1// The template and inlines for the numeric_limits classes. -*- C++ -*-
2
3// Copyright (C) 1999-2018 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
378  // _GLIBCXX_RESOLVE_LIB_DEFECTS
379  // 184. numeric_limits<bool> wording problems
380
381  /// numeric_limits<bool> specialization.
382  template<>
383    struct numeric_limits<bool>
384    {
385      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
386
387      static _GLIBCXX_CONSTEXPR bool
388      min() _GLIBCXX_USE_NOEXCEPT { return false; }
389
390      static _GLIBCXX_CONSTEXPR bool
391      max() _GLIBCXX_USE_NOEXCEPT { return true; }
392
393#if __cplusplus >= 201103L
394      static constexpr bool
395      lowest() noexcept { return min(); }
396#endif
397      static _GLIBCXX_USE_CONSTEXPR int digits = 1;
398      static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
399#if __cplusplus >= 201103L
400      static constexpr int max_digits10 = 0;
401#endif
402      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
403      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
404      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
405      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
406
407      static _GLIBCXX_CONSTEXPR bool
408      epsilon() _GLIBCXX_USE_NOEXCEPT { return false; }
409
410      static _GLIBCXX_CONSTEXPR bool
411      round_error() _GLIBCXX_USE_NOEXCEPT { return false; }
412
413      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
414      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
415      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
416      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
417
418      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
419      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
420      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
421      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
422       = denorm_absent;
423      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
424
425      static _GLIBCXX_CONSTEXPR bool
426      infinity() _GLIBCXX_USE_NOEXCEPT { return false; }
427
428      static _GLIBCXX_CONSTEXPR bool
429      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
430
431      static _GLIBCXX_CONSTEXPR bool
432      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }
433
434      static _GLIBCXX_CONSTEXPR bool
435      denorm_min() _GLIBCXX_USE_NOEXCEPT { return false; }
436
437      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
438      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
439      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
440
441      // It is not clear what it means for a boolean type to trap.
442      // This is a DR on the LWG issue list.  Here, I use integer
443      // promotion semantics.
444      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
445      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
446      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
447       = round_toward_zero;
448    };
449
450  /// numeric_limits<char> specialization.
451  template<>
452    struct numeric_limits<char>
453    {
454      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
455
456      static _GLIBCXX_CONSTEXPR char
457      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min(char); }
458
459      static _GLIBCXX_CONSTEXPR char
460      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max(char); }
461
462#if __cplusplus >= 201103L
463      static constexpr char
464      lowest() noexcept { return min(); }
465#endif
466
467      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (char);
468      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (char);
469#if __cplusplus >= 201103L
470      static constexpr int max_digits10 = 0;
471#endif
472      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (char);
473      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
474      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
475      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
476
477      static _GLIBCXX_CONSTEXPR char
478      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
479
480      static _GLIBCXX_CONSTEXPR char
481      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
482
483      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
484      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
485      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
486      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
487
488      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
489      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
490      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
491      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
492       = denorm_absent;
493      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
494
495      static _GLIBCXX_CONSTEXPR
496      char infinity() _GLIBCXX_USE_NOEXCEPT { return char(); }
497
498      static _GLIBCXX_CONSTEXPR char
499      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
500
501      static _GLIBCXX_CONSTEXPR char
502      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }
503
504      static _GLIBCXX_CONSTEXPR char
505      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<char>(0); }
506
507      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
508      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
509      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
510
511      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
512      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
513      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
514       = round_toward_zero;
515    };
516
517  /// numeric_limits<signed char> specialization.
518  template<>
519    struct numeric_limits<signed char>
520    {
521      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
522
523      static _GLIBCXX_CONSTEXPR signed char
524      min() _GLIBCXX_USE_NOEXCEPT { return -__SCHAR_MAX__ - 1; }
525
526      static _GLIBCXX_CONSTEXPR signed char
527      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__; }
528
529#if __cplusplus >= 201103L
530      static constexpr signed char
531      lowest() noexcept { return min(); }
532#endif
533
534      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (signed char);
535      static _GLIBCXX_USE_CONSTEXPR int digits10
536       = __glibcxx_digits10 (signed char);
537#if __cplusplus >= 201103L
538      static constexpr int max_digits10 = 0;
539#endif
540      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
541      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
542      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
543      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
544
545      static _GLIBCXX_CONSTEXPR signed char
546      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
547
548      static _GLIBCXX_CONSTEXPR signed char
549      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
550
551      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
552      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
553      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
554      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
555
556      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
557      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
558      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
559      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
560       = denorm_absent;
561      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
562
563      static _GLIBCXX_CONSTEXPR signed char
564      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
565
566      static _GLIBCXX_CONSTEXPR signed char
567      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }
568
569      static _GLIBCXX_CONSTEXPR signed char
570      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
571      { return static_cast<signed char>(0); }
572
573      static _GLIBCXX_CONSTEXPR signed char
574      denorm_min() _GLIBCXX_USE_NOEXCEPT
575      { return static_cast<signed char>(0); }
576
577      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
578      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
579      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
580
581      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
582      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
583      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
584       = round_toward_zero;
585    };
586
587  /// numeric_limits<unsigned char> specialization.
