1// The template and inlines for the numeric_limits classes. -*- C++ -*-
2
3// Copyright (C) 1999-2020 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_b(T,B)	((T)(-1) < 0)
129
130#define __glibcxx_min_b(T,B)					\
131  (__glibcxx_signed_b (T,B) ? -__glibcxx_max_b (T,B) - 1 : (T)0)
132
133#define __glibcxx_max_b(T,B)						\
134  (__glibcxx_signed_b (T,B) ?						\
135   (((((T)1 << (__glibcxx_digits_b (T,B) - 1)) - 1) << 1) + 1) : ~(T)0)
136
137#define __glibcxx_digits_b(T,B)				\
138  (B - __glibcxx_signed_b (T,B))
139
140// The fraction 643/2136 approximates log10(2) to 7 significant digits.
141#define __glibcxx_digits10_b(T,B)		\
142  (__glibcxx_digits_b (T,B) * 643L / 2136)
143
144#define __glibcxx_signed(T) \
145  __glibcxx_signed_b (T, sizeof(T) * __CHAR_BIT__)
146#define __glibcxx_min(T) \
147  __glibcxx_min_b (T, sizeof(T) * __CHAR_BIT__)
148#define __glibcxx_max(T) \
149  __glibcxx_max_b (T, sizeof(T) * __CHAR_BIT__)
150#define __glibcxx_digits(T) \
151  __glibcxx_digits_b (T, sizeof(T) * __CHAR_BIT__)
152#define __glibcxx_digits10(T) \
153  __glibcxx_digits10_b (T, sizeof(T) * __CHAR_BIT__)
154
155#define __glibcxx_max_digits10(T) \
156  (2 + (T) * 643L / 2136)
157
158namespace std _GLIBCXX_VISIBILITY(default)
159{
160_GLIBCXX_BEGIN_NAMESPACE_VERSION
161
162  /**
163   *  @brief Describes the rounding style for floating-point types.
164   *
165   *  This is used in the std::numeric_limits class.
166  */
167  enum float_round_style
168  {
169    round_indeterminate       = -1,    /// Intermediate.
170    round_toward_zero         = 0,     /// To zero.
171    round_to_nearest          = 1,     /// To the nearest representable value.
172    round_toward_infinity     = 2,     /// To infinity.
173    round_toward_neg_infinity = 3      /// To negative infinity.
174  };
175
176  /**
177   *  @brief Describes the denormalization for floating-point types.
178   *
179   *  These values represent the presence or absence of a variable number
180   *  of exponent bits.  This type is used in the std::numeric_limits class.
181  */
182  enum float_denorm_style
183  {
184    /// Indeterminate at compile time whether denormalized values are allowed.
185    denorm_indeterminate = -1,
186    /// The type does not allow denormalized values.
187    denorm_absent        = 0,
188    /// The type allows denormalized values.
189    denorm_present       = 1
190  };
191
192  /**
193   *  @brief Part of std::numeric_limits.
194   *
195   *  The @c static @c const members are usable as integral constant
196   *  expressions.
197   *
198   *  @note This is a separate class for purposes of efficiency; you
199   *        should only access these members as part of an instantiation
200   *        of the std::numeric_limits class.
201  */
202  struct __numeric_limits_base
203  {
204    /** This will be true for all fundamental types (which have
205	specializations), and false for everything else.  */
206    static _GLIBCXX_USE_CONSTEXPR bool is_specialized = false;
207
208    /** The number of @c radix digits that be represented without change:  for
209	integer types, the number of non-sign bits in the mantissa; for
210	floating types, the number of @c radix digits in the mantissa.  */
211    static _GLIBCXX_USE_CONSTEXPR int digits = 0;
212
213    /** The number of base 10 digits that can be represented without change. */
214    static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
215
216#if __cplusplus >= 201103L
217    /** The number of base 10 digits required to ensure that values which
218	differ are always differentiated.  */
219    static constexpr int max_digits10 = 0;
220#endif
221
222    /** True if the type is signed.  */
223    static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
224
225    /** True if the type is integer.  */
226    static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
227
228    /** True if the type uses an exact representation. All integer types are
229	exact, but not all exact types are integer.  For example, rational and
230	fixed-exponent representations are exact but not integer. */
231    static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
232
233    /** For integer types, specifies the base of the representation.  For
234	floating types, specifies the base of the exponent representation.  */
235    static _GLIBCXX_USE_CONSTEXPR int radix = 0;
236
237    /** The minimum negative integer such that @c radix raised to the power of
238	(one less than that integer) is a normalized floating point number.  */
239    static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
240
241    /** The minimum negative integer such that 10 raised to that power is in
242	the range of normalized floating point numbers.  */
243    static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
244
245    /** The maximum positive integer such that @c radix raised to the power of
246	(one less than that integer) is a representable finite floating point
247	number.  */
248    static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
249
250    /** The maximum positive integer such that 10 raised to that power is in
251	the range of representable finite floating point numbers.  */
252    static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
253
254    /** True if the type has a representation for positive infinity.  */
255    static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
256
257    /** True if the type has a representation for a quiet (non-signaling)
258	Not a Number.  */
259    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
260
261    /** True if the type has a representation for a signaling
262	Not a Number.  */
263    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
264
265    /** See std::float_denorm_style for more information.  */
266    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm = denorm_absent;
267
268    /** True if loss of accuracy is detected as a denormalization loss,
269	rather than as an inexact result. */
270    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
271
272    /** True if-and-only-if the type adheres to the IEC 559 standard, also
273	known as IEEE 754.  (Only makes sense for floating point types.)  */
274    static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
275
276    /** True if the set of values representable by the type is
277	finite.  All built-in types are bounded, this member would be
278	false for arbitrary precision types. */
279    static _GLIBCXX_USE_CONSTEXPR bool is_bounded = false;
280
281    /** True if the type is @e modulo. A type is modulo if, for any
282	operation involving +, -, or * on values of that type whose
283	result would fall outside the range [min(),max()], the value
284	returned differs from the true value by an integer multiple of
285	max() - min() + 1. On most machines, this is false for floating
286	types, true for unsigned integers, and true for signed integers.
287	See PR22200 about signed integers.  */
288    static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
289
290    /** True if trapping is implemented for this type.  */
291    static _GLIBCXX_USE_CONSTEXPR bool traps = false;
292
293    /** True if tininess is detected before rounding.  (see IEC 559)  */
294    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
295
296    /** See std::float_round_style for more information.  This is only
297	meaningful for floating types; integer types will all be
298	round_toward_zero.  */
299    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style =
300						    round_toward_zero;
301  };
302
303  /**
304   *  @brief Properties of fundamental types.
