text: ///////////////////////////////////////////////////////////////////////////
  //
  // Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
  // Digital Ltd. LLC
  // 
  // All rights reserved.
  // 
  // Redistribution and use in source and binary forms, with or without
  // modification, are permitted provided that the following conditions are
  // met:
  // *       Redistributions of source code must retain the above copyright
  // notice, this list of conditions and the following disclaimer.
  // *       Redistributions in binary form must reproduce the above
  // copyright notice, this list of conditions and the following disclaimer
  // in the documentation and/or other materials provided with the
  // distribution.
  // *       Neither the name of Industrial Light & Magic nor the names of
  // its contributors may be used to endorse or promote products derived
  // from this software without specific prior written permission. 
  // 
  // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  //
  ///////////////////////////////////////////////////////////////////////////
  
  // Primary authors:
  //     Florian Kainz <kainz@ilm.com>
  //     Rod Bogart <rgb@ilm.com>
  
  //---------------------------------------------------------------------------
  //
  //	half -- a 16-bit floating point number class:
  //
  //	Type half can represent positive and negative numbers whose
  //	magnitude is between roughly 6.1e-5 and 6.5e+4 with a relative
  //	error of 9.8e-4; numbers smaller than 6.1e-5 can be represented
  //	with an absolute error of 6.0e-8.  All integers from -2048 to
  //	+2048 can be represented exactly.
  //
  //	Type half behaves (almost) like the built-in C++ floating point
  //	types.  In arithmetic expressions, half, float and double can be
  //	mixed freely.  Here are a few examples:
  //
  //	    half a (3.5);
  //	    float b (a + sqrt (a));
  //	    a += b;
  //	    b += a;
  //	    b = a + 7;
  //
  //	Conversions from half to float are lossless; all half numbers
  //	are exactly representable as floats.
  //
  //	Conversions from float to half may not preserve a float's value
  //	exactly.  If a float is not representable as a half, then the
  //	float value is rounded to the nearest representable half.  If a
  //	float value is exactly in the middle between the two closest
  //	representable half values, then the float value is rounded to
  //	the closest half whose least significant bit is zero.
  //
  //	Overflows during float-to-half conversions cause arithmetic
  //	exceptions.  An overflow occurs when the float value to be
  //	converted is too large to be represented as a half, or if the
  //	float value is an infinity or a NAN.
  //
  //	The implementation of type half makes the following assumptions
  //	about the implementation of the built-in C++ types:
  //
  //	    float is an IEEE 754 single-precision number
  //	    sizeof (float) == 4
  //	    sizeof (unsigned int) == sizeof (float)
  //	    alignof (unsigned int) == alignof (float)
  //	    sizeof (unsigned short) == 2
  //
  //---------------------------------------------------------------------------
  
  #ifndef _HALF_H_
  #define _HALF_H_
  
  #define HALF_EXPORT
  #include <iostream>
  namespace RadeonProRender
  {
      class half
      {
      public:
  
          //-------------
          // Constructors
          //-------------
  
          half();			// no initialization
          half(float f);
  
  
          //--------------------
          // Conversion to float
          //--------------------
  
          operator float() const;
  
  
          //------------
          // Unary minus
          //------------
  
          half		operator - () const;
  
  
          //-----------
          // Assignment
          //-----------
  
          half& operator = (half  h);
          half& operator = (float f);
  
          half& operator += (half  h);
          half& operator += (float f);
  
          half& operator -= (half  h);
          half& operator -= (float f);
  
          half& operator *= (half  h);
          half& operator *= (float f);
  
          half& operator /= (half  h);
          half& operator /= (float f);
  
  
          //---------------------------------------------------------
          // Round to n-bit precision (n should be between 0 and 10).
          // After rounding, the significand's 10-n least significant
          // bits will be zero.
          //---------------------------------------------------------
  
          half		round(unsigned int n) const;
  
  
          //--------------------------------------------------------------------
          // Classification:
          //
          //	h.isFinite()		returns true if h is a normalized number,
          //				a denormalized number or zero
          //
          //	h.isNormalized()	returns true if h is a normalized number
          //
          //	h.isDenormalized()	returns true if h is a denormalized number
          //
          //	h.isZero()		returns true if h is zero
          //
          //	h.isNan()		returns true if h is a NAN
          //
          //	h.isInfinity()		returns true if h is a positive
          //				or a negative infinity
          //
          //	h.isNegative()		returns true if the sign bit of h
          //				is set (negative)
          //--------------------------------------------------------------------
  
          bool		isFinite() const;
          bool		isNormalized() const;
          bool		isDenormalized() const;
          bool		isZero() const;
          bool		isNan() const;
          bool		isInfinity() const;
          bool		isNegative() const;
  
