__complex__ long double
__clogl (__complex__ long double x)
{
__complex__ long double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (rcls == FP_ZERO && icls == FP_ZERO)
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
__imag__ result = __copysignl (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsl (__real__ x);
}
else if (rcls != FP_NAN && icls != FP_NAN)
{
/* Neither real nor imaginary part is NaN. */
__real__ result = __ieee754_logl (__ieee754_hypotl (__real__ x,
__imag__ x));
__imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanl ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALL;
else
__real__ result = __nanl ("");
}
return result;
}
__complex__ long double
__catanl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (rcls == FP_INFINITE)
{
__real__ res = __copysignl (M_PI_2l, __real__ x);
__imag__ res = __copysignl (0.0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = __copysignl (M_PI_2l, __real__ x);
else
__real__ res = __nanl ("");
__imag__ res = __copysignl (0.0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = __nanl ("");
__imag__ res = __copysignl (0.0, __imag__ x);
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
long double r2, num, den;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5 * __ieee754_atan2l (2.0 * __real__ x, den);
num = __imag__ x + 1.0;
num = r2 + num * num;
den = __imag__ x - 1.0;
den = r2 + den * den;
__imag__ res = 0.25 * __ieee754_logl (num / den);
}
return res;
}
__complex__ long double
__clogl (__complex__ long double x)
{
__complex__ long double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
__imag__ result = __copysignl (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsl (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
long double d;
int scale = 0;
if (fabsl (__real__ x) > LDBL_MAX / 2.0L
|| fabsl (__imag__ x) > LDBL_MAX / 2.0L)
{
scale = -1;
__real__ x = __scalbnl (__real__ x, scale);
__imag__ x = __scalbnl (__imag__ x, scale);
}
else if (fabsl (__real__ x) < LDBL_MIN
&& fabsl (__imag__ x) < LDBL_MIN)
{
scale = LDBL_MANT_DIG;
__real__ x = __scalbnl (__real__ x, scale);
__imag__ x = __scalbnl (__imag__ x, scale);
}
d = __ieee754_hypotl (__real__ x, __imag__ x);
__real__ result = __ieee754_logl (d) - scale * M_LN2l;
__imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanl ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALL;
else
__real__ result = __nanl ("");
}
return result;
}
__complex__ long double
__catanhl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (icls == FP_INFINITE)
{
__real__ res = __copysignl (0.0, __real__ x);
__imag__ res = __copysignl (M_PI_2l, __imag__ x);
}
else if (rcls == FP_INFINITE || rcls == FP_ZERO)
{
__real__ res = __copysignl (0.0, __real__ x);
if (icls >= FP_ZERO)
__imag__ res = __copysignl (M_PI_2l, __imag__ x);
else
__imag__ res = __nanl ("");
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
long double i2 = __imag__ x * __imag__ x;
long double num = 1.0 + __real__ x;
num = i2 + num * num;
long double den = 1.0 - __real__ x;
den = i2 + den * den;
__real__ res = 0.25 * (__ieee754_logl (num) - __ieee754_logl (den));
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5 * __ieee754_atan2l (2.0 * __imag__ x, den);
}
return res;
}
__complex__ long double
__casinhl (__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 = __copysignl (HUGE_VALL, __real__ x);
if (rcls == FP_NAN)
__imag__ res = __nanl ("");
else
__imag__ res = __copysignl (rcls >= FP_ZERO ? M_PI_2l : M_PI_4l,
__imag__ x);
}
else if (rcls <= FP_INFINITE)
{
__real__ res = __real__ x;
if ((rcls == FP_INFINITE && icls >= FP_ZERO)
|| (rcls == FP_NAN && icls == FP_ZERO))
__imag__ res = __copysignl (0.0, __imag__ x);
else
__imag__ res = __nanl ("");
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
res = x;
}
else
{
res = __kernel_casinhl (x, 0);
}
return res;
}
__complex__ long double
__ctanl (__complex__ long double x)
{
__complex__ long double res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinfl (__imag__ x))
{
__real__ res = __copysignl (0.0, __real__ x);
__imag__ res = __copysignl (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
#ifdef FE_INVALID
if (__isinfl (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
long double sin2rx, cos2rx;
long double den;
__sincosl (2.0 * __real__ x, &sin2rx, &cos2rx);
den = cos2rx + __ieee754_coshl (2.0 * __imag__ x);
