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Fix catan, catanh spurious overflows (bug 15409).

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This commit is contained in:
Joseph Myers
2013-04-27 14:56:34 +00:00
parent d5ba74f764
commit 5b4217d71f
11 changed files with 510 additions and 109 deletions
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63
math/s_catanl.c
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@ -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
__catanl (__complex__ long double x)
{
@ -61,27 +68,45 @@ __catanl (__complex__ long double x)
}
else
{
long double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
num = __imag__ x + 1.0L;
num = r2 + num * num;
den = __imag__ x - 1.0L;
den = r2 + den * den;
f = num / den;
if (f < 0.5L)
__imag__ res = 0.25L * __ieee754_logl (f);
if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON
|| fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON)
{
__real__ res = __copysignl (M_PI_2l, __real__ x);
if (fabsl (__real__ x) <= 1.0L)
__imag__ res = 1.0L / __imag__ x;
else if (fabsl (__imag__ x) <= 1.0L)
__imag__ res = __imag__ x / __real__ x / __real__ x;
else
{
long double h = __ieee754_hypotl (__real__ x / 2.0L,
__imag__ x / 2.0L);
__imag__ res = __imag__ x / h / h / 4.0L;
}
}
else
{
num = 4.0L * __imag__ x;
__imag__ res = 0.25L * __log1pl (num / den);
long double r2, num, den, f;
r2 = __real__ x * __real__ x;
den = 1 - r2 - __imag__ x * __imag__ x;
__real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den);
num = __imag__ x + 1.0L;
num = r2 + num * num;
den = __imag__ x - 1.0L;
den = r2 + den * den;
f = num / den;
if (f < 0.5L)
__imag__ res = 0.25L * __ieee754_logl (f);
else
{
num = 4.0L * __imag__ x;
__imag__ res = 0.25L * __log1pl (num / den);
}
}
if (fabsl (__real__ res) < LDBL_MIN)