///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 – 2015 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.
///
/// Restrictions:
/// By making use of the Software for military purposes, you choose to make
/// a Bunny unhappy.
///
/// 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/detail/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 for loop 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