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__
38static const double atanhi[] = {
39#else
40static 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__
49static const double atanlo[] = {
50#else
51static 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__
60static const double aT[] = {
61#else
62static 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
82one   = 1.0,
83huge   = 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