588  template<>
589    struct numeric_limits<unsigned char>
590    {
591      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
592
593      static _GLIBCXX_CONSTEXPR unsigned char
594      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
595
596      static _GLIBCXX_CONSTEXPR unsigned char
597      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__ * 2U + 1; }
598
599#if __cplusplus >= 201103L
600      static constexpr unsigned char
601      lowest() noexcept { return min(); }
602#endif
603
604      static _GLIBCXX_USE_CONSTEXPR int digits
605       = __glibcxx_digits (unsigned char);
606      static _GLIBCXX_USE_CONSTEXPR int digits10
607       = __glibcxx_digits10 (unsigned char);
608#if __cplusplus >= 201103L
609      static constexpr int max_digits10 = 0;
610#endif
611      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
612      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
613      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
614      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
615
616      static _GLIBCXX_CONSTEXPR unsigned char
617      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
618
619      static _GLIBCXX_CONSTEXPR unsigned char
620      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
621
622      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
623      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
624      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
625      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
626
627      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
628      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
629      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
630      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
631       = denorm_absent;
632      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
633
634      static _GLIBCXX_CONSTEXPR unsigned char
635      infinity() _GLIBCXX_USE_NOEXCEPT
636      { return static_cast<unsigned char>(0); }
637
638      static _GLIBCXX_CONSTEXPR unsigned char
639      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
640      { return static_cast<unsigned char>(0); }
641
642      static _GLIBCXX_CONSTEXPR unsigned char
643      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
644      { return static_cast<unsigned char>(0); }
645
646      static _GLIBCXX_CONSTEXPR unsigned char
647      denorm_min() _GLIBCXX_USE_NOEXCEPT
648      { return static_cast<unsigned char>(0); }
649
650      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
651      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
652      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
653
654      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
655      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
656      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
657       = round_toward_zero;
658    };
659
660  /// numeric_limits<wchar_t> specialization.
661  template<>
662    struct numeric_limits<wchar_t>
663    {
664      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
665
666      static _GLIBCXX_CONSTEXPR wchar_t
667      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (wchar_t); }
668
669      static _GLIBCXX_CONSTEXPR wchar_t
670      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (wchar_t); }
671
672#if __cplusplus >= 201103L
673      static constexpr wchar_t
674      lowest() noexcept { return min(); }
675#endif
676
677      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (wchar_t);
678      static _GLIBCXX_USE_CONSTEXPR int digits10
679       = __glibcxx_digits10 (wchar_t);
680#if __cplusplus >= 201103L
681      static constexpr int max_digits10 = 0;
682#endif
683      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (wchar_t);
684      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
685      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
686      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
687
688      static _GLIBCXX_CONSTEXPR wchar_t
689      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
690
691      static _GLIBCXX_CONSTEXPR wchar_t
692      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
693
694      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
695      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
696      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
697      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
698
699      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
700      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
701      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
702      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
703       = denorm_absent;
704      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
705
706      static _GLIBCXX_CONSTEXPR wchar_t
707      infinity() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
708
709      static _GLIBCXX_CONSTEXPR wchar_t
710      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
711
712      static _GLIBCXX_CONSTEXPR wchar_t
713      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
714
715      static _GLIBCXX_CONSTEXPR wchar_t
716      denorm_min() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }
717
718      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
719      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
720      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;
721
722      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
723      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
724      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
725       = round_toward_zero;
726    };
727
728#if __cplusplus >= 201103L
729  /// numeric_limits<char16_t> specialization.
730  template<>
731    struct numeric_limits<char16_t>
732    {
733      static constexpr bool is_specialized = true;
734
735      static constexpr char16_t
736      min() noexcept { return __glibcxx_min (char16_t); }
737
738      static constexpr char16_t
739      max() noexcept { return __glibcxx_max (char16_t); }
740
741      static constexpr char16_t
742      lowest() noexcept { return min(); }
743
744      static constexpr int digits = __glibcxx_digits (char16_t);
745      static constexpr int digits10 = __glibcxx_digits10 (char16_t);
746      static constexpr int max_digits10 = 0;
747      static constexpr bool is_signed = __glibcxx_signed (char16_t);
748      static constexpr bool is_integer = true;
749      static constexpr bool is_exact = true;
750      static constexpr int radix = 2;
751
752      static constexpr char16_t
753      epsilon() noexcept { return 0; }
754
755      static constexpr char16_t
756      round_error() noexcept { return 0; }
757
758      static constexpr int min_exponent = 0;
759      static constexpr int min_exponent10 = 0;
760      static constexpr int max_exponent = 0;
761      static constexpr int max_exponent10 = 0;
762
763      static constexpr bool has_infinity = false;
764      static constexpr bool has_quiet_NaN = false;
765      static constexpr bool has_signaling_NaN = false;
766      static constexpr float_denorm_style has_denorm = denorm_absent;
767      static constexpr bool has_denorm_loss = false;
768
769      static constexpr char16_t
770      infinity() noexcept { return char16_t(); }
771
772      static constexpr char16_t
773      quiet_NaN() noexcept { return char16_t(); }
774
775      static constexpr char16_t
776      signaling_NaN() noexcept { return char16_t(); }
777
778      static constexpr char16_t
779      denorm_min() noexcept { return char16_t(); }
780
781      static constexpr bool is_iec559 = false;
782      static constexpr bool is_bounded = true;
783      static constexpr bool is_modulo = !is_signed;
784
785      static constexpr bool traps = __glibcxx_integral_traps;
786      static constexpr bool tinyness_before = false;
787      static constexpr float_round_style round_style = round_toward_zero;
788    };
789
790  /// numeric_limits<char32_t> specialization.
