diff options
Diffstat (limited to 'math/s_catanh.c')
| -rw-r--r-- | math/s_catanh.c | 80 |
1 files changed, 71 insertions, 9 deletions
diff --git a/math/s_catanh.c b/math/s_catanh.c index 5371f44b67..54be9f9e41 100644 --- a/math/s_catanh.c +++ b/math/s_catanh.c @@ -20,7 +20,7 @@ #include <complex.h> #include <math.h> #include <math_private.h> - +#include <float.h> __complex__ double __catanh (__complex__ double x) @@ -56,19 +56,81 @@ __catanh (__complex__ double x) } else { - double i2 = __imag__ x * __imag__ x; + 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 num = 1.0 + __real__ x; - num = i2 + num * num; + double den = 1.0 - __real__ x; + den = i2 + den * den; - 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); + } + } - __real__ res = 0.25 * (__ieee754_log (num) - __ieee754_log (den)); + double absx, absy, den; - den = 1 - __real__ x * __real__ x - i2; + absx = fabs (__real__ x); + absy = fabs (__imag__ x); + if (absx < absy) + { + double t = absx; + absx = absy; + absy = t; + } - __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den); + if (absy < DBL_EPSILON / 2.0) + den = (1.0 - absx) * (1.0 + absx); + 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); + } + + if (fabs (__real__ res) < DBL_MIN) + { + volatile double force_underflow = __real__ res * __real__ res; + (void) force_underflow; + } + if (fabs (__imag__ res) < DBL_MIN) + { + volatile double force_underflow = __imag__ res * __imag__ res; + (void) force_underflow; + } } return res; |