305   *
306   *  This class allows a program to obtain information about the
307   *  representation of a fundamental type on a given platform.  For
308   *  non-fundamental types, the functions will return 0 and the data
309   *  members will all be @c false.
310  */
311  template<typename _Tp>
312    struct numeric_limits : public __numeric_limits_base
313    {
314      /** The minimum finite value, or for floating types with
315	  denormalization, the minimum positive normalized value.  */
316      static _GLIBCXX_CONSTEXPR _Tp
317      min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
318
319      /** The maximum finite value.  */
320      static _GLIBCXX_CONSTEXPR _Tp
321      max() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
322
323#if __cplusplus >= 201103L
324      /** A finite value x such that there is no other finite value y
325       *  where y < x.  */
326      static constexpr _Tp
327      lowest() noexcept { return _Tp(); }
328#endif
329
330      /** The @e machine @e epsilon:  the difference between 1 and the least
331	  value greater than 1 that is representable.  */
332      static _GLIBCXX_CONSTEXPR _Tp
333      epsilon() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
334
335      /** The maximum rounding error measurement (see LIA-1).  */
336      static _GLIBCXX_CONSTEXPR _Tp
337      round_error() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
338
339      /** The representation of positive infinity, if @c has_infinity.  */
340      static _GLIBCXX_CONSTEXPR _Tp
341      infinity() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
342
343      /** The representation of a quiet Not a Number,
344	  if @c has_quiet_NaN. */
345      static _GLIBCXX_CONSTEXPR _Tp
346      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
347
348      /** The representation of a signaling Not a Number, if
349	  @c has_signaling_NaN. */
350      static _GLIBCXX_CONSTEXPR _Tp
351      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
352
353      /** The minimum positive denormalized value.  For types where
354	  @c has_denorm is false, this is the minimum positive normalized
355	  value.  */
356      static _GLIBCXX_CONSTEXPR _Tp
357      denorm_min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
358    };
359
360  // _GLIBCXX_RESOLVE_LIB_DEFECTS
361  // 559. numeric_limits<const T>
362
363  template<typename _Tp>
364    struct numeric_limits<const _Tp>
365    : public numeric_limits<_Tp> { };
366
367  template<typename _Tp>
368    struct numeric_limits<volatile _Tp>
369    : public numeric_limits<_Tp> { };
370
371  template<typename _Tp>
372    struct numeric_limits<const volatile _Tp>
373    : public numeric_limits<_Tp> { };
374
375  // Now there follow 16 explicit specializations.  Yes, 16.  Make sure
376  // you get the count right. (18 in C++11 mode, with char16_t and char32_t.)
377  // (+1 if char8_t is enabled.)
378
379  // _GLIBCXX_RESOLVE_LIB_DEFECTS
380  // 184. numeric_limits<bool> wording problems
381
382  /// numeric_limits<bool> specialization.
383  template<>
384    struct numeric_limits<bool>
385    {
386      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
387
388      static _GLIBCXX_CONSTEXPR bool
389      min() _GLIBCXX_USE_NOEXCEPT { return false; }
390
391      static _GLIBCXX_CONSTEXPR bool
392      max() _GLIBCXX_USE_NOEXCEPT { return true; }
393
394#if __cplusplus >= 201103L
395      static constexpr bool
396      lowest() noexcept { return min(); }
397#endif
398      static _GLIBCXX_USE_CONSTEXPR int digits = 1;
399      static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
400#if __cplusplus >= 201103L
401      static constexpr int max_digits10 = 0;
402#endif
403      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
404      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
405      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
406      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
407
408      static _GLIBCXX_CONSTEXPR bool
409      epsilon() _GLIBCXX_USE_NOEXCEPT { return false; }
410
411      static _GLIBCXX_CONSTEXPR bool
412      round_error() _GLIBCXX_USE_NOEXCEPT { return false; }
413
414      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
415      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
416      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
417      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
418
419      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
420      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
421      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
422      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
423       = denorm_absent;
424      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
425
426      static _GLIBCXX_CONSTEXPR bool
427      infinity() _GLIBCXX_USE_NOEXCEPT { return false; }
428
429      static _GLIBCXX_CONSTEXPR bool
430      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
431
432      static _GLIBCXX_CONSTEXPR bool
433      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
434
435      static _GLIBCXX_CONSTEXPR bool
436      denorm_min() _GLIBCXX_USE_NOEXCEPT { return false; }
437
438      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
439      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
440      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
441
442      // It is not clear what it means for a boolean type to trap.
443      // This is a DR on the LWG issue list.  Here, I use integer
444      // promotion semantics.
445      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
446      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
447      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
448       = round_toward_zero;
449    };
450
451  /// numeric_limits<char> specialization.
452  template<>
453    struct numeric_limits<char>
454    {
455      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
456
457      static _GLIBCXX_CONSTEXPR char
458      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min(char); }
459
460      static _GLIBCXX_CONSTEXPR char
461      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max(char); }
462
463#if __cplusplus >= 201103L
464      static constexpr char
465      lowest() noexcept { return min(); }
466#endif
467
468      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (char);
469      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (char);
470#if __cplusplus >= 201103L
471      static constexpr int max_digits10 = 0;
472#endif
473      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (char);
474      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
475      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
476      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
477
478      static _GLIBCXX_CONSTEXPR char
479      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
480
481      static _GLIBCXX_CONSTEXPR char
482      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
483
484      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
485      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
486      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
487      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
488
489      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
490      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
491      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
492      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
493       = denorm_absent;
494      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
495
496      static _GLIBCXX_CONSTEXPR
497      char infinity() _GLIBCXX_USE_NOEXCEPT { return char(); }
498
499      static _GLIBCXX_CONSTEXPR char
500      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
501
502      static _GLIBCXX_CONSTEXPR char
503      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
504
505      static _GLIBCXX_CONSTEXPR char
506      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<char>(0); }
507
508      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
509      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
510      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
511
512      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
513      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
514      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
515       = round_toward_zero;
516    };
517
518  /// numeric_limits<signed char> specialization.
