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 // Copyright (c) 1998-1999 Matra Datavision
 // Copyright (c) 1999-2014 OPEN CASCADE SAS
 //
 // This file is part of Open CASCADE Technology software library.
 //
 // This library is free software; you can redistribute it and/or modify it under
 // the terms of the GNU Lesser General Public License version 2.1 as published
 // by the Free Software Foundation, with special exception defined in the file
 // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
 // distribution for complete text of the license and disclaimer of any warranty.
 //
 // Alternatively, this file may be used under the terms of Open CASCADE
 // commercial license or contractual agreement.
 
 #ifndef _Standard_Real_HeaderFile
 #define _Standard_Real_HeaderFile
 
 #include <cmath>
 #include <float.h>
 #include <Standard_values.h>
 #include <Standard_math.hxx>
 #include <Standard_TypeDef.hxx>
 
 // ===============================================
 // Methods from Standard_Entity class which are redefined:  
 //    - Hascode
 //    - IsEqual
 // ===============================================
 
 // ==================================
 // Methods implemented in Standard_Real.cxx
 // ==================================
 
 //! Computes a hash code for the given real, in the range [1, theUpperBound]
 //! @param theReal the real value which hash code is to be computed
 //! @param theUpperBound the upper bound of the range a computing hash code must be within
 //! @return a computed hash code, in the range [1, theUpperBound]
 Standard_EXPORT Standard_Integer HashCode    (Standard_Real theReal, Standard_Integer theUpperBound);
 
 Standard_EXPORT Standard_Real    ACos        (const Standard_Real );
 Standard_EXPORT Standard_Real    ACosApprox  (const Standard_Real );
 Standard_EXPORT Standard_Real    ASin        (const Standard_Real );
 Standard_EXPORT Standard_Real    ATan2       (const Standard_Real , const Standard_Real );
 Standard_EXPORT Standard_Real    NextAfter   (const Standard_Real , const Standard_Real );
 
 //! Returns |a| if b >= 0; -|a| if b < 0.
 Standard_EXPORT Standard_Real    Sign(const Standard_Real a, const Standard_Real b);
 
 Standard_EXPORT Standard_Real    ATanh       (const Standard_Real );
 Standard_EXPORT Standard_Real    ACosh       (const Standard_Real );
 Standard_EXPORT Standard_Real    Sinh       (const Standard_Real );
 Standard_EXPORT Standard_Real    Cosh       (const Standard_Real );
 Standard_EXPORT Standard_Real    Log         (const Standard_Real );
 Standard_EXPORT Standard_Real    Sqrt        (const Standard_Real );
 
 //-------------------------------------------------------------------
 // RealSmall : Returns the smallest positive real
 //-------------------------------------------------------------------
 inline Standard_Real     RealSmall() 
 { return DBL_MIN; }
 
 //-------------------------------------------------------------------
 // Abs : Returns the absolute value of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Abs(const Standard_Real Value) 
 { return fabs(Value); }
 
 
 //-------------------------------------------------------------------
 // IsEqual : Returns Standard_True if two reals are equal
 //-------------------------------------------------------------------
 inline Standard_Boolean  IsEqual (const Standard_Real Value1, 
                   const Standard_Real Value2) 
 { return Abs((Value1 - Value2)) < RealSmall(); }
 
          //  *********************************** //
          //       Class methods                  //
          //                                      //
          //  Machine-dependent values            //
          //  Should be taken from include file   //
          //  *********************************** //
 
 
 //-------------------------------------------------------------------
 // RealDigit : Returns the number of digits of precision in a real
 //-------------------------------------------------------------------
 inline Standard_Integer  RealDigits() 
 { return DBL_DIG; }
 
 //-------------------------------------------------------------------
 // RealEpsilon : Returns the minimum positive real such that 
 //               1.0 + x is not equal to 1.0
 //-------------------------------------------------------------------
 inline Standard_Real     RealEpsilon() 
 { return DBL_EPSILON; }
 
