<iso646.h>: Avoid conflicts w/ C++ keywords.
[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 *
74dfd0cf 12 * $NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos
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13 */
14
15/* hypot(x,y)
16 *
17 * Method :
18 * If (assume round-to-nearest) z=x*x+y*y
19 * has error less than sqrt(2)/2 ulp, than
20 * sqrt(z) has error less than 1 ulp (exercise).
21 *
22 * So, compute sqrt(x*x+y*y) with some care as
23 * follows to get the error below 1 ulp:
24 *
25 * Assume x>y>0;
26 * (if possible, set rounding to round-to-nearest)
27 * 1. if x > 2y use
28 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
29 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
30 * 2. if x <= 2y use
74dfd0cf 31 * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y))
b34b60bc 32 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
74dfd0cf 33 * yy1= y with lower 32 bits chopped, y2 = y-yy1.
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34 *
35 * NOTE: scaling may be necessary if some argument is too
36 * large or too tiny
37 *
38 * Special cases:
39 * hypot(x,y) is INF if x or y is +INF or -INF; else
40 * hypot(x,y) is NAN if x or y is NAN.
41 *
42 * Accuracy:
43 * hypot(x,y) returns sqrt(x^2+y^2) with error less
44 * than 1 ulps (units in the last place)
45 */
46
47#include <math.h>
48#include "math_private.h"
49
50double
51hypot(double x, double y)
52{
74dfd0cf 53 double a=x,b=y,t1,t2,yy1,y2,w;
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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 SET_HIGH_WORD(a,ha); /* a <- |a| */
62 SET_HIGH_WORD(b,hb); /* b <- |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 w = a+b; /* for sNaN */
69 GET_LOW_WORD(low,a);
70 if(((ha&0xfffff)|low)==0) w = a;
71 GET_LOW_WORD(low,b);
72 if(((hb^0x7ff00000)|low)==0) w = b;
73 return w;
74 }
75 /* scale a and b by 2**-600 */
76 ha -= 0x25800000; hb -= 0x25800000; k += 600;
77 SET_HIGH_WORD(a,ha);
78 SET_HIGH_WORD(b,hb);
79 }
80 if(hb < 0x20b00000) { /* b < 2**-500 */
81 if(hb <= 0x000fffff) { /* subnormal b or 0 */
82 u_int32_t low;
83 GET_LOW_WORD(low,b);
84 if((hb|low)==0) return a;
85 t1=0;
86 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
87 b *= t1;
88 a *= t1;
89 k -= 1022;
90 } else { /* scale a and b by 2^600 */
91 ha += 0x25800000; /* a *= 2^600 */
92 hb += 0x25800000; /* b *= 2^600 */
93 k -= 600;
94 SET_HIGH_WORD(a,ha);
95 SET_HIGH_WORD(b,hb);
96 }
97 }
98 /* medium size a and b */
99 w = a-b;
100 if (w>b) {
101 t1 = 0;
102 SET_HIGH_WORD(t1,ha);
103 t2 = a-t1;
104 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
105 } else {
106 a = a+a;
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107 yy1 = 0;
108 SET_HIGH_WORD(yy1,hb);
109 y2 = b - yy1;
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110 t1 = 0;
111 SET_HIGH_WORD(t1,ha+0x00100000);
112 t2 = a - t1;
74dfd0cf 113 w = sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b)));
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114 }
115 if(k!=0) {
116 u_int32_t high;
117 t1 = 1.0;
118 GET_HIGH_WORD(high,t1);
119 SET_HIGH_WORD(t1,high+(k<<20));
120 return t1*w;
121 } else return w;
122}