cplusplus >= 201103L
206    /** The number of base 10 digits required to ensure that values which
207	differ are always differentiated.  */
208    static constexpr int max_digits10 = 0;
209#endif
210
211    /** True if the type is signed.  */
212    static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
213
214    /** True if the type is integer.  */
215    static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
216
217    /** True if the type uses an exact representation. All integer types are
218	exact, but not all exact types are integer.  For example, rational and
219	fixed-exponent representations are exact but not integer. */
220    static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
221
222    /** For integer types, specifies the base of the representation.  For
223	floating types, specifies the base of the exponent representation.  */
224    static _GLIBCXX_USE_CONSTEXPR int radix = 0;
225
226    /** The minimum negative integer such that @c radix raised to the power of
227	(one less than that integer) is a normalized floating point number.  */
228    static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
229
230    /** The minimum negative integer such that 10 raised to that power is in
231	the range of normalized floating point numbers.  */
232    static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
233
234    /** The maximum positive integer such that @c radix raised to the power of
235	(one less than that integer) is a representable finite floating point
236	number.  */
237    static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
238
239    /** The maximum positive integer such that 10 raised to that power is in
240	the range of representable finite floating point numbers.  */
241    static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
242
243    /** True if the type has a representation for positive infinity.  */
244    static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
245
246    /** True if the type has a representation for a quiet (non-signaling)
247	Not a Number.  */
248    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
249
250    /** True if the type has a representation for a signaling
251	Not a Number.  */
252    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
253
254    /** See std::float_denorm_style for more information.  */
255    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
256
257    /** True if loss of accuracy is detected as a denormalization loss,
258	rather than as an inexact result. */
259    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
260
261    /** True if-and-only-if the type adheres to the IEC 559 standard, also
262	known as IEEE 754.  (Only makes sense for floating point types.)  */
263    static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
264
265    /** True if the set of values representable by the type is
266	finite.  All built-in types are bounded, this member would be
267	false for arbitrary precision types. */
268    static _GLIBCXX_USE_CONSTEXPR bool is_bounded = false;
269
270    /** True if the type is @e modulo. A type is modulo if, for any
271	operation involving +, -, or * on values of that type whose
272	result would fall outside the range [min(),max()], the value
273	returned differs from the true value by an integer multiple of
274	max() - min() + 1. On most machines, this is false for floating
275	types, true for unsigned integers, and true for signed integers.
276	See PR22200 about signed integers.  */
277    static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
278
279    /** True if trapping is implemented for this type.  */
280    static _GLIBCXX_USE_CONSTEXPR bool traps = false;
281
282    /** True if tininess is detected before rounding.  (see IEC 559)  */
283    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
284
285    /** See std::float_round_style for more information.  This is only
286	meaningful for floating types; integer types will all be
287	round_toward_zero.  */
288    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style =
289						    round_toward_zero;
290  };
291
292  /**
293   *  @brief Properties of fundamental types.
294   *
295   *  This class allows a program to obtain information about the
296   *  representation of a fundamental type on a given platform.  For
297   *  non-fundamental types, the functions will return 0 and the data
298   *  members will all be @c false.
299   *
300   *  _GLIBCXX_RESOLVE_LIB_DEFECTS:  DRs 201 and 184 (hi Gaby!) are
301   *  noted, but not incorporated in this documented (yet).
302  */
303  template<typename _Tp>
304    struct numeric_limits : public __numeric_limits_base
305    {
306      /** The minimum finite value, or for floating types with
307	  denormalization, the minimum positive normalized value.  */
308      static _GLIBCXX_CONSTEXPR _Tp
309      min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
310
311      /** The maximum finite value.  */
312      static _GLIBCXX_CONSTEXPR _Tp
313      max() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
314
315#if __cplusplus >= 201103L
316      /** A finite value x such that there is no other finite value y
317       *  where y < x.  */
318      static constexpr _Tp
319      lowest() noexcept { return _Tp(); }
320#endif
321
322      /** The @e machine @e epsilon:  the difference between 1 and the least
323	  value greater than 1 that is representable.  */
324      static _GLIBCXX_CONSTEXPR _Tp
325      epsilon() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
326
327      /** The maximum rounding error measurement (see LIA-1).  */
328      static _GLIBCXX_CONSTEXPR _Tp
329      round_error() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
330
331      /** The representation of positive infinity, if @c has_infinity.  */
332      static _GLIBCXX_CONSTEXPR _Tp
333      infinity() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
334
335      /** The representation of a quiet Not a Number,
336	  if @c has_quiet_NaN. */
337      static _GLIBCXX_CONSTEXPR _Tp
338      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
339
340      /** The representation of a signaling Not a Number, if
341	  @c has_signaling_NaN. */
342      static _GLIBCXX_CONSTEXPR _Tp
343      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
344
345      /** The minimum positive denormalized value.  For types where
346	  @c has_denorm is false, this is the minimum positive normalized
347	  value.  */
348      static _GLIBCXX_CONSTEXPR _Tp
349      denorm_min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
350    };
351
352#if __cplusplus >= 201103L
353  template<typename _Tp>
354    struct numeric_limits<const _Tp>
355    : public numeric_limits<_Tp> { };
356
357  template<typename _Tp>
358    struct numeric_limits<volatile _Tp>
359    : public numeric_limits<_Tp> { };
360
361  template<typename _Tp>
362    struct numeric_limits<const volatile _Tp>
363    : public numeric_limits<_Tp> { };
364#endif
365
366  // Now there follow 16 explicit specializations.  Yes, 16.  Make sure
367  // you get the count right. (18 in c++0x mode)
368
369  /// numeric_limits<bool> specialization.