 //-------------------------------------------------------------------
 // RealFirst : Returns the minimum negative value of a real
 //-------------------------------------------------------------------
 inline Standard_Real     RealFirst() 
 { return -DBL_MAX; }
   
 //-------------------------------------------------------------------
 // RealFirst10Exp : Returns the minimum value of exponent(base 10) of
 //                  a real.
 //-------------------------------------------------------------------
 inline Standard_Integer  RealFirst10Exp() 
 { return DBL_MIN_10_EXP; }
 
 //-------------------------------------------------------------------
 // RealLast : Returns the maximum value of a real
 //-------------------------------------------------------------------
 inline Standard_Real     RealLast() 
 { return  DBL_MAX; }
 
 //-------------------------------------------------------------------
 // RealLast10Exp : Returns the maximum value of exponent(base 10) of
 //                 a real.
 //-------------------------------------------------------------------
 inline Standard_Integer  RealLast10Exp() 
 { return  DBL_MAX_10_EXP; }
 
 //-------------------------------------------------------------------
 // RealMantissa : Returns the size in bits of the matissa part of a 
 //                real.
 //-------------------------------------------------------------------
 inline Standard_Integer  RealMantissa() 
 { return  DBL_MANT_DIG; }
 
 //-------------------------------------------------------------------
 // RealRadix : Returns the radix of exponent representation
 //-------------------------------------------------------------------
 inline Standard_Integer  RealRadix() 
 { return  FLT_RADIX; }
 
 //-------------------------------------------------------------------
 // RealSize : Returns the size in bits of an integer
 //-------------------------------------------------------------------
 inline Standard_Integer  RealSize() 
 { return BITS(Standard_Real); }
 
 
 
          //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=//
          //   End of machine-dependent values   //
          //=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=//
 
 
 //-------------------------------------------------------------------
 // IntToReal : Converts an integer in a real
 //-------------------------------------------------------------------
 inline Standard_Real     IntToReal(const Standard_Integer Value) 
 { return Value; }
 
 //-------------------------------------------------------------------
 // ATan : Returns the value of the arc tangent of a real
 //-------------------------------------------------------------------
 inline Standard_Real     ATan(const Standard_Real Value) 
 { return atan(Value); }
 
 
 //-------------------------------------------------------------------
 // Ceiling : Returns the smallest integer not less than a real
 //-------------------------------------------------------------------
 inline Standard_Real     Ceiling (const Standard_Real Value) 
 { return ceil(Value); }
 
 //-------------------------------------------------------------------
 // Cos : Returns the cosine of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Cos (const Standard_Real Value) 
 { return cos(Value); }
 
 
 //-------------------------------------------------------------------
 // Epsilon : The function returns absolute value of difference
 //           between 'Value' and other nearest value of
 //           Standard_Real type.
 //           Nearest value is chosen in direction of infinity
 //           the same sign as 'Value'.
 //           If 'Value' is 0 then returns minimal positive value
 //           of Standard_Real type.
 //-------------------------------------------------------------------
 inline Standard_Real     Epsilon (const Standard_Real Value) 
 {
   Standard_Real aEpsilon;
 
   if (Value>=0.0){
     aEpsilon = NextAfter(Value, RealLast()) - Value;
   } else {
     aEpsilon = Value - NextAfter(Value, RealFirst());
   }
   return aEpsilon;
 }
 
 //-------------------------------------------------------------------
 // Exp : Returns the exponential function of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Exp (const Standard_Real Value) 
 { return exp(Value); }
 
 //-------------------------------------------------------------------
 // Floor : Return the largest integer not greater than a real
 //-------------------------------------------------------------------
 inline Standard_Real     Floor (const Standard_Real Value) 
 { return floor(Value); }
 
 //-------------------------------------------------------------------
 // IntegerPart : Returns the integer part of a real
 //-------------------------------------------------------------------
 inline Standard_Real     IntegerPart (const Standard_Real Value) 
 { return ( (Value>0) ? floor(Value) : ceil(Value) ); }
 
