J.T. Conklin's latest version of the Sun math library.

-- Begin comments from J.T. Conklin:
The most significant improvement is the addition of "float" versions
of the math functions that take float arguments, return floats, and do
all operations in floating point.  This doesn't help (performance)
much on the i386, but they are still nice to have.

The float versions were orginally done by Cygnus' Ian Taylor when
fdlibm was integrated into the libm we support for embedded systems.
I gave Ian a copy of my libm as a starting point since I had already
fixed a lot of bugs & problems in Sun's original code.  After he was
done, I cleaned it up a bit and integrated the changes back into my
libm.
-- End comments

Reviewed by:	jkh
Submitted by:	jtc

1 files changed, 128 insertions, 0 deletions

diff --git a/lib/msun/src/e_hypot.c b/lib/msun/src/e_hypot.c
new file mode 100644
index 0000000..045f8a3
--- /dev/null
+++ b/lib/msun/src/e_hypot.c
@@ -0,0 +1,128 @@
+/* @(#)e_hypot.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+#ifndef lint
+static char rcsid[] = "$Id: e_hypot.c,v 1.6 1994/08/18 23:05:24 jtc Exp $";
+#endif
+
+/* __ieee754_hypot(x,y)
+ *
+ * Method :                  
+ *	If (assume round-to-nearest) z=x*x+y*y 
+ *	has error less than sqrt(2)/2 ulp, than 
+ *	sqrt(z) has error less than 1 ulp (exercise).
+ *
+ *	So, compute sqrt(x*x+y*y) with some care as 
+ *	follows to get the error below 1 ulp:
+ *
+ *	Assume x>y>0;
+ *	(if possible, set rounding to round-to-nearest)
+ *	1. if x > 2y  use
+ *		x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *	where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ *	2. if x <= 2y use
+ *		t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *	where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 
+ *	y1= y with lower 32 bits chopped, y2 = y-y1.
+ *		
+ *	NOTE: scaling may be necessary if some argument is too 
+ *	      large or too tiny
+ *
+ * Special cases:
+ *	hypot(x,y) is INF if x or y is +INF or -INF; else
+ *	hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ * 	hypot(x,y) returns sqrt(x^2+y^2) with error less 
+ * 	than 1 ulps (units in the last place) 
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+	double __ieee754_hypot(double x, double y)
+#else
+	double __ieee754_hypot(x,y)
+	double x, y;
+#endif
+{
+	double a=x,b=y,t1,t2,y1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_HIGH_WORD(ha,x);
+	ha &= 0x7fffffff;
+	GET_HIGH_WORD(hb,y);
+	hb &= 0x7fffffff;
+	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
+	SET_HIGH_WORD(a,ha);	/* a <- |a| */
+	SET_HIGH_WORD(b,hb);	/* b <- |b| */
+	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
+	k=0;
+	if(ha > 0x5f300000) {	/* a>2**500 */
+	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
+	       u_int32_t low;
+	       w = a+b;			/* for sNaN */
+	       GET_LOW_WORD(low,a);
+	       if(((ha&0xfffff)|low)==0) w = a;
+	       GET_LOW_WORD(low,b);
+	       if(((hb^0x7ff00000)|low)==0) w = b;
+	       return w;
+	   }
+	   /* scale a and b by 2**-600 */
+	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
+	   SET_HIGH_WORD(a,ha);
+	   SET_HIGH_WORD(b,hb);
+	}
+	if(hb < 0x20b00000) {	/* b < 2**-500 */
+	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */	
+	        u_int32_t low;
+		GET_LOW_WORD(low,b);
+		if((hb|low)==0) return a;
+		t1=0;
+		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
+		b *= t1;
+		a *= t1;
+		k -= 1022;
+	    } else {		/* scale a and b by 2^600 */
+	        ha += 0x25800000; 	/* a *= 2^600 */
+		hb += 0x25800000;	/* b *= 2^600 */
+		k -= 600;
+		SET_HIGH_WORD(a,ha);
+		SET_HIGH_WORD(b,hb);
+	    }
+	}
+    /* medium size a and b */
+	w = a-b;
+	if (w>b) {
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha);
+	    t2 = a-t1;
+	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+	    a  = a+a;
+	    y1 = 0;
+	    SET_HIGH_WORD(y1,hb);
+	    y2 = b - y1;
+	    t1 = 0;
+	    SET_HIGH_WORD(t1,ha+0x00100000);
+	    t2 = a - t1;
+	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if(k!=0) {
+	    u_int32_t high;
+	    t1 = 1.0;
+	    GET_HIGH_WORD(high,t1);
+	    SET_HIGH_WORD(t1,high+(k<<20));
+	    return t1*w;
+	} else return w;
+}