union ieee754dp ieee754dp_abs(union ieee754dp x)
{
unsigned int oldrm;
union ieee754dp y;
oldrm = ieee754_csr.rm;
ieee754_csr.rm = FPU_CSR_RD;
if (DPSIGN(x))
y = ieee754dp_sub(ieee754dp_zero(0), x);
else
y = ieee754dp_add(ieee754dp_zero(0), x);
ieee754_csr.rm = oldrm;
return y;
}
/* modf function is always exact for a finite number
*/
ieee754dp ieee754dp_modf(ieee754dp x, ieee754dp *ip)
{
COMPXDP;
CLEARCX;
EXPLODEXDP;
switch (xc) {
case IEEE754_CLASS_SNAN:
case IEEE754_CLASS_QNAN:
case IEEE754_CLASS_INF:
case IEEE754_CLASS_ZERO:
*ip = x;
return x;
case IEEE754_CLASS_DNORM:
/* far to small */
*ip = ieee754dp_zero(xs);
return x;
case IEEE754_CLASS_NORM:
break;
}
if (xe < 0) {
*ip = ieee754dp_zero(xs);
return x;
}
if (xe >= DP_MBITS) {
*ip = x;
return ieee754dp_zero(xs);
}
/* generate ipart mantissa by clearing bottom bits
*/
*ip = builddp(xs, xe + DP_EBIAS,
((xm >> (DP_MBITS - xe)) << (DP_MBITS - xe)) &
~DP_HIDDEN_BIT);
/* generate fpart mantissa by clearing top bits
* and normalizing (must be able to normalize)
*/
xm = (xm << (64 - (DP_MBITS - xe))) >> (64 - (DP_MBITS - xe));
if (xm == 0)
return ieee754dp_zero(xs);
while ((xm >> DP_MBITS) == 0) {
xm <<= 1;
xe--;
}
return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
}
ieee754dp ieee754dp_ceil(ieee754dp x)
{
ieee754dp i;
if (ieee754dp_gt(ieee754dp_modf(x, &i), ieee754dp_zero(0)))
return ieee754dp_add(i, ieee754dp_one(0));
else
return i;
}
ieee754dp ieee754dp_floor(ieee754dp x)
{
ieee754dp i;
if (ieee754dp_lt(ieee754dp_modf(x, &i), ieee754dp_zero(0)))
return ieee754dp_sub(i, ieee754dp_one(0));
else
return i;
}
union ieee754dp ieee754dp_neg(union ieee754dp x)
{
unsigned int oldrm;
union ieee754dp y;
oldrm = ieee754_csr.rm;
ieee754_csr.rm = FPU_CSR_RD;
y = ieee754dp_sub(ieee754dp_zero(0), x);
ieee754_csr.rm = oldrm;
return y;
}
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));
}
ieee754dp ieee754dp_fsp(ieee754sp x)
{
COMPXSP;
EXPLODEXSP;
CLEARCX;
FLUSHXSP;
switch (xc) {
case IEEE754_CLASS_SNAN:
SETCX(IEEE754_INVALID_OPERATION);
return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp");
case IEEE754_CLASS_QNAN:
return ieee754dp_nanxcpt(builddp(xs,
DP_EMAX + 1 + DP_EBIAS,
((u64) xm
<< (DP_MBITS -
SP_MBITS))), "fsp",
x);
case IEEE754_CLASS_INF:
return ieee754dp_inf(xs);
case IEEE754_CLASS_ZERO:
return ieee754dp_zero(xs);
case IEEE754_CLASS_DNORM:
/* normalize */
while ((xm >> SP_MBITS) == 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_MBITS - SP_MBITS));
}
ieee754dp ieee754dp_fsp(ieee754sp x)
{
COMPXSP;
EXPLODEXSP;
CLEARCX;
FLUSHXSP;
switch (xc) {
case IEEE754_CLASS_SNAN:
SETCX(IEEE754_INVALID_OPERATION);
return ieee754dp_nanxcpt(ieee754dp_indef(), "fsp");
case IEEE754_CLASS_QNAN:
return ieee754dp_nanxcpt(builddp(xs,
DP_EMAX + 1 + DP_EBIAS,
((u64) xm
<< (DP_MBITS -
SP_MBITS))), "fsp",
x);
case IEEE754_CLASS_INF:
return ieee754dp_inf(xs);
case IEEE754_CLASS_ZERO:
return ieee754dp_zero(xs);
case IEEE754_CLASS_DNORM:
while ((xm >> SP_MBITS) == 0) {
xm <<= 1;
xe--;
}
break;
case IEEE754_CLASS_NORM:
break;
}
xm &= ~SP_HIDDEN_BIT;
return builddp(xs, xe + DP_EBIAS,
