Fix catan, catanh spurious underflows (bug 15423).

1 files changed, 26 insertions, 16 deletions

diff --git a/math/s_catan.c b/math/s_catan.c
index 3a041f2..4da0a0d 100644
--- a/math/s_catan.c
+++ b/math/s_catan.c
@@ -77,7 +77,7 @@ __catan (__complex__ double x)
 	}
       else
 	{
-	  double r2, num, den, f, absx, absy;
+	  double den, absx, absy;
 
 	  absx = fabs (__real__ x);
 	  absy = fabs (__imag__ x);
@@ -88,10 +88,10 @@ __catan (__complex__ double x)
 	      absy = t;
 	    }
 
-	  if (absx >= 1.0)
-	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
-	  else if (absx >= 0.75 && absy < DBL_EPSILON / 2.0)
+	  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
@@ -99,21 +99,31 @@ __catan (__complex__ double x)
 
 	  __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
 
-	  r2 = __real__ x * __real__ x;
+	  if (fabs (__imag__ x) == 1.0
+	      && fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
+	    __imag__ res = (__copysign (0.5, __imag__ x)
+			    * (M_LN2 - __ieee754_log (fabs (__real__ x))));
+	  else
+	    {
+	      double r2 = 0.0, num, f;
 
-	  num = __imag__ x + 1.0;
-	  num = r2 + num * num;
+	      if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
+		r2 = __real__ x * __real__ x;
 
-	  den = __imag__ x - 1.0;
-	  den = r2 + den * den;
+	      num = __imag__ x + 1.0;
+	      num = r2 + num * num;
 
-	  f = num / den;
-	  if (f < 0.5)
-	    __imag__ res = 0.25 * __ieee754_log (f);
-	  else
-	    {
-	      num = 4.0 * __imag__ x;
-	      __imag__ res = 0.25 * __log1p (num / den);
+	      den = __imag__ x - 1.0;
+	      den = r2 + den * den;
+
+	      f = num / den;
+	      if (f < 0.5)
+		__imag__ res = 0.25 * __ieee754_log (f);
+	      else
+		{
+		  num = 4.0 * __imag__ x;
+		  __imag__ res = 0.25 * __log1p (num / den);
+		}
 	    }
 	}