__complex__ long double
__cacoshl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
if (rcls == FP_NAN)
__imag__ res = __nanl ("");
else
__imag__ res = __copysignl ((rcls == FP_INFINITE
? (__real__ x < 0.0
? M_PIl - M_PI_4l : M_PI_4l)
: M_PI_2l), __imag__ x);
}
else if (rcls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
if (icls >= FP_ZERO)
__imag__ res = __copysignl (signbit (__real__ x) ? M_PIl : 0.0,
__imag__ x);
else
__imag__ res = __nanl ("");
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
__real__ res = 0.0;
__imag__ res = __copysignl (M_PI_2l, __imag__ x);
}
/* The factor 16 is just a guess. */
else if (16.0L * fabsl (__imag__ x) < fabsl (__real__ x))
{
/* Kahan's formula which avoid cancellation through subtraction in
some cases. */
res = 2.0L * __clogl (__csqrtl ((x + 1.0L) / 2.0L)
+ __csqrtl ((x - 1.0L) / 2.0L));
if (signbit (__real__ res))
__real__ res = 0.0L;
}
else
{
__complex__ long double y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = __csqrtl (y);
if (signbit (__real__ x))
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = __clogl (y);
}
return res;
}
__complex__ long double
__kernel_casinhl (__complex__ long double x, int adj)
{
__complex__ long double res;
long double rx, ix;
__complex__ long double y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsl (__real__ x);
ix = fabsl (__imag__ x);
if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
long double t = __real__ y;
__real__ y = __copysignl (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogl (y);
__real__ res += M_LN2l;
}
else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
{
long double s = __ieee754_hypotl (1.0L, rx);
__real__ res = __ieee754_logl (rx + s);
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
{
long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
__real__ res = __ieee754_logl (ix + s);
if (adj)
__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
else
__imag__ res = __ieee754_atan2l (s, rx);
}
else if (ix > 1.0L && ix < 1.5L && rx < 0.5L)
{
if (rx < LDBL_EPSILON * LDBL_EPSILON)
{
long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
long double s = __ieee754_sqrtl (ix2m1);
__real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
else
__imag__ res = __ieee754_atan2l (s, rx);
}
else
{
long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
long double rx2 = rx * rx;
long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f);
long double dp = d + ix2m1;
long double dm = f / dp;
long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L);
long double r2 = rx * ix / r1;
__real__ res
= __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
}
}
else if (ix == 1.0L && rx < 0.5L)
{
if (rx < LDBL_EPSILON / 8.0L)
{
__real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx),
__copysignl (1.0L, __imag__ x));
else
__imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx));
}
else
{
long double d = rx * __ieee754_sqrtl (4.0L + rx * rx);
long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L);
long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L);
__real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + s1,
__copysignl (1.0L + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1);
}
}
else if (ix < 1.0L && rx < 0.5L)
{
if (ix >= LDBL_EPSILON)
{
if (rx < LDBL_EPSILON * LDBL_EPSILON)
{
long double onemix2 = (1.0L + ix) * (1.0L - ix);
long double s = __ieee754_sqrtl (onemix2);
__real__ res = __log1pl (2.0L * rx / s) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
else
{
long double onemix2 = (1.0L + ix) * (1.0L - ix);
long double rx2 = rx * rx;
long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
long double d = __ieee754_sqrtl (onemix2 * onemix2 + f);
long double dp = d + onemix2;
long double dm = f / dp;
long double r1 = __ieee754_sqrtl ((dp + rx2) / 2.0L);
long double r2 = rx * ix / r1;
__real__ res
= __log1pl (rx2 + dm + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (rx + r1,
__copysignl (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
}
}
else
{
long double s = __ieee754_hypotl (1.0L, rx);
__real__ res = __log1pl (2.0L * rx * (rx + s)) / 2.0L;
if (adj)
__imag__ res = __ieee754_atan2l (s, __imag__ x);
else
__imag__ res = __ieee754_atan2l (ix, s);
}
if (__real__ res < LDBL_MIN)
{
volatile long double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0L;
__imag__ y = 2.0L * rx * ix;
y = __csqrtl (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
long double t = __real__ y;
__real__ y = __copysignl (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogl (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysignl (__real__ res, __real__ x);
__imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
return res;
}
__complex__ long double
__cacoshl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls <= FP_INFINITE || icls <= FP_INFINITE)
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
if (rcls == FP_NAN)
__imag__ res = __nanl ("");
else
__imag__ res = __copysignl ((rcls == FP_INFINITE
? (__real__ x < 0.0
? M_PIl - M_PI_4l : M_PI_4l)
: M_PI_2l), __imag__ x);
}
else if (rcls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
if (icls >= FP_ZERO)
__imag__ res = __copysignl (signbit (__real__ x) ? M_PIl : 0.0,
__imag__ x);
else
__imag__ res = __nanl ("");
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
__real__ res = 0.0;
__imag__ res = __copysignl (M_PI_2l, __imag__ x);
}
else
{
__complex__ long double y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = __csqrtl (y);
if (__real__ x < 0.0)
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = __clogl (y);
}
return res;
}