370  template<>
371    struct numeric_limits<bool>
372    {
373      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
374
375      static _GLIBCXX_CONSTEXPR bool
376      min() _GLIBCXX_USE_NOEXCEPT { return false; }
377
378      static _GLIBCXX_CONSTEXPR bool
379      max() _GLIBCXX_USE_NOEXCEPT { return true; }
380
381#if __cplusplus >= 201103L
382      static constexpr bool
383      lowest() noexcept { return min(); }
384#endif
385      static _GLIBCXX_USE_CONSTEXPR int digits = 1;
386      static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
387#if __cplusplus >= 201103L
388      static constexpr int max_digits10 = 0;
389#endif
390      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
391      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
392      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
393      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
394
395      static _GLIBCXX_CONSTEXPR bool
396      epsilon() _GLIBCXX_USE_NOEXCEPT { return false; }
397
398      static _GLIBCXX_CONSTEXPR bool
399      round_error() _GLIBCXX_USE_NOEXCEPT { return false; }
400
401      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
402      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
403      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
404      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
405
406      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
407      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
408      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
409      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
410       = denorm_absent;
411      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
412
413      static _GLIBCXX_CONSTEXPR bool
414      infinity() _GLIBCXX_USE_NOEXCEPT { return false; }
415
416      static _GLIBCXX_CONSTEXPR bool
417      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
418
419      static _GLIBCXX_CONSTEXPR bool
420      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
421
422      static _GLIBCXX_CONSTEXPR bool
423      denorm_min() _GLIBCXX_USE_NOEXCEPT { return false; }
424
425      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
426      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
427      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
428
429      // It is not clear what it means for a boolean type to trap.
430      // This is a DR on the LWG issue list.  Here, I use integer
431      // promotion semantics.
432      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
433      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
434      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
435       = round_toward_zero;
436    };
437
438  /// numeric_limits<char> specialization.
439  template<>
440    struct numeric_limits<char>
441    {
442      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
443
444      static _GLIBCXX_CONSTEXPR char
445      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min(char); }
446
447      static _GLIBCXX_CONSTEXPR char
448      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max(char); }
449
450#if __cplusplus >= 201103L
451      static constexpr char
452      lowest() noexcept { return min(); }
453#endif
454
455      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (char);
456      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (char);
457#if __cplusplus >= 201103L
458      static constexpr int max_digits10 = 0;
459#endif
460      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (char);
461      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
462      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
463      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
464
465      static _GLIBCXX_CONSTEXPR char
466      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
467
468      static _GLIBCXX_CONSTEXPR char
469      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
470
471      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
472      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
473      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
474      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
475
476      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
477      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
478      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
479      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
480       = denorm_absent;
481      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
482
483      static _GLIBCXX_CONSTEXPR
484      char infinity() _GLIBCXX_USE_NOEXCEPT { return char(); }
485
486      static _GLIBCXX_CONSTEXPR char
487      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
488
489      static _GLIBCXX_CONSTEXPR char
490      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
491
492      static _GLIBCXX_CONSTEXPR char
493      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<char>(0); }
494
495      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
496      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
497      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
498
499      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
500      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
501      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
502       = round_toward_zero;
503    };
504
505  /// numeric_limits<signed char> specialization.
506  template<>
507    struct numeric_limits<signed char>
508    {
509      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
510
511      static _GLIBCXX_CONSTEXPR signed char
512      min() _GLIBCXX_USE_NOEXCEPT { return -__SCHAR_MAX__ - 1; }
513
514      static _GLIBCXX_CONSTEXPR signed char
515      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__; }
516
517#if __cplusplus >= 201103L
518      static constexpr signed char
519      lowest() noexcept { return min(); }
520#endif
521
522      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (signed char);
523      static _GLIBCXX_USE_CONSTEXPR int digits10
524       = __glibcxx_digits10 (signed char);
525#if __cplusplus >= 201103L
526      static constexpr int max_digits10 = 0;
527#endif
528      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
529      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
530      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
531      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
532
533      static _GLIBCXX_CONSTEXPR signed char
534      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
535
536      static _GLIBCXX_CONSTEXPR signed char
537      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
538
539      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
540      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
541      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
542      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
543
544      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
545      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
546      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
547      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
548       = denorm_absent;
549      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
550
551      static _GLIBCXX_CONSTEXPR signed char
552      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
553
554      static _GLIBCXX_CONSTEXPR signed char
555      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
556
557      static _GLIBCXX_CONSTEXPR signed char
558      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
559      { return static_cast<signed char>(0); }
560
561      static _GLIBCXX_CONSTEXPR signed char
562      denorm_min() _GLIBCXX_USE_NOEXCEPT
563      { return static_cast<signed char>(0); }
564
565      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
566      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
567      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
568
569      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
570      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
571      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
572       = round_toward_zero;
573    };
574
575  /// numeric_limits<unsigned char> specialization.
