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

// Copyright (C) 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007,

// 2008, 2009, 2010, 2011, 2012 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

// .

/** @file include/limits

 *  This is a Standard C++ Library header.

 */

// Note: this is not a conforming implementation.

// Written by Gabriel Dos Reis 

//

// ISO 14882:1998

// 18.2.1

//

#ifndef _GLIBCXX_NUMERIC_LIMITS

#define _GLIBCXX_NUMERIC_LIMITS 1

#pragma GCC system_header

#include 

//

// 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.

     *  Is this supposed to be if the type is integral?  */

    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.

        [18.2.1.2]/15  */

    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. [18.2.1.2]/42  */

    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. [18.2.1.2]/54  */

    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

    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

    struct numeric_limits

    : public numeric_limits<_Tp> { };

  template

    struct numeric_limits

    : public numeric_limits<_Tp> { };

  template

    struct numeric_limits

    : 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 specialization.

  template<>

    struct numeric_limits

    {

      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 specialization.

  template<>

    struct numeric_limits

    {

      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(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 specialization.

  template<>

    struct numeric_limits

    {

      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(0); }

      static _GLIBCXX_CONSTEXPR signed char

      quiet_NaN() _GLIBCXX_USE_NOEXCEPT { return static_cast(0); }

      static _GLIBCXX_CONSTEXPR signed char

      signaling_NaN() _GLIBCXX_USE_NOEXCEPT

      { return static_cast(0); }

      static _GLIBCXX_CONSTEXPR signed char

      denorm_min() _GLIBCXX_USE_NOEXCEPT

      { return static_cast(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 specialization.

  template<>

    struct numeric_limits

    {

      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(0); }

      static _GLIBCXX_CONSTEXPR unsigned char

      quiet_NaN() _GLIBCXX_USE_NOEXCEPT

      { return static_cast(0); }

      static _GLIBCXX_CONSTEXPR unsigned char

      signaling_NaN() _GLIBCXX_USE_NOEXCEPT

      { return static_cast(0); }

      static _GLIBCXX_CONSTEXPR unsigned char

      denorm_min() _GLIBCXX_USE_NOEXCEPT

      { return static_cast(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 specialization.

  template<>

    struct numeric_limits

    {

      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 specialization.

  template<>

    struct numeric_limits

    {

      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 specialization.

  template<>

    struct numeric_limits

    {

      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 specialization.

  template<>

    struct numeric_limits

    {

      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 specialization.

  template<>

    struct numeric_limits

    {

      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;