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+// Copyright 2001 John Maddock
+// Distributed under the Boost Software License, Version 1.0. (See accompany-
+// ing file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+/*
+ * Copyright (c) 1997
+ * Silicon Graphics Computer Systems, Inc.
+ *
+ * Permission to use, copy, modify, distribute and sell this software
+ * and its documentation for any purpose is hereby granted without fee,
+ * provided that the above copyright notice appear in all copies and
+ * that both that copyright notice and this permission notice appear
+ * in supporting documentation.  Silicon Graphics makes no
+ * representations about the suitability of this software for any
+ * purpose.  It is provided "as is" without express or implied warranty.
+ */
+
+/* NOTE: This is not portable code.  Parts of numeric_limits<> are
+ * inherently machine-dependent, and this file is written for the MIPS
+ * architecture and the SGI MIPSpro C++ compiler.  Parts of it (in
+ * particular, some of the characteristics of floating-point types)
+ * are almost certainly incorrect for any other platform.
+ */
+
+/* The above comment is almost certainly out of date. This file works
+ * on systems other than SGI MIPSpro C++ now.
+ */
+
+/*
+ * Revision history:
+ * 21 Sep 2001:
+ *    Only include <cwchar> if BOOST_NO_CWCHAR is defined. (Darin Adler)
+ * 10 Aug 2001:
+ *    Added MIPS (big endian) to the big endian family. (Jens Maurer)
+ * 13 Apr 2001:
+ *    Added powerpc to the big endian family. (Jeremy Siek)
+ * 5 Apr 2001:
+ *    Added sparc (big endian) processor support (John Maddock).
+ * Initial sub:
+ *      Modified by Jens Maurer for gcc 2.95 on x86.
+ */
+
+#ifndef BOOST_SGI_CPP_LIMITS
+#define BOOST_SGI_CPP_LIMITS
+
+#include <climits>
+#include <cfloat>
+#include <boost/config.hpp>
+#include <boost/detail/endian.hpp>
+
+#ifndef BOOST_NO_CWCHAR
+#include <cwchar> // for WCHAR_MIN and WCHAR_MAX
+#endif
+
+namespace std {
+
+enum float_round_style {
+  round_indeterminate       = -1,
+  round_toward_zero         =  0,
+  round_to_nearest          =  1,
+  round_toward_infinity     =  2,
+  round_toward_neg_infinity =  3
+};
+
+enum float_denorm_style {
+  denorm_indeterminate = -1,
+  denorm_absent        =  0,
+  denorm_present       =  1
+};
+
+// The C++ standard (section 18.2.1) requires that some of the members of
+// numeric_limits be static const data members that are given constant-
+// initializers within the class declaration.  On compilers where the
+// BOOST_NO_INCLASS_MEMBER_INITIALIZATION macro is defined, it is impossible to write
+// a standard-conforming numeric_limits class.
+//
+// There are two possible workarounds: either initialize the data
+// members outside the class, or change them from data members to
+// enums.  Neither workaround is satisfactory: the former makes it
+// impossible to use the data members in constant-expressions, and the
+// latter means they have the wrong type and that it is impossible to
+// take their addresses.  We choose the former workaround.
+
+#ifdef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
+# define BOOST_STL_DECLARE_LIMITS_MEMBER(__mem_type, __mem_name, __mem_value) \
+  enum { __mem_name = __mem_value }
+#else /* BOOST_NO_INCLASS_MEMBER_INITIALIZATION */
+# define BOOST_STL_DECLARE_LIMITS_MEMBER(__mem_type, __mem_name, __mem_value) \
+  static const __mem_type __mem_name = __mem_value
+#endif /* BOOST_NO_INCLASS_MEMBER_INITIALIZATION */
+
+// Base class for all specializations of numeric_limits.