791  template<>
792    struct numeric_limits<char32_t>
793    {
794      static constexpr bool is_specialized = true;
795
796      static constexpr char32_t
797      min() noexcept { return __glibcxx_min (char32_t); }
798
799      static constexpr char32_t
800      max() noexcept { return __glibcxx_max (char32_t); }
801
802      static constexpr char32_t
803      lowest() noexcept { return min(); }
804
805      static constexpr int digits = __glibcxx_digits (char32_t);
806      static constexpr int digits10 = __glibcxx_digits10 (char32_t);
807      static constexpr int max_digits10 = 0;
808      static constexpr bool is_signed = __glibcxx_signed (char32_t);
809      static constexpr bool is_integer = true;
810      static constexpr bool is_exact = true;
811      static constexpr int radix = 2;
812
813      static constexpr char32_t
814      epsilon() noexcept { return 0; }
815
816      static constexpr char32_t
817      round_error() noexcept { return 0; }
818
819      static constexpr int min_exponent = 0;
820      static constexpr int min_exponent10 = 0;
821      static constexpr int max_exponent = 0;
822      static constexpr int max_exponent10 = 0;
823
824      static constexpr bool has_infinity = false;
825      static constexpr bool has_quiet_NaN = false;
826      static constexpr bool has_signaling_NaN = false;
827      static constexpr float_denorm_style has_denorm = denorm_absent;
828      static constexpr bool has_denorm_loss = false;
829
830      static constexpr char32_t
831      infinity() noexcept { return char32_t(); }
832
833      static constexpr char32_t
834      quiet_NaN() noexcept { return char32_t(); }
835
836      static constexpr char32_t
837      signaling_NaN() noexcept { return char32_t(); }
838
839      static constexpr char32_t
840      denorm_min() noexcept { return char32_t(); }
841
842      static constexpr bool is_iec559 = false;
843      static constexpr bool is_bounded = true;
844      static constexpr bool is_modulo = !is_signed;
845
846      static constexpr bool traps = __glibcxx_integral_traps;
847      static constexpr bool tinyness_before = false;
848      static constexpr float_round_style round_style = round_toward_zero;
849    };
850#endif
851
852  /// numeric_limits<short> specialization.
853  template<>
854    struct numeric_limits<short>
855    {
856      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
857
858      static _GLIBCXX_CONSTEXPR short
859      min() _GLIBCXX_USE_NOEXCEPT { return -__SHRT_MAX__ - 1; }
860
861      static _GLIBCXX_CONSTEXPR short
862      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__; }
863
864#if __cplusplus >= 201103L
865      static constexpr short
866      lowest() noexcept { return min(); }
867#endif
868
869      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (short);
870      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (short);
871#if __cplusplus >= 201103L
872      static constexpr int max_digits10 = 0;
873#endif
874      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
875      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
876      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
877      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
878
879      static _GLIBCXX_CONSTEXPR short
880      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
881
882      static _GLIBCXX_CONSTEXPR short
883      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
884
885      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
886      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
887      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
888      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
889
890      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
891      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
892      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
893      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
894       = denorm_absent;
895      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
896
897      static _GLIBCXX_CONSTEXPR short
898      infinity() _GLIBCXX_USE_NOEXCEPT { return short(); }
899
900      static _GLIBCXX_CONSTEXPR short
901      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
902
903      static _GLIBCXX_CONSTEXPR short
904      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }
905
906      static _GLIBCXX_CONSTEXPR short
907      denorm_min() _GLIBCXX_USE_NOEXCEPT { return short(); }
908
909      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
910      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
911      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
912
913      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
914      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
915      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
916       = round_toward_zero;
917    };
918
919  /// numeric_limits<unsigned short> specialization.
920  template<>
921    struct numeric_limits<unsigned short>
922    {
923      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
924
925      static _GLIBCXX_CONSTEXPR unsigned short
926      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
927
928      static _GLIBCXX_CONSTEXPR unsigned short
929      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__ * 2U + 1; }
930
931#if __cplusplus >= 201103L
932      static constexpr unsigned short
933      lowest() noexcept { return min(); }
934#endif
935
936      static _GLIBCXX_USE_CONSTEXPR int digits
937       = __glibcxx_digits (unsigned short);
938      static _GLIBCXX_USE_CONSTEXPR int digits10
939       = __glibcxx_digits10 (unsigned short);
940#if __cplusplus >= 201103L
941      static constexpr int max_digits10 = 0;
942#endif
943      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
944      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
945      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
946      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
947
948      static _GLIBCXX_CONSTEXPR unsigned short
949      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
950
951      static _GLIBCXX_CONSTEXPR unsigned short
952      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
953
954      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
955      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
956      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
957      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
958
959      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
960      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
961      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
962      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
963       = denorm_absent;
964      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
965
966      static _GLIBCXX_CONSTEXPR unsigned short
967      infinity() _GLIBCXX_USE_NOEXCEPT
968      { return static_cast<unsigned short>(0); }
969
970      static _GLIBCXX_CONSTEXPR unsigned short
971      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
972      { return static_cast<unsigned short>(0); }
973
974      static _GLIBCXX_CONSTEXPR unsigned short
975      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
976      { return static_cast<unsigned short>(0); }
977
978      static _GLIBCXX_CONSTEXPR unsigned short
979      denorm_min() _GLIBCXX_USE_NOEXCEPT
980      { return static_cast<unsigned short>(0); }
981
982      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
983      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
984      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
985
986      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
987      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
988      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
989       = round_toward_zero;
990    };
991
992  /// numeric_limits<int> specialization.
