__complex__ float
__clog10f (__complex__ float x)
{
__complex__ float 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_PI : 0.0;
__imag__ result = __copysignf (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsf (__real__ x);
}
else if (rcls != FP_NAN && icls != FP_NAN)
{
/* Neither real nor imaginary part is NaN. */
__real__ result = __ieee754_log10f (__ieee754_hypotf (__real__ x,
__imag__ x));
__imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanf ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALF;
else
__real__ result = __nanf ("");
}
return result;
}
float
atan2f(float y, float x) /* wrapper atan2f */
{
#ifdef _IEEE_LIBM
return __ieee754_atan2f(y,x);
#else
float z;
z = __ieee754_atan2f(y,x);
if(_LIB_VERSION == _IEEE_||isnanf(x)||isnanf(y)) return z;
if(x==(float)0.0&&y==(float)0.0) {
/* atan2f(+-0,+-0) */
return (float)__kernel_standard((double)y,(double)x,103);
} else
return z;
#endif
}
float
__atan2f (float y, float x)
{
if (__builtin_expect (x == 0.0f && y == 0.0f, 0) && _LIB_VERSION == _SVID_)
return __kernel_standard_f (y, x, 103); /* atan2(+-0,+-0) */
return __ieee754_atan2f (y, x);
}
__complex__ float
__clog10f (__complex__ float x)
{
__complex__ float 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_PI : 0.0;
__imag__ result = __copysignf (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsf (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
float d;
int scale = 0;
if (fabsf (__real__ x) > FLT_MAX / 2.0f
|| fabsf (__imag__ x) > FLT_MAX / 2.0f)
{
scale = -1;
__real__ x = __scalbnf (__real__ x, scale);
__imag__ x = __scalbnf (__imag__ x, scale);
}
else if (fabsf (__real__ x) < FLT_MIN
&& fabsf (__imag__ x) < FLT_MIN)
{
scale = FLT_MANT_DIG;
__real__ x = __scalbnf (__real__ x, scale);
__imag__ x = __scalbnf (__imag__ x, scale);
}
d = __ieee754_hypotf (__real__ x, __imag__ x);
__real__ result = __ieee754_log10f (d) - scale * M_LOG10_2f;
__imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanf ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALF;
else
__real__ result = __nanf ("");
}
return result;
}
float
__atan2f (float y, float x)
{
float z;
if (__builtin_expect (x == 0.0f && y == 0.0f, 0) && _LIB_VERSION == _SVID_)
return __kernel_standard_f (y, x, 103); /* atan2(+-0,+-0) */
z = __ieee754_atan2f (y, x);
if (__glibc_unlikely (z == 0.0f && y != 0.0f && isfinite (x)))
__set_errno (ERANGE);
return z;
}
__complex__ float
__catanhf (__complex__ float x)
{
__complex__ float 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 = __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 (__builtin_expect (rcls == FP_ZERO && icls == FP_ZERO, 0))
{
res = x;
}
else
{
float i2 = __imag__ x * __imag__ x;
float num = 1.0 + __real__ x;
num = i2 + num * num;
float den = 1.0 - __real__ x;
den = i2 + den * den;
__real__ res = 0.25 * (__ieee754_logf (num) - __ieee754_logf (den));
den = 1 - __real__ x * __real__ x - i2;
__imag__ res = 0.5 * __ieee754_atan2f (2.0 * __imag__ x, den);
}
return res;
}
__complex__ float
__cacoshf (__complex__ float x)
{
__complex__ float 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_VALF;
if (rcls == FP_NAN)
__imag__ res = __nanf ("");
else
__imag__ res = __copysignf ((rcls == FP_INFINITE
? (__real__ x < 0.0
? M_PI - M_PI_4 : M_PI_4)
: M_PI_2), __imag__ x);
}
else if (rcls == FP_INFINITE)
{
__real__ res = HUGE_VALF;
if (icls >= FP_ZERO)
