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      1 /* @(#)s_atan.c 5.1 93/09/24 */
      2 /* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunPro, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 #include <sys/cdefs.h>
     15 __FBSDID("$FreeBSD$");
     16 
     17 /*
     18  * See comments in s_atan.c.
     19  * Converted to long double by David Schultz <das (at) FreeBSD.ORG>.
     20  */
     21 
     22 #include <float.h>
     23 
     24 #include "invtrig.h"
     25 #include "math.h"
     26 #include "math_private.h"
     27 
     28 static const long double
     29 one   = 1.0,
     30 huge   = 1.0e300;
     31 
     32 long double
     33 atanl(long double x)
     34 {
     35 	union IEEEl2bits u;
     36 	long double w,s1,s2,z;
     37 	int id;
     38 	int16_t expsign, expt;
     39 	int32_t expman;
     40 
     41 	u.e = x;
     42 	expsign = u.xbits.expsign;
     43 	expt = expsign & 0x7fff;
     44 	if(expt >= ATAN_CONST) {	/* if |x| is large, atan(x)~=pi/2 */
     45 	    if(expt == BIAS + LDBL_MAX_EXP &&
     46 	       ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
     47 		return x+x;		/* NaN */
     48 	    if(expsign>0) return  atanhi[3]+atanlo[3];
     49 	    else     return -atanhi[3]-atanlo[3];
     50 	}
     51 	/* Extract the exponent and the first few bits of the mantissa. */
     52 	/* XXX There should be a more convenient way to do this. */
     53 	expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
     54 	if (expman < ((BIAS - 2) << 8) + 0xc0) {	/* |x| < 0.4375 */
     55 	    if (expt < ATAN_LINEAR) {	/* if |x| is small, atanl(x)~=x */
     56 		if(huge+x>one) return x;	/* raise inexact */
     57 	    }
     58 	    id = -1;
     59 	} else {
     60 	x = fabsl(x);
     61 	if (expman < (BIAS << 8) + 0x30) {		/* |x| < 1.1875 */
     62 	    if (expman < ((BIAS - 1) << 8) + 0x60) {	/* 7/16 <=|x|<11/16 */
     63 		id = 0; x = (2.0*x-one)/(2.0+x);
     64 	    } else {			/* 11/16<=|x|< 19/16 */
     65 		id = 1; x  = (x-one)/(x+one);
     66 	    }
     67 	} else {
     68 	    if (expman < ((BIAS + 1) << 8) + 0x38) {	/* |x| < 2.4375 */
     69 		id = 2; x  = (x-1.5)/(one+1.5*x);
     70 	    } else {			/* 2.4375 <= |x| < 2^ATAN_CONST */
     71 		id = 3; x  = -1.0/x;
     72 	    }
     73 	}}
     74     /* end of argument reduction */
     75 	z = x*x;
     76 	w = z*z;
     77     /* break sum aT[i]z**(i+1) into odd and even poly */
     78 	s1 = z*T_even(w);
     79 	s2 = w*T_odd(w);
     80 	if (id<0) return x - x*(s1+s2);
     81 	else {
     82 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
     83 	    return (expsign<0)? -z:z;
     84 	}
     85 }
     86