117303c62SDavid Schultz
217303c62SDavid Schultz /* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
317303c62SDavid Schultz /*
417303c62SDavid Schultz * ====================================================
517303c62SDavid Schultz * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
617303c62SDavid Schultz *
717303c62SDavid Schultz * Developed at SunSoft, a Sun Microsystems, Inc. business.
817303c62SDavid Schultz * Permission to use, copy, modify, and distribute this
917303c62SDavid Schultz * software is freely granted, provided that this notice
1017303c62SDavid Schultz * is preserved.
1117303c62SDavid Schultz * ====================================================
1217303c62SDavid Schultz */
1317303c62SDavid Schultz
1417303c62SDavid Schultz /*
1517303c62SDavid Schultz * See comments in e_acos.c.
1617303c62SDavid Schultz * Converted to long double by David Schultz <das@FreeBSD.ORG>.
1717303c62SDavid Schultz */
1817303c62SDavid Schultz
1917303c62SDavid Schultz #include <float.h>
2017303c62SDavid Schultz
2117303c62SDavid Schultz #include "invtrig.h"
2217303c62SDavid Schultz #include "math.h"
2317303c62SDavid Schultz #include "math_private.h"
2417303c62SDavid Schultz
2517303c62SDavid Schultz static const long double
261192a80eSDavid Schultz one= 1.00000000000000000000e+00;
271192a80eSDavid Schultz
281192a80eSDavid Schultz #ifdef __i386__
291192a80eSDavid Schultz /* XXX Work around the fact that gcc truncates long double constants on i386 */
301192a80eSDavid Schultz static volatile double
311192a80eSDavid Schultz pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
321192a80eSDavid Schultz pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
331192a80eSDavid Schultz #define pi ((long double)pi1 + pi2)
341192a80eSDavid Schultz #else
351192a80eSDavid Schultz static const long double
3617303c62SDavid Schultz pi = 3.14159265358979323846264338327950280e+00L;
371192a80eSDavid Schultz #endif
3817303c62SDavid Schultz
3917303c62SDavid Schultz long double
acosl(long double x)4017303c62SDavid Schultz acosl(long double x)
4117303c62SDavid Schultz {
4217303c62SDavid Schultz union IEEEl2bits u;
4317303c62SDavid Schultz long double z,p,q,r,w,s,c,df;
4417303c62SDavid Schultz int16_t expsign, expt;
4517303c62SDavid Schultz u.e = x;
4617303c62SDavid Schultz expsign = u.xbits.expsign;
4717303c62SDavid Schultz expt = expsign & 0x7fff;
4817303c62SDavid Schultz if(expt >= BIAS) { /* |x| >= 1 */
4917303c62SDavid Schultz if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
5017303c62SDavid Schultz if (expsign>0) return 0.0; /* acos(1) = 0 */
5117303c62SDavid Schultz else return pi+2.0*pio2_lo; /* acos(-1)= pi */
5217303c62SDavid Schultz }
5317303c62SDavid Schultz return (x-x)/(x-x); /* acos(|x|>1) is NaN */
5417303c62SDavid Schultz }
5517303c62SDavid Schultz if(expt<BIAS-1) { /* |x| < 0.5 */
5617303c62SDavid Schultz if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
5717303c62SDavid Schultz z = x*x;
5817303c62SDavid Schultz p = P(z);
5917303c62SDavid Schultz q = Q(z);
6017303c62SDavid Schultz r = p/q;
6117303c62SDavid Schultz return pio2_hi - (x - (pio2_lo-x*r));
6217303c62SDavid Schultz } else if (expsign<0) { /* x < -0.5 */
6317303c62SDavid Schultz z = (one+x)*0.5;
6417303c62SDavid Schultz p = P(z);
6517303c62SDavid Schultz q = Q(z);
6617303c62SDavid Schultz s = sqrtl(z);
6717303c62SDavid Schultz r = p/q;
6817303c62SDavid Schultz w = r*s-pio2_lo;
6917303c62SDavid Schultz return pi - 2.0*(s+w);
7017303c62SDavid Schultz } else { /* x > 0.5 */
7117303c62SDavid Schultz z = (one-x)*0.5;
7217303c62SDavid Schultz s = sqrtl(z);
7317303c62SDavid Schultz u.e = s;
7417303c62SDavid Schultz u.bits.manl = 0;
7517303c62SDavid Schultz df = u.e;
7617303c62SDavid Schultz c = (z-df*df)/(s+df);
7717303c62SDavid Schultz p = P(z);
7817303c62SDavid Schultz q = Q(z);
7917303c62SDavid Schultz r = p/q;
8017303c62SDavid Schultz w = r*s+c;
8117303c62SDavid Schultz return 2.0*(df+w);
8217303c62SDavid Schultz }
8317303c62SDavid Schultz }
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