576  template<>
577    struct numeric_limits<unsigned char>
578    {
579      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
580
581      static _GLIBCXX_CONSTEXPR unsigned char
582      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
583
584      static _GLIBCXX_CONSTEXPR unsigned char
585      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__ * 2U + 1; }
586
587#if __cplusplus >= 201103L
588      static constexpr unsigned char
589      lowest() noexcept { return min(); }
590#endif
591
592      static _GLIBCXX_USE_CONSTEXPR int digits
593       = __glibcxx_digits (unsigned char);
594      static _GLIBCXX_USE_CONSTEXPR int digits10
595       = __glibcxx_digits10 (unsigned char);
596#if __cplusplus >= 201103L
597      static constexpr int max_digits10 = 0;
598#endif
599      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
600      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
601      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
602      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
603
604      static _GLIBCXX_CONSTEXPR unsigned char
605      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
606
607      static _GLIBCXX_CONSTEXPR unsigned char
608      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
609
610      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
611      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
612      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
613      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
614
615      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
616      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
617      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
618      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
619       = denorm_absent;
620      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
621
622      static _GLIBCXX_CONSTEXPR unsigned char
623      infinity() _GLIBCXX_USE_NOEXCEPT
624      { return static_cast<unsigned char>(0); }
625
626      static _GLIBCXX_CONSTEXPR unsigned char
627      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
628      { return static_cast<unsigned char>(0); }
629
630      static _GLIBCXX_CONSTEXPR unsigned char
631      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
632      { return static_cast<unsigned char>(0); }
633
634      static _GLIBCXX_CONSTEXPR unsigned char
635      denorm_min() _GLIBCXX_USE_NOEXCEPT
636      { return static_cast<unsigned char>(0); }
637
638      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
639      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
640      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
641
642      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
643      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
644      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
645       = round_toward_zero;
646    };
647
648  /// numeric_limits<wchar_t> specialization.
649  template<>
650    struct numeric_limits<wchar_t>
651    {
652      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
653
654      static _GLIBCXX_CONSTEXPR wchar_t
655      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (wchar_t); }
656
657      static _GLIBCXX_CONSTEXPR wchar_t
658      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (wchar_t); }
659
660#if __cplusplus >= 201103L
661      static constexpr wchar_t
662      lowest() noexcept { return min(); }
663#endif
664
665      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (wchar_t);
666      static _GLIBCXX_USE_CONSTEXPR int digits10
667       = __glibcxx_digits10 (wchar_t);
668#if __cplusplus >= 201103L
669      static constexpr int max_digits10 = 0;
670#endif
671      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (wchar_t);
672      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
673      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
674      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
675
676      static _GLIBCXX_CONSTEXPR wchar_t
677      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
678
679      static _GLIBCXX_CONSTEXPR wchar_t
680      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
681
682      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
683      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
684      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
685      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
686
687      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
688      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
689      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
690      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
691       = denorm_absent;
692      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
693
694      static _GLIBCXX_CONSTEXPR wchar_t
695      infinity() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
696
697      static _GLIBCXX_CONSTEXPR wchar_t
698      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
699
700      static _GLIBCXX_CONSTEXPR wchar_t
701      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
702
703      static _GLIBCXX_CONSTEXPR wchar_t
704      denorm_min() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
705
706      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
707      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
708      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
709
710      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
711      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
712      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
713       = round_toward_zero;
714    };
715
716#if __cplusplus >= 201103L
717  /// numeric_limits<char16_t> specialization.
718  template<>
719    struct numeric_limits<char16_t>
720    {
721      static constexpr bool is_specialized = true;
722
723      static constexpr char16_t
724      min() noexcept { return __glibcxx_min (char16_t); }
725
726      static constexpr char16_t
727      max() noexcept { return __glibcxx_max (char16_t); }
728
729      static constexpr char16_t
730      lowest() noexcept { return min(); }
731
732      static constexpr int digits = __glibcxx_digits (char16_t);
733      static constexpr int digits10 = __glibcxx_digits10 (char16_t);
734      static constexpr int max_digits10 = 0;
735      static constexpr bool is_signed = __glibcxx_signed (char16_t);
736      static constexpr bool is_integer = true;
737      static constexpr bool is_exact = true;
738      static constexpr int radix = 2;
739
740      static constexpr char16_t
741      epsilon() noexcept { return 0; }
742
743      static constexpr char16_t
744      round_error() noexcept { return 0; }
745
746      static constexpr int min_exponent = 0;
747      static constexpr int min_exponent10 = 0;
748      static constexpr int max_exponent = 0;
749      static constexpr int max_exponent10 = 0;
750
751      static constexpr bool has_infinity = false;
752      static constexpr bool has_quiet_NaN = false;
753      static constexpr bool has_signaling_NaN = false;
754      static constexpr float_denorm_style has_denorm = denorm_absent;
755      static constexpr bool has_denorm_loss = false;
756
757      static constexpr char16_t
758      infinity() noexcept { return char16_t(); }
759
760      static constexpr char16_t
761      quiet_NaN() noexcept { return char16_t(); }
762
763      static constexpr char16_t
764      signaling_NaN() noexcept { return char16_t(); }
765
766      static constexpr char16_t
767      denorm_min() noexcept { return char16_t(); }
768
769      static constexpr bool is_iec559 = false;
770      static constexpr bool is_bounded = true;
771      static constexpr bool is_modulo = !is_signed;
772
773      static constexpr bool traps = __glibcxx_integral_traps;
774      static constexpr bool tinyness_before = false;
775      static constexpr float_round_style round_style = round_toward_zero;
776    };
777
778  /// numeric_limits<char32_t> specialization.
