CFLOAT
M_DECL_FUNC (__csin) (CFLOAT x)
{
CFLOAT retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = M_FABS (__real__ x);
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2));
FLOAT sinix, cosix;
if (__glibc_likely (__real__ x > M_MIN))
{
M_SINCOS (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1;
}
if (negate)
sinix = -sinix;
if (M_FABS (__imag__ x) > t)
{
FLOAT exp_t = M_EXP (t);
FLOAT ix = M_FABS (__imag__ x);
if (signbit (__imag__ x))
cosix = -cosix;
ix -= t;
sinix *= exp_t / 2;
cosix *= exp_t / 2;
if (ix > t)
{
ix -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (ix > t)
{
/* Overflow (original imaginary part of x > 3t). */
__real__ retval = M_MAX * sinix;
__imag__ retval = M_MAX * cosix;
}
else
{
FLOAT exp_val = M_EXP (ix);
__real__ retval = exp_val * sinix;
__imag__ retval = exp_val * cosix;
}
}
else
{
__real__ retval = M_COSH (__imag__ x) * sinix;
__imag__ retval = M_SINH (__imag__ x) * cosix;
}
math_check_force_underflow_complex (retval);
}
else
{
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = __real__ x - __real__ x;
__imag__ retval = __imag__ x;
}
else
{
__real__ retval = M_NAN;
__imag__ retval = M_NAN;
feraiseexcept (FE_INVALID);
}
}
}
else if (icls == FP_INFINITE)
{
/* Imaginary part is infinite. */
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = M_COPYSIGN (0, negate ? -1 : 1);
__imag__ retval = __imag__ x;
}
else if (rcls > FP_ZERO)
{
/* Real part is finite. */
FLOAT sinix, cosix;
if (__glibc_likely (__real__ x > M_MIN))
{
M_SINCOS (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1;
}
__real__ retval = M_COPYSIGN (M_HUGE_VAL, sinix);
__imag__ retval = M_COPYSIGN (M_HUGE_VAL, cosix);
if (negate)
__real__ retval = -__real__ retval;
if (signbit (__imag__ x))
__imag__ retval = -__imag__ retval;
}
else
{
__real__ retval = __real__ x - __real__ x;
__imag__ retval = M_HUGE_VAL;
}
}
else
{
if (rcls == FP_ZERO)
__real__ retval = M_COPYSIGN (0, negate ? -1 : 1);
else
__real__ retval = M_NAN;
__imag__ retval = M_NAN;
}
return retval;
}
CFLOAT
M_DECL_FUNC (__ctanh) (CFLOAT x)
{
CFLOAT res;
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
{
if (isinf (__real__ x))
{
__real__ res = M_COPYSIGN (1, __real__ x);
if (isfinite (__imag__ x) && M_FABS (__imag__ x) > 1)
{
FLOAT sinix, cosix;
M_SINCOS (__imag__ x, &sinix, &cosix);
__imag__ res = M_COPYSIGN (0, sinix * cosix);
}
else
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
else if (__imag__ x == 0)
{
res = x;
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
if (isinf (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
FLOAT sinix, cosix;
FLOAT den;
const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (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 (M_FABS (__imag__ x) > M_MIN))
{
M_SINCOS (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1;
}
if (M_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). */
FLOAT exp_2t = M_EXP (2 * t);
__real__ res = M_COPYSIGN (1, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = M_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 /= M_EXP (2 * __real__ x);
}
else
{
FLOAT sinhrx, coshrx;
if (M_FABS (__real__ x) > M_MIN)
{
sinhrx = M_SINH (__real__ x);
coshrx = M_COSH (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1;
}
if (M_FABS (sinhrx) > M_FABS (cosix) * M_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
math_check_force_underflow_complex (res);
}
return res;
}
