1/*	$NetBSD: e_acosl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $	*/
2
3/* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15#include <sys/cdefs.h>
16__RCSID("$NetBSD: e_acosl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $");
17
18/*
19 * See comments in e_acos.c.
20 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
21 */
22
23#include "namespace.h"
24
25#include <float.h>
26#include <machine/ieee.h>
27
28#include "math.h"
29#include "math_private.h"
30
31#ifdef __HAVE_LONG_DOUBLE
32
33__weak_alias(acosl, _acosl)
34
35#if LDBL_MANT_DIG == 64
36#include "../ld80/invtrig.h"
37#elif LDBL_MANT_DIG == 113
38#include "../ld128/invtrig.h"
39#else
40#error "Unsupported long double format"
41#endif
42
43#ifdef LDBL_IMPLICIT_NBIT
44#define	LDBL_NBIT	0
45#endif
46
47static const long double
48one=  1.00000000000000000000e+00;
49
50#ifdef __i386__
51/* XXX Work around the fact that gcc truncates long double constants on i386 */
52static volatile double
53pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
54pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
55#define	pi	((long double)pi1 + pi2)
56#else
57static const long double
58pi =  3.14159265358979323846264338327950280e+00L;
59#endif
60
61long double
62acosl(long double x)
63{
64	union ieee_ext_u u;
65	long double z,p,q,r,w,s,c,df;
66	int16_t expsign, expt;
67	u.extu_ld = x;
68	expsign = GET_EXPSIGN(&u);
69	expt = expsign & 0x7fff;
70	if(expt >= BIAS) {	/* |x| >= 1 */
71	    if(expt==BIAS && ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)==0) {
72		if (expsign>0) return 0.0;	/* acos(1) = 0  */
73		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
74	    }
75	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
76	}
77	if(expt<BIAS-1) {	/* |x| < 0.5 */
78	    if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
79	    z = x*x;
80	    p = P(z);
81	    q = Q(z);
82	    r = p/q;
83	    return pio2_hi - (x - (pio2_lo-x*r));
84	} else  if (expsign<0) {	/* x < -0.5 */
85	    z = (one+x)*0.5;
86	    p = P(z);
87	    q = Q(z);
88	    s = sqrtl(z);
89	    r = p/q;
90	    w = r*s-pio2_lo;
91	    return pi - 2.0*(s+w);
92	} else {			/* x > 0.5 */
93	    z = (one-x)*0.5;
94	    s = sqrtl(z);
95	    u.extu_ld = s;
96	    u.extu_fracl = 0;
97	    df = u.extu_ld;
98	    c  = (z-df*df)/(s+df);
99	    p = P(z);
100	    q = Q(z);
101	    r = p/q;
102	    w = r*s+c;
103	    return 2.0*(df+w);
104	}
105}
106#endif
107