union ieee754dp ieee754dp_fsp(union ieee754sp x)
{
COMPXSP;
EXPLODEXSP;
ieee754_clearcx();
FLUSHXSP;
switch (xc) {
case IEEE754_CLASS_SNAN:
return ieee754dp_nanxcpt(ieee754dp_nan_fsp(xs, xm));
case IEEE754_CLASS_QNAN:
return ieee754dp_nan_fsp(xs, xm);
case IEEE754_CLASS_INF:
return ieee754dp_inf(xs);
case IEEE754_CLASS_ZERO:
return ieee754dp_zero(xs);
case IEEE754_CLASS_DNORM:
/* normalize */
while ((xm >> SP_FBITS) == 0) {
xm <<= 1;
xe--;
}
break;
case IEEE754_CLASS_NORM:
break;
}
/*
* Can't possibly overflow,underflow, or need rounding
*/
/* drop the hidden bit */
xm &= ~SP_HIDDEN_BIT;
return builddp(xs, xe + DP_EBIAS,
(u64) xm << (DP_FBITS - SP_FBITS));
}
int ieee754sp_cmp(union ieee754sp x, union ieee754sp y, int cmp, int sig)
{
int vx;
int vy;
COMPXSP;
COMPYSP;
EXPLODEXSP;
EXPLODEYSP;
FLUSHXSP;
FLUSHYSP;
ieee754_clearcx(); /* Even clear inexact flag here */
if (ieee754sp_isnan(x) || ieee754sp_isnan(y)) {
if (sig || xc == IEEE754_CLASS_SNAN || yc == IEEE754_CLASS_SNAN)
ieee754_setcx(IEEE754_INVALID_OPERATION);
if (cmp & IEEE754_CUN)
return 1;
if (cmp & (IEEE754_CLT | IEEE754_CGT)) {
if (sig && ieee754_setandtestcx(IEEE754_INVALID_OPERATION))
return 0;
}
return 0;
} else {
vx = x.bits;
vy = y.bits;
if (vx < 0)
vx = -vx ^ SP_SIGN_BIT;
if (vy < 0)
vy = -vy ^ SP_SIGN_BIT;
if (vx < vy)
return (cmp & IEEE754_CLT) != 0;
else if (vx == vy)
return (cmp & IEEE754_CEQ) != 0;
else
return (cmp & IEEE754_CGT) != 0;
}
}
union ieee754dp ieee754dp_div(union ieee754dp x, union ieee754dp y)
{
u64 rm;
int re;
u64 bm;
COMPXDP;
COMPYDP;
EXPLODEXDP;
EXPLODEYDP;
ieee754_clearcx();
FLUSHXDP;
FLUSHYDP;
switch (CLPAIR(xc, yc)) {
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
return ieee754dp_nanxcpt(y);
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
return ieee754dp_nanxcpt(x);
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
return y;
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
return x;
/*
* Infinity handling
*/
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
ieee754_setcx(IEEE754_INVALID_OPERATION);
return ieee754dp_indef();
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
return ieee754dp_zero(xs ^ ys);
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
return ieee754dp_inf(xs ^ ys);
/*
* Zero handling
*/
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
ieee754_setcx(IEEE754_INVALID_OPERATION);
return ieee754dp_indef();
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
ieee754_setcx(IEEE754_ZERO_DIVIDE);
return ieee754dp_inf(xs ^ ys);
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
return ieee754dp_zero(xs == ys ? 0 : 1);
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
DPDNORMX;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
DPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
DPDNORMX;
break;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_NORM):
break;
}
assert(xm & DP_HIDDEN_BIT);
assert(ym & DP_HIDDEN_BIT);
/* provide rounding space */
xm <<= 3;
ym <<= 3;
/* now the dirty work */
rm = 0;
re = xe - ye;
for (bm = DP_MBIT(DP_FBITS + 2); bm; bm >>= 1) {
if (xm >= ym) {
xm -= ym;
rm |= bm;
if (xm == 0)
break;
}
xm <<= 1;
}
rm <<= 1;
if (xm)
rm |= 1; /* have remainder, set sticky */
assert(rm);
/*
* Normalise rm to rounding precision ?