519  template<>
520    struct numeric_limits<signed char>
521    {
522      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
523
524      static _GLIBCXX_CONSTEXPR signed char
525      min() _GLIBCXX_USE_NOEXCEPT { return -__SCHAR_MAX__ - 1; }
526
527      static _GLIBCXX_CONSTEXPR signed char
528      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__; }
529
530#if __cplusplus >= 201103L
531      static constexpr signed char
532      lowest() noexcept { return min(); }
533#endif
534
535      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (signed char);
536      static _GLIBCXX_USE_CONSTEXPR int digits10
537       = __glibcxx_digits10 (signed char);
538#if __cplusplus >= 201103L
539      static constexpr int max_digits10 = 0;
540#endif
541      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
542      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
543      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
544      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
545
546      static _GLIBCXX_CONSTEXPR signed char
547      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
548
549      static _GLIBCXX_CONSTEXPR signed char
550      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
551
552      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
553      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
554      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
555      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
556
557      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
558      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
559      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
560      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
561       = denorm_absent;
562      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
563
564      static _GLIBCXX_CONSTEXPR signed char
565      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
566
567      static _GLIBCXX_CONSTEXPR signed char
568      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
569
570      static _GLIBCXX_CONSTEXPR signed char
571      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
572      { return static_cast<signed char>(0); }
573
574      static _GLIBCXX_CONSTEXPR signed char
575      denorm_min() _GLIBCXX_USE_NOEXCEPT
576      { return static_cast<signed char>(0); }
577
578      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
579      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
580      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
581
582      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
583      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
584      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
585       = round_toward_zero;
586    };
587
588  /// numeric_limits<unsigned char> specialization.
589  template<>
590    struct numeric_limits<unsigned char>
591    {
592      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
593
594      static _GLIBCXX_CONSTEXPR unsigned char
595      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
596
597      static _GLIBCXX_CONSTEXPR unsigned char
598      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__ * 2U + 1; }
599
600#if __cplusplus >= 201103L
601      static constexpr unsigned char
602      lowest() noexcept { return min(); }
603#endif
604
605      static _GLIBCXX_USE_CONSTEXPR int digits
606       = __glibcxx_digits (unsigned char);
607      static _GLIBCXX_USE_CONSTEXPR int digits10
608       = __glibcxx_digits10 (unsigned char);
609#if __cplusplus >= 201103L
610      static constexpr int max_digits10 = 0;
611#endif
612      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
613      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
614      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
615      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
616
617      static _GLIBCXX_CONSTEXPR unsigned char
618      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
619
620      static _GLIBCXX_CONSTEXPR unsigned char
621      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
622
623      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
624      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
625      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
626      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
627
628      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
629      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
630      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
631      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
632       = denorm_absent;
633      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
634
635      static _GLIBCXX_CONSTEXPR unsigned char
636      infinity() _GLIBCXX_USE_NOEXCEPT
637      { return static_cast<unsigned char>(0); }
638
639      static _GLIBCXX_CONSTEXPR unsigned char
640      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
641      { return static_cast<unsigned char>(0); }
642
643      static _GLIBCXX_CONSTEXPR unsigned char
644      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
645      { return static_cast<unsigned char>(0); }
646
647      static _GLIBCXX_CONSTEXPR unsigned char
648      denorm_min() _GLIBCXX_USE_NOEXCEPT
649      { return static_cast<unsigned char>(0); }
650
651      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
652      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
653      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
654
655      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
656      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
657      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
658       = round_toward_zero;
659    };
660
661  /// numeric_limits<wchar_t> specialization.
662  template<>
663    struct numeric_limits<wchar_t>
664    {
665      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
666
667      static _GLIBCXX_CONSTEXPR wchar_t
668      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (wchar_t); }
669
670      static _GLIBCXX_CONSTEXPR wchar_t
671      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (wchar_t); }
672
673#if __cplusplus >= 201103L
674      static constexpr wchar_t
675      lowest() noexcept { return min(); }
676#endif
677
678      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (wchar_t);
679      static _GLIBCXX_USE_CONSTEXPR int digits10
680       = __glibcxx_digits10 (wchar_t);
681#if __cplusplus >= 201103L
682      static constexpr int max_digits10 = 0;
683#endif
684      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (wchar_t);
685      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
686      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
687      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
688
689      static _GLIBCXX_CONSTEXPR wchar_t
690      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
691
692      static _GLIBCXX_CONSTEXPR wchar_t
693      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
694
695      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
696      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
697      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
698      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
699
700      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
701      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
702      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
703      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
704       = denorm_absent;
705      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
706
707      static _GLIBCXX_CONSTEXPR wchar_t
708      infinity() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
709
710      static _GLIBCXX_CONSTEXPR wchar_t
711      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
712
713      static _GLIBCXX_CONSTEXPR wchar_t
714      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
715
716      static _GLIBCXX_CONSTEXPR wchar_t
717      denorm_min() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
718
719      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
720      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
721      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
722
723      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
724      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
725      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
726       = round_toward_zero;
727    };
728
729#if _GLIBCXX_USE_CHAR8_T
730  /// numeric_limits<char8_t> specialization.
731  template<>
732    struct numeric_limits<char8_t>
733    {
734      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
735
736      static _GLIBCXX_CONSTEXPR char8_t
737      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (char8_t); }
738
739      static _GLIBCXX_CONSTEXPR char8_t
740      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (char8_t); }
741
742      static _GLIBCXX_CONSTEXPR char8_t
743      lowest() _GLIBCXX_USE_NOEXCEPT { return min(); }
744
745      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (char8_t);
746      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (char8_t);
747      static _GLIBCXX_USE_CONSTEXPR int max_digits10 = 0;
748      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (char8_t);
749      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
750      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
751      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
752
753      static _GLIBCXX_CONSTEXPR char8_t
754      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
755
756      static _GLIBCXX_CONSTEXPR char8_t
757      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
758
759      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
760      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
761      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
762      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
763
764      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
765      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
766      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
767      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
768	= denorm_absent;
769      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
770
771      static _GLIBCXX_CONSTEXPR char8_t
772      infinity() _GLIBCXX_USE_NOEXCEPT { return char8_t(); }
773
774      static _GLIBCXX_CONSTEXPR char8_t
775      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return char8_t(); }
776
777      static _GLIBCXX_CONSTEXPR char8_t
778      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return char8_t(); }
779
780      static _GLIBCXX_CONSTEXPR char8_t
781      denorm_min() _GLIBCXX_USE_NOEXCEPT { return char8_t(); }
782
783      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
784      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
785      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
786
787      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
788      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
789      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
790	= round_toward_zero;
791    };
792#endif
793
794#if __cplusplus >= 201103L
795  /// numeric_limits<char16_t> specialization.
