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// The template and inlines for the numeric_limits classes. -*- C++ -*-

// Copyright (C) 1999-2013 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file include/limits
 *  This is a Standard C++ Library header.
 */

// Note: this is not a conforming implementation.
// Written by Gabriel Dos Reis <gdr@codesourcery.com>

//
// ISO 14882:1998
// 18.2.1
//

#ifndef _GLIBCXX_NUMERIC_LIMITS
#define _GLIBCXX_NUMERIC_LIMITS 1

#pragma GCC system_header

#include <bits/c++config.h>

//
// The numeric_limits<> traits document implementation-defined aspects
// of fundamental arithmetic data types (integers and floating points).
// From Standard C++ point of view, there are 14 such types:
//   * integers
//         bool							(1)
//         char, signed char, unsigned char, wchar_t            (4)
//         short, unsigned short				(2)
//         int, unsigned					(2)
//         long, unsigned long					(2)
//
//   * floating points
//         float						(1)
//         double						(1)
//         long double						(1)
//
// GNU C++ understands (where supported by the host C-library)
//   * integer
//         long long, unsigned long long			(2)
//
// which brings us to 16 fundamental arithmetic data types in GNU C++.
//
//
// Since a numeric_limits<> is a bit tricky to get right, we rely on
// an interface composed of macros which should be defined in config/os
// or config/cpu when they differ from the generic (read arbitrary)
// definitions given here.
//

// These values can be overridden in the target configuration file.
// The default values are appropriate for many 32-bit targets.

// GCC only intrinsically supports modulo integral types.  The only remaining
// integral exceptional values is division by zero.  Only targets that do not
// signal division by zero in some "hard to ignore" way should use false.
#ifndef __glibcxx_integral_traps
# define __glibcxx_integral_traps true
#endif

// float
//

// Default values.  Should be overridden in configuration files if necessary.

#ifndef __glibcxx_float_has_denorm_loss
#  define __glibcxx_float_has_denorm_loss false
#endif
#ifndef __glibcxx_float_traps
#  define __glibcxx_float_traps false
#endif
#ifndef __glibcxx_float_tinyness_before
#  define __glibcxx_float_tinyness_before false
#endif

// double

// Default values.  Should be overridden in configuration files if necessary.

#ifndef __glibcxx_double_has_denorm_loss
#  define __glibcxx_double_has_denorm_loss false
#endif
#ifndef __glibcxx_double_traps
#  define __glibcxx_double_traps false
#endif
#ifndef __glibcxx_double_tinyness_before
#  define __glibcxx_double_tinyness_before false
#endif

// long double

// Default values.  Should be overridden in configuration files if necessary.

#ifndef __glibcxx_long_double_has_denorm_loss
#  define __glibcxx_long_double_has_denorm_loss false
#endif
#ifndef __glibcxx_long_double_traps
#  define __glibcxx_long_double_traps false
#endif
#ifndef __glibcxx_long_double_tinyness_before
#  define __glibcxx_long_double_tinyness_before false
#endif

// You should not need to define any macros below this point.

#define __glibcxx_signed(T)	((T)(-1) < 0)

#define __glibcxx_min(T) \
  (__glibcxx_signed (T) ? -__glibcxx_max (T) - 1 : (T)0)

#define __glibcxx_max(T) \
  (__glibcxx_signed (T) ? \
   (((((T)1 << (__glibcxx_digits (T) - 1)) - 1) << 1) + 1) : ~(T)0)

#define __glibcxx_digits(T) \
  (sizeof(T) * __CHAR_BIT__ - __glibcxx_signed (T))

// The fraction 643/2136 approximates log10(2) to 7 significant digits.
#define __glibcxx_digits10(T) \
  (__glibcxx_digits (T) * 643L / 2136)

#define __glibcxx_max_digits10(T) \
  (2 + (T) * 643L / 2136)

namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION

  /**
   *  @brief Describes the rounding style for floating-point types.
   *
   *  This is used in the std::numeric_limits class.
  */
  enum float_round_style
  {
    round_indeterminate       = -1,    /// Intermediate.
    round_toward_zero         = 0,     /// To zero.
    round_to_nearest          = 1,     /// To the nearest representable value.
    round_toward_infinity     = 2,     /// To infinity.
    round_toward_neg_infinity = 3      /// To negative infinity.
  };

