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This commit is contained in:
choelzl
2022-04-07 18:46:57 +02:00
parent 88cb3426ad
commit 15e7120d6d
5316 changed files with 4563444 additions and 6 deletions
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16
cs440-acg/ext/openexr/IlmBase/Half/.cvsignore Normal file
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Makefile
Makefile.in
config.h.in
config.h
config.log
config.status
configure
libtool
stamp-h
aclocal.m4
OpenEXR.pc
autom4te.cache
ltmain.sh
stamp-h.in
depcomp
.deps

58
cs440-acg/ext/openexr/IlmBase/Half/CMakeLists.txt Normal file
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# yue.nicholas@gmail.com
ADD_EXECUTABLE ( eLut eLut.cpp )
ADD_CUSTOM_COMMAND(
OUTPUT ${CMAKE_CURRENT_BINARY_DIR}/eLut.h
COMMAND eLut ARGS > ${CMAKE_CURRENT_BINARY_DIR}/eLut.h
DEPENDS eLut
WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
)
SET_SOURCE_FILES_PROPERTIES(
${CMAKE_CURRENT_BINARY_DIR}/eLut.h
PROPERTIES HEADER_FILE_ONLY TRUE
)
ADD_EXECUTABLE ( toFloat toFloat.cpp )
ADD_CUSTOM_COMMAND(
OUTPUT ${CMAKE_CURRENT_BINARY_DIR}/toFloat.h
COMMAND toFloat ARGS > ${CMAKE_CURRENT_BINARY_DIR}/toFloat.h
DEPENDS toFloat
WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
)
SET_SOURCE_FILES_PROPERTIES(
${CMAKE_CURRENT_BINARY_DIR}/toFloat.h
PROPERTIES HEADER_FILE_ONLY TRUE
)
SET_SOURCE_FILES_PROPERTIES(
half.cpp
PROPERTIES
OBJECT_DEPENDS
"${CMAKE_CURRENT_BINARY_DIR}/eLut.h;${CMAKE_CURRENT_BINARY_DIR}/toFloat.h"
)
IF(ILMBASE_BUILD_SHARED_LIBS)
ADD_DEFINITIONS(-DHALF_EXPORTS)
ENDIF()
ADD_LIBRARY ( Half ${LIB_TYPE}
half.cpp
)
ADD_DEPENDENCIES ( Half toFloat eLut )
INSTALL ( TARGETS
Half
DESTINATION
${OPENEXR_INSTALL_LIB_DEST}
)
INSTALL ( FILES
half.h
halfFunction.h
halfExport.h
halfLimits.h
DESTINATION
${OPENEXR_INSTALL_HEADER_DEST}
)

32
cs440-acg/ext/openexr/IlmBase/Half/Makefile.am Normal file
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## Process this file with automake to produce Makefile.in
INCLUDES = -I$(top_srcdir)/config
lib_LTLIBRARIES = libHalf.la
libHalf_la_SOURCES = half.cpp half.h halfFunction.h halfLimits.h
libHalf_la_LDFLAGS = -version-info @LIBTOOL_VERSION@ -no-undefined
libHalfincludedir = $(includedir)/OpenEXR
libHalfinclude_HEADERS = half.h halfFunction.h halfLimits.h halfExport.h
# these are used to build eLut.h and toFloat.h dynamically
EXTRA_DIST = eLut.cpp toFloat.cpp CMakeLists.txt
CLEANFILES = eLut eLut.h toFloat toFloat.h
eLut_SOURCES = eLut.cpp
toFloat_SOURCES = toFloat.cpp
eLut.h: eLut
./eLut > eLut.h
toFloat.h: toFloat
./toFloat > toFloat.h
BUILT_SOURCES = eLut.h toFloat.h
noinst_PROGRAMS = eLut toFloat