__real__ res = sin2rx / den;
__imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den;
}
return res;
}
__complex__ long double
__casinl (__complex__ long double x)
{
__complex__ long double res;
if (isnan (__real__ x) || isnan (__imag__ x))
{
if (__real__ x == 0.0)
{
res = x;
}
else if (__isinfl (__real__ x) || __isinfl (__imag__ x))
{
__real__ res = __nanl ("");
__imag__ res = __copysignl (HUGE_VALL, __imag__ x);
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else
{
__complex__ long double y;
__real__ y = -__imag__ x;
__imag__ y = __real__ x;
y = __casinhl (y);
__real__ res = __imag__ y;
__imag__ res = -__real__ y;
}
return res;
}
__complex__ long double
__ctanl (__complex__ long double x)
{
__complex__ long double res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_nsl (__imag__ x))
{
__real__ res = __copysignl (0.0, __real__ x);
__imag__ res = __copysignl (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
if (__isinf_nsl (__real__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
long double sinrx, cosrx;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2);
int rcls = fpclassify (__real__ x);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0;
}
if (fabsl (__imag__ x) > t)
{
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
long double exp_2t = __ieee754_expl (2 * t);
__imag__ res = __copysignl (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsl (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= __ieee754_expl (2 * __imag__ x);
}
else
{
long double sinhix, coshix;
if (fabsl (__imag__ x) > LDBL_MIN)
{
sinhix = __ieee754_sinhl (__imag__ x);
coshix = __ieee754_coshl (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0L;
}
if (fabsl (sinhix) > fabsl (cosrx) * LDBL_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
}
return res;
}
__complex__ long double
__catanl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (rcls == FP_INFINITE)
{
__real__ res = __copysignl (M_PI_2l, __real__ x);
__imag__ res = __copysignl (0.0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = __copysignl (M_PI_2l, __real__ x);
else
__real__ res = __nanl ("");
__imag__ res = __copysignl (0.0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = __nanl ("");
__imag__ res = __copysignl (0.0, __imag__ x);
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
{
__real__ res = __copysignl (M_PI_2l, __real__ x);
if (fabsl (__real__ x) <= 1.0L)
__imag__ res = 1.0L / __imag__ x;
else if (fabsl (__imag__ x) <= 1.0L)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
long double h = __ieee754_hypotl (__real__ x / 2.0L,
__imag__ x / 2.0L);
__imag__ res = __imag__ x / h / h / 4.0L;
}
}
else
{
long double den, absx, absy;
absx = fabsl (__real__ x);
absy = fabsl (__imag__ x);
if (absx < absy)
{
long double t = absx;
absx = absy;
absy = t;
}
if (absy < LDBL_EPSILON / 2.0L)
den = (1.0L - absx) * (1.0L + absx);
else if (absx >= 1.0L)
den = (1.0L - absx) * (1.0L + absx) - absy * absy;
else if (absx >= 0.75L || absy >= 0.5L)
den = -__x2y2m1l (absx, absy);
else
den = (1.0L - absx) * (1.0L + absx) - absy * absy;
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
if (fabsl (__imag__ x) == 1.0L
&& fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON)
__imag__ res = (__copysignl (0.5L, __imag__ x)
* (M_LN2l - __ieee754_logl (fabsl (__real__ x))));
else
{
long double r2 = 0.0L, num, f;
if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON)
r2 = __real__ x * __real__ x;
num = __imag__ x + 1.0L;
num = r2 + num * num;
den = __imag__ x - 1.0L;
den = r2 + den * den;
f = num / den;
if (f < 0.5L)
__imag__ res = 0.25L * __ieee754_logl (f);
else
{
num = 4.0L * __imag__ x;
__imag__ res = 0.25L * __log1pl (num / den);
}
}
}
if (fabsl (__real__ res) < LDBL_MIN)
{
volatile long double force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
if (fabsl (__imag__ res) < LDBL_MIN)
{
volatile long double force_underflow = __imag__ res * __imag__ res;
(void) force_underflow;
}
}
return res;
}
__complex__ long double
__clog10l (__complex__ long double x)
{
__complex__ long double result;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
/* Real and imaginary part are 0.0. */
__imag__ result = signbit (__real__ x) ? M_PIl : 0.0;
__imag__ result = __copysignl (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsl (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
int scale = 0;