  /**
   *  @brief Describes the denormalization for floating-point types.
   *
   *  These values represent the presence or absence of a variable number
   *  of exponent bits.  This type is used in the std::numeric_limits class.
  */
  enum float_denorm_style
  {
    /// Indeterminate at compile time whether denormalized values are allowed.
    denorm_indeterminate = -1,
    /// The type does not allow denormalized values.
    denorm_absent        = 0,
    /// The type allows denormalized values.
    denorm_present       = 1
  };

  /**
   *  @brief Part of std::numeric_limits.
   *
   *  The @c static @c const members are usable as integral constant
   *  expressions.
   *
   *  @note This is a separate class for purposes of efficiency; you
   *        should only access these members as part of an instantiation
   *        of the std::numeric_limits class.
  */
  struct __numeric_limits_base
  {
    /** This will be true for all fundamental types (which have
	specializations), and false for everything else.  */
    static _GLIBCXX_USE_CONSTEXPR bool is_specialized = false;

    /** The number of @c radix digits that be represented without change:  for
	integer types, the number of non-sign bits in the mantissa; for
	floating types, the number of @c radix digits in the mantissa.  */
    static _GLIBCXX_USE_CONSTEXPR int digits = 0;

    /** The number of base 10 digits that can be represented without change. */
    static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;

#if __cplusplus >= 201103L
    /** The number of base 10 digits required to ensure that values which
	differ are always differentiated.  */
    static constexpr int max_digits10 = 0;
#endif

    /** True if the type is signed.  */
    static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;

    /** True if the type is integer.  */
    static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;

    /** True if the type uses an exact representation. All integer types are
	exact, but not all exact types are integer.  For example, rational and
	fixed-exponent representations are exact but not integer. */
    static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;

    /** For integer types, specifies the base of the representation.  For
	floating types, specifies the base of the exponent representation.  */
    static _GLIBCXX_USE_CONSTEXPR int radix = 0;

    /** The minimum negative integer such that @c radix raised to the power of
	(one less than that integer) is a normalized floating point number.  */
    static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;

    /** The minimum negative integer such that 10 raised to that power is in
	the range of normalized floating point numbers.  */
    static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;

    /** The maximum positive integer such that @c radix raised to the power of
	(one less than that integer) is a representable finite floating point
	number.  */
    static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;

    /** The maximum positive integer such that 10 raised to that power is in
	the range of representable finite floating point numbers.  */
    static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

    /** True if the type has a representation for positive infinity.  */
    static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;

    /** True if the type has a representation for a quiet (non-signaling)
	Not a Number.  */
    static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;

    /** True if the type has a representation for a signaling
	Not a Number.  */
    static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;

    /** See std::float_denorm_style for more information.  */
    static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm = denorm_absent;

    /** True if loss of accuracy is detected as a denormalization loss,
	rather than as an inexact result. */
    static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

    /** True if-and-only-if the type adheres to the IEC 559 standard, also
	known as IEEE 754.  (Only makes sense for floating point types.)  */
    static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;

    /** True if the set of values representable by the type is
	finite.  All built-in types are bounded, this member would be
	false for arbitrary precision types. */
    static _GLIBCXX_USE_CONSTEXPR bool is_bounded = false;

    /** True if the type is @e modulo. A type is modulo if, for any
	operation involving +, -, or * on values of that type whose
	result would fall outside the range [min(),max()], the value
	returned differs from the true value by an integer multiple of
	max() - min() + 1. On most machines, this is false for floating
	types, true for unsigned integers, and true for signed integers.
	See PR22200 about signed integers.  */
    static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

    /** True if trapping is implemented for this type.  */
    static _GLIBCXX_USE_CONSTEXPR bool traps = false;

    /** True if tininess is detected before rounding.  (see IEC 559)  */
    static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;

    /** See std::float_round_style for more information.  This is only
	meaningful for floating types; integer types will all be
	round_toward_zero.  */
    static _GLIBCXX_USE_CONSTEXPR float_round_style round_style = 
						    round_toward_zero;
  };

  /**
   *  @brief Properties of fundamental types.
   *
   *  This class allows a program to obtain information about the
   *  representation of a fundamental type on a given platform.  For
   *  non-fundamental types, the functions will return 0 and the data
   *  members will all be @c false.
   *
   *  _GLIBCXX_RESOLVE_LIB_DEFECTS:  DRs 201 and 184 (hi Gaby!) are
   *  noted, but not incorporated in this documented (yet).
  */
  template<typename _Tp>
    struct numeric_limits : public __numeric_limits_base
    {
      /** The minimum finite value, or for floating types with
	  denormalization, the minimum positive normalized value.  */
      static _GLIBCXX_CONSTEXPR _Tp
      min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The maximum finite value.  */
      static _GLIBCXX_CONSTEXPR _Tp
      max() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

