xref: /freebsd/lib/msun/src/e_hypotl.c (revision 783d3ff6d7fae619db8a7990b8a6387de0c677b5)
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 /* long double version of hypot().  See e_hypot.c for most comments. */
13 
14 #include <float.h>
15 
16 #include "fpmath.h"
17 #include "math.h"
18 #include "math_private.h"
19 
20 #define	GET_LDBL_MAN(h, l, v) do {	\
21 	union IEEEl2bits uv;		\
22 					\
23 	uv.e = v;			\
24 	h = uv.bits.manh;		\
25 	l = uv.bits.manl;		\
26 } while (0)
27 
28 #undef GET_HIGH_WORD
29 #define	GET_HIGH_WORD(i, v)	GET_LDBL_EXPSIGN(i, v)
30 #undef SET_HIGH_WORD
31 #define	SET_HIGH_WORD(v, i)	SET_LDBL_EXPSIGN(v, i)
32 
33 #define	DESW(exp)	(exp)		/* delta expsign word */
34 #define	ESW(exp)	(MAX_EXP - 1 + (exp))	/* expsign word */
35 #define	MANT_DIG	LDBL_MANT_DIG
36 #define	MAX_EXP		LDBL_MAX_EXP
37 
38 #if LDBL_MANL_SIZE > 32
39 typedef	uint64_t man_t;
40 #else
41 typedef	uint32_t man_t;
42 #endif
43 
44 long double
45 hypotl(long double x, long double y)
46 {
47 	long double a=x,b=y,t1,t2,y1,y2,w;
48 	int32_t j,k,ha,hb;
49 
50 	GET_HIGH_WORD(ha,x);
51 	ha &= 0x7fff;
52 	GET_HIGH_WORD(hb,y);
53 	hb &= 0x7fff;
54 	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
55 	a = fabsl(a);
56 	b = fabsl(b);
57 	if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
58 	k=0;
59 	if(ha > ESW(MAX_EXP/2-12)) {	/* a>2**(MAX_EXP/2-12) */
60 	   if(ha >= ESW(MAX_EXP)) {	/* Inf or NaN */
61 	       man_t manh, manl;
62 	       /* Use original arg order iff result is NaN; quieten sNaNs. */
63 	       w = fabsl(x+0.0L)-fabsl(y+0);
64 	       GET_LDBL_MAN(manh,manl,a);
65 	       if (manh == LDBL_NBIT && manl == 0) w = a;
66 	       GET_LDBL_MAN(manh,manl,b);
67 	       if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
68 	       return w;
69 	   }
70 	   /* scale a and b by 2**-(MAX_EXP/2+88) */
71 	   ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
72 	   k += MAX_EXP/2+88;
73 	   SET_HIGH_WORD(a,ha);
74 	   SET_HIGH_WORD(b,hb);
75 	}
76 	if(hb < ESW(-(MAX_EXP/2-12))) {	/* b < 2**-(MAX_EXP/2-12) */
77 	    if(hb <= 0) {		/* subnormal b or 0 */
78 	        man_t manh, manl;
79 		GET_LDBL_MAN(manh,manl,b);
80 		if((manh|manl)==0) return a;
81 		t1=1;
82 		SET_HIGH_WORD(t1,ESW(MAX_EXP-2));	/* t1=2^(MAX_EXP-2) */
83 		b *= t1;
84 		a *= t1;
85 		k -= MAX_EXP-2;
86 	    } else {		/* scale a and b by 2^(MAX_EXP/2+88) */
87 		ha += DESW(MAX_EXP/2+88);
88 		hb += DESW(MAX_EXP/2+88);
89 		k -= MAX_EXP/2+88;
90 		SET_HIGH_WORD(a,ha);
91 		SET_HIGH_WORD(b,hb);
92 	    }
93 	}
94     /* medium size a and b */
95 	w = a-b;
96 	if (w>b) {
97 	    t1 = a;
98 	    union IEEEl2bits uv;
99 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
100 	    t2 = a-t1;
101 	    w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
102 	} else {
103 	    a  = a+a;
104 	    y1 = b;
105 	    union IEEEl2bits uv;
106 	    uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
107 	    y2 = b - y1;
108 	    t1 = a;
109 	    uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
110 	    t2 = a - t1;
111 	    w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
112 	}
113 	if(k!=0) {
114 	    u_int32_t high;
115 	    t1 = 1.0;
116 	    GET_HIGH_WORD(high,t1);
117 	    SET_HIGH_WORD(t1,high+DESW(k));
118 	    return t1*w;
119 	} else return w;
120 }
121