__float128
nextafterq (__float128 x, __float128 y)
{
int64_t hx,hy,ix,iy;
uint64_t lx,ly;
GET_FLT128_WORDS64(hx,lx,x);
GET_FLT128_WORDS64(hy,ly,y);
ix = hx&0x7fffffffffffffffLL; /* |x| */
iy = hy&0x7fffffffffffffffLL; /* |y| */
if(((ix>=0x7fff000000000000LL)&&((ix-0x7fff000000000000LL)|lx)!=0) || /* x is nan */
((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) /* y is nan */
return x+y;
if(x==y) return y; /* x=y, return y */
if((ix|lx)==0) { /* x == 0 */
SET_FLT128_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */
/* here we should raise an underflow flag */
return x;
}
if(hx>=0) { /* x > 0 */
if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */
if(lx==0) hx--;
lx--;
} else { /* x < y, x += ulp */
lx++;
if(lx==0) hx++;
}
} else { /* x < 0 */
if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */
if(lx==0) hx--;
lx--;
} else { /* x > y, x += ulp */
lx++;
if(lx==0) hx++;
}
}
hy = hx&0x7fff000000000000LL;
if(hy==0x7fff000000000000LL) {
__float128 u = x + x; /* overflow */
math_force_eval (u);
errno = ERANGE;
}
if(hy==0) {
__float128 u = x*x; /* underflow */
math_force_eval (u); /* raise underflow flag */
errno = ERANGE;
}
SET_FLT128_WORDS64(x,hx,lx);
return x;
}
int
ilogbq (__float128 x)
{
int64_t hx,lx;
int ix;
GET_FLT128_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
if(hx <= 0x0001000000000000LL) {
if((hx|lx)==0)
{
errno = EDOM;
#ifdef USE_FENV_H
feraiseexcept (FE_INVALID);
#endif
return FP_ILOGB0; /* ilogbl(0) = FP_ILOGB0 */
}
else /* subnormal x */
if(hx==0) {
for (ix = -16431; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -16382, hx<<=15; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7fff000000000000LL) return (hx>>48)-0x3fff;
else if (FP_ILOGBNAN != INT_MAX) {
int
isnanq (const __float128 x)
{
int64_t hx,lx;
GET_FLT128_WORDS64(hx,lx,x);
hx &= 0x7fffffffffffffffLL;
hx |= (uint64_t)(lx|(-lx))>>63;
hx = 0x7fff000000000000LL - hx;
return (int)((uint64_t)hx>>63);
}
__float128
frexpq (__float128 x, int *eptr)
{
uint64_t hx, lx, ix;
GET_FLT128_WORDS64(hx,lx,x);
ix = 0x7fffffffffffffffULL&hx;
*eptr = 0;
if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x; /* 0,inf,nan */
if (ix<0x0001000000000000ULL) { /* subnormal */
x *= two114;
GET_FLT128_MSW64(hx,x);
ix = hx&0x7fffffffffffffffULL;
*eptr = -114;
}
*eptr += (ix>>48)-16382;
hx = (hx&0x8000ffffffffffffULL) | 0x3ffe000000000000ULL;
SET_FLT128_MSW64(x,hx);
return x;
}
__float128
log2q (__float128 x)
{
__float128 z;
__float128 y;
int e;
int64_t hx, lx;
/* Test for domain */
GET_FLT128_WORDS64 (hx, lx, x);
if (((hx & 0x7fffffffffffffffLL) | lx) == 0)
return (-1.0Q / fabsq (x)); /* log2l(+-0)=-inf */
if (hx < 0)
return (x - x) / (x - x);
if (hx >= 0x7fff000000000000LL)
return (x + x);
if (x == 1.0Q)
return 0.0Q;
/* separate mantissa from exponent */
/* Note, frexp is used so that denormal numbers
* will be handled properly.
*/
x = frexpq (x, &e);
/* logarithm using log(x) = z + z**3 P(z)/Q(z),
* where z = 2(x-1)/x+1)
*/
if ((e > 2) || (e < -2))
{
if (x < SQRTH)
{ /* 2( 2x-1 )/( 2x+1 ) */
e -= 1;
z = x - 0.5Q;
y = 0.5Q * z + 0.5Q;
}
else
{ /* 2 (x-1)/(x+1) */
z = x - 0.5Q;
z -= 0.5Q;
y = 0.5Q * x + 0.5Q;
}
x = z / y;
z = x * x;
y = x * (z * neval (z, R, 5) / deval (z, S, 5));
goto done;
}
/* logarithm using log(1+x) = x - .5x**2 + x**3 P(x)/Q(x) */
if (x < SQRTH)
{
e -= 1;
x = 2.0 * x - 1.0Q; /* 2x - 1 */
}
else
{
x = x - 1.0Q;
}
z = x * x;
y = x * (z * neval (x, P, 12) / deval (x, Q, 11));
y = y - 0.5 * z;
done:
/* Multiply log of fraction by log2(e)
* and base 2 exponent by 1
*/
z = y * LOG2EA;
z += x * LOG2EA;
z += y;
z += x;
z += e;
return (z);
}
__float128
remquoq (__float128 x, __float128 y, int *quo)
{
int64_t hx,hy;
uint64_t sx,lx,ly,qs;
int cquo;
GET_FLT128_WORDS64 (hx, lx, x);
GET_FLT128_WORDS64 (hy, ly, y);
sx = hx & 0x8000000000000000ULL;
qs = sx ^ (hy & 0x8000000000000000ULL);
hy &= 0x7fffffffffffffffLL;
hx &= 0x7fffffffffffffffLL;
/* Purge off exception values. */
if ((hy | ly) == 0)
return (x * y) / (x * y); /* y = 0 */
if ((hx >= 0x7fff000000000000LL) /* x not finite */
|| ((hy >= 0x7fff000000000000LL) /* y is NaN */
&& (((hy - 0x7fff000000000000LL) | ly) != 0)))
return (x * y) / (x * y);
if (hy <= 0x7ffbffffffffffffLL)
x = fmodq (x, 8 * y); /* now x < 8y */
if (((hx - hy) | (lx - ly)) == 0)
{
*quo = qs ? -1 : 1;
return zero * x;
}
x = fabsq (x);
y = fabsq (y);
cquo = 0;
if (hy <= 0x7ffcffffffffffffLL && x >= 4 * y)
{
x -= 4 * y;
cquo += 4;
}
if (hy <= 0x7ffdffffffffffffLL && x >= 2 * y)
{
x -= 2 * y;
cquo += 2;
}
if (hy < 0x0002000000000000LL)
{
if (x + x > y)
{
x -= y;
++cquo;
if (x + x >= y)
{
x -= y;
++cquo;
}
}
}
else
{
__float128 y_half = 0.5Q * y;
if (x > y_half)
{
x -= y;
++cquo;
if (x >= y_half)
{
x -= y;
++cquo;
}
}
}
*quo = qs ? -cquo : cquo;
/* Ensure correct sign of zero result in round-downward mode. */
if (x == 0.0Q)
x = 0.0Q;
if (sx)
x = -x;
return x;
}