#if __cplusplus >= 201103L
      /** A finite value x such that there is no other finite value y
       *  where y < x.  */
      static constexpr _Tp
      lowest() noexcept { return _Tp(); }
#endif

      /** The @e machine @e epsilon:  the difference between 1 and the least
	  value greater than 1 that is representable.  */
      static _GLIBCXX_CONSTEXPR _Tp
      epsilon() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The maximum rounding error measurement (see LIA-1).  */
      static _GLIBCXX_CONSTEXPR _Tp
      round_error() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The representation of positive infinity, if @c has_infinity.  */
      static _GLIBCXX_CONSTEXPR _Tp
      infinity() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The representation of a quiet Not a Number,
	  if @c has_quiet_NaN. */
      static _GLIBCXX_CONSTEXPR _Tp
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The representation of a signaling Not a Number, if
	  @c has_signaling_NaN. */
      static _GLIBCXX_CONSTEXPR _Tp
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }

      /** The minimum positive denormalized value.  For types where
	  @c has_denorm is false, this is the minimum positive normalized
	  value.  */
      static _GLIBCXX_CONSTEXPR _Tp
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return _Tp(); }
    };

#if __cplusplus >= 201103L
  template<typename _Tp>
    struct numeric_limits<const _Tp>
    : public numeric_limits<_Tp> { };

  template<typename _Tp>
    struct numeric_limits<volatile _Tp>
    : public numeric_limits<_Tp> { };

  template<typename _Tp>
    struct numeric_limits<const volatile _Tp>
    : public numeric_limits<_Tp> { };
#endif

  // Now there follow 16 explicit specializations.  Yes, 16.  Make sure
  // you get the count right. (18 in c++0x mode)

  /// numeric_limits<bool> specialization.
  template<>
    struct numeric_limits<bool>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR bool 
      min() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_CONSTEXPR bool 
      max() _GLIBCXX_USE_NOEXCEPT { return true; }

#if __cplusplus >= 201103L
      static constexpr bool
      lowest() noexcept { return min(); }
#endif
      static _GLIBCXX_USE_CONSTEXPR int digits = 1;
      static _GLIBCXX_USE_CONSTEXPR int digits10 = 0;
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR bool 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_CONSTEXPR bool 
      round_error() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR bool 
      infinity() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_CONSTEXPR bool 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_CONSTEXPR bool 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_CONSTEXPR bool 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return false; }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      // It is not clear what it means for a boolean type to trap.
      // This is a DR on the LWG issue list.  Here, I use integer
      // promotion semantics.
      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<char> specialization.
  template<>
    struct numeric_limits<char>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR char 
      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min(char); }

      static _GLIBCXX_CONSTEXPR char 
      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max(char); }

#if __cplusplus >= 201103L
      static constexpr char 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (char);
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (char);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (char);
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR char 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR char 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR 
      char infinity() _GLIBCXX_USE_NOEXCEPT { return char(); }

      static _GLIBCXX_CONSTEXPR char 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }

      static _GLIBCXX_CONSTEXPR char 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return char(); }

      static _GLIBCXX_CONSTEXPR char 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<char>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<signed char> specialization.
  template<>
    struct numeric_limits<signed char>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR signed char 
      min() _GLIBCXX_USE_NOEXCEPT { return -__SCHAR_MAX__ - 1; }

      static _GLIBCXX_CONSTEXPR signed char 
      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__; }

#if __cplusplus >= 201103L
      static constexpr signed char 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (signed char);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (signed char);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR signed char 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR signed char 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR signed char 
      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }

      static _GLIBCXX_CONSTEXPR signed char 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<signed char>(0); }

      static _GLIBCXX_CONSTEXPR signed char 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<signed char>(0); }

      static _GLIBCXX_CONSTEXPR signed char 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<signed char>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<unsigned char> specialization.
  template<>
    struct numeric_limits<unsigned char>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned char 
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned char 
      max() _GLIBCXX_USE_NOEXCEPT { return __SCHAR_MAX__ * 2U + 1; }

