xref: /freebsd/lib/msun/src/e_hypotl.c (revision 4b9d605768acabc460aa6dcfe8a1f8db35b16794)
1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunSoft, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 #include <sys/cdefs.h>
13 /* long double version of hypot().  See e_hypot.c for most comments. */
14 
15 #include <float.h>
16 
17 #include "fpmath.h"
18 #include "math.h"
19 #include "math_private.h"
20 
21 #define	GET_LDBL_MAN(h, l, v) do {	\
22 	union IEEEl2bits uv;		\
23 					\
24 	uv.e = v;			\
25 	h = uv.bits.manh;		\
26 	l = uv.bits.manl;		\
27 } while (0)
28 
29 #undef GET_HIGH_WORD
30 #define	GET_HIGH_WORD(i, v)	GET_LDBL_EXPSIGN(i, v)
31 #undef SET_HIGH_WORD
32 #define	SET_HIGH_WORD(v, i)	SET_LDBL_EXPSIGN(v, i)
33 
34 #define	DESW(exp)	(exp)		/* delta expsign word */
35 #define	ESW(exp)	(MAX_EXP - 1 + (exp))	/* expsign word */
36 #define	MANT_DIG	LDBL_MANT_DIG
37 #define	MAX_EXP		LDBL_MAX_EXP
38 
39 #if LDBL_MANL_SIZE > 32
40 typedef	uint64_t man_t;
41 #else
42 typedef	uint32_t man_t;
43 #endif
44 
45 long double
46 hypotl(long double x, long double y)
47 {
48 	long double a=x,b=y,t1,t2,y1,y2,w;
49 	int32_t j,k,ha,hb;
50 
51 	GET_HIGH_WORD(ha,x);
52 	ha &= 0x7fff;
53 	GET_HIGH_WORD(hb,y);
54 	hb &= 0x7fff;
55 	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
56 	a = fabsl(a);
57 	b = fabsl(b);
58 	if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
59 	k=0;
60 	if(ha > ESW(MAX_EXP/2-12)) {	/* a>2**(MAX_EXP/2-12) */
61 	   if(ha >= ESW(MAX_EXP)) {	/* Inf or NaN */
62 	       man_t manh, manl;
63 	       /* Use original arg order iff result is NaN; quieten sNaNs. */
64 	       w = fabsl(x+0.0L)-fabsl(y+0);
65 	       GET_LDBL_MAN(manh,manl,a);
66 	       if (manh == LDBL_NBIT && manl == 0) w = a;
67 	       GET_LDBL_MAN(manh,manl,b);
68 	       if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
69 	       return w;
70 	   }
71 	   /* scale a and b by 2**-(MAX_EXP/2+88) */
72 	   ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
73 	   k += MAX_EXP/2+88;
74 	   SET_HIGH_WORD(a,ha);
75 	   SET_HIGH_WORD(b,hb);
76 	}
77 	if(hb < ESW(-(MAX_EXP/2-12))) {	/* b < 2**-(MAX_EXP/2-12) */
78 	    if(hb <= 0) {		/* subnormal b or 0 */
79 	        man_t manh, manl;
80 		GET_LDBL_MAN(manh,manl,b);
81 		if((manh|manl)==0) return a;
82 		t1=1;
83 		SET_HIGH_WORD(t1,ESW(MAX_EXP-2));	/* t1=2^(MAX_EXP-2) */
84 		b *= t1;
85 		a *= t1;
86 		k -= MAX_EXP-2;
87 	    } else {		/* scale a and b by 2^(MAX_EXP/2+88) */
88 		ha += DESW(MAX_EXP/2+88);
89 		hb += DESW(MAX_EXP/2+88);
90 		k -= MAX_EXP/2+88;
91 		SET_HIGH_WORD(a,ha);
92 		SET_HIGH_WORD(b,hb);
93 	    }
94 	}
95     /* medium size a and b */
96 	w = a-b;
97 	if (w>b) {
98 	    t1 = a;
99 	    union IEEEl2bits uv;
100 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
101 	    t2 = a-t1;
102 	    w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
103 	} else {
104 	    a  = a+a;
105 	    y1 = b;
106 	    union IEEEl2bits uv;
107 	    uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
108 	    y2 = b - y1;
109 	    t1 = a;
110 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
111 	    t2 = a - t1;
112 	    w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
113 	}
114 	if(k!=0) {
115 	    u_int32_t high;
116 	    t1 = 1.0;
117 	    GET_HIGH_WORD(high,t1);
118 	    SET_HIGH_WORD(t1,high+DESW(k));
119 	    return t1*w;
120 	} else return w;
121 }
122