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---
e_hypot.c (3306B)
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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 #ifndef lint
14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_hypot.c,v 1.8 2002/05/28 18:15:03 alfred Exp $";
15 #endif
16
17 /* __ieee754_hypot(x,y)
18 *
19 * Method :
20 * If (assume round-to-nearest) z=x*x+y*y
21 * has error less than sqrt(2)/2 ulp, than
22 * sqrt(z) has error less than 1 ulp (exercise).
23 *
24 * So, compute sqrt(x*x+y*y) with some care as
25 * follows to get the error below 1 ulp:
26 *
27 * Assume x>y>0;
28 * (if possible, set rounding to round-to-nearest)
29 * 1. if x > 2y use
30 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
31 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
32 * 2. if x <= 2y use
33 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
34 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
35 * y1= y with lower 32 bits chopped, y2 = y-y1.
36 *
37 * NOTE: scaling may be necessary if some argument is too
38 * large or too tiny
39 *
40 * Special cases:
41 * hypot(x,y) is INF if x or y is +INF or -INF; else
42 * hypot(x,y) is NAN if x or y is NAN.
43 *
44 * Accuracy:
45 * hypot(x,y) returns sqrt(x^2+y^2) with error less
46 * than 1 ulps (units in the last place)
47 */
48
49 #include "math.h"
50 #include "math_private.h"
51
52 double
53 __ieee754_hypot(double x, double y)
54 {
55 double a=x,b=y,t1,t2,y1,y2,w;
56 int32_t j,k,ha,hb;
57
58 GET_HIGH_WORD(ha,x);
59 ha &= 0x7fffffff;
60 GET_HIGH_WORD(hb,y);
61 hb &= 0x7fffffff;
62 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
63 SET_HIGH_WORD(a,ha); /* a <- |a| */
64 SET_HIGH_WORD(b,hb); /* b <- |b| */
65 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
66 k=0;
67 if(ha > 0x5f300000) { /* a>2**500 */
68 if(ha >= 0x7ff00000) { /* Inf or NaN */
69 u_int32_t low;
70 w = a+b; /* for sNaN */
71 GET_LOW_WORD(low,a);
72 if(((ha&0xfffff)|low)==0) w = a;
73 GET_LOW_WORD(low,b);
74 if(((hb^0x7ff00000)|low)==0) w = b;
75 return w;
76 }
77 /* scale a and b by 2**-600 */
78 ha -= 0x25800000; hb -= 0x25800000; k += 600;
79 SET_HIGH_WORD(a,ha);
80 SET_HIGH_WORD(b,hb);
81 }
82 if(hb < 0x20b00000) { /* b < 2**-500 */
83 if(hb <= 0x000fffff) { /* subnormal b or 0 */
84 u_int32_t low;
85 GET_LOW_WORD(low,b);
86 if((hb|low)==0) return a;
87 t1=0;
88 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
89 b *= t1;
90 a *= t1;
91 k -= 1022;
92 } else { /* scale a and b by 2^600 */
93 ha += 0x25800000; /* a *= 2^600 */
94 hb += 0x25800000; /* b *= 2^600 */
95 k -= 600;
96 SET_HIGH_WORD(a,ha);
97 SET_HIGH_WORD(b,hb);
98 }
99 }
100 /* medium size a and b */
101 w = a-b;
102 if (w>b) {
103 t1 = 0;
104 SET_HIGH_WORD(t1,ha);
105 t2 = a-t1;
106 w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
107 } else {
108 a = a+a;
109 y1 = 0;
110 SET_HIGH_WORD(y1,hb);
111 y2 = b - y1;
112 t1 = 0;
113 SET_HIGH_WORD(t1,ha+0x00100000);
114 t2 = a - t1;
115 w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
116 }
117 if(k!=0) {
118 u_int32_t high;
119 t1 = 1.0;
120 GET_HIGH_WORD(high,t1);
121 SET_HIGH_WORD(t1,high+(k<<20));
122 return t1*w;
123 } else return w;
124 }