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/*
* IEEE754 floating point arithmetic
* single precision: MADDF.f (Fused Multiply Add)
* MADDF.fmt: FPR[fd] = FPR[fd] + (FPR[fs] x FPR[ft])
*
* MIPS floating point support
* Copyright (C) 2015 Imagination Technologies, Ltd.
* Author: Markos Chandras <markos.chandras@imgtec.com>
*
* This program is free software; you can distribute it and/or modify it
* under the terms of the GNU General Public License as published by the
* Free Software Foundation; version 2 of the License.
*/
#include "ieee754sp.h"
enum maddf_flags {
maddf_negate_product = 1 << 0,
};
static union ieee754sp _sp_maddf(union ieee754sp z, union ieee754sp x,
union ieee754sp y, enum maddf_flags flags)
{
int re;
int rs;
unsigned rm;
unsigned short lxm;
unsigned short hxm;
unsigned short lym;
unsigned short hym;
unsigned lrm;
unsigned hrm;
unsigned t;
unsigned at;
int s;
COMPXSP;
COMPYSP;
COMPZSP;
EXPLODEXSP;
EXPLODEYSP;
EXPLODEZSP;
FLUSHXSP;
FLUSHYSP;
FLUSHZSP;
ieee754_clearcx();
/*
* Handle the cases when at least one of x, y or z is a NaN.
* Order of precedence is sNaN, qNaN and z, x, y.
*/
if (zc == IEEE754_CLASS_SNAN)
return ieee754sp_nanxcpt(z);
if (xc == IEEE754_CLASS_SNAN)
return ieee754sp_nanxcpt(x);
if (yc == IEEE754_CLASS_SNAN)
return ieee754sp_nanxcpt(y);
if (zc == IEEE754_CLASS_QNAN)
return z;
if (xc == IEEE754_CLASS_QNAN)
return x;
if (yc == IEEE754_CLASS_QNAN)
return y;
if (zc == IEEE754_CLASS_DNORM)
SPDNORMZ;
/* ZERO z cases are handled separately below */
switch (CLPAIR(xc, yc)) {
/*
* Infinity handling
*/
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
ieee754_setcx(IEEE754_INVALID_OPERATION);
return ieee754sp_indef();
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
if ((zc == IEEE754_CLASS_INF) &&
((!(flags & maddf_negate_product) && (zs != (xs ^ ys))) ||
((flags & maddf_negate_product) && (zs == (xs ^ ys))))) {
/*
* Cases of addition of infinities with opposite signs
* or subtraction of infinities with same signs.
*/
ieee754_setcx(IEEE754_INVALID_OPERATION);
return ieee754sp_indef();
}
/*
* z is here either not an infinity, or an infinity having the
* same sign as product (x*y) (in case of MADDF.D instruction)
* or product -(x*y) (in MSUBF.D case). The result must be an
* infinity, and its sign is determined only by the value of
* (flags & maddf_negate_product) and the signs of x and y.
*/
if (flags & maddf_negate_product)
return ieee754sp_inf(1 ^ (xs ^ ys));
else
return ieee754sp_inf(xs ^ ys);
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
if (zc == IEEE754_CLASS_INF)
return ieee754sp_inf(zs);
if (zc == IEEE754_CLASS_ZERO) {
/* Handle cases +0 + (-0) and similar ones. */
if ((!(flags & maddf_negate_product)
&& (zs == (xs ^ ys))) ||
((flags & maddf_negate_product)
&& (zs != (xs ^ ys))))
/*
* Cases of addition of zeros of equal signs
* or subtraction of zeroes of opposite signs.
* The sign of the resulting zero is in any
* such case determined only by the sign of z.