  
          //--------------------------------------------
          // Special values
          //
          //	posInf()	returns +infinity
          //
          //	negInf()	returns -infinity
          //
          //	qNan()		returns a NAN with the bit
          //			pattern 0111111111111111
          //
          //	sNan()		returns a NAN with the bit
          //			pattern 0111110111111111
          //--------------------------------------------
  
          static half		posInf();
          static half		negInf();
          static half		qNan();
          static half		sNan();
  
  
          //--------------------------------------
          // Access to the internal representation
          //--------------------------------------
  
          HALF_EXPORT unsigned short	bits() const;
          HALF_EXPORT void		setBits(unsigned short bits);
  
  
      public:
  
          union uif
          {
              unsigned int	i;
              float		f;
          };
  
      private:
  
          HALF_EXPORT static short                  convert(int i);
          HALF_EXPORT static float                  overflow();
  
          unsigned short                            _h;
  
          HALF_EXPORT static const uif              _toFloat[1 << 16];
          HALF_EXPORT static const unsigned short   _eLut[1 << 9];
      };
  
  
  
      //-----------
      // Stream I/O
      //-----------
  
      HALF_EXPORT std::ostream& operator << (std::ostream& os, half  h);
      HALF_EXPORT std::istream& operator >> (std::istream& is, half& h);
  
  
      //----------
      // Debugging
      //----------
  
      HALF_EXPORT void        printBits(std::ostream& os, half  h);
      HALF_EXPORT void        printBits(std::ostream& os, float f);
      HALF_EXPORT void        printBits(char  c[19], half  h);
      HALF_EXPORT void        printBits(char  c[35], float f);
  
  
      //-------------------------------------------------------------------------
      // Limits
      //
      // Visual C++ will complain if HALF_MIN, HALF_NRM_MIN etc. are not float
      // constants, but at least one other compiler (gcc 2.96) produces incorrect
      // results if they are.
      //-------------------------------------------------------------------------
  
  #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
  
  #define HALF_MIN	5.96046448e-08f	// Smallest positive half
  
  #define HALF_NRM_MIN	6.10351562e-05f	// Smallest positive normalized half
  
  #define HALF_MAX	65504.0f	// Largest positive half
  
  #define HALF_EPSILON	0.00097656f	// Smallest positive e for which
                    // half (1.0 + e) != half (1.0)
  #else
  
  #define HALF_MIN	5.96046448e-08	// Smallest positive half
  
  #define HALF_NRM_MIN	6.10351562e-05	// Smallest positive normalized half
  
  #define HALF_MAX	65504.0		// Largest positive half
  
  #define HALF_EPSILON	0.00097656	// Smallest positive e for which
                    // half (1.0 + e) != half (1.0)
  #endif
  
  
  #define HALF_MANT_DIG	11		// Number of digits in mantissa
                      // (significand + hidden leading 1)
  
  #define HALF_DIG	2		// Number of base 10 digits that
                      // can be represented without change
  
  #define HALF_RADIX	2		// Base of the exponent
  
  #define HALF_MIN_EXP	-13		// Minimum negative integer such that
                      // HALF_RADIX raised to the power of
                      // one less than that integer is a
                      // normalized half
  
  #define HALF_MAX_EXP	16		// Maximum positive integer such that
                      // HALF_RADIX raised to the power of
                      // one less than that integer is a
                      // normalized half
  
  #define HALF_MIN_10_EXP	-4		// Minimum positive integer such
                      // that 10 raised to that power is
                      // a normalized half
  
  #define HALF_MAX_10_EXP	4		// Maximum positive integer such
                      // that 10 raised to that power is
                      // a normalized half
  
