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: stable/11/lib/msun/src/e_hypotl.c 369301 2021-02-19 16:21:12Z dim $");
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
43typedef	uint64_t man_t;
44#else
45typedef	uint32_t man_t;
46#endif
47
48long double
49hypotl(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=1;
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