if (absx < absy)
{
long double t = absx;
absx = absy;
absy = t;
}
if (absx > LDBL_MAX / 2.0L)
{
scale = -1;
absx = __scalbnl (absx, scale);
absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
}
else if (absx < LDBL_MIN && absy < LDBL_MIN)
{
scale = LDBL_MANT_DIG;
absx = __scalbnl (absx, scale);
absy = __scalbnl (absy, scale);
}
if (absx == 1.0L && scale == 0)
{
long double absy2 = absy * absy;
if (absy2 <= LDBL_MIN * 2.0L * M_LN10l)
__real__ result
= (absy2 / 2.0L - absy2 * absy2 / 4.0L) * M_LOG10El;
else
__real__ result = __log1pl (absy2) * (M_LOG10El / 2.0L);
}
else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
if (absy >= LDBL_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
}
else if (absx < 1.0L
&& absx >= 0.75L
&& absy < LDBL_EPSILON / 2.0L
&& scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
__real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
}
else if (absx < 1.0L && (absx >= 0.75L || absy >= 0.5L) && scale == 0)
{
long double d2m1 = __x2y2m1l (absx, absy);
__real__ result = __log1pl (d2m1) * (M_LOG10El / 2.0L);
}
else
{
long double d = __ieee754_hypotl (absx, absy);
__real__ result = __ieee754_log10l (d) - scale * M_LOG10_2l;
}
__imag__ result = M_LOG10El * __ieee754_atan2l (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanl ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALL;
else
__real__ result = __nanl ("");
}
return result;
}
__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;
}
//
// atanhl
//
long double atanhl(long double x)
{
if(fabsl(x) >= 1) {errno = EDOM; return __nanl();}
return logl((1 + x) / (1 - x)) >> 1;
}
__complex__ long double
__ctanhl (__complex__ long double x)
{
__complex__ long double res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinfl (__real__ x))
{
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = __copysignl (0.0L, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
#ifdef FE_INVALID
if (__isinfl (__imag__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
long double sinix, cosix;
long double den;
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L);
/* 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). */
__sincosl (__imag__ x, &sinix, &cosix);
if (fabsl (__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). */
long double exp_2t = __ieee754_expl (2 * t);
__real__ res = __copysignl (1.0L, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsl (__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_expl (2.0L * __real__ x);
}
else
{
long double sinhrx, coshrx;
if (fabs (__real__ x) > LDBL_MIN)
{
sinhrx = __ieee754_sinhl (__real__ x);
coshrx = __ieee754_coshl (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0L;
}
if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * (coshrx / den);
__imag__ res = sinix * (cosix / den);
}
/* __gcc_qmul does not respect -0.0 so we need the following fixup. */
if ((__real__ res == 0.0L) && (__real__ x == 0.0L))
__real__ res = __real__ x;
if ((__real__ res == 0.0L) && (__imag__ x == 0.0L))
__imag__ res = __imag__ x;
}
return res;
}
__complex__ long double
__cexpl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls >= FP_ZERO, 1))
{
/* Real part is finite. */
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
__sincosl (__imag__ x, &sinix, &cosix);
if (__real__ x > t)
{
long double exp_t = __ieee754_expl (t);
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
if (__real__ x > t)
{
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
}
}
if (__real__ x > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
else if (__builtin_expect (rcls == FP_INFINITE, 1))
{
/* Real part is infinite. */
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
long double value = signbit (__real__ x) ? 0.0 : HUGE_VALL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
long double sinix, cosix;
__sincosl (__imag__ x, &sinix, &cosix);
__real__ retval = __copysignl (value, cosix);
__imag__ retval = __copysignl (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysignl (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
return retval;
}
__complex__ long double
__clogl (__complex__ long double x)
{
