FLOAT
M_DECL_FUNC (__fminmag) (FLOAT x, FLOAT y)
{
FLOAT ax = M_FABS (x);
FLOAT ay = M_FABS (y);
if (isless (ax, ay))
return x;
else if (isgreater (ax, ay))
return y;
else if (ax == ay)
return x < y ? x : y;
else if (issignaling (x) || issignaling (y))
return x + y;
else
return isnan (y) ? x : y;
}
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 (__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;
}
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 (__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 (__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;
}
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;
}