 
 //-------------------------------------------------------------------
 // Log10 : Returns the base-10 logarithm of a real 
 //-------------------------------------------------------------------
 inline Standard_Real     Log10 (const Standard_Real Value) 
 { return log10(Value); }
 
 //-------------------------------------------------------------------
 // Max : Returns the maximum value of two reals
 //-------------------------------------------------------------------
 inline Standard_Real     Max (const Standard_Real Val1, 
                               const Standard_Real Val2) 
 {
   return Val1 >= Val2 ? Val1 : Val2;
 }
 
 //-------------------------------------------------------------------
 // Min : Returns the minimum value of two reals
 //-------------------------------------------------------------------
 inline Standard_Real     Min (const Standard_Real Val1, 
                               const Standard_Real Val2)
 {
   return Val1 <= Val2 ? Val1 : Val2;
 }
 
 //-------------------------------------------------------------------
 // Pow : Returns a real to a given power
 //-------------------------------------------------------------------
 inline Standard_Real     Pow (const Standard_Real Value, const Standard_Real P)
 { return pow(Value,P); }
 
 //-------------------------------------------------------------------
 // RealPart : Returns the fractional part of a real.
 //-------------------------------------------------------------------
 inline  Standard_Real    RealPart (const Standard_Real Value) 
 { return fabs(IntegerPart(Value) - Value); }
 
 //-------------------------------------------------------------------
 // RealToInt : Returns the real converted to nearest valid integer.
 //             If input value is out of valid range for integers,
 //             minimal or maximal possible integer is returned.
 //-------------------------------------------------------------------
 inline Standard_Integer RealToInt (const Standard_Real theValue)
 { 
   // Note that on WNT under MS VC++ 8.0 conversion of double value less 
   // than INT_MIN or greater than INT_MAX to integer will cause signal 
   // "Floating point multiple trap" (OCC17861)
   return theValue < static_cast<Standard_Real>(INT_MIN)
        ? static_cast<Standard_Integer>(INT_MIN)
        : (theValue > static_cast<Standard_Real>(INT_MAX)
         ? static_cast<Standard_Integer>(INT_MAX)
         : static_cast<Standard_Integer>(theValue));
 }
 
 // =======================================================================
 // function : RealToShortReal
 // purpose  : Converts Standard_Real value to the nearest valid
 //            Standard_ShortReal. If input value is out of valid range
 //            for Standard_ShortReal, minimal or maximal
 //            Standard_ShortReal is returned.
 // =======================================================================
 inline Standard_ShortReal RealToShortReal (const Standard_Real theVal)
 {
   return theVal < -FLT_MAX ? -FLT_MAX
     : theVal > FLT_MAX ? FLT_MAX
     : (Standard_ShortReal)theVal;
 }
 
 //-------------------------------------------------------------------
 // Round : Returns the nearest integer of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Round (const Standard_Real Value) 
 { return IntegerPart(Value + (Value > 0 ? 0.5 : -0.5)); }
 
 //-------------------------------------------------------------------
 // Sin : Returns the sine of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Sin (const Standard_Real Value) 
 { return sin(Value); }
 
 
 //-------------------------------------------------------------------
 // ASinh : Returns the hyperbolic arc sine of a real
 //-------------------------------------------------------------------
 inline Standard_Real     ASinh(const Standard_Real Value)
 #if defined(__QNX__)
 { return std::asinh(Value); }
 #else
 { return asinh(Value); }
 #endif
 
 //-------------------------------------------------------------------
 // Square : Returns a real to the power 2
 //-------------------------------------------------------------------
 inline Standard_Real     Square(const Standard_Real Value) 
 { return Value * Value; }
 
 //-------------------------------------------------------------------
 // Tan : Returns the tangent of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Tan (const Standard_Real Value) 
 { return tan(Value); }
 
 //-------------------------------------------------------------------
 // Tanh : Returns the hyperbolic tangent of a real
 //-------------------------------------------------------------------
 inline Standard_Real     Tanh (const Standard_Real Value) 
 { return tanh(Value); }
 
 #endif

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