1*05a0b428SJohn Marino /* $OpenBSD: e_acosl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */
2*05a0b428SJohn Marino /* @(#)e_acos.c 1.3 95/01/18 */
3*05a0b428SJohn Marino /* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
4*05a0b428SJohn Marino /*
5*05a0b428SJohn Marino * ====================================================
6*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7*05a0b428SJohn Marino *
8*05a0b428SJohn Marino * Developed at SunSoft, a Sun Microsystems, Inc. business.
9*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
10*05a0b428SJohn Marino * software is freely granted, provided that this notice
11*05a0b428SJohn Marino * is preserved.
12*05a0b428SJohn Marino * ====================================================
13*05a0b428SJohn Marino */
14*05a0b428SJohn Marino
15*05a0b428SJohn Marino /*
16*05a0b428SJohn Marino * See comments in e_acos.c.
17*05a0b428SJohn Marino * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18*05a0b428SJohn Marino * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
19*05a0b428SJohn Marino */
20*05a0b428SJohn Marino
21*05a0b428SJohn Marino #include <float.h>
22*05a0b428SJohn Marino #include <math.h>
23*05a0b428SJohn Marino
24*05a0b428SJohn Marino #include "invtrig.h"
25*05a0b428SJohn Marino #include "math_private.h"
26*05a0b428SJohn Marino
27*05a0b428SJohn Marino #ifdef EXT_IMPLICIT_NBIT
28*05a0b428SJohn Marino #define LDBL_NBIT 0
29*05a0b428SJohn Marino #else /* EXT_IMPLICIT_NBIT */
30*05a0b428SJohn Marino #define LDBL_NBIT 0x80000000
31*05a0b428SJohn Marino #endif /* EXT_IMPLICIT_NBIT */
32*05a0b428SJohn Marino
33*05a0b428SJohn Marino static const long double
34*05a0b428SJohn Marino one= 1.00000000000000000000e+00;
35*05a0b428SJohn Marino
36*05a0b428SJohn Marino #if defined(__amd64__) || defined(__i386__)
37*05a0b428SJohn Marino /* XXX Work around the fact that gcc truncates long double constants on i386 */
38*05a0b428SJohn Marino static volatile double
39*05a0b428SJohn Marino pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
40*05a0b428SJohn Marino pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
41*05a0b428SJohn Marino #define pi ((long double)pi1 + pi2)
42*05a0b428SJohn Marino #else
43*05a0b428SJohn Marino static const long double
44*05a0b428SJohn Marino pi = 3.14159265358979323846264338327950280e+00L;
45*05a0b428SJohn Marino #endif
46*05a0b428SJohn Marino
47*05a0b428SJohn Marino long double
acosl(long double x)48*05a0b428SJohn Marino acosl(long double x)
49*05a0b428SJohn Marino {
50*05a0b428SJohn Marino union {
51*05a0b428SJohn Marino long double e;
52*05a0b428SJohn Marino struct ieee_ext bits;
53*05a0b428SJohn Marino } u;
54*05a0b428SJohn Marino long double z,p,q,r,w,s,c,df;
55*05a0b428SJohn Marino int16_t expsign, expt;
56*05a0b428SJohn Marino u.e = x;
57*05a0b428SJohn Marino expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
58*05a0b428SJohn Marino expt = expsign & 0x7fff;
59*05a0b428SJohn Marino if(expt >= BIAS) { /* |x| >= 1 */
60*05a0b428SJohn Marino if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT)
61*05a0b428SJohn Marino #ifdef EXT_FRACHMBITS
62*05a0b428SJohn Marino | u.bits.ext_frachm
63*05a0b428SJohn Marino #endif /* EXT_FRACHMBITS */
64*05a0b428SJohn Marino #ifdef EXT_FRACLMBITS
65*05a0b428SJohn Marino | u.bits.ext_fraclm
66*05a0b428SJohn Marino #endif /* EXT_FRACLMBITS */
67*05a0b428SJohn Marino | u.bits.ext_fracl)==0) {
68*05a0b428SJohn Marino if (expsign>0) return 0.0; /* acos(1) = 0 */
69*05a0b428SJohn Marino else return pi+2.0*pio2_lo; /* acos(-1)= pi */
70*05a0b428SJohn Marino }
71*05a0b428SJohn Marino return (x-x)/(x-x); /* acos(|x|>1) is NaN */
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino if(expt<BIAS-1) { /* |x| < 0.5 */
74*05a0b428SJohn Marino if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
75*05a0b428SJohn Marino z = x*x;
76*05a0b428SJohn Marino p = P(z);
77*05a0b428SJohn Marino q = Q(z);
78*05a0b428SJohn Marino r = p/q;
79*05a0b428SJohn Marino return pio2_hi - (x - (pio2_lo-x*r));
80*05a0b428SJohn Marino } else if (expsign<0) { /* x < -0.5 */
81*05a0b428SJohn Marino z = (one+x)*0.5;
82*05a0b428SJohn Marino p = P(z);
83*05a0b428SJohn Marino q = Q(z);
84*05a0b428SJohn Marino s = sqrtl(z);
85*05a0b428SJohn Marino r = p/q;
86*05a0b428SJohn Marino w = r*s-pio2_lo;
87*05a0b428SJohn Marino return pi - 2.0*(s+w);
88*05a0b428SJohn Marino } else { /* x > 0.5 */
89*05a0b428SJohn Marino z = (one-x)*0.5;
90*05a0b428SJohn Marino s = sqrtl(z);
91*05a0b428SJohn Marino u.e = s;
92*05a0b428SJohn Marino u.bits.ext_fracl = 0;
93*05a0b428SJohn Marino #ifdef EXT_FRACLMBITS
94*05a0b428SJohn Marino u.bits.ext_fraclm = 0;
95*05a0b428SJohn Marino #endif /* EXT_FRACLMBITS */
96*05a0b428SJohn Marino df = u.e;
97*05a0b428SJohn Marino c = (z-df*df)/(s+df);
98*05a0b428SJohn Marino p = P(z);
99*05a0b428SJohn Marino q = Q(z);
100*05a0b428SJohn Marino r = p/q;
101*05a0b428SJohn Marino w = r*s+c;
102*05a0b428SJohn Marino return 2.0*(df+w);
103*05a0b428SJohn Marino }
104*05a0b428SJohn Marino }
105