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 "namespace.h"
16
17
18#include <float.h>
19#include <math.h>
20
21#include <machine/ieee.h>
22
23__weak_alias(hypotl, _hypotl)
24
25#ifdef __HAVE_LONG_DOUBLE
26#include "math.h"
27#include "math_private.h"
28
29#ifdef LDBL_IMPLICIT_NBIT
30#define	LDBL_NBIT	0
31#endif
32
33#define	GET_LDBL_MAN(h, l, v) do {	\
34	union ieee_ext_u uv;		\
35					\
36	uv.extu_ld = v;			\
37	h = uv.extu_frach;		\
38	l = uv.extu_fracl;		\
39} while (0)
40
41#undef GET_HIGH_WORD
42#define	GET_HIGH_WORD(i, v)	GET_LDBL_EXPSIGN(i, v)
43#undef SET_HIGH_WORD
44#define	SET_HIGH_WORD(v, i)	SET_LDBL_EXPSIGN(v, i)
45
46#define	DESW(exp)	(exp)		/* delta expsign word */
47#define	ESW(exp)	(MAX_EXP - 1 + (exp))	/* expsign word */
48#define	MANT_DIG	LDBL_MANT_DIG
49#define	MAX_EXP		LDBL_MAX_EXP
50
51#if EXT_FRACLBITS > 32
52typedef	uint64_t man_t;
53#else
54typedef	uint32_t man_t;
55#endif
56
57long double
58hypotl(long double x, long double y)
59{
60	long double a=x,b=y,t1,t2,y1,y2,w;
61	int32_t j,k,ha,hb;
62
63	GET_HIGH_WORD(ha,x);
64	ha &= 0x7fff;
65	GET_HIGH_WORD(hb,y);
66	hb &= 0x7fff;
67	if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
68	a = fabsl(a);
69	b = fabsl(b);
70	if((ha-hb)>DESW(MANT_DIG+7)) {return a+b;} /* x/y > 2**(MANT_DIG+7) */
71	k=0;
72	if(ha > ESW(MAX_EXP/2-12)) {	/* a>2**(MAX_EXP/2-12) */
73	   if(ha >= ESW(MAX_EXP)) {	/* Inf or NaN */
74	       man_t manh, manl;
75	       /* Use original arg order iff result is NaN; quieten sNaNs. */
76	       w = fabsl(x+0.0L)-fabsl(y+0);
77	       GET_LDBL_MAN(manh,manl,a);
78	       if (manh == LDBL_NBIT && manl == 0) w = a;
79	       GET_LDBL_MAN(manh,manl,b);
80	       if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
81	       return w;
82	   }
83	   /* scale a and b by 2**-(MAX_EXP/2+88) */
84	   ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
85	   k += MAX_EXP/2+88;
86	   SET_HIGH_WORD(a,ha);
87	   SET_HIGH_WORD(b,hb);
88	}
89	if(hb < ESW(-(MAX_EXP/2-12))) {	/* b < 2**-(MAX_EXP/2-12) */
90	    if(hb <= 0) {		/* subnormal b or 0 */
91	        man_t manh, manl;
92		GET_LDBL_MAN(manh,manl,b);
93		if((manh|manl)==0) return a;
94		t1=1;
95		SET_HIGH_WORD(t1,ESW(MAX_EXP-2));	/* t1=2^(MAX_EXP-2) */
96		b *= t1;
97		a *= t1;
98		k -= MAX_EXP-2;
99	    } else {		/* scale a and b by 2^(MAX_EXP/2+88) */
100		ha += DESW(MAX_EXP/2+88);
101		hb += DESW(MAX_EXP/2+88);
102		k -= MAX_EXP/2+88;
103		SET_HIGH_WORD(a,ha);
104		SET_HIGH_WORD(b,hb);
105	    }
106	}
107    /* medium size a and b */
108	w = a-b;
109	if (w>b) {
110	    t1 = a;
111	    union ieee_ext_u uv;
112	    uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld;
113	    t2 = a-t1;
114	    w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
115	} else {
116	    a  = a+a;
117	    y1 = b;
118	    union ieee_ext_u uv;
119	    uv.extu_ld = y1; uv.extu_fracl = 0; y1 = uv.extu_ld;
120	    y2 = b - y1;
121	    t1 = a;
122	    uv.extu_ld = t1; uv.extu_fracl = 0; t1 = uv.extu_ld;
123	    t2 = a - t1;
124	    w  = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
125	}
126	if(k!=0) {
127	    u_int32_t high;
128	    t1 = 1.0;
129	    GET_HIGH_WORD(high,t1);
130	    SET_HIGH_WORD(t1,high+DESW(k));
131	    return t1*w;
132	} else return w;
133}
134#else
135#include "math.h"
136
137long double
138hypotl(long double x, long double y)
139{
140	return hypot(x, y);
141}
142#endif
143