long
__lrintl (long double x)
{
double xh, xl;
long res, hi, lo;
int save_round;
ldbl_unpack (x, &xh, &xl);
/* Limit the range of values handled by the conversion to long.
We do this because we aren't sure whether that conversion properly
raises FE_INVALID. */
if (
#if __LONG_MAX__ == 2147483647
__builtin_expect
((__builtin_fabs (xh) <= (double) __LONG_MAX__ + 2), 1)
#else
__builtin_expect
((__builtin_fabs (xh) <= -(double) (-__LONG_MAX__ - 1)), 1)
#endif
#if !defined (FE_INVALID)
|| 1
#endif
)
{
save_round = __fegetround ();
#if __LONG_MAX__ == 2147483647
long long llhi = (long long) xh;
if (llhi != (long) llhi)
hi = llhi < 0 ? -__LONG_MAX__ - 1 : __LONG_MAX__;
else
hi = llhi;
xh -= hi;
#else
if (__glibc_unlikely ((xh == -(double) (-__LONG_MAX__ - 1))))
{
/* When XH is 9223372036854775808.0, converting to long long will
overflow, resulting in an invalid operation. However, XL might
be negative and of sufficient magnitude that the overall long
double is in fact in range. Avoid raising an exception. In any
case we need to convert this value specially, because
the converted value is not exactly represented as a double
thus subtracting HI from XH suffers rounding error. */
hi = __LONG_MAX__;
xh = 1.0;
}
else
{
hi = (long) xh;
xh -= hi;
}
#endif
ldbl_canonicalize (&xh, &xl);
lo = (long) xh;
/* Peg at max/min values, assuming that the above conversions do so.
Strictly speaking, we can return anything for values that overflow,
but this is more useful. */
res = hi + lo;
/* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */
if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0)))
goto overflow;
xh -= lo;
ldbl_canonicalize (&xh, &xl);
hi = res;
switch (save_round)
{
case FE_TONEAREST:
if (fabs (xh) < 0.5
|| (fabs (xh) == 0.5
&& ((xh > 0.0 && xl < 0.0)
|| (xh < 0.0 && xl > 0.0)
|| (xl == 0.0 && (res & 1) == 0))))
return res;
if (xh < 0.0)
res -= 1;
else
res += 1;
break;
case FE_TOWARDZERO:
if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0)))
res -= 1;
else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0)))
res += 1;
return res;
break;
case FE_UPWARD:
if (xh > 0.0 || (xh == 0.0 && xl > 0.0))
res += 1;
break;
case FE_DOWNWARD:
if (xh < 0.0 || (xh == 0.0 && xl < 0.0))
res -= 1;
break;
}
if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0)))
goto overflow;
return res;
}
else
{
if (xh > 0.0)
hi = __LONG_MAX__;
else if (xh < 0.0)
hi = -__LONG_MAX__ - 1;
else
/* Nan */
hi = 0;
}
overflow:
#ifdef FE_INVALID
feraiseexcept (FE_INVALID);
#endif
return hi;
}
double
__ieee754_sqrt (double x)
{
#include "uroot.h"
static const double
rt0 = 9.99999999859990725855365213134618E-01,
rt1 = 4.99999999495955425917856814202739E-01,
rt2 = 3.75017500867345182581453026130850E-01,
rt3 = 3.12523626554518656309172508769531E-01;
static const double big = 134217728.0;
double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
mynumber a, c = { { 0, 0 } };
int4 k;
a.x = x;
k = a.i[HIGH_HALF];
a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
t = inroot[(k & 0x001fffff) >> 14];
s = a.x;
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k > 0x000fffff && k < 0x7ff00000)
{
int rm = __fegetround ();
fenv_t env;
libc_feholdexcept_setround (&env, FE_TONEAREST);
double ret;
y = 1.0 - t * (t * s);
t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
y = t * s;
hy = (y + big) - big;
del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
res = y + del;
if (res == (res + 1.002 * ((y - res) + del)))
ret = res * c.x;
else
{
res1 = res + 1.5 * ((y - res) + del);
EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
res = ((((z - s) + zz) < 0) ? max (res, res1) :
min (res, res1));
ret = res * c.x;
}
math_force_eval (ret);
libc_fesetenv (&env);
double dret = x / ret;
if (dret != ret)
{
double force_inexact = 1.0 / 3.0;
math_force_eval (force_inexact);
/* The square root is inexact, ret is the round-to-nearest
value which may need adjusting for other rounding
modes. */
switch (rm)
{
#ifdef FE_UPWARD
case FE_UPWARD:
if (dret > ret)
ret = (res + 0x1p-1022) * c.x;
break;
#endif
#ifdef FE_DOWNWARD
case FE_DOWNWARD:
#endif
#ifdef FE_TOWARDZERO
case FE_TOWARDZERO:
#endif
#if defined FE_DOWNWARD || defined FE_TOWARDZERO
if (dret < ret)
ret = (res - 0x1p-1022) * c.x;
break;
#endif
default:
break;
}
}
/* Otherwise (x / ret == ret), either the square root was exact or
the division was inexact. */
return ret;
}
