__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;
}
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;
}
__complex__ double
__ctanh (__complex__ double x)
{
__complex__ double res;
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
{
if (isinf (__real__ x))
{
__real__ res = __copysign (1.0, __real__ x);
if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0)
{
double sinix, cosix;
__sincos (__imag__ x, &sinix, &cosix);
__imag__ res = __copysign (0.0, sinix * cosix);
}
else
__imag__ res = __copysign (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
if (isinf (__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;
}
math_check_force_underflow_complex (res);
}
return res;
}
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;
}
__complex__ double
__catanh (__complex__ double x)
{
__complex__ double 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 = __copysign (0.0, __real__ x);
__imag__ res = __copysign (M_PI_2, __imag__ x);
}
else if (rcls == FP_INFINITE || rcls == FP_ZERO)
{
__real__ res = __copysign (0.0, __real__ x);
if (icls >= FP_ZERO)
__imag__ res = __copysign (M_PI_2, __imag__ x);
else
__imag__ res = __nan ("");
}
else
{
__real__ res = __nan ("");
__imag__ res = __nan ("");
}
}
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
res = x;
}
else
{
if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
|| fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
{
__imag__ res = __copysign (M_PI_2, __imag__ x);
if (fabs (__imag__ x) <= 1.0)
__real__ res = 1.0 / __real__ x;
else if (fabs (__real__ x) <= 1.0)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
__real__ res = __real__ x / h / h / 4.0;
}
}
else
{
if (fabs (__real__ x) == 1.0
&& fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON)
__real__ res = (__copysign (0.5, __real__ x)
* (M_LN2 - __ieee754_log (fabs (__imag__ x))));
else
{
double i2 = 0.0;
if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON)
i2 = __imag__ x * __imag__ x;
double num = 1.0 + __real__ x;
num = i2 + num * num;
double den = 1.0 - __real__ x;
den = i2 + den * den;
double f = num / den;
if (f < 0.5)
__real__ res = 0.25 * __ieee754_log (f);
else
{
num = 4.0 * __real__ x;
__real__ res = 0.25 * __log1p (num / den);
}
}
double absx, absy, den;
absx = fabs (__real__ x);
absy = fabs (__imag__ x);
if (absx < absy)
{
double t = absx;
absx = absy;
absy = t;
}
if (absy < DBL_EPSILON / 2.0)
{
den = (1.0 - absx) * (1.0 + absx);
if (den == -0.0)
den = 0.0;
}
else if (absx >= 1.0)
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
else if (absx >= 0.75 || absy >= 0.5)
den = -__x2y2m1 (absx, absy);
else
den = (1.0 - absx) * (1.0 + absx) - absy * absy;
__imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
}
math_check_force_underflow_complex (res);
}
return res;
}
__complex__ float
__ccoshf (__complex__ float x)
{
__complex__ float 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) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
if (__glibc_likely (fabsf (__imag__ x) > FLT_MIN))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__real__ x) > t)
{
float exp_t = __ieee754_expf (t);
float rx = fabsf (__real__ x);
if (signbit (__real__ x))
sinix = -sinix;
rx -= t;
sinix *= exp_t / 2.0f;
cosix *= exp_t / 2.0f;
if (rx > t)
{
rx -= t;
sinix *= exp_t;
cosix *= exp_t;
}
if (rx > t)
{
/* Overflow (original real part of x > 3t). */
__real__ retval = FLT_MAX * cosix;
__imag__ retval = FLT_MAX * sinix;
}
else
{
float exp_val = __ieee754_expf (rx);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
}
else
{
__real__ retval = __ieee754_coshf (__real__ x) * cosix;
__imag__ retval = __ieee754_sinhf (__real__ x) * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
__imag__ retval = __real__ x == 0.0 ? 0.0 : __nanf ("");
__real__ retval = __nanf ("");
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. */
float sinix, cosix;
if (__glibc_likely (fabsf (__imag__ x) > FLT_MIN))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = (__copysignf (HUGE_VALF, sinix)
* __copysignf (1.0, __real__ x));
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = HUGE_VALF;
__imag__ retval = __imag__ x * __copysignf (1.0, __real__ x);
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
CFLOAT
M_DECL_FUNC (__cexp) (CFLOAT x)
{
CFLOAT 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) ((M_MAX_EXP - 1) * M_MLIT (M_LN2));
FLOAT sinix, cosix;
if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
{
M_SINCOS (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1;
}
if (__real__ x > t)
{
FLOAT exp_t = M_EXP (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 = M_MAX * cosix;
__imag__ retval = M_MAX * sinix;
}
else
{
FLOAT exp_val = M_EXP (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = M_NAN;
__imag__ retval = M_NAN;
feraiseexcept (FE_INVALID);
}