  
  //---------------------------------------------------------------------------
  //
  // Implementation --
  //
  // Representation of a float:
  //
  //	We assume that a float, f, is an IEEE 754 single-precision
  //	floating point number, whose bits are arranged as follows:
  //
  //	    31 (msb)
  //	    | 
  //	    | 30     23
  //	    | |      | 
  //	    | |      | 22                    0 (lsb)
  //	    | |      | |                     |
  //	    X XXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX
  //
  //	    s e        m
  //
  //	S is the sign-bit, e is the exponent and m is the significand.
  //
  //	If e is between 1 and 254, f is a normalized number:
  //
  //	            s    e-127
  //	    f = (-1)  * 2      * 1.m
  //
  //	If e is 0, and m is not zero, f is a denormalized number:
  //
  //	            s    -126
  //	    f = (-1)  * 2      * 0.m
  //
  //	If e and m are both zero, f is zero:
  //
  //	    f = 0.0
  //
  //	If e is 255, f is an "infinity" or "not a number" (NAN),
  //	depending on whether m is zero or not.
  //
  //	Examples:
  //
  //	    0 00000000 00000000000000000000000 = 0.0
  //	    0 01111110 00000000000000000000000 = 0.5
  //	    0 01111111 00000000000000000000000 = 1.0
  //	    0 10000000 00000000000000000000000 = 2.0
  //	    0 10000000 10000000000000000000000 = 3.0
  //	    1 10000101 11110000010000000000000 = -124.0625
  //	    0 11111111 00000000000000000000000 = +infinity
  //	    1 11111111 00000000000000000000000 = -infinity
  //	    0 11111111 10000000000000000000000 = NAN
  //	    1 11111111 11111111111111111111111 = NAN
  //
  // Representation of a half:
  //
  //	Here is the bit-layout for a half number, h:
  //
  //	    15 (msb)
  //	    | 
  //	    | 14  10
  //	    | |   |
  //	    | |   | 9        0 (lsb)
  //	    | |   | |        |
  //	    X XXXXX XXXXXXXXXX
  //
  //	    s e     m
  //
  //	S is the sign-bit, e is the exponent and m is the significand.
  //
  //	If e is between 1 and 30, h is a normalized number:
  //
  //	            s    e-15
  //	    h = (-1)  * 2     * 1.m
  //
  //	If e is 0, and m is not zero, h is a denormalized number:
  //
  //	            S    -14
  //	    h = (-1)  * 2     * 0.m
  //
  //	If e and m are both zero, h is zero:
  //
  //	    h = 0.0
  //
  //	If e is 31, h is an "infinity" or "not a number" (NAN),
  //	depending on whether m is zero or not.
  //
  //	Examples:
  //
  //	    0 00000 0000000000 = 0.0
  //	    0 01110 0000000000 = 0.5
  //	    0 01111 0000000000 = 1.0
  //	    0 10000 0000000000 = 2.0
  //	    0 10000 1000000000 = 3.0
  //	    1 10101 1111000001 = -124.0625
  //	    0 11111 0000000000 = +infinity
  //	    1 11111 0000000000 = -infinity
  //	    0 11111 1000000000 = NAN
  //	    1 11111 1111111111 = NAN
  //
  // Conversion:
  //
  //	Converting from a float to a half requires some non-trivial bit
  //	manipulations.  In some cases, this makes conversion relatively
  //	slow, but the most common case is accelerated via table lookups.
  //
  //	Converting back from a half to a float is easier because we don't
  //	have to do any rounding.  In addition, there are only 65536
  //	different half numbers; we can convert each of those numbers once
  //	and store the results in a table.  Later, all conversions can be
  //	done using only simple table lookups.
  //
  //---------------------------------------------------------------------------
  
  
  //--------------------
  // Simple constructors
  //--------------------
  
      inline
          half::half()
      {
          // no initialization
      }
  
  
      //----------------------------
      // Half-from-float constructor
      //----------------------------
  
      inline
          half::half(float f)
      {
          uif x;
  
          x.f = f;
  
          if (f == 0)
          {
              //
              // Common special case - zero.
              // Preserve the zero's sign bit.
              //
  
              _h = (x.i >> 16);
          }
          else
          {
              //
              // We extract the combined sign and exponent, e, from our
              // floating-point number, f.  Then we convert e to the sign
              // and exponent of the half number via a table lookup.
              //
              // For the most common case, where a normalized half is produced,
              // the table lookup returns a non-zero value; in this case, all
              // we have to do is round f's significand to 10 bits and combine
              // the result with e.
              //
              // For all other cases (overflow, zeroes, denormalized numbers
              // resulting from underflow, infinities and NANs), the table
              // lookup returns zero, and we call a longer, non-inline function
              // to do the float-to-half conversion.
              //
  
              register int e = (x.i >> 23) & 0x000001ff;
  
              e = _eLut[e];
  
              if (e)
              {
                  //
                  // Simple case - round the significand, m, to 10
                  // bits and combine it with the sign and exponent.
                  //
  
                  register int m = x.i & 0x007fffff;
                  _h = e + ((m + 0x00000fff + ((m >> 13) & 1)) >> 13);
              }
              else
              {
                  //
                  // Difficult case - call a function.
                  //
  
