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Diffstat (limited to 'Source/OpenEXR/Half/half.h')
| -rw-r--r-- | Source/OpenEXR/Half/half.h | 776 |
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diff --git a/Source/OpenEXR/Half/half.h b/Source/OpenEXR/Half/half.h new file mode 100644 index 0000000..bfb0116 --- /dev/null +++ b/Source/OpenEXR/Half/half.h @@ -0,0 +1,776 @@ +/////////////////////////////////////////////////////////////////////////// +// +// 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 the float's +// value exactly. If a float is not representable as a half, 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 half with the greater magnitude. +// +// 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 <iostream> + +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 + //-------------------------------------- + + 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; + + //--------------------------------------------------- + // Windows dynamic libraries don't like static + // member variables. + //--------------------------------------------------- +#ifndef OPENEXR_DLL + static const uif _toFloat[1 << 16]; + static const unsigned short _eLut[1 << 9]; +#endif +}; + +#if defined(OPENEXR_DLL) + //-------------------------------------- + // Lookup tables defined for Windows DLL + //-------------------------------------- + #if defined(HALF_EXPORTS) + extern __declspec(dllexport) half::uif _toFloat[1 << 16]; + extern __declspec(dllexport) unsigned short _eLut[1 << 9]; + #else + extern __declspec(dllimport) half::uif _toFloat[1 << 16]; + extern __declspec(dllimport) unsigned short _eLut[1 << 9]; + #endif +#endif + + +//----------- +// Stream I/O +//----------- + +std::ostream & operator << (std::ostream &os, half h); +std::istream & operator >> (std::istream &is, half &h); + + +//---------- +// Debugging +//---------- + +void printBits (std::ostream &os, half h); +void printBits (std::ostream &os, float f); +void printBits (char c[19], half h); +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; +} + +#undef HALF_EXPORT_CONST + +#endif |