#if __cplusplus >= 201103L
      static constexpr unsigned char 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (unsigned char);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (unsigned char);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned char 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned char 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned char 
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned char>(0); }

      static _GLIBCXX_CONSTEXPR unsigned char 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned char>(0); }

      static _GLIBCXX_CONSTEXPR unsigned char 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned char>(0); }

      static _GLIBCXX_CONSTEXPR unsigned char 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned char>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<wchar_t> specialization.
  template<>
    struct numeric_limits<wchar_t>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR wchar_t 
      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (wchar_t); }

      static _GLIBCXX_CONSTEXPR wchar_t 
      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (wchar_t); }

#if __cplusplus >= 201103L
      static constexpr wchar_t
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (wchar_t);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (wchar_t);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = __glibcxx_signed (wchar_t);
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR wchar_t 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR wchar_t 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR wchar_t 
      infinity() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }

      static _GLIBCXX_CONSTEXPR wchar_t 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }

      static _GLIBCXX_CONSTEXPR wchar_t 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }

      static _GLIBCXX_CONSTEXPR wchar_t 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return wchar_t(); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = !is_signed;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

#if __cplusplus >= 201103L
  /// numeric_limits<char16_t> specialization.
  template<>
    struct numeric_limits<char16_t>
    {
      static constexpr bool is_specialized = true;

      static constexpr char16_t 
      min() noexcept { return __glibcxx_min (char16_t); }

      static constexpr char16_t 
      max() noexcept { return __glibcxx_max (char16_t); }

      static constexpr char16_t 
      lowest() noexcept { return min(); }

      static constexpr int digits = __glibcxx_digits (char16_t);
      static constexpr int digits10 = __glibcxx_digits10 (char16_t);
      static constexpr int max_digits10 = 0;
      static constexpr bool is_signed = __glibcxx_signed (char16_t);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr char16_t 
      epsilon() noexcept { return 0; }

      static constexpr char16_t 
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr char16_t 
      infinity() noexcept { return char16_t(); }

      static constexpr char16_t 
      quiet_NaN() noexcept { return char16_t(); }

      static constexpr char16_t 
      signaling_NaN() noexcept { return char16_t(); }

      static constexpr char16_t 
      denorm_min() noexcept { return char16_t(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = __glibcxx_integral_traps;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style = round_toward_zero;
    };

  /// numeric_limits<char32_t> specialization.
  template<>
    struct numeric_limits<char32_t>
    {
      static constexpr bool is_specialized = true;

      static constexpr char32_t 
      min() noexcept { return __glibcxx_min (char32_t); }

      static constexpr char32_t 
      max() noexcept { return __glibcxx_max (char32_t); }

      static constexpr char32_t 
      lowest() noexcept { return min(); }

      static constexpr int digits = __glibcxx_digits (char32_t);
      static constexpr int digits10 = __glibcxx_digits10 (char32_t);
      static constexpr int max_digits10 = 0;
      static constexpr bool is_signed = __glibcxx_signed (char32_t);
      static constexpr bool is_integer = true;
      static constexpr bool is_exact = true;
      static constexpr int radix = 2;

      static constexpr char32_t 
      epsilon() noexcept { return 0; }

      static constexpr char32_t 
      round_error() noexcept { return 0; }

      static constexpr int min_exponent = 0;
      static constexpr int min_exponent10 = 0;
      static constexpr int max_exponent = 0;
      static constexpr int max_exponent10 = 0;

      static constexpr bool has_infinity = false;
      static constexpr bool has_quiet_NaN = false;
      static constexpr bool has_signaling_NaN = false;
      static constexpr float_denorm_style has_denorm = denorm_absent;
      static constexpr bool has_denorm_loss = false;

      static constexpr char32_t 
      infinity() noexcept { return char32_t(); }

      static constexpr char32_t 
      quiet_NaN() noexcept { return char32_t(); }

      static constexpr char32_t 
      signaling_NaN() noexcept { return char32_t(); }

      static constexpr char32_t 
      denorm_min() noexcept { return char32_t(); }

      static constexpr bool is_iec559 = false;
      static constexpr bool is_bounded = true;
      static constexpr bool is_modulo = !is_signed;

      static constexpr bool traps = __glibcxx_integral_traps;
      static constexpr bool tinyness_before = false;
      static constexpr float_round_style round_style = round_toward_zero;
    };
#endif

