diff options
Diffstat (limited to 'math/s_catanhl.c')
| -rw-r--r-- | math/s_catanhl.c | 55 |
1 files changed, 40 insertions, 15 deletions
diff --git a/math/s_catanhl.c b/math/s_catanhl.c index 30fd27703b..64c30b5573 100644 --- a/math/s_catanhl.c +++ b/math/s_catanhl.c @@ -22,6 +22,13 @@ #include <math_private.h> #include <float.h> +/* To avoid spurious overflows, use this definition to treat IBM long + double as approximating an IEEE-style format. */ +#if LDBL_MANT_DIG == 106 +# undef LDBL_EPSILON +# define LDBL_EPSILON 0x1p-106L +#endif + __complex__ long double __catanhl (__complex__ long double x) { @@ -56,26 +63,44 @@ __catanhl (__complex__ long double x) } else { - long double i2 = __imag__ x * __imag__ x; + if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON + || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON) + { + __imag__ res = __copysignl (M_PI_2l, __imag__ x); + if (fabsl (__imag__ x) <= 1.0L) + __real__ res = 1.0L / __real__ x; + else if (fabsl (__real__ x) <= 1.0L) + __real__ res = __real__ x / __imag__ x / __imag__ x; + else + { + long double h = __ieee754_hypotl (__real__ x / 2.0L, + __imag__ x / 2.0L); + __real__ res = __real__ x / h / h / 4.0L; + } + } + else + { + long double i2 = __imag__ x * __imag__ x; - long double num = 1.0L + __real__ x; - num = i2 + num * num; + long double num = 1.0L + __real__ x; + num = i2 + num * num; - long double den = 1.0L - __real__ x; - den = i2 + den * den; + long double den = 1.0L - __real__ x; + den = i2 + den * den; - long double f = num / den; - if (f < 0.5L) - __real__ res = 0.25L * __ieee754_logl (f); - else - { - num = 4.0L * __real__ x; - __real__ res = 0.25L * __log1pl (num / den); - } + long double f = num / den; + if (f < 0.5L) + __real__ res = 0.25L * __ieee754_logl (f); + else + { + num = 4.0L * __real__ x; + __real__ res = 0.25L * __log1pl (num / den); + } - den = 1 - __real__ x * __real__ x - i2; + den = 1 - __real__ x * __real__ x - i2; - __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den); + __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den); + } if (fabsl (__real__ res) < LDBL_MIN) { |