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
47 static const long double
48 one= 1.00000000000000000000e+00;
49
50 #ifdef __i386__
51 /* XXX Work around the fact that gcc truncates long double constants on i386 */
52 static volatile double
53 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
54 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
55 #define pi ((long double)pi1 + pi2)
56 #else
57 static const long double
58 pi = 3.14159265358979323846264338327950280e+00L;
59 #endif
60
61 long double
acosl(long double x)62 acosl(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