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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.
//-----------------------------------------------
HALF_EXPORT 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.
//-----------------------------------------------------
HALF_EXPORT 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
//---------------------
HALF_EXPORT ostream &
operator << (ostream &os, half h)
{
os << float (h);
return os;
}
HALF_EXPORT 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
//---------------------------------------
HALF_EXPORT 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 << ' ';
}
}
HALF_EXPORT 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 << ' ';
}
}
HALF_EXPORT 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;
}
HALF_EXPORT 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;
}