  /// numeric_limits<short> specialization.
  template<>
    struct numeric_limits<short>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR short 
      min() _GLIBCXX_USE_NOEXCEPT { return -__SHRT_MAX__ - 1; }

      static _GLIBCXX_CONSTEXPR short 
      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__; }

#if __cplusplus >= 201103L
      static constexpr short 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (short);
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (short);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR short 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR short 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR short 
      infinity() _GLIBCXX_USE_NOEXCEPT { return short(); }

      static _GLIBCXX_CONSTEXPR short 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }

      static _GLIBCXX_CONSTEXPR short 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return short(); }

      static _GLIBCXX_CONSTEXPR short 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return short(); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<unsigned short> specialization.
  template<>
    struct numeric_limits<unsigned short>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned short 
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned short 
      max() _GLIBCXX_USE_NOEXCEPT { return __SHRT_MAX__ * 2U + 1; }

#if __cplusplus >= 201103L
      static constexpr unsigned short 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (unsigned short);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (unsigned short);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned short 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned short 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned short 
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned short>(0); }

      static _GLIBCXX_CONSTEXPR unsigned short 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned short>(0); }

      static _GLIBCXX_CONSTEXPR unsigned short 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned short>(0); }

      static _GLIBCXX_CONSTEXPR unsigned short 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned short>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<int> specialization.
  template<>
    struct numeric_limits<int>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR int 
      min() _GLIBCXX_USE_NOEXCEPT { return -__INT_MAX__ - 1; }

      static _GLIBCXX_CONSTEXPR int 
      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__; }

#if __cplusplus >= 201103L
      static constexpr int 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (int);
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (int);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR int 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR int 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR int 
      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }

      static _GLIBCXX_CONSTEXPR int 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }

      static _GLIBCXX_CONSTEXPR int 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }

      static _GLIBCXX_CONSTEXPR int 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<int>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<unsigned int> specialization.
  template<>
    struct numeric_limits<unsigned int>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned int 
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned int 
      max() _GLIBCXX_USE_NOEXCEPT { return __INT_MAX__ * 2U + 1; }

#if __cplusplus >= 201103L
      static constexpr unsigned int 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (unsigned int);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (unsigned int);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned int 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned int 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned int 
      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<unsigned int>(0); }

      static _GLIBCXX_CONSTEXPR unsigned int 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned int>(0); }

      static _GLIBCXX_CONSTEXPR unsigned int 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned int>(0); }

      static _GLIBCXX_CONSTEXPR unsigned int 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned int>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<long> specialization.
  template<>
    struct numeric_limits<long>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR long
      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_MAX__ - 1; }

      static _GLIBCXX_CONSTEXPR long 
      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__; }

#if __cplusplus >= 201103L
      static constexpr long 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __glibcxx_digits (long);
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __glibcxx_digits10 (long);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR long 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR long 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR long 
      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }

      static _GLIBCXX_CONSTEXPR long 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }

      static _GLIBCXX_CONSTEXPR long 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }

      static _GLIBCXX_CONSTEXPR long 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<unsigned long> specialization.
  template<>
    struct numeric_limits<unsigned long>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned long 
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned long 
      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_MAX__ * 2UL + 1; }

#if __cplusplus >= 201103L
      static constexpr unsigned long 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (unsigned long);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (unsigned long);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned long 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned long 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned long 
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<long long> specialization.
  template<>
    struct numeric_limits<long long>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR long long 
      min() _GLIBCXX_USE_NOEXCEPT { return -__LONG_LONG_MAX__ - 1; }

      static _GLIBCXX_CONSTEXPR long long 
      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__; }

#if __cplusplus >= 201103L
      static constexpr long long 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (long long);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (long long);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR long long 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR long long 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR long long 
      infinity() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }

      static _GLIBCXX_CONSTEXPR long long 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }

      static _GLIBCXX_CONSTEXPR long long 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<long long>(0); }

      static _GLIBCXX_CONSTEXPR long long 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return static_cast<long long>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

  /// numeric_limits<unsigned long long> specialization.
  template<>
    struct numeric_limits<unsigned long long>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned long long 
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned long long 
      max() _GLIBCXX_USE_NOEXCEPT { return __LONG_LONG_MAX__ * 2ULL + 1; }

