CFLOAT
M_DECL_FUNC (__csqrt) (CFLOAT x)
{
CFLOAT res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
{
if (icls == FP_INFINITE)
{
__real__ res = M_HUGE_VAL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0)
{
__real__ res = icls == FP_NAN ? M_NAN : 0;
__imag__ res = M_COPYSIGN (M_HUGE_VAL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? M_NAN : M_COPYSIGN (0, __imag__ x));
}
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
}
}
else
{
if (__glibc_unlikely (icls == FP_ZERO))
{
if (__real__ x < 0)
{
__real__ res = 0;
__imag__ res = M_COPYSIGN (M_SQRT (-__real__ x), __imag__ x);
}
else
{
__real__ res = M_FABS (M_SQRT (__real__ x));
__imag__ res = M_COPYSIGN (0, __imag__ x);
}
}
else if (__glibc_unlikely (rcls == FP_ZERO))
{
FLOAT r;
if (M_FABS (__imag__ x) >= 2 * M_MIN)
r = M_SQRT (M_LIT (0.5) * M_FABS (__imag__ x));
else
r = M_LIT (0.5) * M_SQRT (2 * M_FABS (__imag__ x));
__real__ res = r;
__imag__ res = M_COPYSIGN (r, __imag__ x);
}
else
{
FLOAT d, r, s;
int scale = 0;
if (M_FABS (__real__ x) > M_MAX / 4)
{
scale = 1;
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__imag__ x) > M_MAX / 4)
{
scale = 1;
if (M_FABS (__real__ x) >= 4 * M_MIN)
__real__ x = M_SCALBN (__real__ x, -2 * scale);
else
__real__ x = 0;
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
else if (M_FABS (__real__ x) < 2 * M_MIN
&& M_FABS (__imag__ x) < 2 * M_MIN)
{
scale = -((M_MANT_DIG + 1) / 2);
__real__ x = M_SCALBN (__real__ x, -2 * scale);
__imag__ x = M_SCALBN (__imag__ x, -2 * scale);
}
d = M_HYPOT (__real__ x, __imag__ x);
/* Use the identity 2 Re res Im res = Im x
to avoid cancellation error in d +/- Re x. */
if (__real__ x > 0)
{
r = M_SQRT (M_LIT (0.5) * (d + __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
s = __imag__ x / r;
r = M_SCALBN (r, scale);
scale = 0;
}
else
s = M_LIT (0.5) * (__imag__ x / r);
}
else
{
s = M_SQRT (M_LIT (0.5) * (d - __real__ x));
if (scale == 1 && M_FABS (__imag__ x) < 1)
{
/* Avoid possible intermediate underflow. */
r = M_FABS (__imag__ x / s);
s = M_SCALBN (s, scale);
scale = 0;
}
else
r = M_FABS (M_LIT (0.5) * (__imag__ x / s));
}
if (scale)
{
r = M_SCALBN (r, scale);
s = M_SCALBN (s, scale);
}
math_check_force_underflow (r);
math_check_force_underflow (s);
__real__ res = r;
__imag__ res = M_COPYSIGN (s, __imag__ x);
}
}
return res;
}
CFLOAT
M_DECL_FUNC (__catanh) (CFLOAT x)
{
CFLOAT res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
{
if (icls == FP_INFINITE)
{
__real__ res = M_COPYSIGN (0, __real__ x);
__imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
}
else if (rcls == FP_INFINITE || rcls == FP_ZERO)
{
__real__ res = M_COPYSIGN (0, __real__ x);
if (icls >= FP_ZERO)
__imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
else
__imag__ res = M_NAN;
}
else
{
__real__ res = M_NAN;
__imag__ res = M_NAN;
}
}
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
res = x;
}
else
{
if (M_FABS (__real__ x) >= 16 / M_EPSILON
|| M_FABS (__imag__ x) >= 16 / M_EPSILON)
{
