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### Annotation of src/lib/libm/src/s_atan.c, Revision 1.9

```1.1       jtc         1: /* @(#)s_atan.c 5.1 93/09/24 */
2: /*
3:  * ====================================================
5:  *
6:  * Developed at SunPro, a Sun Microsystems, Inc. business.
7:  * Permission to use, copy, modify, and distribute this
8:  * software is freely granted, provided that this notice
9:  * is preserved.
10:  * ====================================================
11:  */
1.3       jtc        12:
1.9     ! lukem      13: #include <sys/cdefs.h>
1.7       jtc        14: #if defined(LIBM_SCCS) && !defined(lint)
1.9     ! lukem      15: __RCSID("\$NetBSD\$");
1.3       jtc        16: #endif
1.1       jtc        17:
18: /* atan(x)
19:  * Method
20:  *   1. Reduce x to positive by atan(x) = -atan(-x).
21:  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
22:  *      is further reduced to one of the following intervals and the
23:  *      arctangent of t is evaluated by the corresponding formula:
24:  *
25:  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
26:  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
27:  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
28:  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
29:  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
30:  *
31:  * Constants:
32:  * The hexadecimal values are the intended ones for the following
33:  * constants. The decimal values may be used, provided that the
34:  * compiler will convert from decimal to binary accurately enough
35:  * to produce the hexadecimal values shown.
36:  */
37:
1.5       jtc        38: #include "math.h"
39: #include "math_private.h"
1.1       jtc        40:
41: #ifdef __STDC__
42: static const double atanhi[] = {
43: #else
44: static double atanhi[] = {
45: #endif
46:   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
47:   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
48:   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
49:   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
50: };
51:
52: #ifdef __STDC__
53: static const double atanlo[] = {
54: #else
55: static double atanlo[] = {
56: #endif
57:   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
58:   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
59:   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
60:   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
61: };
62:
63: #ifdef __STDC__
64: static const double aT[] = {
65: #else
66: static double aT[] = {
67: #endif
68:   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
69:  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
70:   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
71:  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
72:   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
73:  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
74:   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
75:  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
76:   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
77:  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
78:   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
79: };
80:
81: #ifdef __STDC__
82:        static const double
83: #else
84:        static double
85: #endif
86: one   = 1.0,
87: huge   = 1.0e300;
88:
89: #ifdef __STDC__
90:        double atan(double x)
91: #else
92:        double atan(x)
93:        double x;
94: #endif
95: {
96:        double w,s1,s2,z;
1.6       jtc        97:        int32_t ix,hx,id;
1.1       jtc        98:
1.5       jtc        99:        GET_HIGH_WORD(hx,x);
1.1       jtc       100:        ix = hx&0x7fffffff;
101:        if(ix>=0x44100000) {    /* if |x| >= 2^66 */
1.6       jtc       102:            u_int32_t low;
1.5       jtc       103:            GET_LOW_WORD(low,x);
1.1       jtc       104:            if(ix>0x7ff00000||
1.5       jtc       105:                (ix==0x7ff00000&&(low!=0)))
1.1       jtc       106:                return x+x;             /* NaN */
107:            if(hx>0) return  atanhi[3]+atanlo[3];
108:            else     return -atanhi[3]-atanlo[3];
109:        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
110:            if (ix < 0x3e200000) {      /* |x| < 2^-29 */
111:                if(huge+x>one) return x;        /* raise inexact */
112:            }
113:            id = -1;
114:        } else {
115:        x = fabs(x);
116:        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
117:            if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
118:                id = 0; x = (2.0*x-one)/(2.0+x);
119:            } else {                    /* 11/16<=|x|< 19/16 */
120:                id = 1; x  = (x-one)/(x+one);
121:            }
122:        } else {
123:            if (ix < 0x40038000) {      /* |x| < 2.4375 */
124:                id = 2; x  = (x-1.5)/(one+1.5*x);
125:            } else {                    /* 2.4375 <= |x| < 2^66 */
126:                id = 3; x  = -1.0/x;
127:            }
128:        }}
129:     /* end of argument reduction */
130:        z = x*x;
131:        w = z*z;
132:     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
133:        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
134:        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
135:        if (id<0) return x - x*(s1+s2);
136:        else {
137:            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
138:            return (hx<0)? -z:z;
139:        }
140: }
```

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