1 /* @(#)e_hypot.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos Exp $");
16 #endif
17
18 /* __ieee754_hypot(x,y)
19 *
20 * Method :
21 * If (assume round-to-nearest) z=x*x+y*y
22 * has error less than sqrt(2)/2 ulp, than
23 * sqrt(z) has error less than 1 ulp (exercise).
24 *
25 * So, compute sqrt(x*x+y*y) with some care as
26 * follows to get the error below 1 ulp:
27 *
28 * Assume x>y>0;
29 * (if possible, set rounding to round-to-nearest)
30 * 1. if x > 2y use
31 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
32 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
33 * 2. if x <= 2y use
34 * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
35 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
36 * yy1= y with lower 32 bits chopped, y2 = y-yy1.
37 *
38 * NOTE: scaling may be necessary if some argument is too
39 * large or too tiny
40 *
41 * Special cases:
42 * hypot(x,y) is INF if x or y is +INF or -INF; else
43 * hypot(x,y) is NAN if x or y is NAN.
44 *
45 * Accuracy:
46 * hypot(x,y) returns sqrt(x^2+y^2) with error less
47 * than 1 ulps (units in the last place)
48 */
49
50 #include "math.h"
51 #include "math_private.h"
52
53 double
__ieee754_hypot(double x,double y)54 __ieee754_hypot(double x, double y)
55 {
56 double a=x,b=y,t1,t2,yy1,y2,w;
57 int32_t j,k,ha,hb;
58
59 GET_HIGH_WORD(ha,x);
60 ha &= 0x7fffffff;
61 GET_HIGH_WORD(hb,y);
62 hb &= 0x7fffffff;
63 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
64 SET_HIGH_WORD(a,ha); /* a <- |a| */
65 SET_HIGH_WORD(b,hb); /* b <- |b| */
66 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
67 k=0;
68 if(ha > 0x5f300000) { /* a>2**500 */
69 if(ha >= 0x7ff00000) { /* Inf or NaN */
70 u_int32_t low;
71 w = a+b; /* for sNaN */
72 GET_LOW_WORD(low,a);
73 if(((ha&0xfffff)|low)==0) w = a;
74 GET_LOW_WORD(low,b);
75 if(((hb^0x7ff00000)|low)==0) w = b;
76 return w;
77 }
78 /* scale a and b by 2**-600 */
79 ha -= 0x25800000; hb -= 0x25800000; k += 600;
80 SET_HIGH_WORD(a,ha);
81 SET_HIGH_WORD(b,hb);
82 }
83 if(hb < 0x20b00000) { /* b < 2**-500 */
84 if(hb <= 0x000fffff) { /* subnormal b or 0 */
85 u_int32_t low;
86 GET_LOW_WORD(low,b);
87 if((hb|low)==0) return a;
88 t1=0;
89 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
90 b *= t1;
91 a *= t1;
92 k -= 1022;
93 } else { /* scale a and b by 2^600 */
94 ha += 0x25800000; /* a *= 2^600 */
95 hb += 0x25800000; /* b *= 2^600 */
96 k -= 600;
97 SET_HIGH_WORD(a,ha);
98 SET_HIGH_WORD(b,hb);
99 }
100 }
101 /* medium size a and b */
102 w = a-b;
103 if (w>b) {
104 t1 = 0;
105 SET_HIGH_WORD(t1,ha);
106 t2 = a-t1;
107 w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
108 } else {
109 a = a+a;
110 yy1 = 0;
111 SET_HIGH_WORD(yy1,hb);
112 y2 = b - yy1;
113 t1 = 0;
114 SET_HIGH_WORD(t1,ha+0x00100000);
115 t2 = a - t1;
116 w = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
117 }
118 if(k!=0) {
119 u_int32_t high;
120 t1 = 1.0;
121 GET_HIGH_WORD(high,t1);
122 SET_HIGH_WORD(t1,high+(k<<20));
123 return t1*w;
124 } else return w;
125 }
126