796  template<>
797    struct numeric_limits<char16_t>
798    {
799      static constexpr bool is_specialized = true;
800
801      static constexpr char16_t
802      min() noexcept { return __glibcxx_min (char16_t); }
803
804      static constexpr char16_t
805      max() noexcept { return __glibcxx_max (char16_t); }
806
807      static constexpr char16_t
808      lowest() noexcept { return min(); }
809
810      static constexpr int digits = __glibcxx_digits (char16_t);
811      static constexpr int digits10 = __glibcxx_digits10 (char16_t);
812      static constexpr int max_digits10 = 0;
813      static constexpr bool is_signed = __glibcxx_signed (char16_t);
814      static constexpr bool is_integer = true;
815      static constexpr bool is_exact = true;
816      static constexpr int radix = 2;
817
818      static constexpr char16_t
819      epsilon() noexcept { return 0; }
820
821      static constexpr char16_t
822      round_error() noexcept { return 0; }
823
824      static constexpr int min_exponent = 0;
825      static constexpr int min_exponent10 = 0;
826      static constexpr int max_exponent = 0;
827      static constexpr int max_exponent10 = 0;
828
829      static constexpr bool has_infinity = false;
830      static constexpr bool has_quiet_NaN = false;
831      static constexpr bool has_signaling_NaN = false;
832      static constexpr float_denorm_style has_denorm = denorm_absent;
833      static constexpr bool has_denorm_loss = false;
834
835      static constexpr char16_t
836      infinity() noexcept { return char16_t(); }
837
838      static constexpr char16_t
839      quiet_NaN() noexcept { return char16_t(); }
840
841      static constexpr char16_t
842      signaling_NaN() noexcept { return char16_t(); }
843
844      static constexpr char16_t
845      denorm_min() noexcept { return char16_t(); }
846
847      static constexpr bool is_iec559 = false;
848      static constexpr bool is_bounded = true;
849      static constexpr bool is_modulo = !is_signed;
850
851      static constexpr bool traps = __glibcxx_integral_traps;
852      static constexpr bool tinyness_before = false;
853      static constexpr float_round_style round_style = round_toward_zero;
854    };
855
856  /// numeric_limits<char32_t> specialization.
857  template<>
858    struct numeric_limits<char32_t>
859    {
860      static constexpr bool is_specialized = true;
861
862      static constexpr char32_t
863      min() noexcept { return __glibcxx_min (char32_t); }
864
865      static constexpr char32_t
866      max() noexcept { return __glibcxx_max (char32_t); }
867
868      static constexpr char32_t
869      lowest() noexcept { return min(); }
870
871      static constexpr int digits = __glibcxx_digits (char32_t);
872      static constexpr int digits10 = __glibcxx_digits10 (char32_t);
873      static constexpr int max_digits10 = 0;
874      static constexpr bool is_signed = __glibcxx_signed (char32_t);
875      static constexpr bool is_integer = true;
876      static constexpr bool is_exact = true;
877      static constexpr int radix = 2;
878
879      static constexpr char32_t
880      epsilon() noexcept { return 0; }
881
882      static constexpr char32_t
883      round_error() noexcept { return 0; }
884
885      static constexpr int min_exponent = 0;
886      static constexpr int min_exponent10 = 0;
887      static constexpr int max_exponent = 0;
888      static constexpr int max_exponent10 = 0;
889
890      static constexpr bool has_infinity = false;
891      static constexpr bool has_quiet_NaN = false;
892      static constexpr bool has_signaling_NaN = false;
893      static constexpr float_denorm_style has_denorm = denorm_absent;
894      static constexpr bool has_denorm_loss = false;
895
896      static constexpr char32_t
897      infinity() noexcept { return char32_t(); }
898
899      static constexpr char32_t
900      quiet_NaN() noexcept { return char32_t(); }
901
902      static constexpr char32_t
903      signaling_NaN() noexcept { return char32_t(); }
904
905      static constexpr char32_t
906      denorm_min() noexcept { return char32_t(); }
907
908      static constexpr bool is_iec559 = false;
909      static constexpr bool is_bounded = true;
910      static constexpr bool is_modulo = !is_signed;
911
912      static constexpr bool traps = __glibcxx_integral_traps;
913      static constexpr bool tinyness_before = false;
914      static constexpr float_round_style round_style = round_toward_zero;
915    };
916#endif
917
918  /// numeric_limits<short> specialization.
919  template<>
920    struct numeric_limits<short>
921    {
922      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
923
924      static _GLIBCXX_CONSTEXPR short
925      min() _GLIBCXX_USE_NOEXCEPT { return -__SHRT_MAX__ - 1; }
926
927      static _GLIBCXX_CONSTEXPR short
928      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__; }
929
930#if __cplusplus >= 201103L
931      static constexpr short
932      lowest() noexcept { return min(); }
933#endif
934
935      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (short);
936      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (short);
937#if __cplusplus >= 201103L
938      static constexpr int max_digits10 = 0;
939#endif
940      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
941      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
942      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
943      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
944
945      static _GLIBCXX_CONSTEXPR short
946      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
947
948      static _GLIBCXX_CONSTEXPR short
949      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
950
951      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
952      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
953      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
954      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
955
956      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
957      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
958      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
959      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
960       = denorm_absent;
961      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
962
963      static _GLIBCXX_CONSTEXPR short
964      infinity() _GLIBCXX_USE_NOEXCEPT { return short(); }
965
966      static _GLIBCXX_CONSTEXPR short
967      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
968
969      static _GLIBCXX_CONSTEXPR short
970      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
971
972      static _GLIBCXX_CONSTEXPR short
973      denorm_min() _GLIBCXX_USE_NOEXCEPT { return short(); }
974
975      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
976      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
977      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
978
979      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
980      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
981      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
982       = round_toward_zero;
983    };
984
985  /// numeric_limits<unsigned short> specialization.