#if __cplusplus >= 201103L
      static constexpr unsigned long long 
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits 
       = __glibcxx_digits (unsigned long long);
      static _GLIBCXX_USE_CONSTEXPR int digits10 
       = __glibcxx_digits10 (unsigned long long);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned long long 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned long long 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm 
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned long long 
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long long 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long long 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long long>(0); }

      static _GLIBCXX_CONSTEXPR unsigned long long 
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned long long>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_toward_zero;
    };

#if !defined(__STRICT_ANSI__) && defined(_GLIBCXX_USE_INT128)
  /// numeric_limits<__int128> specialization.
  template<>
    struct numeric_limits<__int128>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR __int128
      min() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_min (__int128); }

      static _GLIBCXX_CONSTEXPR __int128
      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (__int128); }

#if __cplusplus >= 201103L
      static constexpr __int128
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits
       = __glibcxx_digits (__int128);
      static _GLIBCXX_USE_CONSTEXPR int digits10
       = __glibcxx_digits10 (__int128);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR __int128
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR __int128
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR __int128
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<__int128>(0); }

      static _GLIBCXX_CONSTEXPR __int128
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<__int128>(0); }
      
      static _GLIBCXX_CONSTEXPR __int128
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<__int128>(0); }
      
      static _GLIBCXX_CONSTEXPR __int128
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<__int128>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps
       = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
       = round_toward_zero;
    };

  /// numeric_limits<unsigned __int128> specialization.
  template<>
    struct numeric_limits<unsigned __int128>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR unsigned __int128
      min() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned __int128
      max() _GLIBCXX_USE_NOEXCEPT { return __glibcxx_max (unsigned __int128); }

#if __cplusplus >= 201103L
      static constexpr unsigned __int128
      lowest() noexcept { return min(); }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits
       = __glibcxx_digits (unsigned __int128);
      static _GLIBCXX_USE_CONSTEXPR int digits10
       = __glibcxx_digits10 (unsigned __int128);
#if __cplusplus >= 201103L
      static constexpr int max_digits10 = 0;
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = true;
      static _GLIBCXX_USE_CONSTEXPR int radix = 2;

      static _GLIBCXX_CONSTEXPR unsigned __int128
      epsilon() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_CONSTEXPR unsigned __int128
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = 0;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = 0;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = false;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
       = denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss = false;

      static _GLIBCXX_CONSTEXPR unsigned __int128
      infinity() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned __int128>(0); }

      static _GLIBCXX_CONSTEXPR unsigned __int128
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned __int128>(0); }

      static _GLIBCXX_CONSTEXPR unsigned __int128
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned __int128>(0); }

      static _GLIBCXX_CONSTEXPR unsigned __int128
      denorm_min() _GLIBCXX_USE_NOEXCEPT
      { return static_cast<unsigned __int128>(0); }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559 = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = true;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_integral_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = false;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style
       = round_toward_zero;
    };
#endif

  /// numeric_limits<float> specialization.
  template<>
    struct numeric_limits<float>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR float 
      min() _GLIBCXX_USE_NOEXCEPT { return __FLT_MIN__; }

      static _GLIBCXX_CONSTEXPR float 
      max() _GLIBCXX_USE_NOEXCEPT { return __FLT_MAX__; }

#if __cplusplus >= 201103L
      static constexpr float 
      lowest() noexcept { return -__FLT_MAX__; }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __FLT_MANT_DIG__;
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __FLT_DIG__;
#if __cplusplus >= 201103L
      static constexpr int max_digits10
	 = __glibcxx_max_digits10 (__FLT_MANT_DIG__);
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;

      static _GLIBCXX_CONSTEXPR float 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return __FLT_EPSILON__; }

      static _GLIBCXX_CONSTEXPR float 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5F; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __FLT_MIN_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __FLT_MIN_10_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __FLT_MAX_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __FLT_MAX_10_EXP__;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __FLT_HAS_INFINITY__;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __FLT_HAS_QUIET_NAN__;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
	= bool(__FLT_HAS_DENORM__) ? denorm_present : denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss 
       = __glibcxx_float_has_denorm_loss;

      static _GLIBCXX_CONSTEXPR float 
      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_valf(); }

      static _GLIBCXX_CONSTEXPR float 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanf(""); }

      static _GLIBCXX_CONSTEXPR float 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansf(""); }

      static _GLIBCXX_CONSTEXPR float 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __FLT_DENORM_MIN__; }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_float_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before 
       = __glibcxx_float_tinyness_before;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_to_nearest;
    };

