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 /* hypot(x,y)
15 *
16 * Method :
17 * If (assume round-to-nearest) z=x*x+y*y
18 * has error less than sqrt(2)/2 ulp, than
19 * sqrt(z) has error less than 1 ulp (exercise).
20 *
21 * So, compute sqrt(x*x+y*y) with some care as
22 * follows to get the error below 1 ulp:
23 *
24 * Assume x>y>0;
25 * (if possible, set rounding to round-to-nearest)
26 * 1. if x > 2y use
27 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
28 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
29 * 2. if x <= 2y use
30 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
31 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
32 * y1= y with lower 32 bits chopped, y2 = y-y1.
33 *
34 * NOTE: scaling may be necessary if some argument is too
35 * large or too tiny
36 *
37 * Special cases:
38 * hypot(x,y) is INF if x or y is +INF or -INF; else
39 * hypot(x,y) is NAN if x or y is NAN.
40 *
41 * Accuracy:
42 * hypot(x,y) returns sqrt(x^2+y^2) with error less
43 * than 1 ulps (units in the last place)
44 */
45
46 #include <float.h>
47
48 #include "math.h"
49 #include "math_private.h"
50
51 double
hypot(double x,double y)52 hypot(double x, double y)
53 {
54 double a,b,t1,t2,y1,y2,w;
55 int32_t j,k,ha,hb;
56
57 GET_HIGH_WORD(ha,x);
58 ha &= 0x7fffffff;
59 GET_HIGH_WORD(hb,y);
60 hb &= 0x7fffffff;
61 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
62 a = fabs(a);
63 b = fabs(b);
64 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
65 k=0;
66 if(ha > 0x5f300000) { /* a>2**500 */
67 if(ha >= 0x7ff00000) { /* Inf or NaN */
68 u_int32_t low;
69 /* Use original arg order iff result is NaN; quieten sNaNs. */
70 w = fabsl(x+0.0L)-fabs(y+0);
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 = 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 = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
116 }
117 if(k!=0) {
118 t1 = 0.0;
119 SET_HIGH_WORD(t1,(1023+k)<<20);
120 return t1*w;
121 } else return w;
122 }
123
124 #if LDBL_MANT_DIG == 53
125 __weak_reference(hypot, hypotl);
126 #endif
127