+template <class __number>
+class _Numeric_limits_base {
+public:
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_specialized, false);
+
+  static __number min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return __number(); }
+  static __number max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return __number(); }
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, digits,   0);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, digits10, 0);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_signed,  false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_integer, false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_exact,   false);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, radix, 0);
+
+  static __number epsilon() throw()     { return __number(); }
+  static __number round_error() throw() { return __number(); }
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, min_exponent,   0);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, min_exponent10, 0);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, max_exponent,   0);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, max_exponent10, 0);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_infinity,      false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_quiet_NaN,     false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_signaling_NaN, false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(float_denorm_style,
+                              has_denorm,
+                              denorm_absent);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_denorm_loss,   false);
+
+  static __number infinity() throw()      { return __number(); }
+  static __number quiet_NaN() throw()     { return __number(); }
+  static __number signaling_NaN() throw() { return __number(); }
+  static __number denorm_min() throw()    { return __number(); }
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_iec559,  false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_bounded, false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_modulo,  false);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, traps,            false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, tinyness_before,  false);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(float_round_style,
+                              round_style,
+                              round_toward_zero);
+};
+
+// Base class for integers.
+
+template <class _Int,
+          _Int __imin,
+          _Int __imax,
+          int __idigits = -1>
+class _Integer_limits : public _Numeric_limits_base<_Int> 
+{
+public:
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_specialized, true);
+
+  static _Int min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return __imin; }
+  static _Int max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return __imax; }
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int,
+                              digits,
+                              (__idigits < 0) ? (int)(sizeof(_Int) * CHAR_BIT)
+                                                   - (__imin == 0 ? 0 : 1) 
+                                              : __idigits);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, digits10, (digits * 301) / 1000); 
+                                // log 2 = 0.301029995664...
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_signed,  __imin != 0);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_integer, true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_exact,   true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int,  radix,      2);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_bounded, true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_modulo, true);
+};
+
+#if defined(BOOST_BIG_ENDIAN)
+
+ template<class Number, unsigned int Word>
+ struct float_helper{
+  static Number get_word() throw() {
+    // sizeof(long double) == 16
+    const unsigned int _S_word[4] = { Word, 0, 0, 0 };
+    return *reinterpret_cast<const Number*>(&_S_word);
+  } 
+};
+
+#else
+
+ template<class Number, unsigned int Word>
+ struct float_helper{
+  static Number get_word() throw() {
+    // sizeof(long double) == 12, but only 10 bytes significant
+    const unsigned int _S_word[4] = { 0, 0, 0, Word };
+    return *reinterpret_cast<const Number*>(
+        reinterpret_cast<const char *>(&_S_word)+16-
+                (sizeof(Number) == 12 ? 10 : sizeof(Number)));
+  } 
+};
+
+#endif
+
+// Base class for floating-point numbers.
+template <class __number,
+         int __Digits, int __Digits10,
+         int __MinExp, int __MaxExp,
+         int __MinExp10, int __MaxExp10,
+         unsigned int __InfinityWord,
+         unsigned int __QNaNWord, unsigned int __SNaNWord,
+         bool __IsIEC559,
+         float_round_style __RoundStyle>
+class _Floating_limits : public _Numeric_limits_base<__number>
+{
+public:
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_specialized, true);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, digits,   __Digits);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, digits10, __Digits10);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_signed, true);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, radix, 2);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, min_exponent,   __MinExp);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, max_exponent,   __MaxExp);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, min_exponent10, __MinExp10);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(int, max_exponent10, __MaxExp10);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_infinity,      true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_quiet_NaN,     true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_signaling_NaN, true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(float_denorm_style,
+                              has_denorm,
+                              denorm_indeterminate);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, has_denorm_loss,   false);
+
+ 
+  static __number infinity() throw() {
+    return float_helper<__number, __InfinityWord>::get_word();
+  }
+  static __number quiet_NaN() throw() {
+    return float_helper<__number,__QNaNWord>::get_word();
+  }
+  static __number signaling_NaN() throw() {
+    return float_helper<__number,__SNaNWord>::get_word();
+  }
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_iec559,       __IsIEC559);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, is_bounded,      true);
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, traps,           false /* was: true */ );
+  BOOST_STL_DECLARE_LIMITS_MEMBER(bool, tinyness_before, false);
+
+  BOOST_STL_DECLARE_LIMITS_MEMBER(float_round_style, round_style, __RoundStyle);
+};
+
+// Class numeric_limits
+
+// The unspecialized class.