993  template<>
994    struct numeric_limits<int>
995    {
996      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
997
998      static _GLIBCXX_CONSTEXPR int
999      min() _GLIBCXX_USE_NOEXCEPT { return -__INT_MAX__ - 1; }
1000
1001      static _GLIBCXX_CONSTEXPR int
1002      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__; }
1003
1004#if __cplusplus >= 201103L
1005      static constexpr int
1006      lowest() noexcept { return min(); }
1007#endif
1008
1009      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (int);
1010      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (int);
1011#if __cplusplus >= 201103L
1012      static constexpr int max_digits10 = 0;
1013#endif
1014      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1015      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1016      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1017      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1018
1019      static _GLIBCXX_CONSTEXPR int
1020      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1021
1022      static _GLIBCXX_CONSTEXPR int
1023      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1024
1025      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1026      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1027      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1028      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1029
1030      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1031      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1032      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1033      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1034       = denorm_absent;
1035      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1036
1037      static _GLIBCXX_CONSTEXPR int
1038      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1039
1040      static _GLIBCXX_CONSTEXPR int
1041      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1042
1043      static _GLIBCXX_CONSTEXPR int
1044      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1045
1046      static _GLIBCXX_CONSTEXPR int
1047      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }
1048
1049      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1050      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1051      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1052
1053      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1054      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1055      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1056       = round_toward_zero;
1057    };
1058
1059  /// numeric_limits<unsigned int> specialization.
1060  template<>
1061    struct numeric_limits<unsigned int>
1062    {
1063      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1064
1065      static _GLIBCXX_CONSTEXPR unsigned int
1066      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1067
1068      static _GLIBCXX_CONSTEXPR unsigned int
1069      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__ * 2U + 1; }
1070
1071#if __cplusplus >= 201103L
1072      static constexpr unsigned int
1073      lowest() noexcept { return min(); }
1074#endif
1075
1076      static _GLIBCXX_USE_CONSTEXPR int digits
1077       = __glibcxx_digits (unsigned int);
1078      static _GLIBCXX_USE_CONSTEXPR int digits10
1079       = __glibcxx_digits10 (unsigned int);
1080#if __cplusplus >= 201103L
1081      static constexpr int max_digits10 = 0;
1082#endif
1083      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1084      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1085      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1086      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1087
1088      static _GLIBCXX_CONSTEXPR unsigned int
1089      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1090
1091      static _GLIBCXX_CONSTEXPR unsigned int
1092      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1093
1094      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1095      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1096      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1097      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1098
1099      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1100      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1101      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1102      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1103       = denorm_absent;
1104      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1105
1106      static _GLIBCXX_CONSTEXPR unsigned int
1107      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<unsigned int>(0); }
1108
1109      static _GLIBCXX_CONSTEXPR unsigned int
1110      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1111      { return static_cast<unsigned int>(0); }
1112
1113      static _GLIBCXX_CONSTEXPR unsigned int
1114      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1115      { return static_cast<unsigned int>(0); }
1116
1117      static _GLIBCXX_CONSTEXPR unsigned int
1118      denorm_min() _GLIBCXX_USE_NOEXCEPT
1119      { return static_cast<unsigned int>(0); }
1120
1121      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1122      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1123      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1124
1125      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1126      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1127      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1128       = round_toward_zero;
1129    };
1130
1131  /// numeric_limits<long> specialization.
1132  template<>
1133    struct numeric_limits<long>
1134    {
1135      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1136
1137      static _GLIBCXX_CONSTEXPR long
1138      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_MAX__ - 1; }
1139
1140      static _GLIBCXX_CONSTEXPR long
1141      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__; }
1142
1143#if __cplusplus >= 201103L
1144      static constexpr long
1145      lowest() noexcept { return min(); }
1146#endif
1147
1148      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (long);
1149      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (long);
1150#if __cplusplus >= 201103L
1151      static constexpr int max_digits10 = 0;
1152#endif
1153      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1154      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1155      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1156      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1157
1158      static _GLIBCXX_CONSTEXPR long
1159      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1160
1161      static _GLIBCXX_CONSTEXPR long
1162      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1163
1164      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1165      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1166      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1167      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1168
1169      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1170      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1171      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1172      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1173       = denorm_absent;
1174      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1175
1176      static _GLIBCXX_CONSTEXPR long
1177      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1178
1179      static _GLIBCXX_CONSTEXPR long
1180      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1181
1182      static _GLIBCXX_CONSTEXPR long
1183      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1184
1185      static _GLIBCXX_CONSTEXPR long
1186      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }
1187
1188      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1189      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1190      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1191
1192      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1193      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1194      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1195       = round_toward_zero;
1196    };
1197
1198  /// numeric_limits<unsigned long> specialization.
