--- ray/src/common/tcos.c	2013/01/17 22:48:21	3.6
+++ ray/src/common/tcos.c	2013/02/07 20:19:52	3.7
@@ -1,5 +1,5 @@
 #ifndef lint
-static const char	RCSid[] = "$Id: tcos.c,v 3.6 2013/01/17 22:48:21 greg Exp $";
+static const char	RCSid[] = "$Id: tcos.c,v 3.7 2013/02/07 20:19:52 greg Exp $";
 #endif
 /*
  * Table-based cosine approximation.
@@ -49,4 +49,24 @@ tcos(double x)				/* approximate cosine */
 		return(costab[(4*NCOSENTRY)-i]);
 	}
 	return(0.);		/* should never be reached */
+}
+
+
+/* Fast arctangent approximation due to Rajan et al. 2006 */
+double
+aatan2(double y, double x)
+{
+	double	ratio, aratio, val;
+
+	if (x == 0)
+		return (y > 0) ? PI/2. : 3./2.*PI;
+
+	aratio = (ratio = y/x) >= 0 ? ratio : -ratio;
+
+	if (aratio > 1.01)
+		return PI/2. - aatan2(x, y);
+
+	val = PI/4.*ratio - ratio*(aratio - 1.)*(0.2447 + 0.0663*aratio);
+
+	return val + PI*(x < 0);
 }