+
+template<class T> 
+class numeric_limits : public _Numeric_limits_base<T> {};
+
+// Specializations for all built-in integral types.
+
+template<>
+class numeric_limits<bool>
+  : public _Integer_limits<bool, false, true, 0>
+{};
+
+template<>
+class numeric_limits<char>
+  : public _Integer_limits<char, CHAR_MIN, CHAR_MAX>
+{};
+
+template<>
+class numeric_limits<signed char>
+  : public _Integer_limits<signed char, SCHAR_MIN, SCHAR_MAX>
+{};
+
+template<>
+class numeric_limits<unsigned char>
+  : public _Integer_limits<unsigned char, 0, UCHAR_MAX>
+{};
+
+#ifndef BOOST_NO_INTRINSIC_WCHAR_T
+template<>
+class numeric_limits<wchar_t>
+#if !defined(WCHAR_MAX) || !defined(WCHAR_MIN)
+#if defined(_WIN32) || defined(__CYGWIN__)
+  : public _Integer_limits<wchar_t, 0, USHRT_MAX>
+#elif defined(__hppa)
+// wchar_t has "unsigned int" as the underlying type
+  : public _Integer_limits<wchar_t, 0, UINT_MAX>
+#else
+// assume that wchar_t has "int" as the underlying type
+  : public _Integer_limits<wchar_t, INT_MIN, INT_MAX>
+#endif
+#else
+// we have WCHAR_MIN and WCHAR_MAX defined, so use it
+  : public _Integer_limits<wchar_t, WCHAR_MIN, WCHAR_MAX>
+#endif
+{};
+#endif
+
+template<>
+class numeric_limits<short>
+  : public _Integer_limits<short, SHRT_MIN, SHRT_MAX>
+{};
+
+template<>
+class numeric_limits<unsigned short>
+  : public _Integer_limits<unsigned short, 0, USHRT_MAX>
+{};
+
+template<>
+class numeric_limits<int>
+  : public _Integer_limits<int, INT_MIN, INT_MAX>
+{};
+
+template<>
+class numeric_limits<unsigned int>
+  : public _Integer_limits<unsigned int, 0, UINT_MAX>
+{};
+
+template<>
+class numeric_limits<long>
+  : public _Integer_limits<long, LONG_MIN, LONG_MAX>
+{};
+
+template<>
+class numeric_limits<unsigned long>
+  : public _Integer_limits<unsigned long, 0, ULONG_MAX>
+{};
+
+#ifdef __GNUC__
+
+// Some compilers have long long, but don't define the
+// LONGLONG_MIN and LONGLONG_MAX macros in limits.h.  This
+// assumes that long long is 64 bits.
+#if !defined(LONGLONG_MAX) && !defined(ULONGLONG_MAX)
+
+# define ULONGLONG_MAX 0xffffffffffffffffLLU
+# define LONGLONG_MAX 0x7fffffffffffffffLL
+
+#endif
+
+#if !defined(LONGLONG_MIN)
+# define LONGLONG_MIN (-LONGLONG_MAX - 1)
+#endif 
+
+
+#if !defined(ULONGLONG_MIN)
+# define ULONGLONG_MIN 0
+#endif 
+
+#endif /* __GNUC__ */
+
+// Specializations for all built-in floating-point type.