779  template<>
780    struct numeric_limits<char32_t>
781    {
782      static constexpr bool is_specialized = true;
783
784      static constexpr char32_t
785      min() noexcept { return __glibcxx_min (char32_t); }
786
787      static constexpr char32_t
788      max() noexcept { return __glibcxx_max (char32_t); }
789
790      static constexpr char32_t
791      lowest() noexcept { return min(); }
792
793      static constexpr int digits = __glibcxx_digits (char32_t);
794      static constexpr int digits10 = __glibcxx_digits10 (char32_t);
795      static constexpr int max_digits10 = 0;
796      static constexpr bool is_signed = __glibcxx_signed (char32_t);
797      static constexpr bool is_integer = true;
798      static constexpr bool is_exact = true;
799      static constexpr int radix = 2;
800
801      static constexpr char32_t
802      epsilon() noexcept { return 0; }
803
804      static constexpr char32_t
805      round_error() noexcept { return 0; }
806
807      static constexpr int min_exponent = 0;
808      static constexpr int min_exponent10 = 0;
809      static constexpr int max_exponent = 0;
810      static constexpr int max_exponent10 = 0;
811
812      static constexpr bool has_infinity = false;
813      static constexpr bool has_quiet_NaN = false;
814      static constexpr bool has_signaling_NaN = false;
815      static constexpr float_denorm_style has_denorm = denorm_absent;
816      static constexpr bool has_denorm_loss = false;
817
818      static constexpr char32_t
819      infinity() noexcept { return char32_t(); }
820
821      static constexpr char32_t
822      quiet_NaN() noexcept { return char32_t(); }
823
824      static constexpr char32_t
825      signaling_NaN() noexcept { return char32_t(); }
826
827      static constexpr char32_t
828      denorm_min() noexcept { return char32_t(); }
829
830      static constexpr bool is_iec559 = false;
831      static constexpr bool is_bounded = true;
832      static constexpr bool is_modulo = !is_signed;
833
834      static constexpr bool traps = __glibcxx_integral_traps;
835      static constexpr bool tinyness_before = false;
836      static constexpr float_round_style round_style = round_toward_zero;
837    };
838#endif
839
840  /// numeric_limits<short> specialization.
841  template<>
842    struct numeric_limits<short>
843    {
844      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
845
846      static _GLIBCXX_CONSTEXPR short
847      min() _GLIBCXX_USE_NOEXCEPT { return -__SHRT_MAX__ - 1; }
848
849      static _GLIBCXX_CONSTEXPR short
850      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__; }
851
852#if __cplusplus >= 201103L
853      static constexpr short
854      lowest() noexcept { return min(); }
855#endif
856
857      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (short);
858      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (short);
859#if __cplusplus >= 201103L
860      static constexpr int max_digits10 = 0;
861#endif
862      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
863      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
864      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
865      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
866
867      static _GLIBCXX_CONSTEXPR short
868      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
869
870      static _GLIBCXX_CONSTEXPR short
871      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
872
873      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
874      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
875      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
876      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
877
878      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
879      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
880      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
881      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
882       = denorm_absent;
883      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
884
885      static _GLIBCXX_CONSTEXPR short
886      infinity() _GLIBCXX_USE_NOEXCEPT { return short(); }
887
888      static _GLIBCXX_CONSTEXPR short
889      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
890
891      static _GLIBCXX_CONSTEXPR short
892      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
893
894      static _GLIBCXX_CONSTEXPR short
895      denorm_min() _GLIBCXX_USE_NOEXCEPT { return short(); }
896
897      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
898      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
899      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
900
901      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
902      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
903      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
904       = round_toward_zero;
905    };
906
907  /// numeric_limits<unsigned short> specialization.
908  template<>
909    struct numeric_limits<unsigned short>
910    {
911      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
912
913      static _GLIBCXX_CONSTEXPR unsigned short
914      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
915
916      static _GLIBCXX_CONSTEXPR unsigned short
917      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__ * 2U + 1; }
918
919#if __cplusplus >= 201103L
920      static constexpr unsigned short
921      lowest() noexcept { return min(); }
922#endif
923
924      static _GLIBCXX_USE_CONSTEXPR int digits
925       = __glibcxx_digits (unsigned short);
926      static _GLIBCXX_USE_CONSTEXPR int digits10
927       = __glibcxx_digits10 (unsigned short);
928#if __cplusplus >= 201103L
929      static constexpr int max_digits10 = 0;
930#endif
931      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
932      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
933      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
934      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
935
936      static _GLIBCXX_CONSTEXPR unsigned short
937      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
938
939      static _GLIBCXX_CONSTEXPR unsigned short
940      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
941
942      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
943      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
944      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
945      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
946
947      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
948      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
949      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
950      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
951       = denorm_absent;
952      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
953
954      static _GLIBCXX_CONSTEXPR unsigned short
955      infinity() _GLIBCXX_USE_NOEXCEPT
956      { return static_cast<unsigned short>(0); }
957
958      static _GLIBCXX_CONSTEXPR unsigned short
959      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
960      { return static_cast<unsigned short>(0); }
961
962      static _GLIBCXX_CONSTEXPR unsigned short
963      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
964      { return static_cast<unsigned short>(0); }
965
966      static _GLIBCXX_CONSTEXPR unsigned short
967      denorm_min() _GLIBCXX_USE_NOEXCEPT
968      { return static_cast<unsigned short>(0); }
969
970      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
971      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
972      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
973
974      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
975      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
976      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
977       = round_toward_zero;
978    };
979
980  /// numeric_limits<int> specialization.
