767 lines
18 KiB
C++
767 lines
18 KiB
C++
///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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// Primary authors:
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// Florian Kainz <kainz@ilm.com>
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// Rod Bogart <rgb@ilm.com>
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//---------------------------------------------------------------------------
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//
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// half -- a 16-bit floating point number class:
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//
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// Type half can represent positive and negative numbers whose
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// magnitude is between roughly 6.1e-5 and 6.5e+4 with a relative
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// error of 9.8e-4; numbers smaller than 6.1e-5 can be represented
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// with an absolute error of 6.0e-8. All integers from -2048 to
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// +2048 can be represented exactly.
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//
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// Type half behaves (almost) like the built-in C++ floating point
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// types. In arithmetic expressions, half, float and double can be
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// mixed freely. Here are a few examples:
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//
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// half a (3.5);
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// float b (a + sqrt (a));
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// a += b;
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// b += a;
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// b = a + 7;
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//
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// Conversions from half to float are lossless; all half numbers
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// are exactly representable as floats.
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//
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// Conversions from float to half may not preserve a float's value
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// exactly. If a float is not representable as a half, then the
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// float value is rounded to the nearest representable half. If a
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// float value is exactly in the middle between the two closest
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// representable half values, then the float value is rounded to
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// the closest half whose least significant bit is zero.
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//
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// Overflows during float-to-half conversions cause arithmetic
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// exceptions. An overflow occurs when the float value to be
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// converted is too large to be represented as a half, or if the
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// float value is an infinity or a NAN.
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//
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// The implementation of type half makes the following assumptions
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// about the implementation of the built-in C++ types:
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//
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// float is an IEEE 754 single-precision number
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// sizeof (float) == 4
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// sizeof (unsigned int) == sizeof (float)
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// alignof (unsigned int) == alignof (float)
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// sizeof (unsigned short) == 2
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//
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//---------------------------------------------------------------------------
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#ifndef _HALF_H_
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#define _HALF_H_
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#include <iostream>
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#if defined(OPENEXR_DLL)
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#if defined(HALF_EXPORTS)
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#define HALF_EXPORT __declspec(dllexport)
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#else
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#define HALF_EXPORT __declspec(dllimport)
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#endif
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#define HALF_EXPORT_CONST
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#else
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#define HALF_EXPORT
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#define HALF_EXPORT_CONST const
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#endif
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class HALF_EXPORT half
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{
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public:
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//-------------
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// Constructors
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//-------------
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half (); // no initialization
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half (float f);
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//--------------------
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// Conversion to float
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//--------------------
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operator float () const;
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//------------
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// Unary minus
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//------------
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half operator - () const;
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//-----------
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// Assignment
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//-----------
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half & operator = (half h);
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half & operator = (float f);
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half & operator += (half h);
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half & operator += (float f);
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half & operator -= (half h);
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half & operator -= (float f);
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half & operator *= (half h);
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half & operator *= (float f);
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half & operator /= (half h);
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half & operator /= (float f);
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//---------------------------------------------------------
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// Round to n-bit precision (n should be between 0 and 10).
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// After rounding, the significand's 10-n least significant
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// bits will be zero.
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//---------------------------------------------------------
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half round (unsigned int n) const;
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//--------------------------------------------------------------------
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// Classification:
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//
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// h.isFinite() returns true if h is a normalized number,
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// a denormalized number or zero
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//
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// h.isNormalized() returns true if h is a normalized number
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//
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// h.isDenormalized() returns true if h is a denormalized number
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//
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// h.isZero() returns true if h is zero
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//
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// h.isNan() returns true if h is a NAN
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//
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// h.isInfinity() returns true if h is a positive
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// or a negative infinity
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//
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// h.isNegative() returns true if the sign bit of h
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// is set (negative)
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//--------------------------------------------------------------------
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bool isFinite () const;
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bool isNormalized () const;
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bool isDenormalized () const;
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bool isZero () const;
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bool isNan () const;
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bool isInfinity () const;
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bool isNegative () const;
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//--------------------------------------------
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// Special values
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//
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// posInf() returns +infinity
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//
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// negInf() returns -infinity
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//
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// qNan() returns a NAN with the bit
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// pattern 0111111111111111
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//
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// sNan() returns a NAN with the bit
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// pattern 0111110111111111
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//--------------------------------------------
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static half posInf ();
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static half negInf ();
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static half qNan ();
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static half sNan ();
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//--------------------------------------
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// Access to the internal representation
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//--------------------------------------
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unsigned short bits () const;
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void setBits (unsigned short bits);
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public:
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union uif
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{
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unsigned int i;
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float f;
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};
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private:
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static short convert (int i);
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static float overflow ();
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unsigned short _h;
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static HALF_EXPORT_CONST uif _toFloat[1 << 16];
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static HALF_EXPORT_CONST unsigned short _eLut[1 << 9];
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};
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//-----------
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// Stream I/O
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//-----------
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HALF_EXPORT std::ostream & operator << (std::ostream &os, half h);
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HALF_EXPORT std::istream & operator >> (std::istream &is, half &h);
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//----------
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// Debugging
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//----------
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HALF_EXPORT void printBits (std::ostream &os, half h);
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HALF_EXPORT void printBits (std::ostream &os, float f);
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HALF_EXPORT void printBits (char c[19], half h);
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HALF_EXPORT void printBits (char c[35], float f);
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//-------------------------------------------------------------------------
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// Limits
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//
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// Visual C++ will complain if HALF_MIN, HALF_NRM_MIN etc. are not float
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// constants, but at least one other compiler (gcc 2.96) produces incorrect
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// results if they are.