                  _h = convert(x.i);
              }
          }
      }
  
  
      //------------------------------------------
      // Half-to-float conversion via table lookup
      //------------------------------------------
  
      inline
          half::operator float() const
      {
          return _toFloat[_h].f;
      }
  
  
      //-------------------------
      // Round to n-bit precision
      //-------------------------
  
      inline half
          half::round(unsigned int n) const
      {
          //
          // Parameter check.
          //
  
          if (n >= 10)
              return *this;
  
          //
          // Disassemble h into the sign, s,
          // and the combined exponent and significand, e.
          //
  
          unsigned short s = _h & 0x8000;
          unsigned short e = _h & 0x7fff;
  
          //
          // Round the exponent and significand to the nearest value
          // where ones occur only in the (10-n) most significant bits.
          // Note that the exponent adjusts automatically if rounding
          // up causes the significand to overflow.
          //
  
          e >>= 9 - n;
          e += e & 1;
          e <<= 9 - n;
  
          //
          // Check for exponent overflow.
          //
  
          if (e >= 0x7c00)
          {
              //
              // Overflow occurred -- truncate instead of rounding.
              //
  
              e = _h;
              e >>= 10 - n;
              e <<= 10 - n;
          }
  
          //
          // Put the original sign bit back.
          //
  
          half h;
          h._h = s | e;
  
          return h;
      }
  
  
      //-----------------------
      // Other inline functions
      //-----------------------
  
      inline half
          half::operator - () const
      {
          half h;
          h._h = _h ^ 0x8000;
          return h;
      }
  
  
      inline half&
          half::operator = (half h)
      {
          _h = h._h;
          return *this;
      }
  
  
      inline half&
          half::operator = (float f)
      {
          *this = half(f);
          return *this;
      }
  
  
      inline half&
          half::operator += (half h)
      {
          *this = half(float(*this) + float(h));
          return *this;
      }
  
  
      inline half&
          half::operator += (float f)
      {
          *this = half(float(*this) + f);
          return *this;
      }
  
  
      inline half&
          half::operator -= (half h)
      {
          *this = half(float(*this) - float(h));
          return *this;
      }
  
  
      inline half&
          half::operator -= (float f)
      {
          *this = half(float(*this) - f);
          return *this;
      }
  
  
      inline half&
          half::operator *= (half h)
      {
          *this = half(float(*this) * float(h));
          return *this;
      }
  
  
      inline half&
          half::operator *= (float f)
      {
          *this = half(float(*this) * f);
          return *this;
      }
  
  
      inline half&
          half::operator /= (half h)
      {
          *this = half(float(*this) / float(h));
          return *this;
      }
  
  
      inline half&
          half::operator /= (float f)
      {
          *this = half(float(*this) / f);
          return *this;
      }
  
  
      inline bool
          half::isFinite() const
      {
          unsigned short e = (_h >> 10) & 0x001f;
          return e < 31;
      }
  
  
      inline bool
          half::isNormalized() const
      {
          unsigned short e = (_h >> 10) & 0x001f;
          return e > 0 && e < 31;
      }
  
  
      inline bool
          half::isDenormalized() const
      {
          unsigned short e = (_h >> 10) & 0x001f;
          unsigned short m = _h & 0x3ff;
          return e == 0 && m != 0;
      }
  
  
      inline bool
          half::isZero() const
      {
          return (_h & 0x7fff) == 0;
      }
  
  
      inline bool
          half::isNan() const
      {
          unsigned short e = (_h >> 10) & 0x001f;
          unsigned short m = _h & 0x3ff;
          return e == 31 && m != 0;
      }
  
  
      inline bool
          half::isInfinity() const
      {
          unsigned short e = (_h >> 10) & 0x001f;
          unsigned short m = _h & 0x3ff;
          return e == 31 && m == 0;
      }
  
  
      inline bool
          half::isNegative() const
      {
          return (_h & 0x8000) != 0;
      }
  
  
      inline half
          half::posInf()
      {
          half h;
          h._h = 0x7c00;
          return h;
      }
  
  
      inline half
          half::negInf()
      {
          half h;
          h._h = 0xfc00;
          return h;
      }
  
  
      inline half
          half::qNan()
      {
          half h;
          h._h = 0x7fff;
          return h;
      }
  
  
      inline half
          half::sNan()
      {
          half h;
          h._h = 0x7dff;
          return h;
      }
  
  
      inline unsigned short
          half::bits() const
      {
          return _h;
      }
  
  
      inline void
          half::setBits(unsigned short bits)
      {
          _h = bits;
      }
  }
  #endif
  