glm/detail/type_half.inl

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
///
/// This half implementation is based on OpenEXR which is Copyright (c) 2002,
/// Industrial Light & Magic, a division of Lucas Digital Ltd. LLC
///
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
///
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
///
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref core
/// @file glm/core/type_half.inl
/// @date 2008-08-17 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

namespace glm{
namespace detail
{
	GLM_FUNC_QUALIFIER float overflow()
	{
		volatile float f = 1e10;

		for(int i = 0; i < 10; ++i)
			f *= f;             // this will overflow before
								// the forloop terminates
		return f;
	}

	union uif32
	{
		GLM_FUNC_QUALIFIER uif32() :
			i(0)
		{}

		GLM_FUNC_QUALIFIER uif32(float f) :
			f(f)
		{}

		GLM_FUNC_QUALIFIER uif32(uint32 i) :
			i(i)
		{}

		float f;
		uint32 i;
	};

	GLM_FUNC_QUALIFIER float toFloat32(hdata value)
	{
		int s = (value >> 15) & 0x00000001;
		int e = (value >> 10) & 0x0000001f;
		int m =  value        & 0x000003ff;

		if(e == 0)
		{
			if(m == 0)
			{
				//
				// Plus or minus zero
				//

				detail::uif32 result;
				result.i = (unsigned int)(s << 31);
				return result.f;
			}
			else
			{
				//
				// Denormalized number -- renormalize it
				//

				while(!(m & 0x00000400))
				{
					m <<= 1;
					e -=  1;
				}

				e += 1;
				m &= ~0x00000400;
			}
		}
		else if(e == 31)
		{
			if(m == 0)
			{
				//
				// Positive or negative infinity
				//

				uif32 result;
				result.i = (unsigned int)((s << 31) | 0x7f800000);
				return result.f;
			}
			else
			{
				//
				// Nan -- preserve sign and significand bits
				//

				uif32 result;
				result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13));
				return result.f;
			}
		}

		//
		// Normalized number
		//

		e = e + (127 - 15);
		m = m << 13;

		//
		// Assemble s, e and m.
		//

		uif32 Result;
		Result.i = (unsigned int)((s << 31) | (e << 23) | m);
		return Result.f;
	}

	GLM_FUNC_QUALIFIER hdata toFloat16(float const & f)
	{
		uif32 Entry;
		Entry.f = f;
		int i = (int)Entry.i;

		//
		// Our floating point number, f, is represented by the bit
		// pattern in integer i.  Disassemble that bit pattern into
		// the sign, s, the exponent, e, and the significand, m.
		// Shift s into the position where it will go in in the
		// resulting half number.
		// Adjust e, accounting for the different exponent bias
		// of float and half (127 versus 15).
		//

		int s =  (i >> 16) & 0x00008000;
		int e = ((i >> 23) & 0x000000ff) - (127 - 15);
		int m =   i        & 0x007fffff;

		//
		// Now reassemble s, e and m into a half:
		//

		if(e <= 0)
		{
			if(e < -10)
			{
				//
				// E is less than -10.  The absolute value of f is
				// less than half_MIN (f may be a small normalized
				// float, a denormalized float or a zero).
				//
				// We convert f to a half zero.
				//

				return hdata(s);
			}

			//
			// E is between -10 and 0.  F is a normalized float,
			// whose magnitude is less than __half_NRM_MIN.
			//
			// We convert f to a denormalized half.
			//

			m = (m | 0x00800000) >> (1 - e);

			//
			// Round to nearest, round "0.5" up.
			//
			// Rounding may cause the significand to overflow and make
			// our number normalized.  Because of the way a half's bits
			// are laid out, we don't have to treat this case separately;
			// the code below will handle it correctly.
			//

			if(m & 0x00001000)
				m += 0x00002000;

			//
			// Assemble the half from s, e (zero) and m.
			//

			return hdata(s | (m >> 13));
		}
		else if(e == 0xff - (127 - 15))
		{
			if(m == 0)
			{
				//
				// F is an infinity; convert f to a half
				// infinity with the same sign as f.
				//

				return hdata(s | 0x7c00);
			}
			else
			{
				//
				// F is a NAN; we produce a half NAN that preserves
				// the sign bit and the 10 leftmost bits of the
				// significand of f, with one exception: If the 10
				// leftmost bits are all zero, the NAN would turn
				// into an infinity, so we have to set at least one
				// bit in the significand.
				//

				m >>= 13;

				return hdata(s | 0x7c00 | m | (m == 0));
			}
		}
		else
		{
			//
			// E is greater than zero.  F is a normalized float.
			// We try to convert f to a normalized half.
			//

			//
			// Round to nearest, round "0.5" up
			//

			if(m &  0x00001000)
			{
				m += 0x00002000;

				if(m & 0x00800000)
				{
					m =  0;     // overflow in significand,
					e += 1;     // adjust exponent
				}
			}

			//
			// Handle exponent overflow
			//

			if (e > 30)
			{
				overflow();        // Cause a hardware floating point overflow;

				return hdata(s | 0x7c00);
				// if this returns, the half becomes an
			}   // infinity with the same sign as f.

			//
			// Assemble the half from s, e and m.
			//

			return hdata(s | (e << 10) | (m >> 13));
		}
	}

}//namespace detail
}//namespace glm