__complex__ long double 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) ? M_PIl : 0.0;
__imag__ result = __copysignl (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsl (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
long double absx = fabsl (__real__ x), absy = fabsl (__imag__ x);
int scale = 0;
if (absx < absy)
{
long double t = absx;
absx = absy;
absy = t;
}
if (absx > LDBL_MAX / 2.0L)
{
scale = -1;
absx = __scalbnl (absx, scale);
absy = (absy >= LDBL_MIN * 2.0L ? __scalbnl (absy, scale) : 0.0L);
}
else if (absx < LDBL_MIN && absy < LDBL_MIN)
{
scale = LDBL_MANT_DIG;
absx = __scalbnl (absx, scale);
absy = __scalbnl (absy, scale);
}
if (absx == 1.0L && scale == 0)
{
__real__ result = __log1pl (absy * absy) / 2.0L;
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1.0L && absx < 2.0L && absy < 1.0L && scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
if (absy >= LDBL_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1pl (d2m1) / 2.0L;
}
else if (absx < 1.0L
&& absx >= 0.5L
&& absy < LDBL_EPSILON / 2.0L
&& scale == 0)
{
long double d2m1 = (absx - 1.0L) * (absx + 1.0L);
__real__ result = __log1pl (d2m1) / 2.0L;
}
else if (absx < 1.0L
&& absx >= 0.5L
&& scale == 0
&& absx * absx + absy * absy >= 0.5L)
{
long double d2m1 = __x2y2m1l (absx, absy);
__real__ result = __log1pl (d2m1) / 2.0L;
}
else
{
long double d = __ieee754_hypotl (absx, absy);
__real__ result = __ieee754_logl (d) - scale * M_LN2l;
}
__imag__ result = __ieee754_atan2l (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanl ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALL;
else
__real__ result = __nanl ("");
}
return result;
}
__complex__ long double
__csinl (__complex__ long double x)
{
__complex__ long double retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsl (__real__ x);
if (__builtin_expect (icls >= FP_ZERO, 1))
{
/* Imaginary part is finite. */
if (__builtin_expect (rcls >= FP_ZERO, 1))
{
/* Real part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0;
}
if (fabsl (__imag__ x) > t)
{
long double exp_t = __ieee754_expl (t);
long double ix = fabsl (__imag__ x);
if (signbit (__imag__ x))
cosix = -cosix;
ix -= t;
sinix *= exp_t / 2.0L;
cosix *= exp_t / 2.0L;
if (ix > t)
{
ix -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (ix > t)
{
/* Overflow (original imaginary part of x > 3t). */
__real__ retval = LDBL_MAX * sinix;
__imag__ retval = LDBL_MAX * cosix;
}
else
{
long double exp_val = __ieee754_expl (ix);
__real__ retval = exp_val * sinix;
__imag__ retval = exp_val * cosix;
}
}
else
{
__real__ retval = __ieee754_coshl (__imag__ x) * sinix;
__imag__ retval = __ieee754_sinhl (__imag__ x) * cosix;
}
if (negate)
__real__ retval = -__real__ retval;
if (fabsl (__real__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsl (__imag__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = __nanl ("");
__imag__ retval = __imag__ x;
if (rcls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
}
else if (icls == FP_INFINITE)
{
/* Imaginary part is infinite. */
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = __copysignl (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __imag__ x;
}
else if (rcls > FP_ZERO)
{
/* Real part is finite. */
long double sinix, cosix;
if (__builtin_expect (rcls != FP_SUBNORMAL, 1))
{
__sincosl (__real__ x, &sinix, &cosix);
}
else
{
sinix = __real__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (HUGE_VALL, sinix);
__imag__ retval = __copysignl (HUGE_VALL, cosix);
if (negate)
__real__ retval = -__real__ retval;
if (signbit (__imag__ x))
__imag__ retval = -__imag__ retval;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = __nanl ("");
__imag__ retval = HUGE_VALL;
if (rcls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
if (rcls == FP_ZERO)
__real__ retval = __copysignl (0.0, negate ? -1.0 : 1.0);
else
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
}
return retval;
}
//
// nanl
//
long double nanl(char const *tagp)
{
return __nanl();
}
//
// acoshl
//
long double acoshl(long double x)
{
if(x < 1) {errno = EDOM; return __nanl();}
return logl(x + sqrtl(x * x - 1));
}
__complex__ long double
__cexpl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (__real__ x > t)
{
long double exp_t = __ieee754_expl (t);
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
if (__real__ x > t)
{
__real__ x -= t;
sinix *= exp_t;
cosix *= exp_t;
}
}
if (__real__ x > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