#undef __glibcxx_float_has_denorm_loss
#undef __glibcxx_float_traps
#undef __glibcxx_float_tinyness_before

  /// numeric_limits<double> specialization.
  template<>
    struct numeric_limits<double>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR double 
      min() _GLIBCXX_USE_NOEXCEPT { return __DBL_MIN__; }

      static _GLIBCXX_CONSTEXPR double 
      max() _GLIBCXX_USE_NOEXCEPT { return __DBL_MAX__; }

#if __cplusplus >= 201103L
      static constexpr double 
      lowest() noexcept { return -__DBL_MAX__; }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __DBL_MANT_DIG__;
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __DBL_DIG__;
#if __cplusplus >= 201103L
      static constexpr int max_digits10
	 = __glibcxx_max_digits10 (__DBL_MANT_DIG__);
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;

      static _GLIBCXX_CONSTEXPR double 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return __DBL_EPSILON__; }

      static _GLIBCXX_CONSTEXPR double 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __DBL_MIN_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __DBL_MIN_10_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __DBL_MAX_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __DBL_MAX_10_EXP__;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __DBL_HAS_INFINITY__;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __DBL_HAS_QUIET_NAN__;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
	= bool(__DBL_HAS_DENORM__) ? denorm_present : denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss 
        = __glibcxx_double_has_denorm_loss;

      static _GLIBCXX_CONSTEXPR double 
      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_val(); }

      static _GLIBCXX_CONSTEXPR double 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nan(""); }

      static _GLIBCXX_CONSTEXPR double 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nans(""); }

      static _GLIBCXX_CONSTEXPR double 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __DBL_DENORM_MIN__; }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_double_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before 
       = __glibcxx_double_tinyness_before;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style 
       = round_to_nearest;
    };

#undef __glibcxx_double_has_denorm_loss
#undef __glibcxx_double_traps
#undef __glibcxx_double_tinyness_before

  /// numeric_limits<long double> specialization.
  template<>
    struct numeric_limits<long double>
    {
      static _GLIBCXX_USE_CONSTEXPR bool is_specialized = true;

      static _GLIBCXX_CONSTEXPR long double 
      min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MIN__; }

      static _GLIBCXX_CONSTEXPR long double 
      max() _GLIBCXX_USE_NOEXCEPT { return __LDBL_MAX__; }

#if __cplusplus >= 201103L
      static constexpr long double 
      lowest() noexcept { return -__LDBL_MAX__; }
#endif

      static _GLIBCXX_USE_CONSTEXPR int digits = __LDBL_MANT_DIG__;
      static _GLIBCXX_USE_CONSTEXPR int digits10 = __LDBL_DIG__;
#if __cplusplus >= 201103L
      static _GLIBCXX_USE_CONSTEXPR int max_digits10
	 = __glibcxx_max_digits10 (__LDBL_MANT_DIG__);
#endif
      static _GLIBCXX_USE_CONSTEXPR bool is_signed = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_integer = false;
      static _GLIBCXX_USE_CONSTEXPR bool is_exact = false;
      static _GLIBCXX_USE_CONSTEXPR int radix = __FLT_RADIX__;

      static _GLIBCXX_CONSTEXPR long double 
      epsilon() _GLIBCXX_USE_NOEXCEPT { return __LDBL_EPSILON__; }

      static _GLIBCXX_CONSTEXPR long double 
      round_error() _GLIBCXX_USE_NOEXCEPT { return 0.5L; }

      static _GLIBCXX_USE_CONSTEXPR int min_exponent = __LDBL_MIN_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int min_exponent10 = __LDBL_MIN_10_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent = __LDBL_MAX_EXP__;
      static _GLIBCXX_USE_CONSTEXPR int max_exponent10 = __LDBL_MAX_10_EXP__;

      static _GLIBCXX_USE_CONSTEXPR bool has_infinity = __LDBL_HAS_INFINITY__;
      static _GLIBCXX_USE_CONSTEXPR bool has_quiet_NaN = __LDBL_HAS_QUIET_NAN__;
      static _GLIBCXX_USE_CONSTEXPR bool has_signaling_NaN = has_quiet_NaN;
      static _GLIBCXX_USE_CONSTEXPR float_denorm_style has_denorm
	= bool(__LDBL_HAS_DENORM__) ? denorm_present : denorm_absent;
      static _GLIBCXX_USE_CONSTEXPR bool has_denorm_loss
	= __glibcxx_long_double_has_denorm_loss;

