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      1 
      2 /* @(#)s_atan.c 1.3 95/01/18 */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunSoft, 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 
     15 /* ieee_atan(x)
     16  * Method
     17  *   1. Reduce x to positive by ieee_atan(x) = -ieee_atan(-x).
     18  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
     19  *      is further reduced to one of the following intervals and the
     20  *      arctangent of t is evaluated by the corresponding formula:
     21  *
     22  *      [0,7/16]      ieee_atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
     23  *      [7/16,11/16]  ieee_atan(x) = ieee_atan(1/2) + ieee_atan( (t-0.5)/(1+t/2) )
     24  *      [11/16.19/16] ieee_atan(x) = ieee_atan( 1 ) + ieee_atan( (t-1)/(1+t) )
     25  *      [19/16,39/16] ieee_atan(x) = ieee_atan(3/2) + ieee_atan( (t-1.5)/(1+1.5t) )
     26  *      [39/16,INF]   ieee_atan(x) = ieee_atan(INF) + ieee_atan( -1/t )
     27  *
     28  * Constants:
     29  * The hexadecimal values are the intended ones for the following
     30  * constants. The decimal values may be used, provided that the
     31  * compiler will convert from decimal to binary accurately enough
     32  * to produce the hexadecimal values shown.
     33  */
     34 
     35 #include "fdlibm.h"
     36 
     37 #ifdef __STDC__
     38 static const double atanhi[] = {
     39 #else
     40 static double atanhi[] = {
     41 #endif
     42   4.63647609000806093515e-01, /* ieee_atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
     43   7.85398163397448278999e-01, /* ieee_atan(1.0)hi 0x3FE921FB, 0x54442D18 */
     44   9.82793723247329054082e-01, /* ieee_atan(1.5)hi 0x3FEF730B, 0xD281F69B */
     45   1.57079632679489655800e+00, /* ieee_atan(inf)hi 0x3FF921FB, 0x54442D18 */
     46 };
     47 
     48 #ifdef __STDC__
     49 static const double atanlo[] = {
     50 #else
     51 static double atanlo[] = {
     52 #endif
     53   2.26987774529616870924e-17, /* ieee_atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
     54   3.06161699786838301793e-17, /* ieee_atan(1.0)lo 0x3C81A626, 0x33145C07 */
     55   1.39033110312309984516e-17, /* ieee_atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
     56   6.12323399573676603587e-17, /* ieee_atan(inf)lo 0x3C91A626, 0x33145C07 */
     57 };
     58 
     59 #ifdef __STDC__
     60 static const double aT[] = {
     61 #else
     62 static double aT[] = {
     63 #endif
     64   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
     65  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
     66   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
     67  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
     68   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
     69  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
     70   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
     71  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
     72   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
     73  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
     74   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
     75 };
     76 
     77 #ifdef __STDC__
     78 	static const double
     79 #else
     80 	static double
     81 #endif
     82 one   = 1.0,
     83 huge   = 1.0e300;
     84 
     85 #ifdef __STDC__
     86 	double ieee_atan(double x)
     87 #else
     88 	double ieee_atan(x)
     89 	double x;
     90 #endif
     91 {
     92 	double w,s1,s2,z;
     93 	int ix,hx,id;
     94 
     95 	hx = __HI(x);
     96 	ix = hx&0x7fffffff;
     97 	if(ix>=0x44100000) {	/* if |x| >= 2^66 */
     98 	    if(ix>0x7ff00000||
     99 		(ix==0x7ff00000&&(__LO(x)!=0)))
    100 		return x+x;		/* NaN */
    101 	    if(hx>0) return  atanhi[3]+atanlo[3];
    102 	    else     return -atanhi[3]-atanlo[3];
    103 	} if (ix < 0x3fdc0000) {	/* |x| < 0.4375 */
    104 	    if (ix < 0x3e200000) {	/* |x| < 2^-29 */
    105 		if(huge+x>one) return x;	/* raise inexact */
    106 	    }
    107 	    id = -1;
    108 	} else {
    109 	x = ieee_fabs(x);
    110 	if (ix < 0x3ff30000) {		/* |x| < 1.1875 */
    111 	    if (ix < 0x3fe60000) {	/* 7/16 <=|x|<11/16 */
    112 		id = 0; x = (2.0*x-one)/(2.0+x);
    113 	    } else {			/* 11/16<=|x|< 19/16 */
    114 		id = 1; x  = (x-one)/(x+one);
    115 	    }
    116 	} else {
    117 	    if (ix < 0x40038000) {	/* |x| < 2.4375 */
    118 		id = 2; x  = (x-1.5)/(one+1.5*x);
    119 	    } else {			/* 2.4375 <= |x| < 2^66 */
    120 		id = 3; x  = -1.0/x;
    121 	    }
    122 	}}
    123     /* end of argument reduction */
    124 	z = x*x;
    125 	w = z*z;
    126     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
    127 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
    128 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
    129 	if (id<0) return x - x*(s1+s2);
    130 	else {
    131 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
    132 	    return (hx<0)? -z:z;
    133 	}
    134 }
    135