986  template<>
987    struct numeric_limits<unsigned short>
988    {
989      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
990
991      static _GLIBCXX_CONSTEXPR unsigned short
992      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
993
994      static _GLIBCXX_CONSTEXPR unsigned short
995      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__ * 2U + 1; }
996
997#if __cplusplus >= 201103L
998      static constexpr unsigned short
999      lowest() noexcept { return min(); }
1000#endif
1001
1002      static _GLIBCXX_USE_CONSTEXPR int digits
1003       = __glibcxx_digits (unsigned short);
1004      static _GLIBCXX_USE_CONSTEXPR int digits10
1005       = __glibcxx_digits10 (unsigned short);
1006#if __cplusplus >= 201103L
1007      static constexpr int max_digits10 = 0;
1008#endif
1009      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1010      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1011      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1012      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1013
1014      static _GLIBCXX_CONSTEXPR unsigned short
1015      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1016
1017      static _GLIBCXX_CONSTEXPR unsigned short
1018      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1019
1020      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1021      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1022      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1023      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1024
1025      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1026      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1027      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1028      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1029       = denorm_absent;
1030      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1031
1032      static _GLIBCXX_CONSTEXPR unsigned short
1033      infinity() _GLIBCXX_USE_NOEXCEPT
1034      { return static_cast<unsigned short>(0); }
1035
1036      static _GLIBCXX_CONSTEXPR unsigned short
1037      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1038      { return static_cast<unsigned short>(0); }
1039
1040      static _GLIBCXX_CONSTEXPR unsigned short
1041      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1042      { return static_cast<unsigned short>(0); }
1043
1044      static _GLIBCXX_CONSTEXPR unsigned short
1045      denorm_min() _GLIBCXX_USE_NOEXCEPT
1046      { return static_cast<unsigned short>(0); }
1047
1048      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1049      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1050      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1051
1052      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1053      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1054      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1055       = round_toward_zero;
1056    };
1057
1058  /// numeric_limits<int> specialization.
1059  template<>
1060    struct numeric_limits<int>
1061    {
1062      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1063
1064      static _GLIBCXX_CONSTEXPR int
1065      min() _GLIBCXX_USE_NOEXCEPT { return -__INT_MAX__ - 1; }
1066
1067      static _GLIBCXX_CONSTEXPR int
1068      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__; }
1069
1070#if __cplusplus >= 201103L
1071      static constexpr int
1072      lowest() noexcept { return min(); }
1073#endif
1074
1075      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (int);
1076      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (int);
1077#if __cplusplus >= 201103L
1078      static constexpr int max_digits10 = 0;
1079#endif
1080      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1081      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1082      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1083      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1084
1085      static _GLIBCXX_CONSTEXPR int
1086      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1087
1088      static _GLIBCXX_CONSTEXPR int
1089      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1090
1091      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1092      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1093      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1094      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1095
1096      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1097      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1098      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1099      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1100       = denorm_absent;
1101      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1102
1103      static _GLIBCXX_CONSTEXPR int
1104      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1105
1106      static _GLIBCXX_CONSTEXPR int
1107      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1108
1109      static _GLIBCXX_CONSTEXPR int
1110      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1111
1112      static _GLIBCXX_CONSTEXPR int
1113      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1114
1115      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1116      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1117      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1118
1119      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1120      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1121      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1122       = round_toward_zero;
1123    };
1124
1125  /// numeric_limits<unsigned int> specialization.
1126  template<>
1127    struct numeric_limits<unsigned int>
1128    {
1129      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1130
1131      static _GLIBCXX_CONSTEXPR unsigned int
1132      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1133
1134      static _GLIBCXX_CONSTEXPR unsigned int
1135      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__ * 2U + 1; }
1136
1137#if __cplusplus >= 201103L
1138      static constexpr unsigned int
1139      lowest() noexcept { return min(); }
1140#endif
1141
1142      static _GLIBCXX_USE_CONSTEXPR int digits
1143       = __glibcxx_digits (unsigned int);
1144      static _GLIBCXX_USE_CONSTEXPR int digits10
1145       = __glibcxx_digits10 (unsigned int);
1146#if __cplusplus >= 201103L
1147      static constexpr int max_digits10 = 0;
1148#endif
1149      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1150      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1151      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1152      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1153
1154      static _GLIBCXX_CONSTEXPR unsigned int
1155      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1156
1157      static _GLIBCXX_CONSTEXPR unsigned int
1158      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1159
1160      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1161      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1162      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1163      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1164
1165      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1166      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1167      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1168      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1169       = denorm_absent;
1170      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1171
1172      static _GLIBCXX_CONSTEXPR unsigned int
1173      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<unsigned int>(0); }
1174
1175      static _GLIBCXX_CONSTEXPR unsigned int
1176      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1177      { return static_cast<unsigned int>(0); }
1178
1179      static _GLIBCXX_CONSTEXPR unsigned int
1180      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1181      { return static_cast<unsigned int>(0); }
1182
1183      static _GLIBCXX_CONSTEXPR unsigned int
1184      denorm_min() _GLIBCXX_USE_NOEXCEPT
1185      { return static_cast<unsigned int>(0); }
1186
1187      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1188      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1189      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1190
1191      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1192      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1193      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1194       = round_toward_zero;
1195    };
1196
1197  /// numeric_limits<long> specialization.
1198  template<>
1199    struct numeric_limits<long>
1200    {
1201      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1202
1203      static _GLIBCXX_CONSTEXPR long
1204      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_MAX__ - 1; }
1205
1206      static _GLIBCXX_CONSTEXPR long
1207      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__; }
1208
1209#if __cplusplus >= 201103L
1210      static constexpr long
1211      lowest() noexcept { return min(); }
1212#endif
1213
1214      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (long);
1215      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (long);
1216#if __cplusplus >= 201103L
1217      static constexpr int max_digits10 = 0;
1218#endif
1219      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1220      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1221      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1222      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1223
1224      static _GLIBCXX_CONSTEXPR long
1225      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1226
1227      static _GLIBCXX_CONSTEXPR long
1228      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1229
1230      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1231      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1232      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1233      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1234
1235      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1236      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1237      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1238      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1239       = denorm_absent;
1240      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1241
1242      static _GLIBCXX_CONSTEXPR long
1243      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1244
1245      static _GLIBCXX_CONSTEXPR long
1246      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1247
1248      static _GLIBCXX_CONSTEXPR long
1249      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1250
1251      static _GLIBCXX_CONSTEXPR long
1252      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1253
1254      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1255      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1256      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1257
1258      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1259      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1260      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1261       = round_toward_zero;
1262    };
1263
1264  /// numeric_limits<unsigned long> specialization.