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//-------------------------------------------------------------------------
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#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
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#define HALF_MIN 5.96046448e-08f // Smallest positive half
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#define HALF_NRM_MIN 6.10351562e-05f // Smallest positive normalized half
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#define HALF_MAX 65504.0f // Largest positive half
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#define HALF_EPSILON 0.00097656f // Smallest positive e for which
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// half (1.0 + e) != half (1.0)
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#else
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#define HALF_MIN 5.96046448e-08 // Smallest positive half
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#define HALF_NRM_MIN 6.10351562e-05 // Smallest positive normalized half
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#define HALF_MAX 65504.0 // Largest positive half
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#define HALF_EPSILON 0.00097656 // Smallest positive e for which
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// half (1.0 + e) != half (1.0)
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#endif
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#define HALF_MANT_DIG 11 // Number of digits in mantissa
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// (significand + hidden leading 1)
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#define HALF_DIG 2 // Number of base 10 digits that
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// can be represented without change
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#define HALF_RADIX 2 // Base of the exponent
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#define HALF_MIN_EXP -13 // Minimum negative integer such that
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// HALF_RADIX raised to the power of
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// one less than that integer is a
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// normalized half
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#define HALF_MAX_EXP 16 // Maximum positive integer such that
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// HALF_RADIX raised to the power of
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// one less than that integer is a
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// normalized half
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#define HALF_MIN_10_EXP -4 // Minimum positive integer such
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// that 10 raised to that power is
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// a normalized half
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#define HALF_MAX_10_EXP 4 // Maximum positive integer such
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// that 10 raised to that power is
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// a normalized half
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//---------------------------------------------------------------------------
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//
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// Implementation --
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//
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// Representation of a float:
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//
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// We assume that a float, f, is an IEEE 754 single-precision
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// floating point number, whose bits are arranged as follows:
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//
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// 31 (msb)
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// |
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// | 30 23
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// | | |
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// | | | 22 0 (lsb)
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// | | | | |
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// X XXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX
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//
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// s e m
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//
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// S is the sign-bit, e is the exponent and m is the significand.
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//
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// If e is between 1 and 254, f is a normalized number:
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//
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// s e-127
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// f = (-1) * 2 * 1.m
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//
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// If e is 0, and m is not zero, f is a denormalized number:
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//
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// s -126
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// f = (-1) * 2 * 0.m
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//
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// If e and m are both zero, f is zero:
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//
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// f = 0.0
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//
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// If e is 255, f is an "infinity" or "not a number" (NAN),
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// depending on whether m is zero or not.
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//
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// Examples:
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//
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// 0 00000000 00000000000000000000000 = 0.0
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// 0 01111110 00000000000000000000000 = 0.5
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// 0 01111111 00000000000000000000000 = 1.0
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// 0 10000000 00000000000000000000000 = 2.0
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// 0 10000000 10000000000000000000000 = 3.0
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// 1 10000101 11110000010000000000000 = -124.0625
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// 0 11111111 00000000000000000000000 = +infinity
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// 1 11111111 00000000000000000000000 = -infinity
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// 0 11111111 10000000000000000000000 = NAN
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// 1 11111111 11111111111111111111111 = NAN
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//
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// Representation of a half:
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//
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// Here is the bit-layout for a half number, h:
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//
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// 15 (msb)
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// |
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// | 14 10
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// | | |
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// | | | 9 0 (lsb)
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// | | | | |
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// X XXXXX XXXXXXXXXX
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//
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// s e m
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//
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// S is the sign-bit, e is the exponent and m is the significand.
