--- ray/src/common/tcos.c	2011/02/11 00:35:14	3.5
+++ ray/src/common/tcos.c	2013/07/12 05:16:02	3.10
@@ -1,5 +1,5 @@
 #ifndef lint
-static const char	RCSid[] = "$Id: tcos.c,v 3.5 2011/02/11 00:35:14 greg Exp $";
+static const char	RCSid[] = "$Id: tcos.c,v 3.10 2013/07/12 05:16:02 greg Exp $";
 #endif
 /*
  * Table-based cosine approximation.
@@ -18,11 +18,12 @@ static const char	RCSid[] = "$Id: tcos.c,v 3.5 2011/02
 
 #include "rtmath.h"
 
+#ifndef __FAST_MATH__
+
 #ifndef NCOSENTRY
-#define NCOSENTRY	256
+#define NCOSENTRY	1024
 #endif
 
-
 double
 tcos(double x)				/* approximate cosine */
 {
@@ -49,4 +50,25 @@ tcos(double x)				/* approximate cosine */
 		return(costab[(4*NCOSENTRY)-i]);
 	}
 	return(0.);		/* should never be reached */
+}
+
+#endif
+
+/* Fast arctangent approximation due to Rajan et al. 2006 */
+double
+atan2a(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. - atan2a(x, y);
+
+	val = PI/4.*ratio - ratio*(aratio - 1.)*(0.2447 + 0.0663*aratio);
+
+	return val + PI*(x < 0);
 }