1199  template<>
1200    struct numeric_limits<unsigned long>
1201    {
1202      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1203
1204      static _GLIBCXX_CONSTEXPR unsigned long
1205      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1206
1207      static _GLIBCXX_CONSTEXPR unsigned long
1208      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__ * 2UL + 1; }
1209
1210#if __cplusplus >= 201103L
1211      static constexpr unsigned long
1212      lowest() noexcept { return min(); }
1213#endif
1214
1215      static _GLIBCXX_USE_CONSTEXPR int digits
1216       = __glibcxx_digits (unsigned long);
1217      static _GLIBCXX_USE_CONSTEXPR int digits10
1218       = __glibcxx_digits10 (unsigned long);
1219#if __cplusplus >= 201103L
1220      static constexpr int max_digits10 = 0;
1221#endif
1222      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1223      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1224      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1225      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1226
1227      static _GLIBCXX_CONSTEXPR unsigned long
1228      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1229
1230      static _GLIBCXX_CONSTEXPR unsigned long
1231      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1232
1233      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1234      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1235      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1236      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1237
1238      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1239      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1240      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1241      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1242       = denorm_absent;
1243      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1244
1245      static _GLIBCXX_CONSTEXPR unsigned long
1246      infinity() _GLIBCXX_USE_NOEXCEPT
1247      { return static_cast<unsigned long>(0); }
1248
1249      static _GLIBCXX_CONSTEXPR unsigned long
1250      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1251      { return static_cast<unsigned long>(0); }
1252
1253      static _GLIBCXX_CONSTEXPR unsigned long
1254      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1255      { return static_cast<unsigned long>(0); }
1256
1257      static _GLIBCXX_CONSTEXPR unsigned long
1258      denorm_min() _GLIBCXX_USE_NOEXCEPT
1259      { return static_cast<unsigned long>(0); }
1260
1261      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1262      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1263      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1264
1265      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1266      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1267      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1268       = round_toward_zero;
1269    };
1270
1271  /// numeric_limits<long long> specialization.
1272  template<>
1273    struct numeric_limits<long long>
1274    {
1275      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1276
1277      static _GLIBCXX_CONSTEXPR long long
1278      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_LONG_MAX__ - 1; }
1279
1280      static _GLIBCXX_CONSTEXPR long long
1281      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__; }
1282
1283#if __cplusplus >= 201103L
1284      static constexpr long long
1285      lowest() noexcept { return min(); }
1286#endif
1287
1288      static _GLIBCXX_USE_CONSTEXPR int digits
1289       = __glibcxx_digits (long long);
1290      static _GLIBCXX_USE_CONSTEXPR int digits10
1291       = __glibcxx_digits10 (long long);
1292#if __cplusplus >= 201103L
1293      static constexpr int max_digits10 = 0;
1294#endif
1295      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1296      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1297      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1298      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1299
1300      static _GLIBCXX_CONSTEXPR long long
1301      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1302
1303      static _GLIBCXX_CONSTEXPR long long
1304      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1305
1306      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1307      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1308      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1309      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1310
1311      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1312      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1313      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1314      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1315       = denorm_absent;
1316      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1317
1318      static _GLIBCXX_CONSTEXPR long long
1319      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1320
1321      static _GLIBCXX_CONSTEXPR long long
1322      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1323
1324      static _GLIBCXX_CONSTEXPR long long
1325      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1326      { return static_cast<long long>(0); }
1327
1328      static _GLIBCXX_CONSTEXPR long long
1329      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }
1330
1331      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1332      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1333      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1334
1335      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1336      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1337      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1338       = round_toward_zero;
1339    };
1340
1341  /// numeric_limits<unsigned long long> specialization.