__imag__ res = M_COPYSIGN (M_MLIT (M_PI_2), __imag__ x);
if (M_FABS (__imag__ x) <= 1)
__real__ res = 1 / __real__ x;
else if (M_FABS (__real__ x) <= 1)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
FLOAT h = M_HYPOT (__real__ x / 2, __imag__ x / 2);
__real__ res = __real__ x / h / h / 4;
}
}
else
{
if (M_FABS (__real__ x) == 1
&& M_FABS (__imag__ x) < M_EPSILON * M_EPSILON)
__real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x)
* ((FLOAT) M_MLIT (M_LN2)
- M_LOG (M_FABS (__imag__ x))));
else
{
FLOAT i2 = 0;
if (M_FABS (__imag__ x) >= M_EPSILON * M_EPSILON)
i2 = __imag__ x * __imag__ x;
FLOAT num = 1 + __real__ x;
num = i2 + num * num;
FLOAT den = 1 - __real__ x;
den = i2 + den * den;
FLOAT f = num / den;
if (f < M_LIT (0.5))
__real__ res = M_LIT (0.25) * M_LOG (f);
else
{
num = 4 * __real__ x;
__real__ res = M_LIT (0.25) * M_LOG1P (num / den);
}
}
FLOAT absx, absy, den;
absx = M_FABS (__real__ x);
absy = M_FABS (__imag__ x);
if (absx < absy)
{
FLOAT t = absx;
absx = absy;
absy = t;
}
if (absy < M_EPSILON / 2)
{
den = (1 - absx) * (1 + absx);
if (den == 0)
den = 0;
}
else if (absx >= 1)
den = (1 - absx) * (1 + absx) - absy * absy;
else if (absx >= M_LIT (0.75) || absy >= M_LIT (0.5))
den = -M_SUF (__x2y2m1) (absx, absy);
else
den = (1 - absx) * (1 + absx) - absy * absy;
__imag__ res = M_LIT (0.5) * M_ATAN2 (2 * __imag__ x, den);
}
math_check_force_underflow_complex (res);
}
return res;
}
CFLOAT
M_DECL_FUNC (__clog) (CFLOAT x)
{
CFLOAT result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? (FLOAT) M_MLIT (M_PI) : 0;
__imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1 / M_FABS (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
FLOAT absx = M_FABS (__real__ x), absy = M_FABS (__imag__ x);
int scale = 0;
if (absx < absy)
{
FLOAT t = absx;
absx = absy;
absy = t;
}
if (absx > M_MAX / 2)
{
scale = -1;
absx = M_SCALBN (absx, scale);
absy = (absy >= M_MIN * 2 ? M_SCALBN (absy, scale) : 0);
}
else if (absx < M_MIN && absy < M_MIN)
{
scale = M_MANT_DIG;
absx = M_SCALBN (absx, scale);
absy = M_SCALBN (absy, scale);
}
if (absx == 1 && scale == 0)
{
__real__ result = M_LOG1P (absy * absy) / 2;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
{
FLOAT d2m1 = (absx - 1) * (absx + 1);
if (absy >= M_EPSILON)
d2m1 += absy * absy;
__real__ result = M_LOG1P (d2m1) / 2;
}
else if (absx < 1
&& absx >= M_LIT (0.5)
&& absy < M_EPSILON / 2
&& scale == 0)
{
FLOAT d2m1 = (absx - 1) * (absx + 1);
__real__ result = M_LOG1P (d2m1) / 2;
}
else if (absx < 1
&& absx >= M_LIT (0.5)
&& scale == 0
&& absx * absx + absy * absy >= M_LIT (0.5))
{
FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
__real__ result = M_LOG1P (d2m1) / 2;
}
else
{
FLOAT d = M_HYPOT (absx, absy);
__real__ result = M_LOG (d) - scale * (FLOAT) M_MLIT (M_LN2);
}
__imag__ result = M_ATAN2 (__imag__ x, __real__ x);
}
else
{
__imag__ result = M_NAN;
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = M_HUGE_VAL;
else
__real__ result = M_NAN;
}
return result;
}