if (fabsl (__real__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsl (__imag__ retval) < LDBL_MIN)
{
volatile long double force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = __nanl ("");
__imag__ retval = __nanl ("");
feraiseexcept (FE_INVALID);
}
}
else if (__glibc_likely (rcls == FP_INFINITE))
{
/* Real part is infinite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
long double value = signbit (__real__ x) ? 0.0 : HUGE_VALL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
long double sinix, cosix;
if (__glibc_likely (icls != FP_SUBNORMAL))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (value, cosix);
__imag__ retval = __copysignl (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysignl (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = __nanl ("");
if (icls == FP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = __nanl ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
}
return retval;
}
__complex__ long double
__csqrtl (__complex__ long double x)
{
__complex__ long double res;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
{
if (icls == FP_INFINITE)
{
__real__ res = HUGE_VALL;
__imag__ res = __imag__ x;
}
else if (rcls == FP_INFINITE)
{
if (__real__ x < 0.0)
{
__real__ res = icls == FP_NAN ? __nanl ("") : 0;
__imag__ res = __copysignl (HUGE_VALL, __imag__ x);
}
else
{
__real__ res = __real__ x;
__imag__ res = (icls == FP_NAN
? __nanl ("") : __copysignl (0.0, __imag__ x));
}
}
else
{
__real__ res = __nanl ("");
__imag__ res = __nanl ("");
}
}
else
{
if (__builtin_expect (icls == FP_ZERO, 0))
{
if (__real__ x < 0.0)
{
__real__ res = 0.0;
__imag__ res = __copysignl (__ieee754_sqrtl (-__real__ x),
__imag__ x);
}
else
{
__real__ res = fabsl (__ieee754_sqrtl (__real__ x));
__imag__ res = __copysignl (0.0, __imag__ x);
}
}
else if (__builtin_expect (rcls == FP_ZERO, 0))
{
long double r = __ieee754_sqrtl (0.5 * fabsl (__imag__ x));
__real__ res = r;
__imag__ res = __copysignl (r, __imag__ x);
}
else
{
long double d, r, s;
d = __ieee754_hypotl (__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 = __ieee754_sqrtl (0.5L * d + 0.5L * __real__ x);
s = (0.5L * __imag__ x) / r;
}
else
{
s = __ieee754_sqrtl (0.5L * d - 0.5L * __real__ x);
r = fabsl ((0.5L * __imag__ x) / s);
}
__real__ res = r;
__imag__ res = __copysignl (s, __imag__ x);
}
}
return res;
}
__complex__ long double
__ccoshl (__complex__ long double x)
{
__complex__ long double retval;
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
if (__glibc_likely (rcls >= FP_ZERO))
{
/* Real part is finite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l);
long double sinix, cosix;
if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (fabsl (__real__ x) > t)
{
long double exp_t = __ieee754_expl (t);
long double rx = fabsl (__real__ x);
if (signbit (__real__ x))
sinix = -sinix;
rx -= t;
sinix *= exp_t / 2.0L;
cosix *= exp_t / 2.0L;
if (rx > t)
{
rx -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (rx > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = LDBL_MAX * cosix;
__imag__ retval = LDBL_MAX * sinix;
}
else
{
long double exp_val = __ieee754_expl (rx);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
__real__ retval = __ieee754_coshl (__real__ x) * cosix;
__imag__ retval = __ieee754_sinhl (__real__ x) * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
__imag__ retval = __real__ x == 0.0 ? 0.0 : __nanl ("");
__real__ retval = __nanl ("") + __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else if (rcls == FP_INFINITE)
{
/* Real part is infinite. */
if (__glibc_likely (icls > FP_ZERO))
{
/* Imaginary part is finite. */
long double sinix, cosix;
if (__glibc_likely (fabsl (__imag__ x) > LDBL_MIN))
{
__sincosl (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
__real__ retval = __copysignl (HUGE_VALL, cosix);
__imag__ retval = (__copysignl (HUGE_VALL, sinix)
* __copysignl (1.0, __real__ x));
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = HUGE_VALL;
__imag__ retval = __imag__ x * __copysignl (1.0, __real__ x);
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALL;
__imag__ retval = __nanl ("") + __nanl ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
__real__ retval = __nanl ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanl ("");
}
return retval;
}
__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;
}