__imag__ res = __copysignf (signbit (__real__ x) ? M_PI : 0.0,
__imag__ x);
else
__imag__ res = __nanf ("");
}
else
{
__real__ res = __nanf ("");
__imag__ res = __nanf ("");
}
}
else if (rcls == FP_ZERO && icls == FP_ZERO)
{
__real__ res = 0.0;
__imag__ res = __copysignf (M_PI_2, __imag__ x);
}
else
{
#if 1
__complex__ float y;
__real__ y = (__real__ x - __imag__ x) * (__real__ x + __imag__ x) - 1.0;
__imag__ y = 2.0 * __real__ x * __imag__ x;
y = __csqrtf (y);
if (__real__ x < 0.0)
y = -y;
__real__ y += __real__ x;
__imag__ y += __imag__ x;
res = __clogf (y);
#else
float re2 = __real__ x * __real__ x;
float im2 = __imag__ x * __imag__ x;
float sq = re2 - im2 - 1.0;
float ro = __ieee754_sqrtf (sq * sq + 4 * re2 * im2);
float a = __ieee754_sqrtf ((sq + ro) / 2.0);
float b = __ieee754_sqrtf ((-sq + ro) / 2.0);
__real__ res = 0.5 * __ieee754_logf (re2 + __real__ x * 2 * a
+ im2 + __imag__ x * 2 * b
+ ro);
__imag__ res = __ieee754_atan2f (__imag__ x + b, __real__ x + a);
#endif
/* We have to use the positive branch. */
if (__real__ res < 0.0)
res = -res;
}
return res;
}
__complex__ float
__clog10f (__complex__ float x)
{
__complex__ float 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_PI_LOG10Ef : 0.0;
__imag__ result = __copysignf (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsf (__real__ x);
}
else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
{
/* Neither real nor imaginary part is NaN. */
float absx = fabsf (__real__ x), absy = fabsf (__imag__ x);
int scale = 0;
if (absx < absy)
{
float t = absx;
absx = absy;
absy = t;
}
if (absx > FLT_MAX / 2.0f)
{
scale = -1;
absx = __scalbnf (absx, scale);
absy = (absy >= FLT_MIN * 2.0f ? __scalbnf (absy, scale) : 0.0f);
}
else if (absx < FLT_MIN && absy < FLT_MIN)
{
scale = FLT_MANT_DIG;
absx = __scalbnf (absx, scale);
absy = __scalbnf (absy, scale);
}
if (absx == 1.0f && scale == 0)
{
float absy2 = absy * absy;
if (absy2 <= FLT_MIN * 2.0f * (float) M_LN10)
{
float force_underflow = absy2 * absy2;
__real__ result = absy2 * ((float) M_LOG10E / 2.0f);
math_force_eval (force_underflow);
}
else
__real__ result = __log1pf (absy2) * ((float) M_LOG10E / 2.0f);
}
else if (absx > 1.0f && absx < 2.0f && absy < 1.0f && scale == 0)
{
float d2m1 = (absx - 1.0f) * (absx + 1.0f);
if (absy >= FLT_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f);
}
else if (absx < 1.0f
&& absx >= 0.75f
&& absy < FLT_EPSILON / 2.0f
&& scale == 0)
{
float d2m1 = (absx - 1.0f) * (absx + 1.0f);
__real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f);
}
else if (absx < 1.0f && (absx >= 0.75f || absy >= 0.5f) && scale == 0)
{
float d2m1 = __x2y2m1f (absx, absy);
__real__ result = __log1pf (d2m1) * ((float) M_LOG10E / 2.0f);
}
else
{
float d = __ieee754_hypotf (absx, absy);
__real__ result = __ieee754_log10f (d) - scale * M_LOG10_2f;
}
__imag__ result = M_LOG10E * __ieee754_atan2f (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanf ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALF;
else
__real__ result = __nanf ("");
}
return result;
}
__complex__ float
__clogf (__complex__ float x)
{
__complex__ float 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_PI : 0.0;
__imag__ result = __copysignf (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1.0 / fabsf (__real__ x);
}
else if (__builtin_expect (rcls != FP_NAN && icls != FP_NAN, 1))
{
/* Neither real nor imaginary part is NaN. */
float absx = fabsf (__real__ x), absy = fabsf (__imag__ x);