(u64) xm << (DP_MBITS - SP_MBITS));
}
ieee754dp ieee754dp_fint(int x)
{
u64 xm;
int xe;
int xs;
CLEARCX;
if (x == 0)
return ieee754dp_zero(0);
if (x == 1 || x == -1)
return ieee754dp_one(x < 0);
if (x == 10 || x == -10)
return ieee754dp_ten(x < 0);
xs = (x < 0);
if (xs) {
if (x == (1 << 31))
xm = ((unsigned) 1 << 31); /* max neg can't be safely negated */
else
xm = -x;
} else {
xm = x;
}
#if 1
/* normalize - result can never be inexact or overflow */
xe = DP_MBITS;
while ((xm >> DP_MBITS) == 0) {
xm <<= 1;
xe--;
}
return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
#else
/* normalize */
xe = DP_MBITS + 3;
while ((xm >> (DP_MBITS + 3)) == 0) {
xm <<= 1;
xe--;
}
DPNORMRET1(xs, xe, xm, "fint", x);
#endif
}
ieee754dp ieee754dp_fint(int x)
{
u64 xm;
int xe;
int xs;
CLEARCX;
if (x == 0)
return ieee754dp_zero(0);
if (x == 1 || x == -1)
return ieee754dp_one(x < 0);
if (x == 10 || x == -10)
return ieee754dp_ten(x < 0);
xs = (x < 0);
if (xs) {
if (x == (1 << 31))
xm = ((unsigned) 1 << 31);
else
xm = -x;
} else {
xm = x;
}
#if 1
xe = DP_MBITS;
while ((xm >> DP_MBITS) == 0) {
xm <<= 1;
xe--;
}
return builddp(xs, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
#else
xe = DP_MBITS + 3;
while ((xm >> (DP_MBITS + 3)) == 0) {
xm <<= 1;
xe--;
}
DPNORMRET1(xs, xe, xm, "fint", x);
#endif
}
ieee754dp ieee754dp_div(ieee754dp x, ieee754dp y)
{
COMPXDP;
COMPYDP;
EXPLODEXDP;
EXPLODEYDP;
CLEARCX;
FLUSHXDP;
FLUSHYDP;
switch (CLPAIR(xc, yc)) {
case CLPAIR(IEEE754_CLASS_SNAN, IEEE754_CLASS_QNAN):
case CLPAIR(IEEE754_CLASS_QNAN, IEEE754_CLASS_SNAN):
case CLPAIR(IEEE754_CLASS_SNAN, 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):
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):
SETCX(IEEE754_INVALID_OPERATION);
return ieee754dp_nanxcpt(ieee754dp_indef(), "div", x, y);
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):
SETCX(IEEE754_INVALID_OPERATION);
return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y);
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):
SETCX(IEEE754_INVALID_OPERATION);
return ieee754dp_xcpt(ieee754dp_indef(), "div", x, y);
case CLPAIR(IEEE754_CLASS_NORM, IEEE754_CLASS_ZERO):
case CLPAIR(IEEE754_CLASS_DNORM, IEEE754_CLASS_ZERO):
SETCX(IEEE754_ZERO_DIVIDE);
return ieee754dp_xcpt(ieee754dp_inf(xs ^ ys), "div", x, y);
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 */
u64 rm = 0;
int re = xe - ye;
u64 bm;
for (bm = DP_MBIT(DP_MBITS + 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_MBITS + 3)) == 0) {
rm <<= 1;
re--;
}
DPNORMRET2(xs == ys ? 0 : 1, re, rm, "div", x, 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 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);
/* 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 ? 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):
if (xs == ys)
return x;
return ieee754dp_zero(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;
}
/* 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;
/* Compare exponent */
if (xe > ye)
return x;
else if (xe < ye)
return y;
/* Compare mantissa */
if (xm <= ym)
return y;
return x;
}