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

// Copyright (C) 1999, 2000, 2001, 2002, 2003 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 2, 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.

// You should have received a copy of the GNU General Public License along

// with this library; see the file COPYING.  If not, write to the Free

// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,

// USA.

// As a special exception, you may use this file as part of a free software

// library without restriction.  Specifically, if other files instantiate

// templates or use macros or inline functions from this file, or you compile

// this file and link it with other files to produce an executable, this

// file does not by itself cause the resulting executable to be covered by

// the GNU General Public License.  This exception does not however

// invalidate any other reasons why the executable file might be covered by

// the GNU General Public License.

/** @file 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 13 such types:

//   * integers

//         bool                                                 (1)

//         char, signed char, unsigned char                     (3)

//         short, unsigned short                                (2)

//         int, unsigned                                        (2)

//         long, unsigned long                                  (2)

//

//   * floating points

//         float                                                (1)

//         double                                               (1)

//         long double                                          (1)

//

// GNU C++ undertstands (where supported by the host C-library)

//   * integer

//         long long, unsigned long long                        (2)

//

// which brings us to 15 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 intrinsicly 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 overriden 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 overriden 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 overriden 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) ? (T)1 << __glibcxx_digits (T) : (T)0)

#define __glibcxx_max(T) \

  (__glibcxx_signed (T) ? ((T)1 << __glibcxx_digits (T)) - 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) * 643 / 2136)

namespace std

{

  /**

   *  @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,    ///< Self-explanatory.

    round_toward_zero         = 0,     ///< Self-explanatory.

    round_to_nearest          = 1,     ///< To the nearest representable value.

    round_toward_infinity     = 2,     ///< Self-explanatory.

    round_toward_neg_infinity = 3      ///< Self-explanatory.

  };

  /**

   *  @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 seperate 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 const 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 const int digits = 0;

    /** The number of base 10 digits that can be represented without change. */

    static const int digits10 = 0;

    /** True if the type is signed.  */

    static const bool is_signed = false;

    /** True if the type is integer.

     *  @if maint

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

     *  @endif

    */

    static const 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 const bool is_exact = false;

    /** For integer types, specifies the base of the representation.  For

        floating types, specifies the base of the exponent representation.  */

    static const 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 const 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 const 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 const 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 const int max_exponent10 = 0;

    /** True if the type has a representation for positive infinity.  */

    static const bool has_infinity = false;

    /** True if the type has a representation for a quiet (non-signaling)

        "Not a Number."  */

    static const bool has_quiet_NaN = false;

    /** True if the type has a representation for a signaling

        "Not a Number."  */

    static const bool has_signaling_NaN = false;

    /** See std::float_denorm_style for more information.  */

    static const 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 const 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 const 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 const bool is_bounded = false;

    /** True if the type is @e modulo, that is, if it is possible to add two

        positive numbers and have a result that wraps around to a third number

        that is less.  Typically false for floating types, true for unsigned

        integers, and true for signed integers.  */

    static const bool is_modulo = false;

    /** True if trapping is implemented for this type.  */

    static const bool traps = false;

    /** True if tinyness is detected before rounding.  (see IEC 559)  */

    static const 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 const 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.

   *

   *  @if maint

   *  _GLIBCXX_RESOLVE_LIB_DEFECTS:  DRs 201 and 184 (hi Gaby!) are

   *  noted, but not incorporated in this documented (yet).

   *  @endif

  */

  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 _Tp min() throw() { return static_cast<_Tp>(0); }

      /** The maximum finite value.  */

      static _Tp max() throw() { return static_cast<_Tp>(0); }

      /** The @e machine @e epsilon:  the difference between 1 and the least

          value greater than 1 that is representable.  */

      static _Tp epsilon() throw() { return static_cast<_Tp>(0); }

      /** The maximum rounding error measurement (see LIA-1).  */

      static _Tp round_error() throw() { return static_cast<_Tp>(0); }

      /** The representation of positive infinity, if @c has_infinity.  */

      static _Tp infinity() throw()  { return static_cast<_Tp>(0); }

      /** The representation of a quiet "Not a Number," if @c has_quiet_NaN. */

      static _Tp quiet_NaN() throw() { return static_cast<_Tp>(0); }

      /** The representation of a signaling "Not a Number," if

          @c has_signaling_NaN. */

      static _Tp signaling_NaN() throw() { return static_cast<_Tp>(0); }

      /** The minimum positive denormalized value.  For types where

          @c has_denorm is false, this is the minimum positive normalized

          value.  */

      static _Tp denorm_min() throw() { return static_cast<_Tp>(0); }

    };

  // Now there follow 15 explicit specializations.  Yes, 15.  Make sure

  // you get the count right.

