1 /* From: @(#)e_hypot.c 1.3 95/01/18 */
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 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
15 
16 /* long double version of hypot().  See e_hypot.c for most comments. */
17 
18 #include <float.h>
19 
20 #include "fpmath.h"
21 #include "math.h"
22 #include "math_private.h"
23 
24 #define	GET_LDBL_MAN(h, l, v) do {	\
25 	union IEEEl2bits uv;		\
26 					\
27 	uv.e = v;			\
28 	h = uv.bits.manh;		\
29 	l = uv.bits.manl;		\
30 } while (0)
31 
32 #undef GET_HIGH_WORD
33 #define	GET_HIGH_WORD(i, v)	GET_LDBL_EXPSIGN(i, v)
34 #undef SET_HIGH_WORD
35 #define	SET_HIGH_WORD(v, i)	SET_LDBL_EXPSIGN(v, i)
36 
37 #define	DESW(exp)	(exp)		/* delta expsign word */
38 #define	ESW(exp)	(MAX_EXP - 1 + (exp))	/* expsign word */
39 #define	MANT_DIG	LDBL_MANT_DIG
40 #define	MAX_EXP		LDBL_MAX_EXP
41 
42 #if LDBL_MANL_SIZE > 32
43 typedef	uint64_t man_t;
44 #else
45 typedef	uint32_t man_t;
46 #endif
47 
48 long double
hypotl(long double x,long double y)49 hypotl(long double x, long double y)
50 {
51 	long double a=x,b=y,t1,t2,y1,y2,w;
52 	int32_t j,k,ha,hb;
53 
54 	GET_HIGH_WORD(ha,x);
55 	ha &= 0x7fff;
56 	GET_HIGH_WORD(hb,y);
57 	hb &= 0x7fff;
58 	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
59 	a = fabsl(a);
60 	b = fabsl(b);
61 	if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
62 	k=0;
63 	if(ha > ESW(MAX_EXP/2-12)) {	/* a>2**(MAX_EXP/2-12) */
64 	   if(ha >= ESW(MAX_EXP)) {	/* Inf or NaN */
65 	       man_t manh, manl;
66 	       /* Use original arg order iff result is NaN; quieten sNaNs. */
67 	       w = fabsl(x+0.0)-fabsl(y+0.0);
68 	       GET_LDBL_MAN(manh,manl,a);
69 	       if (manh == LDBL_NBIT && manl == 0) w = a;
70 	       GET_LDBL_MAN(manh,manl,b);
71 	       if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
72 	       return w;
73 	   }
74 	   /* scale a and b by 2**-(MAX_EXP/2+88) */
75 	   ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
76 	   k += MAX_EXP/2+88;
77 	   SET_HIGH_WORD(a,ha);
78 	   SET_HIGH_WORD(b,hb);
79 	}
80 	if(hb < ESW(-(MAX_EXP/2-12))) {	/* b < 2**-(MAX_EXP/2-12) */
81 	    if(hb <= 0) {		/* subnormal b or 0 */
82 	        man_t manh, manl;
83 		GET_LDBL_MAN(manh,manl,b);
84 		if((manh|manl)==0) return a;
85 		t1=0;
86 		SET_HIGH_WORD(t1,ESW(MAX_EXP-2));	/* t1=2^(MAX_EXP-2) */
87 		b *= t1;
88 		a *= t1;
89 		k -= MAX_EXP-2;
90 	    } else {		/* scale a and b by 2^(MAX_EXP/2+88) */
91 		ha += DESW(MAX_EXP/2+88);
92 		hb += DESW(MAX_EXP/2+88);
93 		k -= MAX_EXP/2+88;
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 = a;
102 	    union IEEEl2bits uv;
103 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
104 	    t2 = a-t1;
105 	    w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
106 	} else {
107 	    a  = a+a;
108 	    y1 = b;
109 	    union IEEEl2bits uv;
110 	    uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
111 	    y2 = b - y1;
112 	    t1 = a;
113 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
114 	    t2 = a - t1;
115 	    w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
116 	}
117 	if(k!=0) {
118 	    u_int32_t high;
119 	    t1 = 1.0;
120 	    GET_HIGH_WORD(high,t1);
121 	    SET_HIGH_WORD(t1,high+DESW(k));
122 	    return t1*w;
123 	} else return w;
124 }
125