*/
return z;
return ieee754sp_zero(ieee754_csr.rm == FPU_CSR_RD);
}
/* x*y is here 0, and z is not 0, so just return z */
return z;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
SPDNORMX;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
if (zc == IEEE754_CLASS_INF)
return ieee754sp_inf(zs);
SPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
if (zc == IEEE754_CLASS_INF)
return ieee754sp_inf(zs);
SPDNORMX;
break;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
if (zc == IEEE754_CLASS_INF)
return ieee754sp_inf(zs);
/* fall through to real computations */
}
/* Finally get to do some computation */
/*
* Do the multiplication bit first
*
* rm = xm * ym, re = xe + ye basically
*
* At this point xm and ym should have been normalized.
*/
/* rm = xm * ym, re = xe+ye basically */
assert(xm & SP_HIDDEN_BIT);
assert(ym & SP_HIDDEN_BIT);
re = xe + ye;
rs = xs ^ ys;
if (flags & maddf_negate_product)
rs ^= 1;
/* shunt to top of word */
xm <<= 32 - (SP_FBITS + 1);
ym <<= 32 - (SP_FBITS + 1);
/*
* Multiply 32 bits xm, ym to give high 32 bits rm with stickness.
*/
lxm = xm & 0xffff;
hxm = xm >> 16;
lym = ym & 0xffff;
hym = ym >> 16;
lrm = lxm * lym; /* 16 * 16 => 32 */
hrm = hxm * hym; /* 16 * 16 => 32 */
t = lxm * hym; /* 16 * 16 => 32 */
at = lrm + (t << 16);
hrm += at < lrm;
lrm = at;
hrm = hrm + (t >> 16);
t = hxm * lym; /* 16 * 16 => 32 */
at = lrm + (t << 16);
hrm += at < lrm;
lrm = at;
hrm = hrm + (t >> 16);
rm = hrm | (lrm != 0);
/*
* Sticky shift down to normal rounding precision.
*/
if ((int) rm < 0) {
rm = (rm >> (32 - (SP_FBITS + 1 + 3))) |
((rm << (SP_FBITS + 1 + 3)) != 0);
re++;
} else {
rm = (rm >> (32 - (SP_FBITS + 1 + 3 + 1))) |
((rm << (SP_FBITS + 1 + 3 + 1)) != 0);
}
assert(rm & (SP_HIDDEN_BIT << 3));
if (zc == IEEE754_CLASS_ZERO)
return ieee754sp_format(rs, re, rm);
/* And now the addition */
assert(zm & SP_HIDDEN_BIT);
/*
* Provide guard,round and stick bit space.
*/
zm <<= 3;
if (ze > re) {
/*
* Have to shift r fraction right to align.
*/
s = ze - re;
rm = XSPSRS(rm, s);
re += s;
} else if (re > ze) {
/*
* Have to shift z fraction right to align.
*/
s = re - ze;
zm = XSPSRS(zm, s);
ze += s;
}
assert(ze == re);
assert(ze <= SP_EMAX);
if (zs == rs) {
/*
* Generate 28 bit result of adding two 27 bit numbers
* leaving result in zm, zs and ze.
*/
zm = zm + rm;
if (zm >> (SP_FBITS + 1 + 3)) { /* carry out */
zm = XSPSRS1(zm);
ze++;
}
} else {
if (zm >= rm) {
zm = zm - rm;
} else {
zm = rm - zm;
zs = rs;
}
if (zm == 0)
return ieee754sp_zero(ieee754_csr.rm == FPU_CSR_RD);
/*
* Normalize in extended single precision
*/
while ((zm >> (SP_MBITS + 3)) == 0) {
zm <<= 1;
ze--;
}
}
return ieee754sp_format(zs, ze, zm);
}
union ieee754sp ieee754sp_maddf(union ieee754sp z, union ieee754sp x,
union ieee754sp y)
{
return _sp_maddf(z, x, y, 0);
}
union ieee754sp ieee754sp_msubf(union ieee754sp z, union ieee754sp x,
union ieee754sp y)
{
return _sp_maddf(z, x, y, maddf_negate_product);
}
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