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
39typedef	uint64_t man_t;
40#else
41typedef	uint32_t man_t;
42#endif
43
44long double
45hypotl(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