int scale = 0;
if (absx < absy)
{
float t = absx;
absx = absy;
absy = t;
}
if (absx > FLT_MAX / 2.0f)
{
scale = -1;
absx = __scalbnf (absx, scale);
absy = (absy >= FLT_MIN * 2.0f ? __scalbnf (absy, scale) : 0.0f);
}
else if (absx < FLT_MIN && absy < FLT_MIN)
{
scale = FLT_MANT_DIG;
absx = __scalbnf (absx, scale);
absy = __scalbnf (absy, scale);
}
if (absx == 1.0f && scale == 0)
{
float absy2 = absy * absy;
if (absy2 <= FLT_MIN * 2.0f)
{
#if __FLT_EVAL_METHOD__ == 0
__real__ result = absy2 / 2.0f - absy2 * absy2 / 4.0f;
#else
volatile float force_underflow = absy2 * absy2 / 4.0f;
__real__ result = absy2 / 2.0f - force_underflow;
#endif
}
else
__real__ result = __log1pf (absy2) / 2.0f;
}
else if (absx > 1.0f && absx < 2.0f && absy < 1.0f && scale == 0)
{
float d2m1 = (absx - 1.0f) * (absx + 1.0f);
if (absy >= FLT_EPSILON)
d2m1 += absy * absy;
__real__ result = __log1pf (d2m1) / 2.0f;
}
else if (absx < 1.0f
&& absx >= 0.75f
&& absy < FLT_EPSILON / 2.0f
&& scale == 0)
{
float d2m1 = (absx - 1.0f) * (absx + 1.0f);
__real__ result = __log1pf (d2m1) / 2.0f;
}
else if (absx < 1.0f && (absx >= 0.75f || absy >= 0.5f) && scale == 0)
{
float d2m1 = __x2y2m1f (absx, absy);
__real__ result = __log1pf (d2m1) / 2.0f;
}
else
{
float d = __ieee754_hypotf (absx, absy);
__real__ result = __ieee754_logf (d) - scale * (float) M_LN2;
}
__imag__ result = __ieee754_atan2f (__imag__ x, __real__ x);
}
else
{
__imag__ result = __nanf ("");
if (rcls == FP_INFINITE || icls == FP_INFINITE)
/* Real or imaginary part is infinite. */
__real__ result = HUGE_VALF;
else
__real__ result = __nanf ("");
}
return result;
}
__complex__ float
__catanf (__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 (rcls == FP_INFINITE)
{
__real__ res = __copysignf (M_PI_2, __real__ x);
__imag__ res = __copysignf (0.0, __imag__ x);
}
else if (icls == FP_INFINITE)
{
if (rcls >= FP_ZERO)
__real__ res = __copysignf (M_PI_2, __real__ x);
else
__real__ res = __nanf ("");
__imag__ res = __copysignf (0.0, __imag__ x);
}
else if (icls == FP_ZERO || icls == FP_INFINITE)
{
__real__ res = __nanf ("");
__imag__ res = __copysignf (0.0, __imag__ x);
}
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)
{
__real__ res = __copysignf ((float) M_PI_2, __real__ x);
if (fabsf (__real__ x) <= 1.0f)
__imag__ res = 1.0f / __imag__ x;
else if (fabsf (__imag__ x) <= 1.0f)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
float h = __ieee754_hypotf (__real__ x / 2.0f,
__imag__ x / 2.0f);
__imag__ res = __imag__ x / h / h / 4.0f;
}
}
else
{
float den, absx, absy;
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;
__real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den);
if (fabsf (__imag__ x) == 1.0f
&& fabsf (__real__ x) < FLT_EPSILON * FLT_EPSILON)
__imag__ res = (__copysignf (0.5f, __imag__ x)
* ((float) M_LN2
- __ieee754_logf (fabsf (__real__ x))));
else
{
float r2 = 0.0f, num, f;
if (fabsf (__real__ x) >= FLT_EPSILON * FLT_EPSILON)
r2 = __real__ x * __real__ x;
num = __imag__ x + 1.0f;
num = r2 + num * num;
den = __imag__ x - 1.0f;
den = r2 + den * den;
f = num / den;
if (f < 0.5f)
__imag__ res = 0.25f * __ieee754_logf (f);
else
{
num = 4.0f * __imag__ x;
__imag__ res = 0.25f * __log1pf (num / den);
}
}
}
if (fabsf (__real__ res) < FLT_MIN)
{
volatile float force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
if (fabsf (__imag__ res) < FLT_MIN)
{