1265  template<>
1266    struct numeric_limits<unsigned long>
1267    {
1268      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1269
1270      static _GLIBCXX_CONSTEXPR unsigned long
1271      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1272
1273      static _GLIBCXX_CONSTEXPR unsigned long
1274      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__ * 2UL + 1; }
1275
1276#if __cplusplus >= 201103L
1277      static constexpr unsigned long
1278      lowest() noexcept { return min(); }
1279#endif
1280
1281      static _GLIBCXX_USE_CONSTEXPR int digits
1282       = __glibcxx_digits (unsigned long);
1283      static _GLIBCXX_USE_CONSTEXPR int digits10
1284       = __glibcxx_digits10 (unsigned long);
1285#if __cplusplus >= 201103L
1286      static constexpr int max_digits10 = 0;
1287#endif
1288      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1289      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1290      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1291      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1292
1293      static _GLIBCXX_CONSTEXPR unsigned long
1294      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1295
1296      static _GLIBCXX_CONSTEXPR unsigned long
1297      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1298
1299      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1300      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1301      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1302      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1303
1304      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1305      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1306      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1307      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1308       = denorm_absent;
1309      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1310
1311      static _GLIBCXX_CONSTEXPR unsigned long
1312      infinity() _GLIBCXX_USE_NOEXCEPT
1313      { return static_cast<unsigned long>(0); }
1314
1315      static _GLIBCXX_CONSTEXPR unsigned long
1316      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1317      { return static_cast<unsigned long>(0); }
1318
1319      static _GLIBCXX_CONSTEXPR unsigned long
1320      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1321      { return static_cast<unsigned long>(0); }
1322
1323      static _GLIBCXX_CONSTEXPR unsigned long
1324      denorm_min() _GLIBCXX_USE_NOEXCEPT
1325      { return static_cast<unsigned long>(0); }
1326
1327      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1328      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1329      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1330
1331      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1332      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1333      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1334       = round_toward_zero;
1335    };
1336
1337  /// numeric_limits<long long> specialization.
1338  template<>
1339    struct numeric_limits<long long>
1340    {
1341      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1342
1343      static _GLIBCXX_CONSTEXPR long long
1344      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_LONG_MAX__ - 1; }
1345
1346      static _GLIBCXX_CONSTEXPR long long
1347      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__; }
1348
1349#if __cplusplus >= 201103L
1350      static constexpr long long
1351      lowest() noexcept { return min(); }
1352#endif
1353
1354      static _GLIBCXX_USE_CONSTEXPR int digits
1355       = __glibcxx_digits (long long);
1356      static _GLIBCXX_USE_CONSTEXPR int digits10
1357       = __glibcxx_digits10 (long long);
1358#if __cplusplus >= 201103L
1359      static constexpr int max_digits10 = 0;
1360#endif
1361      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1362      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1363      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1364      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1365
1366      static _GLIBCXX_CONSTEXPR long long
1367      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1368
1369      static _GLIBCXX_CONSTEXPR long long
1370      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1371
1372      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1373      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1374      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1375      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1376
1377      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1378      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1379      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1380      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1381       = denorm_absent;
1382      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1383
1384      static _GLIBCXX_CONSTEXPR long long
1385      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1386
1387      static _GLIBCXX_CONSTEXPR long long
1388      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1389
1390      static _GLIBCXX_CONSTEXPR long long
1391      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1392      { return static_cast<long long>(0); }
1393
1394      static _GLIBCXX_CONSTEXPR long long
1395      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1396
1397      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1398      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1399      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1400
1401      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1402      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1403      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1404       = round_toward_zero;
1405    };
1406
1407  /// numeric_limits<unsigned long long> specialization.
1408  template<>
1409    struct numeric_limits<unsigned long long>
1410    {
1411      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1412
1413      static _GLIBCXX_CONSTEXPR unsigned long long
1414      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1415
1416      static _GLIBCXX_CONSTEXPR unsigned long long
1417      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__ * 2ULL + 1; }
1418
1419#if __cplusplus >= 201103L
1420      static constexpr unsigned long long
1421      lowest() noexcept { return min(); }
1422#endif
1423
1424      static _GLIBCXX_USE_CONSTEXPR int digits
1425       = __glibcxx_digits (unsigned long long);
1426      static _GLIBCXX_USE_CONSTEXPR int digits10
1427       = __glibcxx_digits10 (unsigned long long);
1428#if __cplusplus >= 201103L
1429      static constexpr int max_digits10 = 0;
1430#endif
1431      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1432      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1433      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1434      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1435
1436      static _GLIBCXX_CONSTEXPR unsigned long long
1437      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1438
1439      static _GLIBCXX_CONSTEXPR unsigned long long
1440      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1441
1442      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1443      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1444      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1445      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1446
1447      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1448      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1449      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1450      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1451       = denorm_absent;
1452      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1453
1454      static _GLIBCXX_CONSTEXPR unsigned long long
1455      infinity() _GLIBCXX_USE_NOEXCEPT
1456      { return static_cast<unsigned long long>(0); }
1457
1458      static _GLIBCXX_CONSTEXPR unsigned long long
1459      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1460      { return static_cast<unsigned long long>(0); }
1461
1462      static _GLIBCXX_CONSTEXPR unsigned long long
1463      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1464      { return static_cast<unsigned long long>(0); }
1465
1466      static _GLIBCXX_CONSTEXPR unsigned long long
1467      denorm_min() _GLIBCXX_USE_NOEXCEPT
1468      { return static_cast<unsigned long long>(0); }
1469
1470      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1471      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1472      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1473
1474      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1475      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1476      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1477       = round_toward_zero;
1478    };
1479
1480#define __INT_N(TYPE, BITSIZE, EXT, UEXT)			\
1481  template<> 									\
1482    struct numeric_limits<TYPE> 						\
1483    { 										\
1484      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true; 		\
1485 										\
1486      static _GLIBCXX_CONSTEXPR TYPE 						\
1487	min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min_b (TYPE, BITSIZE); } \
1488 										\
1489      static _GLIBCXX_CONSTEXPR TYPE 						\
1490      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max_b (TYPE, BITSIZE); } 	\
1491 										\
1492      static _GLIBCXX_USE_CONSTEXPR int digits 					\
1493       = BITSIZE - 1; 								\
1494      static _GLIBCXX_USE_CONSTEXPR int digits10 				\
1495       = (BITSIZE - 1) * 643L / 2136; 						\
1496      										\
1497      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true; 			\
1498      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true; 			\
1499      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true; 			\
1500      static _GLIBCXX_USE_CONSTEXPR int radix = 2; 				\
1501 										\
1502      static _GLIBCXX_CONSTEXPR TYPE 						\
1503      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1504 										\
1505      static _GLIBCXX_CONSTEXPR TYPE 						\
1506      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; } 			\
1507 										\
1508      EXT									\
1509 										\
1510      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0; 			\
