inline void eval_frexp(float128_backend& result, const float128_backend& arg, int* exp)
{
result.value() = frexpq(arg.value(), exp);
}
__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);
}