1342  template<>
1343    struct numeric_limits<unsigned long long>
1344    {
1345      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1346
1347      static _GLIBCXX_CONSTEXPR unsigned long long
1348      min() _GLIBCXX_USE_NOEXCEPT { return 0; }
1349
1350      static _GLIBCXX_CONSTEXPR unsigned long long
1351      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__ * 2ULL + 1; }
1352
1353#if __cplusplus >= 201103L
1354      static constexpr unsigned long long
1355      lowest() noexcept { return min(); }
1356#endif
1357
1358      static _GLIBCXX_USE_CONSTEXPR int digits
1359       = __glibcxx_digits (unsigned long long);
1360      static _GLIBCXX_USE_CONSTEXPR int digits10
1361       = __glibcxx_digits10 (unsigned long long);
1362#if __cplusplus >= 201103L
1363      static constexpr int max_digits10 = 0;
1364#endif
1365      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
1366      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
1367      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
1368      static _GLIBCXX_USE_CONSTEXPR int radix = 2;
1369
1370      static _GLIBCXX_CONSTEXPR unsigned long long
1371      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }
1372
1373      static _GLIBCXX_CONSTEXPR unsigned long long
1374      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }
1375
1376      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
1377      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
1378      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
1379      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;
1380
1381      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
1382      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
1383      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
1384      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1385       = denorm_absent;
1386      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;
1387
1388      static _GLIBCXX_CONSTEXPR unsigned long long
1389      infinity() _GLIBCXX_USE_NOEXCEPT
1390      { return static_cast<unsigned long long>(0); }
1391
1392      static _GLIBCXX_CONSTEXPR unsigned long long
1393      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
1394      { return static_cast<unsigned long long>(0); }
1395
1396      static _GLIBCXX_CONSTEXPR unsigned long long
1397      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
1398      { return static_cast<unsigned long long>(0); }
1399
1400      static _GLIBCXX_CONSTEXPR unsigned long long
1401      denorm_min() _GLIBCXX_USE_NOEXCEPT
1402      { return static_cast<unsigned long long>(0); }
1403
1404      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
1405      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1406      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;
1407
1408      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
1409      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
1410      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1411       = round_toward_zero;
1412    };
1413
1414#if !defined(__STRICT_ANSI__)
1415
1416#define __INT_N(TYPE, BITSIZE, EXT, UEXT)			\
1417  template<> 									\
1418    struct numeric_limits<TYPE> 						\
1419    { 										\
1420      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true; 		\
1421 										\
1422      static _GLIBCXX_CONSTEXPR TYPE 						\
1423	min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min_b (TYPE, BITSIZE); } \
1424 										\
1425      static _GLIBCXX_CONSTEXPR TYPE 						\
1426      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max_b (TYPE, BITSIZE); } 	\
1427 										\
1428      static _GLIBCXX_USE_CONSTEXPR int digits 					\
1429       = BITSIZE - 1; 								\
1430      static _GLIBCXX_USE_CONSTEXPR int digits10 				\
1431       = (BITSIZE - 1) * 643L / 2136; 						\
1432      										\
1433      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true; 			\
1434      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true; 			\
1435      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true; 			\
1436      static _GLIBCXX_USE_CONSTEXPR int radix = 2; 				\
1437 										\
1438      static _GLIBCXX_CONSTEXPR TYPE 						\
1439      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1440 										\
1441      static _GLIBCXX_CONSTEXPR TYPE 						\
1442      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; } 			\
1443 										\
1444      EXT									\
1445 										\
1446      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0; 			\
1447      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0; 			\
1448      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0; 			\
1449      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0; 			\
1450 										\
1451      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false; 			\
1452      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false; 		\
1453      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false; 		\
1454      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 		\
1455       = denorm_absent; 							\
1456      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false; 		\
1457 										\
1458      static _GLIBCXX_CONSTEXPR TYPE 						\
1459      infinity() _GLIBCXX_USE_NOEXCEPT 						\
1460      { return static_cast<TYPE>(0); } 						\
1461 										\
1462      static _GLIBCXX_CONSTEXPR TYPE 						\
1463      quiet_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1464      { return static_cast<TYPE>(0); } 						\
1465       										\
1466      static _GLIBCXX_CONSTEXPR TYPE 						\
1467      signaling_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1468      { return static_cast<TYPE>(0); } 						\
1469       										\
1470      static _GLIBCXX_CONSTEXPR TYPE 						\
1471      denorm_min() _GLIBCXX_USE_NOEXCEPT 					\
1472      { return static_cast<TYPE>(0); } 						\
1473 										\
1474      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false; 			\
1475      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true; 			\
1476      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false; 			\
1477 										\
1478      static _GLIBCXX_USE_CONSTEXPR bool traps 					\
1479       = __glibcxx_integral_traps; 						\
1480      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false; 		\
1481      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 		\
1482       = round_toward_zero; 							\
1483    }; 										\
1484 										\
1485  template<> 									\
1486    struct numeric_limits<unsigned TYPE> 					\
1487    { 										\
1488      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true; 		\
1489 										\
1490      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1491      min() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1492 										\
1493      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1494      max() _GLIBCXX_USE_NOEXCEPT						\
1495      { return  __glibcxx_max_b (unsigned TYPE, BITSIZE); }			\
1496 										\
1497      UEXT									\
1498 										\
1499      static _GLIBCXX_USE_CONSTEXPR int digits 					\
1500       = BITSIZE; 								\
1501      static _GLIBCXX_USE_CONSTEXPR int digits10 				\
1502       = BITSIZE * 643L / 2136; 						\
1503      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false; 			\
