FreeBSD and NetBSD both use derivates of Sun's math library. On FreeBSD,
[dragonfly.git] / lib / libm / src / e_hypot.c
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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 * $NetBSD: e_hypot.c,v 1.12 2002/05/26 22:01:50 wiz Exp $
13 * $DragonFly: src/lib/libm/src/e_hypot.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
14 */
15
16/* hypot(x,y)
17 *
18 * Method :
19 * If (assume round-to-nearest) z=x*x+y*y
20 * has error less than sqrt(2)/2 ulp, than
21 * sqrt(z) has error less than 1 ulp (exercise).
22 *
23 * So, compute sqrt(x*x+y*y) with some care as
24 * follows to get the error below 1 ulp:
25 *
26 * Assume x>y>0;
27 * (if possible, set rounding to round-to-nearest)
28 * 1. if x > 2y use
29 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
30 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
31 * 2. if x <= 2y use
32 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
33 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
34 * y1= y with lower 32 bits chopped, y2 = y-y1.
35 *
36 * NOTE: scaling may be necessary if some argument is too
37 * large or too tiny
38 *
39 * Special cases:
40 * hypot(x,y) is INF if x or y is +INF or -INF; else
41 * hypot(x,y) is NAN if x or y is NAN.
42 *
43 * Accuracy:
44 * hypot(x,y) returns sqrt(x^2+y^2) with error less
45 * than 1 ulps (units in the last place)
46 */
47
48#include <math.h>
49#include "math_private.h"
50
51double
52hypot(double x, double y)
53{
54 double a=x,b=y,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 SET_HIGH_WORD(a,ha); /* a <- |a| */
63 SET_HIGH_WORD(b,hb); /* b <- |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 w = a+b; /* for sNaN */
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 u_int32_t high;
118 t1 = 1.0;
119 GET_HIGH_WORD(high,t1);
120 SET_HIGH_WORD(t1,high+(k<<20));
121 return t1*w;
122 } else return w;
123}