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Half.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>
//---------------------------------------------------------------------------
//
// 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 OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
#include <openvdb/Platform.h>
#include <openvdb/version.h>
#include <iostream>
namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {
namespace internal {
class OPENVDB_API half
{
public:
//-------------
// Constructors
//-------------
half () = default; // no initialization
half (float f);
// rule of 5
~half () = default;
half (const half &) = default;
half (half &&) noexcept = default;
//--------------------
// Conversion to float
//--------------------
operator float () const;
//------------
// Unary minus
//------------
half operator - () const;
//-----------
// Assignment
//-----------
half & operator = (const half &h) = default;
half & operator = (half &&h) noexcept = default;
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
//--------------------------------------
unsigned short bits () const;
void setBits (unsigned short bits);
public:
union uif
{
unsigned int i;
float f;
};
private:
static short convert (int i);
static float overflow ();
unsigned short _h;
static const uif _toFloat[1 << 16];
static const unsigned short _eLut[1 << 9];
};
//-----------
// Stream I/O
//-----------
OPENVDB_API std::ostream & operator << (std::ostream &os, half h);
OPENVDB_API std::istream & operator >> (std::istream &is, half &h);
//----------
// Debugging
//----------
OPENVDB_API void printBits (std::ostream &os, half h);
OPENVDB_API void printBits (std::ostream &os, float f);
OPENVDB_API void printBits (char c[19], half h);
OPENVDB_API 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 VDB_HALF_MIN 5.96046448e-08f // Smallest positive half
#define VDB_HALF_NRM_MIN 6.10351562e-05f // Smallest positive normalized half
#define VDB_HALF_MAX 65504.0f // Largest positive half
#define VDB_HALF_EPSILON 0.00097656f // Smallest positive e for which
// half (1.0 + e) != half (1.0)
#else
#define VDB_HALF_MIN 5.96046448e-08 // Smallest positive half
#define VDB_HALF_NRM_MIN 6.10351562e-05 // Smallest positive normalized half
#define VDB_HALF_MAX 65504.0 // Largest positive half
#define VDB_HALF_EPSILON 0.00097656 // Smallest positive e for which
// half (1.0 + e) != half (1.0)
#endif
#define VDB_HALF_MANT_DIG 11 // Number of digits in mantissa
// (significand + hidden leading 1)
//
// floor( (VDB_HALF_MANT_DIG - 1) * log10(2) ) => 3.01... -> 3
#define VDB_HALF_DIG 3 // Number of base 10 digits that
// can be represented without change
// ceil(VDB_HALF_MANT_DIG * log10(2) + 1) => 4.31... -> 5
#define VDB_HALF_DECIMAL_DIG 5 // Number of base-10 digits that are
// necessary to uniquely represent all
// distinct values
#define VDB_HALF_RADIX 2 // Base of the exponent
#define VDB_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 VDB_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 VDB_HALF_MIN_10_EXP -4 // Minimum positive integer such
// that 10 raised to that power is
// a normalized half
#define VDB_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.
//
//---------------------------------------------------------------------------
//----------------------------
// 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 = (unsigned short)(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 = (unsigned short)(e >> (9 - n));
e = (unsigned short)(e + (e & 1));
e = (unsigned short)(e << (9 - n));
//
// Check for exponent overflow.
//
if (e >= 0x7c00)
{
//
// Overflow occurred -- truncate instead of rounding.
//
e = _h;
e = (unsigned short)(e >> (10 - n));
e = (unsigned short)(e << (10 - n));
}
//
// Put the original sign bit back.
//
half h;
h._h = (unsigned short)(s | e);
return h;
}
//-----------------------
// Other inline functions
//-----------------------
inline half
half::operator - () const
{
half h;
h._h = _h ^ 0x8000;
return h;
}
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;
}
} // namespace internal
} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb
#endif // OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
Platform.h
OPENVDB_API
#define OPENVDB_API
Definition Platform.h:251
openvdb::v10_0::math::internal::half
Definition Half.h:99
openvdb::v10_0::math::internal::half::sNan
static half sNan()
Definition Half.h:735
openvdb::v10_0::math::internal::half::round
half round(unsigned int n) const
Definition Half.h:511
openvdb::v10_0::math::internal::half::half
half()=default
openvdb::v10_0::math::internal::half::~half
~half()=default
openvdb::v10_0::math::internal::half::isZero
bool isZero() const
Definition Half.h:676
openvdb::v10_0::math::internal::half::half
half(half &&) noexcept=default
openvdb::v10_0::math::internal::half::bits
unsigned short bits() const
Definition Half.h:744
openvdb::v10_0::math::internal::half::isInfinity
bool isInfinity() const
Definition Half.h:692
openvdb::v10_0::math::internal::half::negInf
static half negInf()
Definition Half.h:717
openvdb::v10_0::math::internal::half::posInf
static half posInf()
Definition Half.h:708
openvdb::v10_0::math::internal::half::isNegative
bool isNegative() const
Definition Half.h:701
openvdb::v10_0::math::internal::half::half
half(const half &)=default
openvdb::v10_0::math::internal::half::setBits
void setBits(unsigned short bits)
Definition Half.h:751
openvdb::v10_0::math::internal::half::qNan
static half qNan()
Definition Half.h:726
openvdb::v10_0::math::internal::half::isNormalized
bool isNormalized() const
Definition Half.h:659
openvdb::v10_0::math::internal::half::isDenormalized
bool isDenormalized() const
Definition Half.h:667
openvdb::v10_0::math::internal::half::isNan
bool isNan() const
Definition Half.h:683
openvdb::v10_0::math::internal::half::isFinite
bool isFinite() const
Definition Half.h:651
openvdb::v10_0::math::internal
Definition Half.h:96
openvdb::v10_0::math::internal::printBits
OPENVDB_API void printBits(std::ostream &os, half h)
openvdb
Definition Exceptions.h:13
openvdb::v10_0::math::internal::half::uif
Definition Half.h:218
openvdb::v10_0::math::internal::half::uif::i
unsigned int i
Definition Half.h:219
openvdb::v10_0::math::internal::half::uif::f
float f
Definition Half.h:220
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212