// SPDX-License-Identifier: GPL-2.0-only
/*
* IEEE754 floating point arithmetic
* double 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>
*/
#include "ieee754dp.h"
/* 128 bits shift right logical with rounding. */
static void srl128(u64 *hptr, u64 *lptr, int count)
{
u64 low;
if (count >= 128) {
*lptr = *hptr != 0 || *lptr != 0;
*hptr = 0;
} else if (count >= 64) {
if (count == 64) {
*lptr = *hptr | (*lptr != 0);
} else {
low = *lptr;
*lptr = *hptr >> (count - 64);
*lptr |= (*hptr << (128 - count)) != 0 || low != 0;
}
*hptr = 0;
} else {
low = *lptr;
*lptr = low >> count | *hptr << (64 - count);
*lptr |= (low << (64 - count)) != 0;
*hptr = *hptr >> count;
}
}
static union ieee754dp _dp_maddf(union ieee754dp z, union ieee754dp x,
union ieee754dp y, enum maddf_flags flags)
{
int re;
int rs;
unsigned int lxm;
unsigned int hxm;
unsigned int lym;
unsigned int hym;
u64 lrm;
u64 hrm;
u64 lzm;
u64 hzm;
u64 t;
u64 at;
int s;
COMPXDP;
COMPYDP;
COMPZDP;
EXPLODEXDP;
EXPLODEYDP;
EXPLODEZDP;
FLUSHXDP;
FLUSHYDP;
FLUSHZDP;
ieee754_clearcx();
rs = xs ^ ys;
if (flags & MADDF_NEGATE_PRODUCT)
rs ^= 1;
if (flags & MADDF_NEGATE_ADDITION)
zs ^= 1;
/*
* 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 ieee754dp_nanxcpt(z);
if (xc == IEEE754_CLASS_SNAN)
return ieee754dp_nanxcpt(x);
if (yc == IEEE754_CLASS_SNAN)
return ieee754dp_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)
DPDNORMZ;
/* 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 ieee754dp_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) && (zs != rs)) {
/*
* Cases of addition of infinities with opposite signs
* or subtraction of infinities with same signs.
*/
ieee754_setcx(IEEE754_INVALID_OPERATION);
return ieee754dp_indef();
}
/*
* z is here either not an infinity, or an infinity having the
* same sign as product (x*y). The result must be an infinity,
* and its sign is determined only by the sign of product (x*y).
*/
return ieee754dp_inf(rs);
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 ieee754dp_inf(zs);
if (zc == IEEE754_CLASS_ZERO) {
/* Handle cases +0 + (-0) and similar ones. */
if (zs == rs)
/*
* 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 ieee754dp_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):
DPDNORMX;
fallthrough;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
if (zc == IEEE754_CLASS_INF)
return ieee754dp_inf(zs);
DPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
if (zc == IEEE754_CLASS_INF)
return ieee754dp_inf(zs);
DPDNORMX;
break;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
if (zc == IEEE754_CLASS_INF)
return ieee754dp_inf(zs);
/* continue 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.
*/
assert(xm & DP_HIDDEN_BIT);
assert(ym & DP_HIDDEN_BIT);
re = xe + ye;
/* shunt to top of word */
xm <<= 64 - (DP_FBITS + 1);
ym <<= 64 - (DP_FBITS + 1);
/*
* Multiply 64 bits xm and ym to give 128 bits result in hrm:lrm.
*/
lxm = xm;
hxm = xm >> 32;
lym = ym;
hym = ym >> 32;
lrm = DPXMULT(lxm, lym);
hrm = DPXMULT(hxm, hym);
t = DPXMULT(lxm, hym);
at = lrm + (t << 32);
hrm += at < lrm;
lrm = at;
hrm = hrm + (t >> 32);
t = DPXMULT(hxm, lym);
at = lrm + (t << 32);
hrm += at < lrm;
lrm = at;
hrm = hrm + (t >> 32);
/* Put explicit bit at bit 126 if necessary */
if ((int64_t)hrm < 0) {
lrm = (hrm << 63) | (lrm >> 1);
hrm = hrm >> 1;
re++;
}
assert(hrm & (1 << 62));
if (zc == IEEE754_CLASS_ZERO) {
/*
* Move explicit bit from bit 126 to bit 55 since the
* ieee754dp_format code expects the mantissa to be
* 56 bits wide (53 + 3 rounding bits).
*/
srl128(&hrm, &lrm, (126 - 55));
return ieee754dp_format(rs, re, lrm);
}
/* Move explicit bit from bit 52 to bit 126 */
lzm = 0;
hzm = zm << 10;
assert(hzm & (1 << 62));
/* Make the exponents the same */
if (ze > re) {
/*
* Have to shift y fraction right to align.
*/
s = ze - re;
srl128(&hrm, &lrm, s);
re += s;
} else if (re > ze) {
/*
* Have to shift x fraction right to align.
*/
s = re - ze;
srl128(&hzm, &lzm, s);
ze += s;
}
assert(ze == re);
assert(ze <= DP_EMAX);
/* Do the addition */
if (zs == rs) {
/*
* Generate 128 bit result by adding two 127 bit numbers
* leaving result in hzm:lzm, zs and ze.
*/
hzm = hzm + hrm + (lzm > (lzm + lrm));
lzm = lzm + lrm;
if ((int64_t)hzm < 0) { /* carry out */
srl128(&hzm, &lzm, 1);
ze++;
}
} else {
if (hzm > hrm || (hzm == hrm && lzm >= lrm)) {
hzm = hzm - hrm - (lzm < lrm);
lzm = lzm - lrm;
} else {
hzm = hrm - hzm - (lrm < lzm);
lzm = lrm - lzm;
zs = rs;
}
if (lzm == 0 && hzm == 0)
return ieee754dp_zero(ieee754_csr.rm == FPU_CSR_RD);
/*
* Put explicit bit at bit 126 if necessary.
*/
if (hzm == 0) {
/* left shift by 63 or 64 bits */
if ((int64_t)lzm < 0) {
/* MSB of lzm is the explicit bit */
hzm = lzm >> 1;
lzm = lzm << 63;
ze -= 63;
} else {
hzm = lzm;
lzm = 0;
ze -= 64;
}
}
t = 0;
while ((hzm >> (62 - t)) == 0)
t++;
assert(t <= 62);
if (t) {
hzm = hzm << t | lzm >> (64 - t);
lzm = lzm << t;
ze -= t;
}
}
/*
* Move explicit bit from bit 126 to bit 55 since the
* ieee754dp_format code expects the mantissa to be
* 56 bits wide (53 + 3 rounding bits).
*/
srl128(&hzm, &lzm, (126 - 55));
return ieee754dp_format(zs, ze, lzm);
}
union ieee754dp ieee754dp_maddf(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, 0);
}
union ieee754dp ieee754dp_msubf(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, MADDF_NEGATE_PRODUCT);
}
union ieee754dp ieee754dp_madd(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, 0);
}
union ieee754dp ieee754dp_msub(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, MADDF_NEGATE_ADDITION);
}
union ieee754dp ieee754dp_nmadd(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, MADDF_NEGATE_PRODUCT|MADDF_NEGATE_ADDITION);
}
union ieee754dp ieee754dp_nmsub(union ieee754dp z, union ieee754dp x,
union ieee754dp y)
{
return _dp_maddf(z, x, y, MADDF_NEGATE_PRODUCT);
}