half.cpp

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//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
// *       Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// *       Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following disclaimer
// in the documentation and/or other materials provided with the
// distribution.
// *       Neither the name of Industrial Light & Magic nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission. 
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
 
// Primary authors:
//     Florian Kainz <kainz@ilm.com>
//     Rod Bogart <rgb@ilm.com>
 
 
//---------------------------------------------------------------------------
//
//      class half --
//      implementation of non-inline members
//
//---------------------------------------------------------------------------
 
#include <assert.h>
#include "half.h"
 
using namespace std;
 
//-------------------------------------------------------------
// Lookup tables for half-to-float and float-to-half conversion
//-------------------------------------------------------------
 
HALF_EXPORT_CONST half::uif half::_toFloat[1 << 16] =
#include "toFloat.h"
HALF_EXPORT_CONST unsigned short half::_eLut[1 << 9] =
#include "eLut.h"
 
 
//-----------------------------------------------
// Overflow handler for float-to-half conversion;
// generates a hardware floating-point overflow,
// which may be trapped by the operating system.
//-----------------------------------------------
 
float
half::overflow ()
{
    volatile float f = 1e10;
 
    for (int i = 0; i < 10; i++)        
        f *= f;                         // this will overflow before
                                        // the for­loop terminates
    return f;
}
 
 
//-----------------------------------------------------
// Float-to-half conversion -- general case, including
// zeroes, denormalized numbers and exponent overflows.
//-----------------------------------------------------
 
short
half::convert (int i)
{
    //
    // Our floating point number, f, is represented by the bit
    // pattern in integer i.  Disassemble that bit pattern into
    // the sign, s, the exponent, e, and the significand, m.
    // Shift s into the position where it will go in in the
    // resulting half number.
    // Adjust e, accounting for the different exponent bias
    // of float and half (127 versus 15).
    //
 
    register int s =  (i >> 16) & 0x00008000;
    register int e = ((i >> 23) & 0x000000ff) - (127 - 15);
    register int m =   i        & 0x007fffff;
 
    //
    // Now reassemble s, e and m into a half:
    //
 
    if (e <= 0)
    {
        if (e < -10)
        {
            //
            // E is less than -10.  The absolute value of f is
            // less than HALF_MIN (f may be a small normalized
            // float, a denormalized float or a zero).
            //
            // We convert f to a half zero with the same sign as f.
            //
 
            return s;
        }
 
        //
        // E is between -10 and 0.  F is a normalized float
        // whose magnitude is less than HALF_NRM_MIN.
        //
        // We convert f to a denormalized half.
        //
 
        //
        // Add an explicit leading 1 to the significand.
        // 
 
        m = m | 0x00800000;
 
        //
        // Round to m to the nearest (10+e)-bit value (with e between
        // -10 and 0); in case of a tie, round to the nearest even value.
        //
        // Rounding may cause the significand to overflow and make
        // our number normalized.  Because of the way a half's bits
        // are laid out, we don't have to treat this case separately;
        // the code below will handle it correctly.
        // 
 
        int t = 14 - e;
        int a = (1 << (t - 1)) - 1;
        int b = (m >> t) & 1;
 
        m = (m + a + b) >> t;
 
        //
        // Assemble the half from s, e (zero) and m.
        //
 
        return s | m;
    }
    else if (e == 0xff - (127 - 15))
    {
        if (m == 0)
        {
            //
            // F is an infinity; convert f to a half
            // infinity with the same sign as f.
            //
 
            return s | 0x7c00;
        }
        else
        {
            //
            // F is a NAN; we produce a half NAN that preserves
            // the sign bit and the 10 leftmost bits of the
            // significand of f, with one exception: If the 10
            // leftmost bits are all zero, the NAN would turn 
            // into an infinity, so we have to set at least one
            // bit in the significand.
            //
 
            m >>= 13;
            return s | 0x7c00 | m | (m == 0);
        }
    }
    else
    {
        //
        // E is greater than zero.  F is a normalized float.
        // We try to convert f to a normalized half.
        //
 
        //
        // Round to m to the nearest 10-bit value.  In case of
        // a tie, round to the nearest even value.
        //
 
        m = m + 0x00000fff + ((m >> 13) & 1);
 
        if (m & 0x00800000)
        {
            m =  0;             // overflow in significand,
            e += 1;             // adjust exponent
        }
 
        //
        // Handle exponent overflow
        //
 
        if (e > 30)
        {
            overflow ();        // Cause a hardware floating point overflow;
            return s | 0x7c00;  // if this returns, the half becomes an
        }                       // infinity with the same sign as f.
 
        //
        // Assemble the half from s, e and m.
        //
 
        return s | (e << 10) | (m >> 13);
    }
}
 
 
//---------------------
// Stream I/O operators
//---------------------
 
ostream &
operator << (ostream &os, half h)
{
    os << float (h);
    return os;
}
 
 
istream &
operator >> (istream &is, half &h)
{
    float f;
    is >> f;
    h = half (f);
    return is;
}
 
 
//---------------------------------------
// Functions to print the bit-layout of
// floats and halfs, mostly for debugging
//---------------------------------------
 
void
printBits (ostream &os, half h)
{
    unsigned short b = h.bits();
 
    for (int i = 15; i >= 0; i--)
    {
        os << (((b >> i) & 1)? '1': '0');
 
        if (i == 15 || i == 10)
            os << ' ';
    }
}
 
 
void
printBits (ostream &os, float f)
{
    half::uif x;
    x.f = f;
 
    for (int i = 31; i >= 0; i--)
    {
        os << (((x.i >> i) & 1)? '1': '0');
 
        if (i == 31 || i == 23)
            os << ' ';
    }
}
 
 
void
printBits (char c[19], half h)
{
    unsigned short b = h.bits();
 
    for (int i = 15, j = 0; i >= 0; i--, j++)
    {
        c[j] = (((b >> i) & 1)? '1': '0');
 
        if (i == 15 || i == 10)
            c[++j] = ' ';
    }
    
    c[18] = 0;
}
 
 
void
printBits (char c[35], float f)
{
    half::uif x;
    x.f = f;
 
    for (int i = 31, j = 0; i >= 0; i--, j++)
    {
        c[j] = (((x.i >> i) & 1)? '1': '0');
 
        if (i == 31 || i == 23)
            c[++j] = ' ';
    }
 
    c[34] = 0;
}