981  template<>
982    struct numeric_limits<int>
983    {
984      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
985
986      static _GLIBCXX_CONSTEXPR int
987      min() _GLIBCXX_USE_NOEXCEPT { return -__INT_MAX__ - 1; }
988
989      static _GLIBCXX_CONSTEXPR int
990      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__; }
991
992#if __cplusplus >= 201103L
993      static constexpr int
994      lowest() noexcept { return min(); }
995#endif
996
997      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (int);
998      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (int);
999#if __cplusplus >= 201103L
1000      static constexpr int max_digits10 = 0;
1001#endif
1002      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1003      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1004      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1005      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1006
1007      static _GLIBCXX_CONSTEXPR int
1008      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1009
1010      static _GLIBCXX_CONSTEXPR int
1011      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1012
1013      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1014      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1015      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1016      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1017
1018      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1019      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1020      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1021      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1022       = denorm_absent;
1023      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1024
1025      static _GLIBCXX_CONSTEXPR int
1026      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1027
1028      static _GLIBCXX_CONSTEXPR int
1029      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1030
1031      static _GLIBCXX_CONSTEXPR int
1032      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1033
1034      static _GLIBCXX_CONSTEXPR int
1035      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1036
1037      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1038      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1039      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1040
1041      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1042      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1043      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1044       = round_toward_zero;
1045    };
1046
1047  /// numeric_limits<unsigned int> specialization.
1048  template<>
1049    struct numeric_limits<unsigned int>
1050    {
1051      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1052
1053      static _GLIBCXX_CONSTEXPR unsigned int
1054      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1055
1056      static _GLIBCXX_CONSTEXPR unsigned int
1057      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__ * 2U + 1; }
1058
1059#if __cplusplus >= 201103L
1060      static constexpr unsigned int
1061      lowest() noexcept { return min(); }
1062#endif
1063
1064      static _GLIBCXX_USE_CONSTEXPR int digits
1065       = __glibcxx_digits (unsigned int);
1066      static _GLIBCXX_USE_CONSTEXPR int digits10
1067       = __glibcxx_digits10 (unsigned int);
1068#if __cplusplus >= 201103L
1069      static constexpr int max_digits10 = 0;
1070#endif
1071      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1072      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1073      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1074      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1075
1076      static _GLIBCXX_CONSTEXPR unsigned int
1077      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1078
1079      static _GLIBCXX_CONSTEXPR unsigned int
1080      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1081
1082      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1083      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1084      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1085      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1086
1087      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1088      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1089      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1090      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1091       = denorm_absent;
1092      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1093
1094      static _GLIBCXX_CONSTEXPR unsigned int
1095      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<unsigned int>(0); }
1096
1097      static _GLIBCXX_CONSTEXPR unsigned int
1098      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1099      { return static_cast<unsigned int>(0); }
1100
1101      static _GLIBCXX_CONSTEXPR unsigned int
1102      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1103      { return static_cast<unsigned int>(0); }
1104
1105      static _GLIBCXX_CONSTEXPR unsigned int
1106      denorm_min() _GLIBCXX_USE_NOEXCEPT
1107      { return static_cast<unsigned int>(0); }
1108
1109      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1110      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1111      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1112
1113      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1114      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1115      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1116       = round_toward_zero;
1117    };
1118
1119  /// numeric_limits<long> specialization.
1120  template<>
1121    struct numeric_limits<long>
1122    {
1123      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1124
1125      static _GLIBCXX_CONSTEXPR long
1126      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_MAX__ - 1; }
1127
1128      static _GLIBCXX_CONSTEXPR long
1129      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__; }
1130
1131#if __cplusplus >= 201103L
1132      static constexpr long
1133      lowest() noexcept { return min(); }
1134#endif
1135
1136      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (long);
1137      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (long);
1138#if __cplusplus >= 201103L
1139      static constexpr int max_digits10 = 0;
1140#endif
1141      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1142      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1143      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1144      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1145
1146      static _GLIBCXX_CONSTEXPR long
1147      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1148
1149      static _GLIBCXX_CONSTEXPR long
1150      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1151
1152      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1153      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1154      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1155      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1156
1157      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1158      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1159      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1160      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1161       = denorm_absent;
1162      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1163
1164      static _GLIBCXX_CONSTEXPR long
1165      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1166
1167      static _GLIBCXX_CONSTEXPR long
1168      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1169
1170      static _GLIBCXX_CONSTEXPR long
1171      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1172
1173      static _GLIBCXX_CONSTEXPR long
1174      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1175
1176      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1177      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1178      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1179
1180      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1181      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1182      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1183       = round_toward_zero;
1184    };
1185
1186  /// numeric_limits<unsigned long> specialization.
1187  template<>
1188    struct numeric_limits<unsigned long>
1189    {
1190      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1191
1192      static _GLIBCXX_CONSTEXPR unsigned long
1193      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1194
1195      static _GLIBCXX_CONSTEXPR unsigned long
1196      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__ * 2UL + 1; }
1197
1198#if __cplusplus >= 201103L
1199      static constexpr unsigned long
1200      lowest() noexcept { return min(); }
1201#endif
1202
1203      static _GLIBCXX_USE_CONSTEXPR int digits
1204       = __glibcxx_digits (unsigned long);
1205      static _GLIBCXX_USE_CONSTEXPR int digits10
1206       = __glibcxx_digits10 (unsigned long);
1207#if __cplusplus >= 201103L
1208      static constexpr int max_digits10 = 0;
1209#endif
1210      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1211      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1212      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1213      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1214
1215      static _GLIBCXX_CONSTEXPR unsigned long
1216      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1217
1218      static _GLIBCXX_CONSTEXPR unsigned long
1219      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1220
1221      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1222      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1223      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1224      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1225
1226      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1227      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1228      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1229      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1230       = denorm_absent;
1231      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1232
1233      static _GLIBCXX_CONSTEXPR unsigned long
1234      infinity() _GLIBCXX_USE_NOEXCEPT
1235      { return static_cast<unsigned long>(0); }
1236
1237      static _GLIBCXX_CONSTEXPR unsigned long
1238      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1239      { return static_cast<unsigned long>(0); }
1240
1241      static _GLIBCXX_CONSTEXPR unsigned long
1242      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1243      { return static_cast<unsigned long>(0); }
1244
1245      static _GLIBCXX_CONSTEXPR unsigned long
1246      denorm_min() _GLIBCXX_USE_NOEXCEPT
1247      { return static_cast<unsigned long>(0); }
1248
1249      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1250      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1251      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1252
1253      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1254      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1255      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1256       = round_toward_zero;
1257    };
1258
1259  /// numeric_limits<long long> specialization.
