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 sqrt(2)/2 ulp, than
18 * sqrt(z) has error less than 1 ulp (exercise).
19 *
20 * So, compute sqrt(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 32 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 32 bits cleared, t2 = 2x-t1,
31 * yy1= y with lower 32 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 * hypot(x,y) is INF if x or y is +INF or -INF; else
38 * hypot(x,y) is NAN if x or y is NAN.
39 *
40 * Accuracy:
41 * hypot(x,y) returns sqrt(x^2+y^2) with error less
42 * than 1 ulps (units in the last place)
43 */
44
45 #include <math.h>
46
47 #include "math_private.h"
48
49 long double
hypotl(long double x,long double y)50 hypotl(long double x, long double y)
51 {
52 long double a,b,t1,t2,yy1,y2,w;
53 u_int32_t j,k,ea,eb;
54
55 GET_LDOUBLE_EXP(ea,x);
56 ea &= 0x7fff;
57 GET_LDOUBLE_EXP(eb,y);
58 eb &= 0x7fff;
59 if(eb > ea) {a=y;b=x;j=ea; ea=eb;eb=j;} else {a=x;b=y;}
60 SET_LDOUBLE_EXP(a,ea); /* a <- |a| */
61 SET_LDOUBLE_EXP(b,eb); /* b <- |b| */
62 if((ea-eb)>0x46) {return a+b;} /* x/y > 2**70 */
63 k=0;
64 if(ea > 0x5f3f) { /* a>2**8000 */
65 if(ea == 0x7fff) { /* Inf or NaN */
66 u_int32_t es,high,low;
67 w = a+b; /* for sNaN */
68 GET_LDOUBLE_WORDS(es,high,low,a);
69 if(((high&0x7fffffff)|low)==0) w = a;
70 GET_LDOUBLE_WORDS(es,high,low,b);
71 if(((eb^0x7fff)|(high&0x7fffffff)|low)==0) w = b;
72 return w;
73 }
74 /* scale a and b by 2**-9600 */
75 ea -= 0x2580; eb -= 0x2580; k += 9600;
76 SET_LDOUBLE_EXP(a,ea);
77 SET_LDOUBLE_EXP(b,eb);
78 }
79 if(eb < 0x20bf) { /* b < 2**-8000 */
80 if(eb == 0) { /* subnormal b or 0 */
81 u_int32_t es,high,low;
82 GET_LDOUBLE_WORDS(es,high,low,b);
83 if((high|low)==0) return a;
84 SET_LDOUBLE_WORDS(t1, 0x7ffd, 0, 0); /* t1=2^16382 */
85 b *= t1;
86 a *= t1;
87 k -= 16382;
88 } else { /* scale a and b by 2^9600 */
89 ea += 0x2580; /* a *= 2^9600 */
90 eb += 0x2580; /* b *= 2^9600 */
91 k -= 9600;
92 SET_LDOUBLE_EXP(a,ea);
93 SET_LDOUBLE_EXP(b,eb);
94 }
95 }
96 /* medium size a and b */
97 w = a-b;
98 if (w>b) {
99 u_int32_t high;
100 GET_LDOUBLE_MSW(high,a);
101 SET_LDOUBLE_WORDS(t1,ea,high,0);
102 t2 = a-t1;
103 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
104 } else {
105 u_int32_t high;
106 GET_LDOUBLE_MSW(high,b);
107 a = a+a;
108 SET_LDOUBLE_WORDS(yy1,eb,high,0);
109 y2 = b - yy1;
110 GET_LDOUBLE_MSW(high,a);
111 SET_LDOUBLE_WORDS(t1,ea+1,high,0);
112 t2 = a - t1;
113 w = sqrtl(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
114 }
115 if(k!=0) {
116 u_int32_t es;
117 t1 = 1.0;
118 GET_LDOUBLE_EXP(es,t1);
119 SET_LDOUBLE_EXP(t1,es+k);
120 return t1*w;
121 } else return w;
122 }
123