1511      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0; 			\
1512      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0; 			\
1513      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0; 			\
1514 										\
1515      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false; 			\
1516      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false; 		\
1517      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false; 		\
1518      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 		\
1519       = denorm_absent; 							\
1520      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false; 		\
1521 										\
1522      static _GLIBCXX_CONSTEXPR TYPE 						\
1523      infinity() _GLIBCXX_USE_NOEXCEPT 						\
1524      { return static_cast<TYPE>(0); } 						\
1525 										\
1526      static _GLIBCXX_CONSTEXPR TYPE 						\
1527      quiet_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1528      { return static_cast<TYPE>(0); } 						\
1529       										\
1530      static _GLIBCXX_CONSTEXPR TYPE 						\
1531      signaling_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1532      { return static_cast<TYPE>(0); } 						\
1533       										\
1534      static _GLIBCXX_CONSTEXPR TYPE 						\
1535      denorm_min() _GLIBCXX_USE_NOEXCEPT 					\
1536      { return static_cast<TYPE>(0); } 						\
1537 										\
1538      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false; 			\
1539      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true; 			\
1540      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false; 			\
1541 										\
1542      static _GLIBCXX_USE_CONSTEXPR bool traps 					\
1543       = __glibcxx_integral_traps; 						\
1544      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false; 		\
1545      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 		\
1546       = round_toward_zero; 							\
1547    }; 										\
1548 										\
1549  template<> 									\
1550    struct numeric_limits<unsigned TYPE> 					\
1551    { 										\
1552      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true; 		\
1553 										\
1554      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1555      min() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1556 										\
1557      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1558      max() _GLIBCXX_USE_NOEXCEPT						\
1559      { return  __glibcxx_max_b (unsigned TYPE, BITSIZE); }			\
1560 										\
1561      UEXT									\
1562 										\
1563      static _GLIBCXX_USE_CONSTEXPR int digits 					\
1564       = BITSIZE; 								\
1565      static _GLIBCXX_USE_CONSTEXPR int digits10 				\
1566       = BITSIZE * 643L / 2136; 						\
1567      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false; 			\
1568      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true; 			\
1569      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true; 			\
1570      static _GLIBCXX_USE_CONSTEXPR int radix = 2; 				\
1571 										\
1572      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1573      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1574 										\
1575      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1576      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; } 			\
1577 										\
1578      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0; 			\
1579      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0; 			\
1580      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0; 			\
1581      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0; 			\
1582 										\
1583      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false; 			\
1584      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false; 		\
1585      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false; 		\
1586      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 		\
1587       = denorm_absent; 							\
1588      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false; 		\
1589 										\
1590      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1591      infinity() _GLIBCXX_USE_NOEXCEPT 						\
1592      { return static_cast<unsigned TYPE>(0); } 				\
1593 										\
1594      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1595      quiet_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1596      { return static_cast<unsigned TYPE>(0); } 				\
1597 										\
1598      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1599      signaling_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1600      { return static_cast<unsigned TYPE>(0); } 				\
1601 										\
1602      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1603      denorm_min() _GLIBCXX_USE_NOEXCEPT 					\
1604      { return static_cast<unsigned TYPE>(0); } 				\
1605 										\
1606      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false; 			\
1607      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true; 			\
1608      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true; 			\
1609 										\
1610      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps; 	\
1611      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false; 		\
1612      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 		\
1613       = round_toward_zero; 							\
1614    };
1615
1616#if __cplusplus >= 201103L
1617
1618#define __INT_N_201103(TYPE)							\
1619      static constexpr TYPE 							\
1620      lowest() noexcept { return min(); }					\
1621      static constexpr int max_digits10 = 0;
1622
1623#define __INT_N_U201103(TYPE)							\
1624      static constexpr unsigned TYPE 						\
1625      lowest() noexcept { return min(); }					\
1626      static constexpr int max_digits10 = 0;
1627
1628#else
1629#define __INT_N_201103(TYPE)
1630#define __INT_N_U201103(TYPE)
1631#endif
1632
1633#if !defined(__STRICT_ANSI__)
1634#ifdef __GLIBCXX_TYPE_INT_N_0
1635  __INT_N(__GLIBCXX_TYPE_INT_N_0, __GLIBCXX_BITSIZE_INT_N_0,
1636	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_0), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_0))
1637#endif
1638#ifdef __GLIBCXX_TYPE_INT_N_1
1639  __INT_N (__GLIBCXX_TYPE_INT_N_1, __GLIBCXX_BITSIZE_INT_N_1,
1640	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_1), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_1))
1641#endif
1642#ifdef __GLIBCXX_TYPE_INT_N_2
1643  __INT_N (__GLIBCXX_TYPE_INT_N_2, __GLIBCXX_BITSIZE_INT_N_2,
1644	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_2), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_2))
1645#endif
1646#ifdef __GLIBCXX_TYPE_INT_N_3
1647  __INT_N (__GLIBCXX_TYPE_INT_N_3, __GLIBCXX_BITSIZE_INT_N_3,
1648	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_3), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_3))
1649#endif
1650
1651#elif defined __STRICT_ANSI__ && defined __SIZEOF_INT128__
1652  __INT_N(__int128, 128,
1653	  __INT_N_201103 (__int128),
1654	  __INT_N_U201103 (__int128))
1655#endif
1656
1657#undef __INT_N
1658#undef __INT_N_201103
1659#undef __INT_N_U201103
1660
1661
1662  /// numeric_limits<float> specialization.
1663  template<>
1664    struct numeric_limits<float>
1665    {
1666      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1667
1668      static _GLIBCXX_CONSTEXPR float
1669      min() _GLIBCXX_USE_NOEXCEPT { return __FLT_MIN__; }
1670
1671      static _GLIBCXX_CONSTEXPR float
1672      max() _GLIBCXX_USE_NOEXCEPT { return __FLT_MAX__; }
1673
1674#if __cplusplus >= 201103L
1675      static constexpr float
1676      lowest() noexcept { return -__FLT_MAX__; }
1677#endif
1678
1679      static _GLIBCXX_USE_CONSTEXPR int digits = __FLT_MANT_DIG__;
1680      static _GLIBCXX_USE_CONSTEXPR int digits10 = __FLT_DIG__;
1681#if __cplusplus >= 201103L
1682      static constexpr int max_digits10
1683	 = __glibcxx_max_digits10 (__FLT_MANT_DIG__);
1684#endif
1685      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1686      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1687      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1688      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1689
1690      static _GLIBCXX_CONSTEXPR float
1691      epsilon() _GLIBCXX_USE_NOEXCEPT { return __FLT_EPSILON__; }
1692
1693      static _GLIBCXX_CONSTEXPR float
1694      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5F; }
1695
1696      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __FLT_MIN_EXP__;
1697      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __FLT_MIN_10_EXP__;
1698      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __FLT_MAX_EXP__;
1699      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __FLT_MAX_10_EXP__;
1700
1701      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __FLT_HAS_INFINITY__;
1702      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __FLT_HAS_QUIET_NAN__;
1703      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1704      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1705	= bool(__FLT_HAS_DENORM__) ? denorm_present : denorm_absent;
1706      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1707       = __glibcxx_float_has_denorm_loss;
1708
1709      static _GLIBCXX_CONSTEXPR float
1710      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_valf(); }
1711
1712      static _GLIBCXX_CONSTEXPR float
1713      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanf(""); }
1714
1715      static _GLIBCXX_CONSTEXPR float
1716      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansf(""); }
1717
1718      static _GLIBCXX_CONSTEXPR float
1719      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __FLT_DENORM_MIN__; }
1720
1721      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1722	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1723      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1724      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1725
1726      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_float_traps;
1727      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1728       = __glibcxx_float_tinyness_before;
1729      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1730       = round_to_nearest;
1731    };
1732
1733#undef __glibcxx_float_has_denorm_loss
1734#undef __glibcxx_float_traps
1735#undef __glibcxx_float_tinyness_before
1736
1737  /// numeric_limits<double> specialization.
