__complex__ double
__ctanh (__complex__ double x)
{
__complex__ double res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_ns (__real__ x))
{
__real__ res = __copysign (1.0, __real__ x);
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
if (__isinf_ns (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
double sin2ix, cos2ix;
double den;
__sincos (2.0 * __imag__ x, &sin2ix, &cos2ix);
den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix);
if (den == 0.0)
{
__complex__ double ez = __cexp (x);
__complex__ double emz = __cexp (-x);
res = (ez - emz) / (ez + emz);
}
else
{
__real__ res = __ieee754_sinh (2.0 * __real__ x) / den;
__imag__ res = sin2ix / den;
}
}
return res;
}
__complex__ double
__cproj (__complex__ double x)
{
if (__isinf_ns (__real__ x) || __isinf_ns (__imag__ x))
{
__complex__ double res;
__real__ res = INFINITY;
__imag__ res = __copysign (0.0, __imag__ x);
return res;
}
return x;
}
/* wrapper remainder */
double
__remainder (double x, double y)
{
if (((__builtin_expect (y == 0.0, 0) && ! __isnan (x))
|| (__builtin_expect (__isinf_ns (x), 0) && ! __isnan (y)))
&& _LIB_VERSION != _IEEE_)
return __kernel_standard (x, y, 28); /* remainder domain */
return __ieee754_remainder (x, y);
}
__complex__ double
__ctanh (__complex__ double x)
{
__complex__ double res;
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
{
if (__isinf_ns (__real__ x))
{
__real__ res = __copysign (1.0, __real__ x);
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
if (__isinf_ns (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
double sinix, cosix;
double den;
const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
/* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
= (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */
if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
{
__sincos (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (fabs (__real__ x) > t)
{
/* Avoid intermediate overflow when the imaginary part of
the result may be subnormal. Ignoring negligible terms,
the real part is +/- 1, the imaginary part is
sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */
double exp_2t = __ieee754_exp (2 * t);
__real__ res = __copysign (1.0, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabs (__real__ x);
__real__ x -= t;
__imag__ res /= exp_2t;
if (__real__ x > t)
{
/* Underflow (original real part of x has absolute value
> 2t). */
__imag__ res /= exp_2t;
}
else
__imag__ res /= __ieee754_exp (2 * __real__ x);
}
else
{
double sinhrx, coshrx;
if (fabs (__real__ x) > DBL_MIN)
{
sinhrx = __ieee754_sinh (__real__ x);
coshrx = __ieee754_cosh (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0;
}
if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
}
return res;
}
