half.cpp

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
//
// All rights reserved.
//
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// modification, are permitted provided that the following conditions are
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// *       Redistributions in binary form must reproduce the above
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// in the documentation and/or other materials provided with the
// distribution.
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// 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
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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///////////////////////////////////////////////////////////////////////////

// Primary authors:
//     Florian Kainz <[email protected]>
//     Rod Bogart <[email protected]>


//---------------------------------------------------------------------------
//
//	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 for�loop 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;
}