1260  template<>
1261    struct numeric_limits<long long>
1262    {
1263      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1264
1265      static _GLIBCXX_CONSTEXPR long long
1266      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_LONG_MAX__ - 1; }
1267
1268      static _GLIBCXX_CONSTEXPR long long
1269      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__; }
1270
1271#if __cplusplus >= 201103L
1272      static constexpr long long
1273      lowest() noexcept { return min(); }
1274#endif
1275
1276      static _GLIBCXX_USE_CONSTEXPR int digits
1277       = __glibcxx_digits (long long);
1278      static _GLIBCXX_USE_CONSTEXPR int digits10
1279       = __glibcxx_digits10 (long long);
1280#if __cplusplus >= 201103L
1281      static constexpr int max_digits10 = 0;
1282#endif
1283      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1284      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1285      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1286      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1287
1288      static _GLIBCXX_CONSTEXPR long long
1289      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1290
1291      static _GLIBCXX_CONSTEXPR long long
1292      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1293
1294      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1295      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1296      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1297      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1298
1299      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1300      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1301      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1302      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1303       = denorm_absent;
1304      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1305
1306      static _GLIBCXX_CONSTEXPR long long
1307      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1308
1309      static _GLIBCXX_CONSTEXPR long long
1310      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1311
1312      static _GLIBCXX_CONSTEXPR long long
1313      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1314      { return static_cast<long long>(0); }
1315
1316      static _GLIBCXX_CONSTEXPR long long
1317      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1318
1319      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1320      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1321      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1322
1323      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1324      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1325      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1326       = round_toward_zero;
1327    };
1328
1329  /// numeric_limits<unsigned long long> specialization.
1330  template<>
1331    struct numeric_limits<unsigned long long>
1332    {
1333      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1334
1335      static _GLIBCXX_CONSTEXPR unsigned long long
1336      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1337
1338      static _GLIBCXX_CONSTEXPR unsigned long long
1339      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__ * 2ULL + 1; }
1340
1341#if __cplusplus >= 201103L
1342      static constexpr unsigned long long
1343      lowest() noexcept { return min(); }
1344#endif
1345
1346      static _GLIBCXX_USE_CONSTEXPR int digits
1347       = __glibcxx_digits (unsigned long long);
1348      static _GLIBCXX_USE_CONSTEXPR int digits10
1349       = __glibcxx_digits10 (unsigned long long);
1350#if __cplusplus >= 201103L
1351      static constexpr int max_digits10 = 0;
1352#endif
1353      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1354      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1355      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1356      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1357
1358      static _GLIBCXX_CONSTEXPR unsigned long long
1359      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1360
1361      static _GLIBCXX_CONSTEXPR unsigned long long
1362      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1363
1364      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1365      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1366      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1367      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1368
1369      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1370      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1371      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1372      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1373       = denorm_absent;
1374      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1375
1376      static _GLIBCXX_CONSTEXPR unsigned long long
1377      infinity() _GLIBCXX_USE_NOEXCEPT
1378      { return static_cast<unsigned long long>(0); }
1379
1380      static _GLIBCXX_CONSTEXPR unsigned long long
1381      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1382      { return static_cast<unsigned long long>(0); }
1383
1384      static _GLIBCXX_CONSTEXPR unsigned long long
1385      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1386      { return static_cast<unsigned long long>(0); }
1387
1388      static _GLIBCXX_CONSTEXPR unsigned long long
1389      denorm_min() _GLIBCXX_USE_NOEXCEPT
1390      { return static_cast<unsigned long long>(0); }
1391
1392      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1393      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1394      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1395
1396      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1397      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1398      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1399       = round_toward_zero;
1400    };
1401
1402#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_INT128)
1403  /// numeric_limits<__int128> specialization.
1404  template<>
1405    struct numeric_limits<__int128>
1406    {
1407      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1408
1409      static _GLIBCXX_CONSTEXPR __int128
1410      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (__int128); }
1411
1412      static _GLIBCXX_CONSTEXPR __int128
1413      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (__int128); }
1414
1415#if __cplusplus >= 201103L
1416      static constexpr __int128
1417      lowest() noexcept { return min(); }
1418#endif
1419
1420      static _GLIBCXX_USE_CONSTEXPR int digits
1421       = __glibcxx_digits (__int128);
1422      static _GLIBCXX_USE_CONSTEXPR int digits10
1423       = __glibcxx_digits10 (__int128);
1424#if __cplusplus >= 201103L
1425      static constexpr int max_digits10 = 0;
1426#endif
1427      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1428      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1429      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1430      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1431
1432      static _GLIBCXX_CONSTEXPR __int128
1433      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1434
1435      static _GLIBCXX_CONSTEXPR __int128
1436      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1437
1438      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1439      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1440      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1441      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1442
1443      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1444      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1445      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1446      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1447       = denorm_absent;
1448      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1449
1450      static _GLIBCXX_CONSTEXPR __int128
1451      infinity() _GLIBCXX_USE_NOEXCEPT
1452      { return static_cast<__int128>(0); }
1453
1454      static _GLIBCXX_CONSTEXPR __int128
1455      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1456      { return static_cast<__int128>(0); }
1457
1458      static _GLIBCXX_CONSTEXPR __int128
1459      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1460      { return static_cast<__int128>(0); }
1461
1462      static _GLIBCXX_CONSTEXPR __int128
1463      denorm_min() _GLIBCXX_USE_NOEXCEPT
1464      { return static_cast<__int128>(0); }
1465
1466      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1467      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1468      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1469
1470      static _GLIBCXX_USE_CONSTEXPR bool traps
1471       = __glibcxx_integral_traps;
1472      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1473      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1474       = round_toward_zero;
1475    };
1476
1477  /// numeric_limits<unsigned __int128> specialization.