      static _GLIBCXX_CONSTEXPR long double 
      infinity() _GLIBCXX_USE_NOEXCEPT { return __builtin_huge_vall(); }

      static _GLIBCXX_CONSTEXPR long double 
      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nanl(""); }

      static _GLIBCXX_CONSTEXPR long double 
      signaling_NaN() _GLIBCXX_USE_NOEXCEPT { return __builtin_nansl(""); }

      static _GLIBCXX_CONSTEXPR long double 
      denorm_min() _GLIBCXX_USE_NOEXCEPT { return __LDBL_DENORM_MIN__; }

      static _GLIBCXX_USE_CONSTEXPR bool is_iec559
	= has_infinity && has_quiet_NaN && has_denorm == denorm_present;
      static _GLIBCXX_USE_CONSTEXPR bool is_bounded = true;
      static _GLIBCXX_USE_CONSTEXPR bool is_modulo = false;

      static _GLIBCXX_USE_CONSTEXPR bool traps = __glibcxx_long_double_traps;
      static _GLIBCXX_USE_CONSTEXPR bool tinyness_before = 
					 __glibcxx_long_double_tinyness_before;
      static _GLIBCXX_USE_CONSTEXPR float_round_style round_style = 
						      round_to_nearest;
    };

#undef __glibcxx_long_double_has_denorm_loss
#undef __glibcxx_long_double_traps
#undef __glibcxx_long_double_tinyness_before

_GLIBCXX_END_NAMESPACE_VERSION
} // namespace

#undef __glibcxx_signed
#undef __glibcxx_min
#undef __glibcxx_max
#undef __glibcxx_digits
#undef __glibcxx_digits10
#undef __glibcxx_max_digits10

#endif // _GLIBCXX_NUMERIC_LIMITS

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climits File 1.84 KB 0644
clocale File 1.86 KB 0644
cmath File 41.45 KB 0644
complex File 51.29 KB 0644
complex.h File 1.43 KB 0644
condition_variable File 7.8 KB 0644
csetjmp File 1.9 KB 0644
csignal File 1.81 KB 0644
cstdalign File 1.37 KB 0644
cstdarg File 1.8 KB 0644
cstdbool File 1.37 KB 0644
cstddef File 1.57 KB 0644
cstdint File 2.12 KB 0644
cstdio File 4.18 KB 0644
cstdlib File 6.01 KB 0644
cstring File 3.05 KB 0644
ctgmath File 1.29 KB 0644
ctime File 2.08 KB 0644
cwchar File 6.34 KB 0644
cwctype File 2.73 KB 0644
cxxabi.h File 21.24 KB 0644
deque File 2.6 KB 0644
exception File 4.95 KB 0644
fenv.h File 1.97 KB 0644
forward_list File 1.54 KB 0644
fstream File 29.31 KB 0644
functional File 79.23 KB 0644
future File 41.7 KB 0644
initializer_list File 2.9 KB 0644
iomanip File 11.21 KB 0644
ios File 1.56 KB 0644
iosfwd File 6.69 KB 0644
iostream File 2.63 KB 0644
istream File 29.25 KB 0644
iterator File 2.58 KB 0644
limits File 65.68 KB 0644
list File 2.53 KB 0644
locale File 1.39 KB 0644
map File 2.5 KB 0644
memory File 2.81 KB 0644
mutex File 19.66 KB 0644
new File 4.09 KB 0644
numeric File 2.72 KB 0644
ostream File 19.19 KB 0644
queue File 2.41 KB 0644
random File 1.67 KB 0644
ratio File 18.69 KB 0644
regex File 1.82 KB 0644
scoped_allocator File 15.65 KB 0644
set File 2.5 KB 0644
sstream File 19.57 KB 0644
stack File 2.33 KB 0644
stdexcept File 4.61 KB 0644
streambuf File 28.71 KB 0644
string File 1.9 KB 0644
system_error File 10.11 KB 0644
tgmath.h File 1.33 KB 0644
thread File 7.08 KB 0644
tuple File 34.85 KB 0644
type_traits File 57.55 KB 0644
typeindex File 3.01 KB 0644
typeinfo File 7.5 KB 0644
unordered_map File 1.81 KB 0644
unordered_set File 1.81 KB 0644
utility File 5.22 KB 0644
valarray File 39.32 KB 0644
vector File 2.66 KB 0644