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 /* hypotl(x,y)
14 *
15 * Method :
16 * If (assume round-to-nearest) z=x*x+y*y
17 * has error less than sqrtl(2)/2 ulp, than
18 * sqrtl(z) has error less than 1 ulp (exercise).
19 *
20 * So, compute sqrtl(x*x+y*y) with some care as
21 * follows to get the error below 1 ulp:
22 *
23 * Assume x>y>0;
24 * (if possible, set rounding to round-to-nearest)
25 * 1. if x > 2y use
26 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
27 * where x1 = x with lower 64 bits cleared, x2 = x-x1; else
28 * 2. if x <= 2y use
29 * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
30 * where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
31 * yy1= y with lower 64 bits chopped, y2 = y-yy1.
32 *
33 * NOTE: scaling may be necessary if some argument is too
34 * large or too tiny
35 *
36 * Special cases:
37 * hypotl(x,y) is INF if x or y is +INF or -INF; else
38 * hypotl(x,y) is NAN if x or y is NAN.
39 *
40 * Accuracy:
41 * hypotl(x,y) returns sqrtl(x^2+y^2) with error less
42 * than 1 ulps (units in the last place)
43 */
44
45
46
47 long double
hypotl(long double x,long double y)48 hypotl(long double x, long double y)
49 {
50 long double a,b,t1,t2,yy1,y2,w;
51 int64_t j,k,ha,hb;
52
53 GET_LDOUBLE_MSW64(ha,x);
54 ha &= 0x7fffffffffffffffLL;
55 GET_LDOUBLE_MSW64(hb,y);
56 hb &= 0x7fffffffffffffffLL;
57 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
58 SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */
59 SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */
60 if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
61 k=0;
62 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
63 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
64 u_int64_t low;
65 w = a+b; /* for sNaN */
66 GET_LDOUBLE_LSW64(low,a);
67 if(((ha&0xffffffffffffLL)|low)==0 && !issignalingl(b))
68 w = a;
69 GET_LDOUBLE_LSW64(low,b);
70 if(((hb^0x7fff000000000000LL)|low)==0 && !issignalingl(a))
71 w = b;
72 return w;
73 }
74 /* scale a and b by 2**-9600 */
75 ha -= 0x2580000000000000LL;
76 hb -= 0x2580000000000000LL; k += 9600;
77 SET_LDOUBLE_MSW64(a,ha);
78 SET_LDOUBLE_MSW64(b,hb);
79 }
80 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
81 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
82 u_int64_t low;
83 GET_LDOUBLE_LSW64(low,b);
84 if((hb|low)==0) return a;
85 t1=0;
86 SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
87 b *= t1;
88 a *= t1;
89 k -= 16382;
90 } else { /* scale a and b by 2^9600 */
91 ha += 0x2580000000000000LL; /* a *= 2^9600 */
92 hb += 0x2580000000000000LL; /* b *= 2^9600 */
93 k -= 9600;
94 SET_LDOUBLE_MSW64(a,ha);
95 SET_LDOUBLE_MSW64(b,hb);
96 }
97 }
98 /* medium size a and b */
99 w = a-b;
100 if (w>b) {
101 t1 = 0;
102 SET_LDOUBLE_MSW64(t1,ha);
103 t2 = a-t1;
104 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
105 } else {
106 a = a+a;
107 yy1 = 0;
108 SET_LDOUBLE_MSW64(yy1,hb);
109 y2 = b - yy1;
110 t1 = 0;
111 SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
112 t2 = a - t1;
113 w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
114 }
115 if(k!=0) {
116 u_int64_t high;
117 t1 = 1.0L;
118 GET_LDOUBLE_MSW64(high,t1);
119 SET_LDOUBLE_MSW64(t1,high+(k<<48));
120 return check_oflowl(t1*w);
121 } else return w;
122 }
123
