initial check-in, version 0.5.0 v0.5.0

1 files changed, 121 insertions, 0 deletions

diff --git a/src/math/e_hypot.c b/src/math/e_hypot.c
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+
+/* @(#)e_hypot.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice 
+ * is preserved.
+ * ====================================================
+ */
+
+/* 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"
+
+double
+hypot(double x, double y)
+{
+        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 */
+               uint32_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 */
+                uint32_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) {
+            uint32_t high;
+            t1 = 1.0;
+            GET_HIGH_WORD(high,t1);
+            SET_HIGH_WORD(t1,high+(k<<20));
+            return t1*w;
+        } else return w;
+}