114
cs440-acg/ext/openexr/IlmBase/Half/eLut.cpp Normal file
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///////////////////////////////////////////////////////////////////////////
//
// 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.
//
///////////////////////////////////////////////////////////////////////////
#include <iostream>
#include <iomanip>
using namespace std;
//-----------------------------------------------------
// Compute a lookup table for float-to-half conversion.
//
// When indexed with the combined sign and exponent of
// a float, the table either returns the combined sign
// and exponent of the corresponding half, or zero if
// the corresponding half may not be normalized (zero,
// denormalized, overflow).
//-----------------------------------------------------
void
initELut (unsigned short eLut[])
{
for (int i = 0; i < 0x100; i++)
{
int e = (i & 0x0ff) - (127 - 15);
if (e <= 0 || e >= 30)
{
//
// Special case
//
eLut[i] = 0;
eLut[i | 0x100] = 0;
}
else
{
//
// Common case - normalized half, no exponent overflow possible
//
eLut[i] = (e << 10);
eLut[i | 0x100] = ((e << 10) | 0x8000);
}
}
}
//------------------------------------------------------------
// Main - prints the sign-and-exponent conversion lookup table
//------------------------------------------------------------
int
main ()
{
const int tableSize = 1 << 9;
unsigned short eLut[tableSize];
initELut (eLut);
cout << "//\n"
"// This is an automatically generated file.\n"
"// Do not edit.\n"
"//\n\n";
cout << "{\n ";
for (int i = 0; i < tableSize; i++)
{
cout << setw (5) << eLut[i] << ", ";
if (i % 8 == 7)
{
cout << "\n";
if (i < tableSize - 1)
cout << " ";
}
}
cout << "};\n";
return 0;
}

310
cs440-acg/ext/openexr/IlmBase/Half/half.cpp Normal file
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///////////////////////////////////////////////////////////////////////////
//
// 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>
//---------------------------------------------------------------------------
//
// class half --
// implementation of non-inline members
//
//---------------------------------------------------------------------------
#include <assert.h>
#include "half.h"
using namespace std;
//-------------------------------------------------------------
// Lookup tables for half-to-float and float-to-half conversion
//-------------------------------------------------------------
HALF_EXPORT const half::uif half::_toFloat[1 << 16] =
#include "toFloat.h"
HALF_EXPORT const unsigned short half::_eLut[1 << 9] =
#include "eLut.h"
//-----------------------------------------------
// Overflow handler for float-to-half conversion;
// generates a hardware floating-point overflow,
// which may be trapped by the operating system.
//-----------------------------------------------
HALF_EXPORT float
half::overflow ()
{
volatile float f = 1e10;
for (int i = 0; i < 10; i++)
f *= f; // this will overflow before
// the for<6F>loop terminates
return f;
}
//-----------------------------------------------------
// Float-to-half conversion -- general case, including
// zeroes, denormalized numbers and exponent overflows.
//-----------------------------------------------------
HALF_EXPORT short
half::convert (int 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 with the same sign as f.
//
return 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.
//
//
// Add an explicit leading 1 to the significand.
//
m = m | 0x00800000;
//
// Round to m to the nearest (10+e)-bit value (with e between
// -10 and 0); in case of a tie, round to the nearest even value.
//
// 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.
//
int t = 14 - e;
int a = (1 << (t - 1)) - 1;
int b = (m >> t) & 1;
m = (m + a + b) >> t;
//
// Assemble the half from s, e (zero) and m.
//
return s | m;
}
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 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 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 m to the nearest 10-bit value. In case of
// a tie, round to the nearest even value.
//
m = m + 0x00000fff + ((m >> 13) & 1);
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 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 s | (e << 10) | (m >> 13);
}
}
//---------------------
// Stream I/O operators
//---------------------
HALF_EXPORT ostream &
operator << (ostream &os, half h)
{
os << float (h);
return os;
}
HALF_EXPORT istream &
operator >> (istream &is, half &h)
{
float f;
is >> f;
h = half (f);
return is;
}
//---------------------------------------
// Functions to print the bit-layout of
// floats and halfs, mostly for debugging
//---------------------------------------
HALF_EXPORT void
printBits (ostream &os, half h)
{
unsigned short b = h.bits();
for (int i = 15; i >= 0; i--)
{
os << (((b >> i) & 1)? '1': '0');
if (i == 15 || i == 10)
os << ' ';
}
}
HALF_EXPORT void
printBits (ostream &os, float f)
{
half::uif x;
x.f = f;
for (int i = 31; i >= 0; i--)
{
os << (((x.i >> i) & 1)? '1': '0');
if (i == 31 || i == 23)
os << ' ';
}
}
HALF_EXPORT void
printBits (char c[19], half h)
{
unsigned short b = h.bits();
for (int i = 15, j = 0; i >= 0; i--, j++)
{
c[j] = (((b >> i) & 1)? '1': '0');
if (i == 15 || i == 10)
c[++j] = ' ';
}
c[18] = 0;
}
HALF_EXPORT void
printBits (char c[35], float f)
{
half::uif x;
x.f = f;
for (int i = 31, j = 0; i >= 0; i--, j++)
{
c[j] = (((x.i >> i) & 1)? '1': '0');
if (i == 31 || i == 23)
c[++j] = ' ';
}
c[34] = 0;
}

