float
__coshf (float x)
{
float z = __ieee754_coshf (x);
if (__builtin_expect (!isfinite (z), 0) && isfinite (x)
&& _LIB_VERSION != _IEEE_)
return __kernel_standard_f (x, x, 105); /* cosh overflow */
return z;
}
__complex__ float
__ctanf (__complex__ float x)
{
__complex__ float res;
if (!isfinite (__real__ x) || !isfinite (__imag__ x))
{
if (__isinff (__imag__ x))
{
__real__ res = __copysignf (0.0, __real__ x);
__imag__ res = __copysignf (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
#ifdef FE_INVALID
if (__isinff (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
float sin2rx, cos2rx;
float den;
__sincosf (2.0 * __real__ x, &sin2rx, &cos2rx);
den = cos2rx + __ieee754_coshf (2.0 * __imag__ x);
__real__ res = sin2rx / den;
__imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den;
}
return res;
}
__complex__ float
__csinhf (__complex__ float x)
{
__complex__ float retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsf (__real__ x);
if (rcls >= FP_ZERO)
{
/* Real part is finite. */
if (icls >= FP_ZERO)
{
/* Imaginary part is finite. */
float sinh_val = __ieee754_sinhf (__real__ x);
float cosh_val = __ieee754_coshf (__real__ x);
float sinix, cosix;
__sincosf (__imag__ x, &sinix, &cosix);
__real__ retval = sinh_val * cosix;
__imag__ retval = cosh_val * sinix;
if (negate)
__real__ retval = -__real__ retval;
}
else
{
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = __copysignf (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __nanf ("");
#ifdef FE_INVALID
feraiseexcept (FE_INVALID);
#endif
}
}
}
else if (rcls == FP_INFINITE)
{
/* Real part is infinite. */
if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = negate ? -HUGE_VALF : HUGE_VALF;
__imag__ retval = __imag__ x;
}
else if (icls > FP_ZERO)
{
/* Imaginary part is finite. */
float sinix, cosix;
__sincosf (__imag__ x, &sinix, &cosix);
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = __copysignf (HUGE_VALF, sinix);
if (negate)
__real__ retval = -__real__ retval;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
__complex__ float
__csinhf (__complex__ float x)
{
__complex__ float retval;
int negate = signbit (__real__ x);
int rcls = fpclassify (__real__ x);
int icls = fpclassify (__imag__ x);
__real__ x = fabsf (__real__ 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) ((FLT_MAX_EXP - 1) * M_LN2);
float sinix, cosix;
if (__builtin_expect (icls != FP_SUBNORMAL, 1))
{
__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))
cosix = -cosix;
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_sinhf (__real__ x) * cosix;
__imag__ retval = __ieee754_coshf (__real__ x) * sinix;
}
if (negate)
__real__ retval = -__real__ retval;
if (fabsf (__real__ retval) < FLT_MIN)
{
volatile float force_underflow
= __real__ retval * __real__ retval;
(void) force_underflow;
}
if (fabsf (__imag__ retval) < FLT_MIN)
{
volatile float force_underflow
= __imag__ retval * __imag__ retval;
(void) force_underflow;
}
}
else
{
if (rcls == FP_ZERO)
{
/* Real part is 0.0. */
__real__ retval = __copysignf (0.0, negate ? -1.0 : 1.0);
__imag__ retval = __nanf ("") + __nanf ("");
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __nanf ("");
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. */
float sinix, cosix;
if (__builtin_expect (icls != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
__real__ retval = __copysignf (HUGE_VALF, cosix);
__imag__ retval = __copysignf (HUGE_VALF, sinix);
if (negate)
__real__ retval = -__real__ retval;
}
else if (icls == FP_ZERO)
{
/* Imaginary part is 0.0. */
__real__ retval = negate ? -HUGE_VALF : HUGE_VALF;
__imag__ retval = __imag__ x;
}
else
{
/* The addition raises the invalid exception. */
__real__ retval = HUGE_VALF;
__imag__ retval = __nanf ("") + __nanf ("");
#ifdef FE_INVALID
if (icls == FP_INFINITE)
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__real__ retval = __nanf ("");
__imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nanf ("");
}
return retval;
}
__complex__ float
__ctanf (__complex__ float x)
{
__complex__ float res;
if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
{
if (isinf (__imag__ x))
{
if (isfinite (__real__ x) && fabsf (__real__ x) > 1.0f)
{
float sinrx, cosrx;
__sincosf (__real__ x, &sinrx, &cosrx);
__real__ res = __copysignf (0.0f, sinrx * cosrx);
}
else
__real__ res = __copysignf (0.0, __real__ x);
__imag__ res = __copysignf (1.0, __imag__ x);
}
else if (__real__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
if (isinf (__real__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
float sinrx, cosrx;
float den;
const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2);
/* 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 (__glibc_likely (fabsf (__real__ x) > FLT_MIN))
{
__sincosf (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0f;
}
if (fabsf (__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). */
float exp_2t = __ieee754_expf (2 * t);
__imag__ res = __copysignf (1.0, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsf (__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_expf (2 * __imag__ x);
}
else
{
float sinhix, coshix;
if (fabsf (__imag__ x) > FLT_MIN)
{
sinhix = __ieee754_sinhf (__imag__ x);
coshix = __ieee754_coshf (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0f;
}
if (fabsf (sinhix) > fabsf (cosrx) * FLT_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / 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;
}
__complex__ float
__ctanhf (__complex__ float x)
{
__complex__ float res;
if (__builtin_expect (!isfinite (__real__ x) || !isfinite (__imag__ x), 0))
{
if (__isinf_nsf (__real__ x))
{
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = __copysignf (0.0, __imag__ x);
}
else if (__imag__ x == 0.0)
{
res = x;
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
if (__isinf_nsf (__imag__ x))
feraiseexcept (FE_INVALID);
}
}
else
{
float sinix, cosix;
float den;
const int t = (int) ((FLT_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 (__builtin_expect (fpclassify(__imag__ x) != FP_SUBNORMAL, 1))
{
__sincosf (__imag__ x, &sinix, &cosix);
}
else
{
sinix = __imag__ x;
cosix = 1.0f;
}
if (fabsf (__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 = __ieee754_expf (2 * t);
__real__ res = __copysignf (1.0, __real__ x);
__imag__ res = 4 * sinix * cosix;
__real__ x = fabsf (__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_expf (2 * __real__ x);
}
else
{
float sinhrx, coshrx;
if (fabsf (__real__ x) > FLT_MIN)
{
sinhrx = __ieee754_sinhf (__real__ x);
coshrx = __ieee754_coshf (__real__ x);
}
else
{
sinhrx = __real__ x;
coshrx = 1.0f;
}
if (fabsf (sinhrx) > fabsf (cosix) * FLT_EPSILON)
den = sinhrx * sinhrx + cosix * cosix;
else
den = cosix * cosix;
__real__ res = sinhrx * coshrx / den;
__imag__ res = sinix * cosix / den;
}
}
return res;
}