+
+template<> class numeric_limits<float>
+  : public _Floating_limits<float, 
+                            FLT_MANT_DIG,   // Binary digits of precision
+                            FLT_DIG,        // Decimal digits of precision
+                            FLT_MIN_EXP,    // Minimum exponent
+                            FLT_MAX_EXP,    // Maximum exponent
+                            FLT_MIN_10_EXP, // Minimum base 10 exponent
+                            FLT_MAX_10_EXP, // Maximum base 10 exponent
+#if defined(BOOST_BIG_ENDIAN)
+                            0x7f80 << (sizeof(int)*CHAR_BIT-16),    // Last word of +infinity
+                            0x7f81 << (sizeof(int)*CHAR_BIT-16),    // Last word of quiet NaN
+                            0x7fc1 << (sizeof(int)*CHAR_BIT-16),    // Last word of signaling NaN
+#else
+                            0x7f800000u,    // Last word of +infinity
+                            0x7f810000u,    // Last word of quiet NaN
+                            0x7fc10000u,    // Last word of signaling NaN
+#endif
+                            true,           // conforms to iec559
+                            round_to_nearest>
+{
+public:
+  static float min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return FLT_MIN; }
+  static float denorm_min() throw() { return FLT_MIN; }
+  static float max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return FLT_MAX; }
+  static float epsilon() throw() { return FLT_EPSILON; }
+  static float round_error() throw() { return 0.5f; } // Units: ulps.
+};
+
+template<> class numeric_limits<double>
+  : public _Floating_limits<double, 
+                            DBL_MANT_DIG,   // Binary digits of precision
+                            DBL_DIG,        // Decimal digits of precision
+                            DBL_MIN_EXP,    // Minimum exponent
+                            DBL_MAX_EXP,    // Maximum exponent
+                            DBL_MIN_10_EXP, // Minimum base 10 exponent
+                            DBL_MAX_10_EXP, // Maximum base 10 exponent
+#if defined(BOOST_BIG_ENDIAN)
+                            0x7ff0 << (sizeof(int)*CHAR_BIT-16),    // Last word of +infinity
+                            0x7ff1 << (sizeof(int)*CHAR_BIT-16),    // Last word of quiet NaN
+                            0x7ff9 << (sizeof(int)*CHAR_BIT-16),    // Last word of signaling NaN
+#else
+                            0x7ff00000u,    // Last word of +infinity
+                            0x7ff10000u,    // Last word of quiet NaN
+                            0x7ff90000u,    // Last word of signaling NaN
+#endif
+                            true,           // conforms to iec559
+                            round_to_nearest>
+{
+public:
+  static double min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return DBL_MIN; }
+  static double denorm_min() throw() { return DBL_MIN; }
+  static double max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return DBL_MAX; }
+  static double epsilon() throw() { return DBL_EPSILON; }
+  static double round_error() throw() { return 0.5; } // Units: ulps.
+};
+
+template<> class numeric_limits<long double>
+  : public _Floating_limits<long double, 
+                            LDBL_MANT_DIG,  // Binary digits of precision
+                            LDBL_DIG,       // Decimal digits of precision
+                            LDBL_MIN_EXP,   // Minimum exponent
+                            LDBL_MAX_EXP,   // Maximum exponent
+                            LDBL_MIN_10_EXP,// Minimum base 10 exponent
+                            LDBL_MAX_10_EXP,// Maximum base 10 exponent
+#if defined(BOOST_BIG_ENDIAN)
+                            0x7ff0 << (sizeof(int)*CHAR_BIT-16),    // Last word of +infinity
+                            0x7ff1 << (sizeof(int)*CHAR_BIT-16),    // Last word of quiet NaN
+                            0x7ff9 << (sizeof(int)*CHAR_BIT-16),    // Last word of signaling NaN
+#else
+                            0x7fff8000u,    // Last word of +infinity
+                            0x7fffc000u,    // Last word of quiet NaN
+                            0x7fff9000u,    // Last word of signaling NaN
+#endif
+                            false,          // Doesn't conform to iec559
+                            round_to_nearest>
+{
+public:
+  static long double min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return LDBL_MIN; }
+  static long double denorm_min() throw() { return LDBL_MIN; }
+  static long double max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return LDBL_MAX; }
+  static long double epsilon() throw() { return LDBL_EPSILON; }
+  static long double round_error() throw() { return 4; } // Units: ulps.
+};
+
+} // namespace std
+
+#endif /* BOOST_SGI_CPP_LIMITS */
+
+// Local Variables:
+// mode:C++
+// End:
+
+
+