1478  template<>
1479    struct numeric_limits<unsigned __int128>
1480    {
1481      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1482
1483      static _GLIBCXX_CONSTEXPR unsigned __int128
1484      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1485
1486      static _GLIBCXX_CONSTEXPR unsigned __int128
1487      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (unsigned __int128); }
1488
1489#if __cplusplus >= 201103L
1490      static constexpr unsigned __int128
1491      lowest() noexcept { return min(); }
1492#endif
1493
1494      static _GLIBCXX_USE_CONSTEXPR int digits
1495       = __glibcxx_digits (unsigned __int128);
1496      static _GLIBCXX_USE_CONSTEXPR int digits10
1497       = __glibcxx_digits10 (unsigned __int128);
1498#if __cplusplus >= 201103L
1499      static constexpr int max_digits10 = 0;
1500#endif
1501      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1502      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1503      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1504      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1505
1506      static _GLIBCXX_CONSTEXPR unsigned __int128
1507      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1508
1509      static _GLIBCXX_CONSTEXPR unsigned __int128
1510      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1511
1512      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1513      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1514      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1515      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1516
1517      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1518      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1519      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1520      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1521       = denorm_absent;
1522      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1523
1524      static _GLIBCXX_CONSTEXPR unsigned __int128
1525      infinity() _GLIBCXX_USE_NOEXCEPT
1526      { return static_cast<unsigned __int128>(0); }
1527
1528      static _GLIBCXX_CONSTEXPR unsigned __int128
1529      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1530      { return static_cast<unsigned __int128>(0); }
1531
1532      static _GLIBCXX_CONSTEXPR unsigned __int128
1533      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1534      { return static_cast<unsigned __int128>(0); }
1535
1536      static _GLIBCXX_CONSTEXPR unsigned __int128
1537      denorm_min() _GLIBCXX_USE_NOEXCEPT
1538      { return static_cast<unsigned __int128>(0); }
1539
1540      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1541      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1542      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1543
1544      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1545      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1546      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1547       = round_toward_zero;
1548    };
1549#endif
1550
1551  /// numeric_limits<float> specialization.
1552  template<>
1553    struct numeric_limits<float>
1554    {
1555      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1556
1557      static _GLIBCXX_CONSTEXPR float
1558      min() _GLIBCXX_USE_NOEXCEPT { return __FLT_MIN__; }
1559
1560      static _GLIBCXX_CONSTEXPR float
1561      max() _GLIBCXX_USE_NOEXCEPT { return __FLT_MAX__; }
1562
1563#if __cplusplus >= 201103L
1564      static constexpr float
1565      lowest() noexcept { return -__FLT_MAX__; }
1566#endif
1567
1568      static _GLIBCXX_USE_CONSTEXPR int digits = __FLT_MANT_DIG__;
1569      static _GLIBCXX_USE_CONSTEXPR int digits10 = __FLT_DIG__;
1570#if __cplusplus >= 201103L
1571      static constexpr int max_digits10
1572	 = __glibcxx_max_digits10 (__FLT_MANT_DIG__);
1573#endif
1574      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1575      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1576      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1577      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1578
1579      static _GLIBCXX_CONSTEXPR float
1580      epsilon() _GLIBCXX_USE_NOEXCEPT { return __FLT_EPSILON__; }
1581
1582      static _GLIBCXX_CONSTEXPR float
1583      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5F; }
1584
1585      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __FLT_MIN_EXP__;
1586      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __FLT_MIN_10_EXP__;
1587      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __FLT_MAX_EXP__;
1588      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __FLT_MAX_10_EXP__;
1589
1590      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __FLT_HAS_INFINITY__;
1591      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __FLT_HAS_QUIET_NAN__;
1592      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1593      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1594	= bool(__FLT_HAS_DENORM__) ? denorm_present : denorm_absent;
1595      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1596       = __glibcxx_float_has_denorm_loss;
1597
1598      static _GLIBCXX_CONSTEXPR float
1599      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_valf(); }
1600
1601      static _GLIBCXX_CONSTEXPR float
1602      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanf(""); }
1603
1604      static _GLIBCXX_CONSTEXPR float
1605      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansf(""); }
1606
1607      static _GLIBCXX_CONSTEXPR float
1608      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __FLT_DENORM_MIN__; }
1609
1610      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1611	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1612      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1613      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1614
1615      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_float_traps;
1616      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1617       = __glibcxx_float_tinyness_before;
1618      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1619       = round_to_nearest;
1620    };
1621
1622#undef __glibcxx_float_has_denorm_loss
1623#undef __glibcxx_float_traps
1624#undef __glibcxx_float_tinyness_before
1625
1626  /// numeric_limits<double> specialization.
