xref: /freebsd/lib/msun/src/e_hypot.c (revision 10b59a9b4add0320d52c15ce057dd697261e7dfc)
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.h"
52  #include "math_private.h"
53  
54  double
55  __ieee754_hypot(double x, double y)
56  {
57  	double a,b,t1,t2,y1,y2,w;
58  	int32_t j,k,ha,hb;
59  
60  	GET_HIGH_WORD(ha,x);
61  	ha &= 0x7fffffff;
62  	GET_HIGH_WORD(hb,y);
63  	hb &= 0x7fffffff;
64  	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
65  	a = fabs(a);
66  	b = fabs(b);
67  	if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
68  	k=0;
69  	if(ha > 0x5f300000) {	/* a>2**500 */
70  	   if(ha >= 0x7ff00000) {	/* Inf or NaN */
71  	       u_int32_t low;
72  	       /* Use original arg order iff result is NaN; quieten sNaNs. */
73  	       w = fabs(x+0.0)-fabs(y+0.0);
74  	       GET_LOW_WORD(low,a);
75  	       if(((ha&0xfffff)|low)==0) w = a;
76  	       GET_LOW_WORD(low,b);
77  	       if(((hb^0x7ff00000)|low)==0) w = b;
78  	       return w;
79  	   }
80  	   /* scale a and b by 2**-600 */
81  	   ha -= 0x25800000; hb -= 0x25800000;	k += 600;
82  	   SET_HIGH_WORD(a,ha);
83  	   SET_HIGH_WORD(b,hb);
84  	}
85  	if(hb < 0x20b00000) {	/* b < 2**-500 */
86  	    if(hb <= 0x000fffff) {	/* subnormal b or 0 */
87  	        u_int32_t low;
88  		GET_LOW_WORD(low,b);
89  		if((hb|low)==0) return a;
90  		t1=0;
91  		SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */
92  		b *= t1;
93  		a *= t1;
94  		k -= 1022;
95  	    } else {		/* scale a and b by 2^600 */
96  	        ha += 0x25800000; 	/* a *= 2^600 */
97  		hb += 0x25800000;	/* b *= 2^600 */
98  		k -= 600;
99  		SET_HIGH_WORD(a,ha);
100  		SET_HIGH_WORD(b,hb);
101  	    }
102  	}
103      /* medium size a and b */
104  	w = a-b;
105  	if (w>b) {
106  	    t1 = 0;
107  	    SET_HIGH_WORD(t1,ha);
108  	    t2 = a-t1;
109  	    w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
110  	} else {
111  	    a  = a+a;
112  	    y1 = 0;
113  	    SET_HIGH_WORD(y1,hb);
114  	    y2 = b - y1;
115  	    t1 = 0;
116  	    SET_HIGH_WORD(t1,ha+0x00100000);
117  	    t2 = a - t1;
118  	    w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
119  	}
120  	if(k!=0) {
121  	    u_int32_t high;
122  	    t1 = 1.0;
123  	    GET_HIGH_WORD(high,t1);
124  	    SET_HIGH_WORD(t1,high+(k<<20));
125  	    return t1*w;
126  	} else return w;
127  }
128  
129  #if LDBL_MANT_DIG == 53
130  __weak_reference(hypot, hypotl);
131  #endif
132