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//
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// If e is between 1 and 30, h is a normalized number:
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//
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// s e-15
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// h = (-1) * 2 * 1.m
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//
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// If e is 0, and m is not zero, h is a denormalized number:
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//
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// S -14
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// h = (-1) * 2 * 0.m
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//
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// If e and m are both zero, h is zero:
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//
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// h = 0.0
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//
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// If e is 31, h is an "infinity" or "not a number" (NAN),
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// depending on whether m is zero or not.
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//
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// Examples:
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//
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// 0 00000 0000000000 = 0.0
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// 0 01110 0000000000 = 0.5
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// 0 01111 0000000000 = 1.0
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// 0 10000 0000000000 = 2.0
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// 0 10000 1000000000 = 3.0
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// 1 10101 1111000001 = -124.0625
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// 0 11111 0000000000 = +infinity
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// 1 11111 0000000000 = -infinity
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// 0 11111 1000000000 = NAN
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// 1 11111 1111111111 = NAN
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//
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// Conversion:
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//
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// Converting from a float to a half requires some non-trivial bit
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// manipulations. In some cases, this makes conversion relatively
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// slow, but the most common case is accelerated via table lookups.
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//
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// Converting back from a half to a float is easier because we don't
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// have to do any rounding. In addition, there are only 65536
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// different half numbers; we can convert each of those numbers once
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// and store the results in a table. Later, all conversions can be
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// done using only simple table lookups.
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//
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//---------------------------------------------------------------------------
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//--------------------
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// Simple constructors
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//--------------------
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inline
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half::half ()
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{
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// no initialization
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}
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//----------------------------
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// Half-from-float constructor
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//----------------------------
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inline
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half::half (float f)
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{
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uif x;
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x.f = f;
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if (f == 0)
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{
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//
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// Common special case - zero.
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// Preserve the zero's sign bit.
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//
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_h = (x.i >> 16);
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}
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else
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{
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//
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// We extract the combined sign and exponent, e, from our
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// floating-point number, f. Then we convert e to the sign
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// and exponent of the half number via a table lookup.
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//
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// For the most common case, where a normalized half is produced,
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// the table lookup returns a non-zero value; in this case, all
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// we have to do is round f's significand to 10 bits and combine
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// the result with e.
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//
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// For all other cases (overflow, zeroes, denormalized numbers
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// resulting from underflow, infinities and NANs), the table
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// lookup returns zero, and we call a longer, non-inline function
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// to do the float-to-half conversion.
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//
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register int e = (x.i >> 23) & 0x000001ff;
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e = _eLut[e];
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if (e)
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{
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//
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// Simple case - round the significand, m, to 10
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// bits and combine it with the sign and exponent.
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//
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register int m = x.i & 0x007fffff;
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_h = e + ((m + 0x00000fff + ((m >> 13) & 1)) >> 13);
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}
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else
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{
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//
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// Difficult case - call a function.
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//
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_h = convert (x.i);
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}
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}
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}
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//------------------------------------------
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// Half-to-float conversion via table lookup
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//------------------------------------------
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inline
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half::operator float () const
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{
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return _toFloat[_h].f;
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}
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//-------------------------
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// Round to n-bit precision
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//-------------------------
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inline half
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half::round (unsigned int n) const
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{
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//
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// Parameter check.
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//
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if (n >= 10)
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return *this;
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//
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// Disassemble h into the sign, s,
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// and the combined exponent and significand, e.
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//
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unsigned short s = _h & 0x8000;
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unsigned short e = _h & 0x7fff;
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//
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// Round the exponent and significand to the nearest value
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// where ones occur only in the (10-n) most significant bits.
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// Note that the exponent adjusts automatically if rounding
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// up causes the significand to overflow.
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//
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e >>= 9 - n;
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e += e & 1;
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e <<= 9 - n;
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//
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// Check for exponent overflow.
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//
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if (e >= 0x7c00)
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{
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//
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// Overflow occurred -- truncate instead of rounding.
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//
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e = _h;
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e >>= 10 - n;
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e <<= 10 - n;
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}
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//
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// Put the original sign bit back.
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//
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half h;
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h._h = s | e;
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return h;
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}
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//-----------------------
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// Other inline functions
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//-----------------------
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inline half
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half::operator - () const
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{
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half h;
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h._h = _h ^ 0x8000;
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return h;
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}
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inline half &
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half::operator = (half h)
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{
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_h = h._h;
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return *this;
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}
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inline half &
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half::operator = (float f)
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{
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*this = half (f);
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return *this;
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}
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inline half &
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half::operator += (half h)
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{
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*this = half (float (*this) + float (h));
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return *this;
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}
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inline half &
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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
|