1504      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true; 			\
1505      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true; 			\
1506      static _GLIBCXX_USE_CONSTEXPR int radix = 2; 				\
1507 										\
1508      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1509      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; } 				\
1510 										\
1511      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1512      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; } 			\
1513 										\
1514      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0; 			\
1515      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0; 			\
1516      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0; 			\
1517      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0; 			\
1518 										\
1519      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false; 			\
1520      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false; 		\
1521      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false; 		\
1522      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 		\
1523       = denorm_absent; 							\
1524      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false; 		\
1525 										\
1526      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1527      infinity() _GLIBCXX_USE_NOEXCEPT 						\
1528      { return static_cast<unsigned TYPE>(0); } 				\
1529 										\
1530      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1531      quiet_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1532      { return static_cast<unsigned TYPE>(0); } 				\
1533 										\
1534      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1535      signaling_NaN() _GLIBCXX_USE_NOEXCEPT 					\
1536      { return static_cast<unsigned TYPE>(0); } 				\
1537 										\
1538      static _GLIBCXX_CONSTEXPR unsigned TYPE 					\
1539      denorm_min() _GLIBCXX_USE_NOEXCEPT 					\
1540      { return static_cast<unsigned TYPE>(0); } 				\
1541 										\
1542      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false; 			\
1543      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true; 			\
1544      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true; 			\
1545 										\
1546      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps; 	\
1547      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false; 		\
1548      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 		\
1549       = round_toward_zero; 							\
1550    };
1551
1552#if __cplusplus >= 201103L
1553
1554#define __INT_N_201103(TYPE)							\
1555      static constexpr TYPE 							\
1556      lowest() noexcept { return min(); }					\
1557      static constexpr int max_digits10 = 0;
1558
1559#define __INT_N_U201103(TYPE)							\
1560      static constexpr unsigned TYPE 						\
1561      lowest() noexcept { return min(); }					\
1562      static constexpr int max_digits10 = 0;
1563
1564#else
1565#define __INT_N_201103(TYPE)
1566#define __INT_N_U201103(TYPE)
1567#endif
1568
1569#ifdef __GLIBCXX_TYPE_INT_N_0
1570  __INT_N(__GLIBCXX_TYPE_INT_N_0, __GLIBCXX_BITSIZE_INT_N_0,
1571	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_0), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_0))
1572#endif
1573#ifdef __GLIBCXX_TYPE_INT_N_1
1574  __INT_N (__GLIBCXX_TYPE_INT_N_1, __GLIBCXX_BITSIZE_INT_N_1,
1575	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_1), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_1))
1576#endif
1577#ifdef __GLIBCXX_TYPE_INT_N_2
1578  __INT_N (__GLIBCXX_TYPE_INT_N_2, __GLIBCXX_BITSIZE_INT_N_2,
1579	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_2), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_2))
1580#endif
1581#ifdef __GLIBCXX_TYPE_INT_N_3
1582  __INT_N (__GLIBCXX_TYPE_INT_N_3, __GLIBCXX_BITSIZE_INT_N_3,
1583	  __INT_N_201103 (__GLIBCXX_TYPE_INT_N_3), __INT_N_U201103 (__GLIBCXX_TYPE_INT_N_3))
1584#endif
1585
1586#undef __INT_N
1587#undef __INT_N_201103
1588#undef __INT_N_U201103
1589
1590#endif
1591
1592  /// numeric_limits<float> specialization.
1593  template<>
1594    struct numeric_limits<float>
1595    {
1596      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1597
1598      static _GLIBCXX_CONSTEXPR float
1599      min() _GLIBCXX_USE_NOEXCEPT { return __FLT_MIN__; }
1600
1601      static _GLIBCXX_CONSTEXPR float
1602      max() _GLIBCXX_USE_NOEXCEPT { return __FLT_MAX__; }
1603
1604#if __cplusplus >= 201103L
1605      static constexpr float
1606      lowest() noexcept { return -__FLT_MAX__; }
1607#endif
1608
1609      static _GLIBCXX_USE_CONSTEXPR int digits = __FLT_MANT_DIG__;
1610      static _GLIBCXX_USE_CONSTEXPR int digits10 = __FLT_DIG__;
1611#if __cplusplus >= 201103L
1612      static constexpr int max_digits10
1613	 = __glibcxx_max_digits10 (__FLT_MANT_DIG__);
1614#endif
1615      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1616      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1617      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1618      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1619
1620      static _GLIBCXX_CONSTEXPR float
1621      epsilon() _GLIBCXX_USE_NOEXCEPT { return __FLT_EPSILON__; }
1622
1623      static _GLIBCXX_CONSTEXPR float
1624      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5F; }
1625
1626      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __FLT_MIN_EXP__;
1627      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __FLT_MIN_10_EXP__;
1628      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __FLT_MAX_EXP__;
1629      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __FLT_MAX_10_EXP__;
1630
1631      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __FLT_HAS_INFINITY__;
1632      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __FLT_HAS_QUIET_NAN__;
1633      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1634      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1635	= bool(__FLT_HAS_DENORM__) ? denorm_present : denorm_absent;
1636      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1637       = __glibcxx_float_has_denorm_loss;
1638
1639      static _GLIBCXX_CONSTEXPR float
1640      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_valf(); }
1641
1642      static _GLIBCXX_CONSTEXPR float
1643      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanf(""); }
1644
1645      static _GLIBCXX_CONSTEXPR float
1646      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansf(""); }
1647
1648      static _GLIBCXX_CONSTEXPR float
1649      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __FLT_DENORM_MIN__; }
1650
1651      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1652	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1653      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1654      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1655
1656      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_float_traps;
1657      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1658       = __glibcxx_float_tinyness_before;
1659      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1660       = round_to_nearest;
1661    };
1662
1663#undef __glibcxx_float_has_denorm_loss
1664#undef __glibcxx_float_traps
1665#undef __glibcxx_float_tinyness_before
1666
1667  /// numeric_limits<double> specialization.