*/
while ((rm >> (DP_FBITS + 3)) == 0) {
rm <<= 1;
re--;
}
return ieee754dp_format(xs == ys ? 0 : 1, re, rm);
}
union ieee754sp ieee754sp_fmin(union ieee754sp x, union ieee754sp y)
{
COMPXSP;
COMPYSP;
EXPLODEXSP;
EXPLODEYSP;
FLUSHXSP;
FLUSHYSP;
ieee754_clearcx();
switch (CLPAIR(xc, yc)) {
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
return ieee754sp_nanxcpt(y);
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
return ieee754sp_nanxcpt(x);
/* numbers are preferred to NaNs */
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
return x;
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
return y;
/*
* Infinity and zero handling
*/
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
return xs ? x : y;
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
return ys ? y : x;
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
if (xs == ys)
return x;
return ieee754sp_zero(1);
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
SPDNORMX;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
SPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
SPDNORMX;
}
/* Finally get to do some computation */
assert(xm & SP_HIDDEN_BIT);
assert(ym & SP_HIDDEN_BIT);
/* Compare signs */
if (xs > ys)
return x;
else if (xs < ys)
return y;
/* Compare exponent */
if (xe > ye)
return y;
else if (xe < ye)
return x;
/* Compare mantissa */
if (xm <= ym)
return x;
return y;
}
union ieee754dp ieee754dp_fmax(union ieee754dp x, union ieee754dp y)
{
COMPXDP;
COMPYDP;
EXPLODEXDP;
EXPLODEYDP;
FLUSHXDP;
FLUSHYDP;
ieee754_clearcx();
switch (CLPAIR(xc, yc)) {
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
return ieee754dp_nanxcpt(y);
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
return ieee754dp_nanxcpt(x);
/*
* Quiet NaN handling
*/
/*
* The case of both inputs quiet NaNs
*/
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
return x;
/*
* The cases of exactly one input quiet NaN (numbers
* are here preferred as returned values to NaNs)
*/
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
return x;
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
return y;
/*
* Infinity and zero handling
*/
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
return xs ? y : x;
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
return ys ? x : y;
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
return ieee754dp_zero(xs & ys);
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
DPDNORMX;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
DPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
DPDNORMX;
}
/* Finally get to do some computation */
assert(xm & DP_HIDDEN_BIT);
assert(ym & DP_HIDDEN_BIT);
/* Compare signs */
if (xs > ys)
return y;
else if (xs < ys)
return x;
/* Signs of inputs are equal, let's compare exponents */
if (xs == 0) {
/* Inputs are both positive */
if (xe > ye)
return x;
else if (xe < ye)
return y;
} else {
/* Inputs are both negative */
if (xe > ye)
return y;
else if (xe < ye)
return x;
}
/* Signs and exponents of inputs are equal, let's compare mantissas */
if (xs == 0) {
/* Inputs are both positive, with equal signs and exponents */
if (xm <= ym)
return y;
return x;
}
/* Inputs are both negative, with equal signs and exponents */
if (xm <= ym)
return x;
return y;
}
union ieee754sp ieee754sp_fmina(union ieee754sp x, union ieee754sp y)
{
COMPXSP;
COMPYSP;
EXPLODEXSP;
EXPLODEYSP;
FLUSHXSP;
FLUSHYSP;
ieee754_clearcx();
switch (CLPAIR(xc, yc)) {
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_SNAN):
return ieee754sp_nanxcpt(y);
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_INF):
return ieee754sp_nanxcpt(x);
/*
* Quiet NaN handling
*/
/*
* The case of both inputs quiet NaNs
*/
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_QNAN):
return x;
/*
* The cases of exactly one input quiet NaN (numbers
* are here preferred as returned values to NaNs)
*/
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_QNAN):
return x;
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_INF):
return y;
/*
* Infinity and zero handling
*/
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_INF):
return ieee754sp_inf(xs | ys);
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_INF, IEEE754_CLASS_DNORM):
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
return y;
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_INF):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_NORM):
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_DNORM):
return x;
case CLPAIR(IEEE754_CLASS_ZERO, IEEE754_CLASS_ZERO):
return ieee754sp_zero(xs | ys);
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_DNORM):
SPDNORMX;
/* fall through */
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_DNORM):
SPDNORMY;
break;
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_NORM):
SPDNORMX;
}
/* Finally get to do some computation */
assert(xm & SP_HIDDEN_BIT);
assert(ym & SP_HIDDEN_BIT);
/* Compare exponent */
if (xe > ye)
return y;
else if (xe < ye)
return x;
/* Compare mantissa */
if (xm < ym)
return x;
else if (xm > ym)
return y;
else if (xs == 1)
return x;
return y;
}
