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      1 
      2 /* @(#)e_acos.c 1.3 95/01/18 */
      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 __FBSDID("$FreeBSD$");
     17 
     18 /*
     19  * See comments in e_acos.c.
     20  * Converted to long double by David Schultz <das (at) FreeBSD.ORG>.
     21  */
     22 
     23 #include <float.h>
     24 
     25 #include "invtrig.h"
     26 #include "math.h"
     27 #include "math_private.h"
     28 
     29 static const long double
     30 one=  1.00000000000000000000e+00;
     31 
     32 #ifdef __i386__
     33 /* XXX Work around the fact that gcc truncates long double constants on i386 */
     34 static volatile double
     35 pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
     36 pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
     37 #define	pi	((long double)pi1 + pi2)
     38 #else
     39 static const long double
     40 pi =  3.14159265358979323846264338327950280e+00L;
     41 #endif
     42 
     43 long double
     44 acosl(long double x)
     45 {
     46 	union IEEEl2bits u;
     47 	long double z,p,q,r,w,s,c,df;
     48 	int16_t expsign, expt;
     49 	u.e = x;
     50 	expsign = u.xbits.expsign;
     51 	expt = expsign & 0x7fff;
     52 	if(expt >= BIAS) {	/* |x| >= 1 */
     53 	    if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
     54 		if (expsign>0) return 0.0;	/* acos(1) = 0  */
     55 		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
     56 	    }
     57 	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
     58 	}
     59 	if(expt<BIAS-1) {	/* |x| < 0.5 */
     60 	    if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
     61 	    z = x*x;
     62 	    p = P(z);
     63 	    q = Q(z);
     64 	    r = p/q;
     65 	    return pio2_hi - (x - (pio2_lo-x*r));
     66 	} else  if (expsign<0) {	/* x < -0.5 */
     67 	    z = (one+x)*0.5;
     68 	    p = P(z);
     69 	    q = Q(z);
     70 	    s = sqrtl(z);
     71 	    r = p/q;
     72 	    w = r*s-pio2_lo;
     73 	    return pi - 2.0*(s+w);
     74 	} else {			/* x > 0.5 */
     75 	    z = (one-x)*0.5;
     76 	    s = sqrtl(z);
     77 	    u.e = s;
     78 	    u.bits.manl = 0;
     79 	    df = u.e;
     80 	    c  = (z-df*df)/(s+df);
     81 	    p = P(z);
     82 	    q = Q(z);
     83 	    r = p/q;
     84 	    w = r*s+c;
     85 	    return 2.0*(df+w);
     86 	}
     87 }
     88