volatile float force_underflow = __imag__ res * __imag__ res;
(void) force_underflow;
}
}
return res;
}
__complex__ float
__kernel_casinhf (__complex__ float x, int adj)
{
__complex__ float res;
float rx, ix;
__complex__ float y;
/* Avoid cancellation by reducing to the first quadrant. */
rx = fabsf (__real__ x);
ix = fabsf (__imag__ x);
if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
{
/* For large x in the first quadrant, x + csqrt (1 + x * x)
is sufficiently close to 2 * x to make no significant
difference to the result; avoid possible overflow from
the squaring and addition. */
__real__ y = rx;
__imag__ y = ix;
if (adj)
{
float t = __real__ y;
__real__ y = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
__real__ res += (float) M_LN2;
}
else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __ieee754_logf (rx + s);
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
{
float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
__real__ res = __ieee754_logf (ix + s);
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else if (ix > 1.0f && ix < 1.5f && rx < 0.5f)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float s = __ieee754_sqrtf (ix2m1);
__real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
else
__imag__ res = __ieee754_atan2f (s, rx);
}
else
{
float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f);
float dp = d + ix2m1;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else if (ix == 1.0f && rx < 0.5f)
{
if (rx < FLT_EPSILON / 8.0f)
{
__real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
__copysignf (1.0f, __imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
}
else
{
float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
__real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + s1,
__copysignf (1.0f + s2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
}
}
else if (ix < 1.0f && rx < 0.5f)
{
if (ix >= FLT_EPSILON)
{
if (rx < FLT_EPSILON * FLT_EPSILON)
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float s = __ieee754_sqrtf (onemix2);
__real__ res = __log1pf (2.0f * rx / s) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
else
{
float onemix2 = (1.0f + ix) * (1.0f - ix);
float rx2 = rx * rx;
float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
float d = __ieee754_sqrtf (onemix2 * onemix2 + f);
float dp = d + onemix2;
float dm = f / dp;
float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f);
float r2 = rx * ix / r1;
__real__ res
= __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (rx + r1,
__copysignf (ix + r2,
__imag__ x));
else
__imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
}
}
else
{
float s = __ieee754_hypotf (1.0f, rx);
__real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f;
if (adj)
__imag__ res = __ieee754_atan2f (s, __imag__ x);
else
__imag__ res = __ieee754_atan2f (ix, s);
}
if (__real__ res < FLT_MIN)
{
volatile float force_underflow = __real__ res * __real__ res;
(void) force_underflow;
}
}
else
{
__real__ y = (rx - ix) * (rx + ix) + 1.0f;
__imag__ y = 2.0f * rx * ix;
y = __csqrtf (y);
__real__ y += rx;
__imag__ y += ix;
if (adj)
{
float t = __real__ y;
__real__ y = __copysignf (__imag__ y, __imag__ x);
__imag__ y = t;
}
res = __clogf (y);
}
/* Give results the correct sign for the original argument. */
__real__ res = __copysignf (__real__ res, __real__ x);
__imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
return res;
}