1668  template<>
1669    struct numeric_limits<double>
1670    {
1671      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1672
1673      static _GLIBCXX_CONSTEXPR double
1674      min() _GLIBCXX_USE_NOEXCEPT { return __DBL_MIN__; }
1675
1676      static _GLIBCXX_CONSTEXPR double
1677      max() _GLIBCXX_USE_NOEXCEPT { return __DBL_MAX__; }
1678
1679#if __cplusplus >= 201103L
1680      static constexpr double
1681      lowest() noexcept { return -__DBL_MAX__; }
1682#endif
1683
1684      static _GLIBCXX_USE_CONSTEXPR int digits = __DBL_MANT_DIG__;
1685      static _GLIBCXX_USE_CONSTEXPR int digits10 = __DBL_DIG__;
1686#if __cplusplus >= 201103L
1687      static constexpr int max_digits10
1688	 = __glibcxx_max_digits10 (__DBL_MANT_DIG__);
1689#endif
1690      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1691      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1692      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1693      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1694
1695      static _GLIBCXX_CONSTEXPR double
1696      epsilon() _GLIBCXX_USE_NOEXCEPT { return __DBL_EPSILON__; }
1697
1698      static _GLIBCXX_CONSTEXPR double
1699      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5; }
1700
1701      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __DBL_MIN_EXP__;
1702      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __DBL_MIN_10_EXP__;
1703      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __DBL_MAX_EXP__;
1704      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __DBL_MAX_10_EXP__;
1705
1706      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __DBL_HAS_INFINITY__;
1707      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __DBL_HAS_QUIET_NAN__;
1708      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1709      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1710	= bool(__DBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1711      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1712        = __glibcxx_double_has_denorm_loss;
1713
1714      static _GLIBCXX_CONSTEXPR double
1715      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_val(); }
1716
1717      static _GLIBCXX_CONSTEXPR double
1718      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nan(""); }
1719
1720      static _GLIBCXX_CONSTEXPR double
1721      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nans(""); }
1722
1723      static _GLIBCXX_CONSTEXPR double
1724      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __DBL_DENORM_MIN__; }
1725
1726      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1727	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1728      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1729      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1730
1731      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_double_traps;
1732      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before
1733       = __glibcxx_double_tinyness_before;
1734      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
1735       = round_to_nearest;
1736    };
1737
1738#undef __glibcxx_double_has_denorm_loss
1739#undef __glibcxx_double_traps
1740#undef __glibcxx_double_tinyness_before
1741
1742  /// numeric_limits<long double> specialization.
1743  template<>
1744    struct numeric_limits<long double>
1745    {
1746      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;
1747
1748      static _GLIBCXX_CONSTEXPR long double
1749      min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MIN__; }
1750
1751      static _GLIBCXX_CONSTEXPR long double
1752      max() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MAX__; }
1753
1754#if __cplusplus >= 201103L
1755      static constexpr long double
1756      lowest() noexcept { return -__LDBL_MAX__; }
1757#endif
1758
1759      static _GLIBCXX_USE_CONSTEXPR int digits = __LDBL_MANT_DIG__;
1760      static _GLIBCXX_USE_CONSTEXPR int digits10 = __LDBL_DIG__;
1761#if __cplusplus >= 201103L
1762      static _GLIBCXX_USE_CONSTEXPR int max_digits10
1763	 = __glibcxx_max_digits10 (__LDBL_MANT_DIG__);
1764#endif
1765      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
1766      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
1767      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
1768      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;
1769
1770      static _GLIBCXX_CONSTEXPR long double
1771      epsilon() _GLIBCXX_USE_NOEXCEPT { return __LDBL_EPSILON__; }
1772
1773      static _GLIBCXX_CONSTEXPR long double
1774      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5L; }
1775
1776      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __LDBL_MIN_EXP__;
1777      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __LDBL_MIN_10_EXP__;
1778      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __LDBL_MAX_EXP__;
1779      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __LDBL_MAX_10_EXP__;
1780
1781      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __LDBL_HAS_INFINITY__;
1782      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __LDBL_HAS_QUIET_NAN__;
1783      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
1784      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
1785	= bool(__LDBL_HAS_DENORM__) ? denorm_present : denorm_absent;
1786      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
1787	= __glibcxx_long_double_has_denorm_loss;
1788
1789      static _GLIBCXX_CONSTEXPR long double
1790      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_vall(); }
1791
1792      static _GLIBCXX_CONSTEXPR long double
1793      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanl(""); }
1794
1795      static _GLIBCXX_CONSTEXPR long double
1796      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansl(""); }
1797
1798      static _GLIBCXX_CONSTEXPR long double
1799      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_DENORM_MIN__; }
1800
1801      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
1802	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
1803      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
1804      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;
1805
1806      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_long_double_traps;
1807      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before =
1808					 __glibcxx_long_double_tinyness_before;
1809      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style =
1810						      round_to_nearest;
1811    };
1812
1813#undef __glibcxx_long_double_has_denorm_loss
1814#undef __glibcxx_long_double_traps
1815#undef __glibcxx_long_double_tinyness_before
1816
1817_GLIBCXX_END_NAMESPACE_VERSION
1818} // namespace
1819
1820#undef __glibcxx_signed
1821#undef __glibcxx_min
1822#undef __glibcxx_max
1823#undef __glibcxx_digits
1824#undef __glibcxx_digits10
1825#undef __glibcxx_max_digits10
1826
1827#endif // _GLIBCXX_NUMERIC_LIMITS
1828