  /// numeric_limits<bool> specialization.

  template<>

    struct numeric_limits<bool>

    {

      static const bool is_specialized = true;

      static bool min() throw()

      { return false; }

      static bool max() throw()

      { return true; }

      static const int digits = 1;

      static const int digits10 = 0;

      static const bool is_signed = false;

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static bool epsilon() throw()

      { return false; }

      static bool round_error() throw()

      { return false; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static bool infinity() throw()

      { return false; }

      static bool quiet_NaN() throw()

      { return false; }

      static bool signaling_NaN() throw()

      { return false; }

      static bool denorm_min() throw()

      { return false; }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const 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 const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<char> specialization.

  template<>

    struct numeric_limits<char>

    {

      static const bool is_specialized = true;

      static char min() throw()

      { return __glibcxx_min(char); }

      static char max() throw()

      { return __glibcxx_max(char); }

      static const int digits = __glibcxx_digits (char);

      static const int digits10 = __glibcxx_digits10 (char);

      static const bool is_signed = __glibcxx_signed (char);

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static char epsilon() throw()

      { return 0; }

      static char round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static char infinity() throw()

      { return char(); }

      static char quiet_NaN() throw()

      { return char(); }

      static char signaling_NaN() throw()

      { return char(); }

      static char denorm_min() throw()

      { return static_cast<char>(0); }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const bool is_modulo = true;

      static const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<signed char> specialization.

  template<>

    struct numeric_limits<signed char>

    {

      static const bool is_specialized = true;

      static signed char min() throw()

      { return -__SCHAR_MAX__ - 1; }

      static signed char max() throw()

      { return __SCHAR_MAX__; }

      static const int digits = __glibcxx_digits (signed char);

      static const int digits10 = __glibcxx_digits10 (signed char);

      static const bool is_signed = true;

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static signed char epsilon() throw()

      { return 0; }

      static signed char round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static signed char infinity() throw()

      { return static_cast<signed char>(0); }

      static signed char quiet_NaN() throw()

      { return static_cast<signed char>(0); }

      static signed char signaling_NaN() throw()

      { return static_cast<signed char>(0); }

      static signed char denorm_min() throw()

      { return static_cast<signed char>(0); }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const bool is_modulo = true;

      static const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<unsigned char> specialization.

  template<>

    struct numeric_limits<unsigned char>

    {

      static const bool is_specialized = true;

      static unsigned char min() throw()

      { return 0; }

      static unsigned char max() throw()

      { return __SCHAR_MAX__ * 2U + 1; }

      static const int digits = __glibcxx_digits (unsigned char);

      static const int digits10 = __glibcxx_digits10 (unsigned char);

      static const bool is_signed = false;

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static unsigned char epsilon() throw()

      { return 0; }

      static unsigned char round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static unsigned char infinity() throw()

      { return static_cast<unsigned char>(0); }

      static unsigned char quiet_NaN() throw()

      { return static_cast<unsigned char>(0); }

      static unsigned char signaling_NaN() throw()

      { return static_cast<unsigned char>(0); }

      static unsigned char denorm_min() throw()

      { return static_cast<unsigned char>(0); }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const bool is_modulo = true;

      static const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<wchar_t> specialization.

  template<>

    struct numeric_limits<wchar_t>

    {

      static const bool is_specialized = true;

      static wchar_t min() throw()

      { return __glibcxx_min (wchar_t); }

      static wchar_t max() throw()

      { return __glibcxx_max (wchar_t); }

      static const int digits = __glibcxx_digits (wchar_t);

      static const int digits10 = __glibcxx_digits10 (wchar_t);

      static const bool is_signed = __glibcxx_signed (wchar_t);

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static wchar_t epsilon() throw()

      { return 0; }

      static wchar_t round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static wchar_t infinity() throw()

      { return wchar_t(); }

      static wchar_t quiet_NaN() throw()

      { return wchar_t(); }

      static wchar_t signaling_NaN() throw()

      { return wchar_t(); }

      static wchar_t denorm_min() throw()

      { return wchar_t(); }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const bool is_modulo = true;

      static const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<short> specialization.

  template<>

    struct numeric_limits<short>

    {

      static const bool is_specialized = true;

      static short min() throw()

      { return -__SHRT_MAX__ - 1; }

      static short max() throw()

      { return __SHRT_MAX__; }

      static const int digits = __glibcxx_digits (short);

      static const int digits10 = __glibcxx_digits10 (short);

      static const bool is_signed = true;

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static short epsilon() throw()

      { return 0; }

      static short round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;

      static short infinity() throw()

      { return short(); }

      static short quiet_NaN() throw()

      { return short(); }

      static short signaling_NaN() throw()

      { return short(); }

      static short denorm_min() throw()

      { return short(); }

      static const bool is_iec559 = false;

      static const bool is_bounded = true;

      static const bool is_modulo = true;

      static const bool traps = __glibcxx_integral_traps;

      static const bool tinyness_before = false;

      static const float_round_style round_style = round_toward_zero;

    };

  /// numeric_limits<unsigned short> specialization.

  template<>

    struct numeric_limits<unsigned short>

    {

      static const bool is_specialized = true;

      static unsigned short min() throw()

      { return 0; }

      static unsigned short max() throw()

      { return __SHRT_MAX__ * 2U + 1; }

      static const int digits = __glibcxx_digits (unsigned short);

      static const int digits10 = __glibcxx_digits10 (unsigned short);

      static const bool is_signed = false;

      static const bool is_integer = true;

      static const bool is_exact = true;

      static const int radix = 2;

      static unsigned short epsilon() throw()

      { return 0; }

      static unsigned short round_error() throw()

      { return 0; }

      static const int min_exponent = 0;

      static const int min_exponent10 = 0;

      static const int max_exponent = 0;

      static const int max_exponent10 = 0;

      static const bool has_infinity = false;

      static const bool has_quiet_NaN = false;

      static const bool has_signaling_NaN = false;

      static const float_denorm_style has_denorm = denorm_absent;

      static const bool has_denorm_loss = false;