1
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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 /* hypot(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*y1+((x-y)*(x-y)+(t1*y2+t2*y))
30 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
31 * y1= y with lower 32 bits chopped, y2 = y-y1.
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 <float.h>
46
47 #include "math.h"
48 #include "math_private.h"
49
50 double
hypot(double x,double y)51 hypot(double x, double y)
52 {
53 double a,b,t1,t2,y1,y2,w;
54 int32_t j,k,ha,hb;
55
56 GET_HIGH_WORD(ha,x);
57 ha &= 0x7fffffff;
58 GET_HIGH_WORD(hb,y);
59 hb &= 0x7fffffff;
60 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
61 a = fabs(a);
62 b = fabs(b);
63 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
64 k=0;
65 if(ha > 0x5f300000) { /* a>2**500 */
66 if(ha >= 0x7ff00000) { /* Inf or NaN */
67 u_int32_t low;
68 /* Use original arg order iff result is NaN; quieten sNaNs. */
69 w = fabsl(x+0.0L)-fabs(y+0);
70 GET_LOW_WORD(low,a);
71 if(((ha&0xfffff)|low)==0) w = a;
72 GET_LOW_WORD(low,b);
73 if(((hb^0x7ff00000)|low)==0) w = b;
74 return w;
75 }
76 /* scale a and b by 2**-600 */
77 ha -= 0x25800000; hb -= 0x25800000; k += 600;
78 SET_HIGH_WORD(a,ha);
79 SET_HIGH_WORD(b,hb);
80 }
81 if(hb < 0x20b00000) { /* b < 2**-500 */
82 if(hb <= 0x000fffff) { /* subnormal b or 0 */
83 u_int32_t low;
84 GET_LOW_WORD(low,b);
85 if((hb|low)==0) return a;
86 t1=0;
87 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
88 b *= t1;
89 a *= t1;
90 k -= 1022;
91 } else { /* scale a and b by 2^600 */
92 ha += 0x25800000; /* a *= 2^600 */
93 hb += 0x25800000; /* b *= 2^600 */
94 k -= 600;
95 SET_HIGH_WORD(a,ha);
96 SET_HIGH_WORD(b,hb);
97 }
98 }
99 /* medium size a and b */
100 w = a-b;
101 if (w>b) {
102 t1 = 0;
103 SET_HIGH_WORD(t1,ha);
104 t2 = a-t1;
105 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
106 } else {
107 a = a+a;
108 y1 = 0;
109 SET_HIGH_WORD(y1,hb);
110 y2 = b - y1;
111 t1 = 0;
112 SET_HIGH_WORD(t1,ha+0x00100000);
113 t2 = a - t1;
114 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
115 }
116 if(k!=0) {
117 t1 = 0.0;
118 SET_HIGH_WORD(t1,(1023+k)<<20);
119 return t1*w;
120 } else return w;
121 }
122
123 #if LDBL_MANT_DIG == 53
124 __weak_reference(hypot, hypotl);
125 #endif
126