inline Complex<Quad> Sqrt( const Complex<Quad>& alphaPre )
{
__complex128 alpha;
__real__(alpha) = alphaPre.real();
__imag__(alpha) = alphaPre.imag();
__complex128 sqrtAlpha = csqrtq(alpha);
return Complex<Quad>(crealq(sqrtAlpha),cimagq(sqrtAlpha));
}
__complex128
cacoshq (__complex128 x)
{
__complex128 res;
int rcls = fpclassifyq (__real__ x);
int icls = fpclassifyq (__imag__ x);
if (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)
{
if (icls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
if (rcls == QUADFP_NAN)
__imag__ res = nanq ("");
else
__imag__ res = copysignq ((rcls == QUADFP_INFINITE
? (__real__ x < 0.0
? M_PIq - M_PI_4q : M_PI_4q)
: M_PI_2q), __imag__ x);
}
else if (rcls == QUADFP_INFINITE)
{
__real__ res = HUGE_VALQ;
if (icls >= QUADFP_ZERO)
__imag__ res = copysignq (signbitq (__real__ x) ? M_PIq : 0.0,
__imag__ x);
else
__imag__ res = nanq ("");
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
}
}
else if (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)
{
__real__ res = 0.0;
__imag__ res = copysignq (M_PI_2q, __imag__ x);
}
/* The factor 16 is just a guess. */
else if (16.0Q * fabsq (__imag__ x) < fabsq (__real__ x))
{
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0Q * clogq (csqrtq ((x + 1.0Q) / 2.0Q)
+ csqrtq ((x - 1.0Q) / 2.0Q));
if (signbitq (__real__ res))
__real__ res = 0.0Q;
}
else
{
__complex128 y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = csqrtq (y);
if (signbitq (x))
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = clogq (y);
}
return res;
}