1738  template<>
1739    struct numeric_limits<double>
1740    {
1741      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1742
1743      static _GLIBCXX_CONSTEXPR double
1744      min() _GLIBCXX_USE_NOEXCEPT { return __DBL_MIN__; }
1745
1746      static _GLIBCXX_CONSTEXPR double
1747      max() _GLIBCXX_USE_NOEXCEPT { return __DBL_MAX__; }
1748
1749#if __cplusplus >= 201103L
1750      static constexpr double
1751      lowest() noexcept { return -__DBL_MAX__; }
1752#endif
1753
1754      static _GLIBCXX_USE_CONSTEXPR int digits = __DBL_MANT_DIG__;
1755      static _GLIBCXX_USE_CONSTEXPR int digits10 = __DBL_DIG__;
1756#if __cplusplus >= 201103L
1757      static constexpr int max_digits10
1758	 = __glibcxx_max_digits10 (__DBL_MANT_DIG__);
1759#endif
1760      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1761      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1762      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1763      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1764
1765      static _GLIBCXX_CONSTEXPR double
1766      epsilon() _GLIBCXX_USE_NOEXCEPT { return __DBL_EPSILON__; }
1767
1768      static _GLIBCXX_CONSTEXPR double
1769      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5; }
1770
1771      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __DBL_MIN_EXP__;
1772      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __DBL_MIN_10_EXP__;
1773      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __DBL_MAX_EXP__;
1774      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __DBL_MAX_10_EXP__;
1775
1776      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __DBL_HAS_INFINITY__;
1777      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __DBL_HAS_QUIET_NAN__;
1778      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1779      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1780	= bool(__DBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1781      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1782        = __glibcxx_double_has_denorm_loss;
1783
1784      static _GLIBCXX_CONSTEXPR double
1785      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_val(); }
1786
1787      static _GLIBCXX_CONSTEXPR double
1788      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nan(""); }
1789
1790      static _GLIBCXX_CONSTEXPR double
1791      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nans(""); }
1792
1793      static _GLIBCXX_CONSTEXPR double
1794      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __DBL_DENORM_MIN__; }
1795
1796      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1797	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1798      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1799      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1800
1801      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_double_traps;
1802      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1803       = __glibcxx_double_tinyness_before;
1804      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1805       = round_to_nearest;
1806    };
1807
1808#undef __glibcxx_double_has_denorm_loss
1809#undef __glibcxx_double_traps
1810#undef __glibcxx_double_tinyness_before
1811
1812  /// numeric_limits<long double> specialization.
1813  template<>
1814    struct numeric_limits<long double>
1815    {
1816      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1817
1818      static _GLIBCXX_CONSTEXPR long double
1819      min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MIN__; }
1820
1821      static _GLIBCXX_CONSTEXPR long double
1822      max() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MAX__; }
1823
1824#if __cplusplus >= 201103L
1825      static constexpr long double
1826      lowest() noexcept { return -__LDBL_MAX__; }
1827#endif
1828
1829      static _GLIBCXX_USE_CONSTEXPR int digits = __LDBL_MANT_DIG__;
1830      static _GLIBCXX_USE_CONSTEXPR int digits10 = __LDBL_DIG__;
1831#if __cplusplus >= 201103L
1832      static _GLIBCXX_USE_CONSTEXPR int max_digits10
1833	 = __glibcxx_max_digits10 (__LDBL_MANT_DIG__);
1834#endif
1835      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1836      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1837      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1838      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1839
1840      static _GLIBCXX_CONSTEXPR long double
1841      epsilon() _GLIBCXX_USE_NOEXCEPT { return __LDBL_EPSILON__; }
1842
1843      static _GLIBCXX_CONSTEXPR long double
1844      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5L; }
1845
1846      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __LDBL_MIN_EXP__;
1847      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __LDBL_MIN_10_EXP__;
1848      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __LDBL_MAX_EXP__;
1849      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __LDBL_MAX_10_EXP__;
1850
1851      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __LDBL_HAS_INFINITY__;
1852      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __LDBL_HAS_QUIET_NAN__;
1853      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1854      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1855	= bool(__LDBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1856      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1857	= __glibcxx_long_double_has_denorm_loss;
1858
1859      static _GLIBCXX_CONSTEXPR long double
1860      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_vall(); }
1861
1862      static _GLIBCXX_CONSTEXPR long double
1863      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanl(""); }
1864
1865      static _GLIBCXX_CONSTEXPR long double
1866      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansl(""); }
1867
1868      static _GLIBCXX_CONSTEXPR long double
1869      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_DENORM_MIN__; }
1870
1871      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1872	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1873      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1874      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1875
1876      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_long_double_traps;
1877      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before =
1878					 __glibcxx_long_double_tinyness_before;
1879      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style =
1880						      round_to_nearest;
1881    };
1882
1883#undef __glibcxx_long_double_has_denorm_loss
1884#undef __glibcxx_long_double_traps
1885#undef __glibcxx_long_double_tinyness_before
1886
1887_GLIBCXX_END_NAMESPACE_VERSION
1888} // namespace
1889
1890#undef __glibcxx_signed
1891#undef __glibcxx_min
1892#undef __glibcxx_max
1893#undef __glibcxx_digits
1894#undef __glibcxx_digits10
1895#undef __glibcxx_max_digits10
1896
1897#endif // _GLIBCXX_NUMERIC_LIMITS
1898