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cs440-acg/ext/openexr/IlmBase/Half/half.h Normal file
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///////////////////////////////////////////////////////////////////////////
//
// 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_
#include "halfExport.h" // for definition of HALF_EXPORT
#include <iostream>
class half
{
public:
//-------------
// Constructors
//-------------
half (); // no initialization
half (float f);
half(const half & h): _h(h._h) { }
//--------------------
// 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.
//
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.
//
int m = x.i & 0x007fffff;
_h = (unsigned short) (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

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#ifndef HALFEXPORT_H
#define HALFEXPORT_H
//
// Copyright (c) 2008 Lucasfilm Entertainment Company Ltd.
// All rights reserved. Used under authorization.
// This material contains the confidential and proprietary
// information of Lucasfilm Entertainment Company and
// may not be copied in whole or in part without the express
// written permission of Lucasfilm Entertainment Company.
// This copyright notice does not imply publication.
//
#if defined(OPENEXR_DLL)
#if defined(HALF_EXPORTS)
#define HALF_EXPORT __declspec(dllexport)
#else
#define HALF_EXPORT __declspec(dllimport)
#endif
#define HALF_EXPORT_CONST
#else
#define HALF_EXPORT
#define HALF_EXPORT_CONST const
#endif
#endif // #ifndef HALFEXPORT_H

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///////////////////////////////////////////////////////////////////////////
//
// 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>
//---------------------------------------------------------------------------
//
// halfFunction<T> -- a class for fast evaluation
// of half --> T functions
//
// The constructor for a halfFunction object,
//
// halfFunction (function,
// domainMin, domainMax,
// defaultValue,
// posInfValue, negInfValue,
// nanValue);
//
// evaluates the function for all finite half values in the interval
// [domainMin, domainMax], and stores the results in a lookup table.
// For finite half values that are not in [domainMin, domainMax], the
// constructor stores defaultValue in the table. For positive infinity,
// negative infinity and NANs, posInfValue, negInfValue and nanValue
// are stored in the table.
//
// The tabulated function can then be evaluated quickly for arbitrary
// half values by calling the the halfFunction object's operator()
// method.
//
// Example:
//
// #include <math.h>
// #include <halfFunction.h>
//
// halfFunction<half> hsin (sin);
//
// halfFunction<half> hsqrt (sqrt, // function
// 0, HALF_MAX, // domain
// half::qNan(), // sqrt(x) for x < 0
// half::posInf(), // sqrt(+inf)
// half::qNan(), // sqrt(-inf)
// half::qNan()); // sqrt(nan)
//
// half x = hsin (1);
// half y = hsqrt (3.5);
//
//---------------------------------------------------------------------------
#ifndef _HALF_FUNCTION_H_
#define _HALF_FUNCTION_H_
#include "half.h"
#include "IlmBaseConfig.h"
#ifndef ILMBASE_HAVE_LARGE_STACK
#include <string.h> // need this for memset
#else
#endif
#include <float.h>
template <class T>
class halfFunction
{
public:
//------------
// Constructor
//------------
template <class Function>
halfFunction (Function f,
half domainMin = -HALF_MAX,
half domainMax = HALF_MAX,
T defaultValue = 0,
T posInfValue = 0,
T negInfValue = 0,
T nanValue = 0);
#ifndef ILMBASE_HAVE_LARGE_STACK
~halfFunction () { delete [] _lut; }
#endif
//-----------
// Evaluation
//-----------
T operator () (half x) const;
private:
#ifdef ILMBASE_HAVE_LARGE_STACK
T _lut[1 << 16];
#else
T * _lut;
#endif
};
//---------------
// Implementation
//---------------
template <class T>
template <class Function>
halfFunction<T>::halfFunction (Function f,
half domainMin,
half domainMax,
T defaultValue,
T posInfValue,
T negInfValue,
T nanValue)
{
#ifndef ILMBASE_HAVE_LARGE_STACK
_lut = new T[1<<16];
memset (_lut, 0 , (1<<16) * sizeof(T));
#endif
for (int i = 0; i < (1 << 16); i++)
{
half x;
x.setBits (i);
if (x.isNan())
_lut[i] = nanValue;
else if (x.isInfinity())
_lut[i] = x.isNegative()? negInfValue: posInfValue;
else if (x < domainMin || x > domainMax)
_lut[i] = defaultValue;
else
_lut[i] = f (x);
}
}
template <class T>
inline T
halfFunction<T>::operator () (half x) const
{
return _lut[x.bits()];
}
#endif

