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1 :
2 : /* @(#)e_hypot.c 1.3 95/01/18 */
3 : /*
4 : * ====================================================
5 : * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 : *
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
10 : * is preserved.
11 : * ====================================================
12 : */
13 :
14 : //#include <sys/cdefs.h>
15 : //__FBSDID("$FreeBSD$");
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 <float.h>
50 :
51 : #include "math_private.h"
52 :
53 : double
54 0 : __ieee754_hypot(double x, double y)
55 : {
56 : double a,b,t1,t2,y1,y2,w;
57 : int32_t j,k,ha,hb;
58 :
59 0 : GET_HIGH_WORD(ha,x);
60 0 : ha &= 0x7fffffff;
61 0 : GET_HIGH_WORD(hb,y);
62 0 : hb &= 0x7fffffff;
63 0 : if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
64 0 : a = fabs(a);
65 0 : b = fabs(b);
66 0 : if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
67 0 : k=0;
68 0 : if(ha > 0x5f300000) { /* a>2**500 */
69 0 : if(ha >= 0x7ff00000) { /* Inf or NaN */
70 : u_int32_t low;
71 : /* Use original arg order iff result is NaN; quieten sNaNs. */
72 0 : w = fabs(x+0.0)-fabs(y+0.0);
73 0 : GET_LOW_WORD(low,a);
74 0 : if(((ha&0xfffff)|low)==0) w = a;
75 0 : GET_LOW_WORD(low,b);
76 0 : if(((hb^0x7ff00000)|low)==0) w = b;
77 0 : return w;
78 : }
79 : /* scale a and b by 2**-600 */
80 0 : ha -= 0x25800000; hb -= 0x25800000; k += 600;
81 0 : SET_HIGH_WORD(a,ha);
82 0 : SET_HIGH_WORD(b,hb);
83 : }
84 0 : if(hb < 0x20b00000) { /* b < 2**-500 */
85 0 : if(hb <= 0x000fffff) { /* subnormal b or 0 */
86 : u_int32_t low;
87 0 : GET_LOW_WORD(low,b);
88 0 : if((hb|low)==0) return a;
89 0 : t1=0;
90 0 : SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
91 0 : b *= t1;
92 0 : a *= t1;
93 0 : k -= 1022;
94 : } else { /* scale a and b by 2^600 */
95 0 : ha += 0x25800000; /* a *= 2^600 */
96 0 : hb += 0x25800000; /* b *= 2^600 */
97 0 : k -= 600;
98 0 : SET_HIGH_WORD(a,ha);
99 0 : SET_HIGH_WORD(b,hb);
100 : }
101 : }
102 : /* medium size a and b */
103 0 : w = a-b;
104 0 : if (w>b) {
105 0 : t1 = 0;
106 0 : SET_HIGH_WORD(t1,ha);
107 0 : t2 = a-t1;
108 0 : w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
109 : } else {
110 0 : a = a+a;
111 0 : y1 = 0;
112 0 : SET_HIGH_WORD(y1,hb);
113 0 : y2 = b - y1;
114 0 : t1 = 0;
115 0 : SET_HIGH_WORD(t1,ha+0x00100000);
116 0 : t2 = a - t1;
117 0 : w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
118 : }
119 0 : if(k!=0) {
120 : u_int32_t high;
121 0 : t1 = 1.0;
122 0 : GET_HIGH_WORD(high,t1);
123 0 : SET_HIGH_WORD(t1,high+(k<<20));
124 0 : return t1*w;
125 0 : } else return w;
126 : }
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