}
else if (__glibc_likely (rcls == FP_INFINITE))
{
/* Real part is infinite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
FLOAT value = signbit (__real__ x) ? 0 : M_HUGE_VAL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
FLOAT sinix, cosix;
if (__glibc_likely (M_FABS (__imag__ x) > M_MIN))
{
M_SINCOS (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1;
}
__real__ retval = M_COPYSIGN (value, cosix);
__imag__ retval = M_COPYSIGN (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = M_HUGE_VAL;
__imag__ retval = __imag__ x - __imag__ x;
}
else
{
__real__ retval = 0;
__imag__ retval = M_COPYSIGN (0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = M_NAN;
if (icls == FP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = M_NAN;
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
}
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;
}
__complex__ float
__catanhf (__complex__ float x)
{
__complex__ float 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 = __copysignf (0.0, __real__ x);
__imag__ res = __copysignf (M_PI_2, __imag__ x);
}
else if (rcls == FP_INFINITE || rcls == FP_ZERO)
{
__real__ res = __copysignf (0.0, __real__ x);
if (icls >= FP_ZERO)
__imag__ res = __copysignf (M_PI_2, __imag__ x);
else
__imag__ res = __nanf ("");
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
res = x;
}
else
{
if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON
|| fabsf (__imag__ x) >= 16.0f / FLT_EPSILON)
{
__imag__ res = __copysignf ((float) M_PI_2, __imag__ x);
if (fabsf (__imag__ x) <= 1.0f)
__real__ res = 1.0f / __real__ x;
else if (fabsf (__real__ x) <= 1.0f)
__real__ res = __real__ x / __imag__ x / __imag__ x;
else
{
float h = __ieee754_hypotf (__real__ x / 2.0f,
__imag__ x / 2.0f);
__real__ res = __real__ x / h / h / 4.0f;
}
}
else
{
if (fabsf (__real__ x) == 1.0f
&& fabsf (__imag__ x) < FLT_EPSILON * FLT_EPSILON)
__real__ res = (__copysignf (0.5f, __real__ x)
* ((float) M_LN2
- __ieee754_logf (fabsf (__imag__ x))));
else
{
float i2 = 0.0f;
if (fabsf (__imag__ x) >= FLT_EPSILON * FLT_EPSILON)
i2 = __imag__ x * __imag__ x;
float num = 1.0f + __real__ x;
num = i2 + num * num;
float den = 1.0f - __real__ x;
den = i2 + den * den;
float f = num / den;
if (f < 0.5f)
__real__ res = 0.25f * __ieee754_logf (f);
else
{
num = 4.0f * __real__ x;
__real__ res = 0.25f * __log1pf (num / den);
}
}
float absx, absy, den;
absx = fabsf (__real__ x);
absy = fabsf (__imag__ x);
if (absx < absy)
{
float t = absx;
absx = absy;
absy = t;
}
if (absy < FLT_EPSILON / 2.0f)
{
den = (1.0f - absx) * (1.0f + absx);
if (den == -0.0f)
den = 0.0f;
}
else if (absx >= 1.0f)
den = (1.0f - absx) * (1.0f + absx) - absy * absy;
else if (absx >= 0.75f || absy >= 0.5f)
den = -__x2y2m1f (absx, absy);
else
den = (1.0f - absx) * (1.0f + absx) - absy * absy;
__imag__ res = 0.5f * __ieee754_atan2f (2.0f * __imag__ x, den);
}
math_check_force_underflow_complex (res);
}
return res;
}
__complex__ double
__cexp (__complex__ double x)
{
__complex__ 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) ((DBL_MAX_EXP - 1) * M_LN2);
double sinix, cosix;
if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
{
__sincos (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
if (__real__ x > t)
{
double exp_t = __ieee754_exp (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 = DBL_MAX * cosix;
__imag__ retval = DBL_MAX * sinix;
}
else
{
double exp_val = __ieee754_exp (__real__ x);
__real__ retval = exp_val * cosix;
__imag__ retval = exp_val * sinix;
}
math_check_force_underflow_complex (retval);
}
else
{
/* If the imaginary part is +-inf or NaN and the real part
is not +-inf the result is NaN + iNaN. */
__real__ retval = __nan ("");
__imag__ retval = __nan ("");
feraiseexcept (FE_INVALID);
}
}
else if (__glibc_likely (rcls == FP_INFINITE))
{
/* Real part is infinite. */
if (__glibc_likely (icls >= FP_ZERO))
{
/* Imaginary part is finite. */
double value = signbit (__real__ x) ? 0.0 : HUGE_VAL;
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = value;
__imag__ retval = __imag__ x;
}
else
{
double sinix, cosix;
if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
{
__sincos (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0;
}
__real__ retval = __copysign (value, cosix);
__imag__ retval = __copysign (value, sinix);
}
}
else if (signbit (__real__ x) == 0)
{
__real__ retval = HUGE_VAL;
__imag__ retval = __nan ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = 0.0;
__imag__ retval = __copysign (0.0, __imag__ x);
}
}
else
{
/* If the real part is NaN the result is NaN + iNaN unless the
imaginary part is zero. */
__real__ retval = __nan ("");
if (icls == FP_ZERO)
__imag__ retval = __imag__ x;
else
{
__imag__ retval = __nan ("");
if (rcls != FP_NAN || icls != FP_NAN)
feraiseexcept (FE_INVALID);
}
}
return retval;
}