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///////////////////////////////////////////////////////////////////////////
//
// 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>
#ifndef INCLUDED_HALF_LIMITS_H
#define INCLUDED_HALF_LIMITS_H
//------------------------------------------------------------------------
//
// C++ standard library-style numeric_limits for class half
//
//------------------------------------------------------------------------
#include <limits>
#include "half.h"
namespace std {
template <>
class numeric_limits <half>
{
public:
static const bool is_specialized = true;
static half min () {return HALF_NRM_MIN;}
static half max () {return HALF_MAX;}
static const int digits = HALF_MANT_DIG;
static const int digits10 = HALF_DIG;
static const bool is_signed = true;
static const bool is_integer = false;
static const bool is_exact = false;
static const int radix = HALF_RADIX;
static half epsilon () {return HALF_EPSILON;}
static half round_error () {return HALF_EPSILON / 2;}
static const int min_exponent = HALF_MIN_EXP;
static const int min_exponent10 = HALF_MIN_10_EXP;
static const int max_exponent = HALF_MAX_EXP;
static const int max_exponent10 = HALF_MAX_10_EXP;
static const bool has_infinity = true;
static const bool has_quiet_NaN = true;
static const bool has_signaling_NaN = true;
static const float_denorm_style has_denorm = denorm_present;
static const bool has_denorm_loss = false;
static half infinity () {return half::posInf();}
static half quiet_NaN () {return half::qNan();}
static half signaling_NaN () {return half::sNan();}
static half denorm_min () {return HALF_MIN;}
static const bool is_iec559 = false;
static const bool is_bounded = false;
static const bool is_modulo = false;
static const bool traps = true;
static const bool tinyness_before = false;
static const float_round_style round_style = round_to_nearest;
};
} // namespace std
#endif

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///////////////////////////////////////////////////////////////////////////
//
// 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.
//
///////////////////////////////////////////////////////////////////////////
//---------------------------------------------------------------------------
//
// toFloat
//
// A program to generate the lookup table for half-to-float
// conversion needed by class half.
// The program loops over all 65536 possible half numbers,
// converts each of them to a float, and prints the result.
//
//---------------------------------------------------------------------------
#include <iostream>
#include <iomanip>
using namespace std;
//---------------------------------------------------
// Interpret an unsigned short bit pattern as a half,
// and convert that half to the corresponding float's
// bit pattern.
//---------------------------------------------------
unsigned int
halfToFloat (unsigned short y)
{
int s = (y >> 15) & 0x00000001;
int e = (y >> 10) & 0x0000001f;
int m = y & 0x000003ff;
if (e == 0)
{
if (m == 0)
{
//
// Plus or minus zero
//
return s << 31;
}
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
//
return (s << 31) | 0x7f800000;
}
else
{
//
// Nan -- preserve sign and significand bits
//
return (s << 31) | 0x7f800000 | (m << 13);
}
}
//
// Normalized number
//
e = e + (127 - 15);
m = m << 13;
//
// Assemble s, e and m.
//
return (s << 31) | (e << 23) | m;
}
//---------------------------------------------
// Main - prints the half-to-float lookup table
//---------------------------------------------
int
main ()
{
cout.precision (9);
cout.setf (ios_base::hex, ios_base::basefield);
cout << "//\n"
"// This is an automatically generated file.\n"
"// Do not edit.\n"
"//\n\n";
cout << "{\n ";
const int iMax = (1 << 16);
for (int i = 0; i < iMax; i++)
{
cout << "{0x" << setfill ('0') << setw (8) << halfToFloat (i) << "}, ";
if (i % 4 == 3)
{
cout << "\n";
if (i < iMax - 1)
cout << " ";
}
}
cout << "};\n";
return 0;
}