2 /* @(#)e_hypot.c 1.3 95/01/18 */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
14 #include <sys/cdefs.h>
18 * If (assume round-to-nearest) z=x*x+y*y
19 * has error less than sqrt(2)/2 ulp, than
20 * sqrt(z) has error less than 1 ulp (exercise).
22 * So, compute sqrt(x*x+y*y) with some care as
23 * follows to get the error below 1 ulp:
26 * (if possible, set rounding to round-to-nearest)
28 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
29 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
31 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
32 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
33 * y1= y with lower 32 bits chopped, y2 = y-y1.
35 * NOTE: scaling may be necessary if some argument is too
39 * hypot(x,y) is INF if x or y is +INF or -INF; else
40 * hypot(x,y) is NAN if x or y is NAN.
43 * hypot(x,y) returns sqrt(x^2+y^2) with error less
44 * than 1 ulps (units in the last place)
50 #include "math_private.h"
53 hypot(double x, double y)
55 double a,b,t1,t2,y1,y2,w;
62 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
65 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
67 if(ha > 0x5f300000) { /* a>2**500 */
68 if(ha >= 0x7ff00000) { /* Inf or NaN */
70 /* Use original arg order iff result is NaN; quieten sNaNs. */
71 w = fabsl(x+0.0L)-fabs(y+0);
73 if(((ha&0xfffff)|low)==0) w = a;
75 if(((hb^0x7ff00000)|low)==0) w = b;
78 /* scale a and b by 2**-600 */
79 ha -= 0x25800000; hb -= 0x25800000; k += 600;
83 if(hb < 0x20b00000) { /* b < 2**-500 */
84 if(hb <= 0x000fffff) { /* subnormal b or 0 */
87 if((hb|low)==0) return a;
89 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
93 } else { /* scale a and b by 2^600 */
94 ha += 0x25800000; /* a *= 2^600 */
95 hb += 0x25800000; /* b *= 2^600 */
101 /* medium size a and b */
105 SET_HIGH_WORD(t1,ha);
107 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
111 SET_HIGH_WORD(y1,hb);
114 SET_HIGH_WORD(t1,ha+0x00100000);
116 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
120 SET_HIGH_WORD(t1,(1023+k)<<20);
125 #if LDBL_MANT_DIG == 53
126 __weak_reference(hypot, hypotl);