1627  template<>
1628    struct numeric_limits<double>
1629    {
1630      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1631
1632      static _GLIBCXX_CONSTEXPR double
1633      min() _GLIBCXX_USE_NOEXCEPT { return __DBL_MIN__; }
1634
1635      static _GLIBCXX_CONSTEXPR double
1636      max() _GLIBCXX_USE_NOEXCEPT { return __DBL_MAX__; }
1637
1638#if __cplusplus >= 201103L
1639      static constexpr double
1640      lowest() noexcept { return -__DBL_MAX__; }
1641#endif
1642
1643      static _GLIBCXX_USE_CONSTEXPR int digits = __DBL_MANT_DIG__;
1644      static _GLIBCXX_USE_CONSTEXPR int digits10 = __DBL_DIG__;
1645#if __cplusplus >= 201103L
1646      static constexpr int max_digits10
1647	 = __glibcxx_max_digits10 (__DBL_MANT_DIG__);
1648#endif
1649      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1650      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1651      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1652      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1653
1654      static _GLIBCXX_CONSTEXPR double
1655      epsilon() _GLIBCXX_USE_NOEXCEPT { return __DBL_EPSILON__; }
1656
1657      static _GLIBCXX_CONSTEXPR double
1658      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5; }
1659
1660      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __DBL_MIN_EXP__;
1661      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __DBL_MIN_10_EXP__;
1662      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __DBL_MAX_EXP__;
1663      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __DBL_MAX_10_EXP__;
1664
1665      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __DBL_HAS_INFINITY__;
1666      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __DBL_HAS_QUIET_NAN__;
1667      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1668      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1669	= bool(__DBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1670      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1671        = __glibcxx_double_has_denorm_loss;
1672
1673      static _GLIBCXX_CONSTEXPR double
1674      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_val(); }
1675
1676      static _GLIBCXX_CONSTEXPR double
1677      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nan(""); }
1678
1679      static _GLIBCXX_CONSTEXPR double
1680      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nans(""); }
1681
1682      static _GLIBCXX_CONSTEXPR double
1683      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __DBL_DENORM_MIN__; }
1684
1685      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1686	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1687      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1688      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1689
1690      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_double_traps;
1691      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1692       = __glibcxx_double_tinyness_before;
1693      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1694       = round_to_nearest;
1695    };
1696
1697#undef __glibcxx_double_has_denorm_loss
1698#undef __glibcxx_double_traps
1699#undef __glibcxx_double_tinyness_before
1700
1701  /// numeric_limits<long double> specialization.
1702  template<>
1703    struct numeric_limits<long double>
1704    {
1705      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1706
1707      static _GLIBCXX_CONSTEXPR long double
1708      min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MIN__; }
1709
1710      static _GLIBCXX_CONSTEXPR long double
1711      max() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MAX__; }
1712
1713#if __cplusplus >= 201103L
1714      static constexpr long double
1715      lowest() noexcept { return -__LDBL_MAX__; }
1716#endif
1717
1718      static _GLIBCXX_USE_CONSTEXPR int digits = __LDBL_MANT_DIG__;
1719      static _GLIBCXX_USE_CONSTEXPR int digits10 = __LDBL_DIG__;
1720#if __cplusplus >= 201103L
1721      static _GLIBCXX_USE_CONSTEXPR int max_digits10
1722	 = __glibcxx_max_digits10 (__LDBL_MANT_DIG__);
1723#endif
1724      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1725      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1726      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1727      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1728
1729      static _GLIBCXX_CONSTEXPR long double
1730      epsilon() _GLIBCXX_USE_NOEXCEPT { return __LDBL_EPSILON__; }
1731
1732      static _GLIBCXX_CONSTEXPR long double
1733      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5L; }
1734
1735      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __LDBL_MIN_EXP__;
1736      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __LDBL_MIN_10_EXP__;
1737      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __LDBL_MAX_EXP__;
1738      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __LDBL_MAX_10_EXP__;
1739
1740      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __LDBL_HAS_INFINITY__;
1741      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __LDBL_HAS_QUIET_NAN__;
1742      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1743      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1744	= bool(__LDBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1745      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1746	= __glibcxx_long_double_has_denorm_loss;
1747
1748      static _GLIBCXX_CONSTEXPR long double
1749      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_vall(); }
1750
1751      static _GLIBCXX_CONSTEXPR long double
1752      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanl(""); }
1753
1754      static _GLIBCXX_CONSTEXPR long double
1755      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansl(""); }
1756
1757      static _GLIBCXX_CONSTEXPR long double
1758      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_DENORM_MIN__; }
1759
1760      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1761	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1762      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1763      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1764
1765      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_long_double_traps;
1766      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before =
1767					 __glibcxx_long_double_tinyness_before;
1768      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style =
1769						      round_to_nearest;
1770    };
1771
1772#undef __glibcxx_long_double_has_denorm_loss
1773#undef __glibcxx_long_double_traps
1774#undef __glibcxx_long_double_tinyness_before
1775
1776_GLIBCXX_END_NAMESPACE_VERSION
1777} // namespace
1778
1779#undef __glibcxx_signed
1780#undef __glibcxx_min
1781#undef __glibcxx_max
1782#undef __glibcxx_digits
1783#undef __glibcxx_digits10
1784#undef __glibcxx_max_digits10
1785
1786#endif // _GLIBCXX_NUMERIC_LIMITS
1787