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Iex.h
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IexBaseExc.h
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IexErrnoExc.h
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IexExport.h
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IexForward.h
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IexMacros.h
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IexMathExc.h
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IexMathFloatExc.h
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IexMathFpu.h
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IexMathIeeeExc.h
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IexNamespace.h
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IexThrowErrnoExc.h
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IlmBaseConfig.h
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IlmThread.h
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IlmThreadExport.h
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IlmThreadForward.h
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IlmThreadMutex.h
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IlmThreadNamespace.h
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IlmThreadPool.h
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IlmThreadSemaphore.h
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ImathBox.h
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ImathBoxAlgo.h
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ImathColor.h
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ImathColorAlgo.h
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ImathEuler.h
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ImathExc.h
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ImathExport.h
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ImathForward.h
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ImathFrame.h
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ImathFrustum.h
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ImathFrustumTest.h
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ImathFun.h
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ImathGL.h
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ImathGLU.h
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ImathHalfLimits.h
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ImathInt64.h
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ImathInterval.h
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ImathLimits.h
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ImathLine.h
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ImathLineAlgo.h
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ImathMath.h
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ImathMatrix.h
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ImathMatrixAlgo.h
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ImathNamespace.h
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ImathPlane.h
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ImathPlatform.h
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ImathQuat.h
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ImathRandom.h
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ImathRoots.h
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ImathShear.h
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ImathSphere.h
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ImathVec.h
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ImathVecAlgo.h
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ImfAcesFile.h
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ImfArray.h
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ImfAttribute.h
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ImfB44Compressor.h
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ImfBoxAttribute.h
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ImfCRgbaFile.h
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ImfChannelList.h
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ImfChannelListAttribute.h
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ImfChromaticities.h
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ImfChromaticitiesAttribute.h
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ImfCompositeDeepScanLine.h
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ImfCompression.h
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ImfCompressionAttribute.h
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ImfConvert.h
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ImfDeepCompositing.h
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ImfDeepFrameBuffer.h
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ImfDeepImageState.h
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ImfDeepImageStateAttribute.h
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ImfDeepScanLineInputFile.h
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ImfDeepScanLineInputPart.h
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ImfDeepScanLineOutputFile.h
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ImfDeepScanLineOutputPart.h
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ImfDeepTiledInputFile.h
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ImfDeepTiledInputPart.h
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ImfDeepTiledOutputFile.h
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ImfDeepTiledOutputPart.h
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ImfDoubleAttribute.h
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ImfEnvmap.h
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ImfEnvmapAttribute.h
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ImfExport.h
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ImfFloatAttribute.h
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ImfForward.h
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ImfFrameBuffer.h
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ImfFramesPerSecond.h
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ImfGenericInputFile.h
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ImfGenericOutputFile.h
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ImfHeader.h
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ImfHuf.h
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ImfIO.h
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ImfInputFile.h
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ImfInputPart.h
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ImfInt64.h
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ImfIntAttribute.h
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ImfKeyCode.h
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ImfKeyCodeAttribute.h
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ImfLineOrder.h
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ImfLineOrderAttribute.h
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ImfLut.h
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ImfMatrixAttribute.h
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ImfMisc.h
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ImfMultiPartInputFile.h
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ImfMultiPartOutputFile.h
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ImfMultiView.h
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ImfName.h
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ImfNamespace.h
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ImfOpaqueAttribute.h
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ImfOutputFile.h
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ImfOutputPart.h
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ImfPartHelper.h
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ImfPartType.h
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ImfPixelType.h
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ImfPreviewImage.h
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ImfPreviewImageAttribute.h
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ImfRational.h
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ImfRationalAttribute.h
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ImfRgba.h
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ImfRgbaFile.h
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ImfRgbaYca.h
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ImfStandardAttributes.h
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ImfStringAttribute.h
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ImfStringVectorAttribute.h
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ImfTestFile.h
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ImfThreading.h
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ImfTileDescription.h
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ImfTileDescriptionAttribute.h
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ImfTiledInputFile.h
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ImfTiledInputPart.h
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ImfTiledOutputFile.h
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ImfTiledOutputPart.h
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ImfTiledRgbaFile.h
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ImfTimeCode.h
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ImfTimeCodeAttribute.h
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ImfVecAttribute.h
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ImfVersion.h
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ImfWav.h
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ImfXdr.h
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OpenEXRConfig.h
1.8
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half.h
17.22
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halfExport.h
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halfFunction.h
4.83
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halfLimits.h
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Code Editor : half.h
/////////////////////////////////////////////////////////////////////////// // // 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); //-------------------- // 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. // 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; } #endif
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