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Annotation of src/lib/libm/src/s_atan.c, Revision 1.1.1.1

```1.1       jtc         1:
2: /* @(#)s_atan.c 5.1 93/09/24 */
3: /*
4:  * ====================================================
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:
15: /* atan(x)
16:  * Method
17:  *   1. Reduce x to positive by atan(x) = -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]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
23:  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
24:  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
25:  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
26:  *      [39/16,INF]   atan(x) = atan(INF) + 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, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
43:   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
44:   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
45:   1.57079632679489655800e+00, /* 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, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
54:   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
55:   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
56:   6.12323399573676603587e-17, /* 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 atan(double x)
87: #else
88:        double atan(x)
89:        double x;
90: #endif
91: {
92:        double w,s1,s2,z;
93:        int n0,ix,hx,id;
94:
95:        n0 = ((*(int*)&one)>>29)^1;
96:        hx = *(n0+(int*)&x);
97:        ix = hx&0x7fffffff;
98:        if(ix>=0x44100000) {    /* if |x| >= 2^66 */
99:            if(ix>0x7ff00000||
100:                (ix==0x7ff00000&&(*(1-n0+(int*)&x)!=0)))
101:                return x+x;             /* NaN */
102:            if(hx>0) return  atanhi[3]+atanlo[3];
103:            else     return -atanhi[3]-atanlo[3];
104:        } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
105:            if (ix < 0x3e200000) {      /* |x| < 2^-29 */
106:                if(huge+x>one) return x;        /* raise inexact */
107:            }
108:            id = -1;
109:        } else {
110:        x = fabs(x);
111:        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
112:            if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
113:                id = 0; x = (2.0*x-one)/(2.0+x);
114:            } else {                    /* 11/16<=|x|< 19/16 */
115:                id = 1; x  = (x-one)/(x+one);
116:            }
117:        } else {
118:            if (ix < 0x40038000) {      /* |x| < 2.4375 */
119:                id = 2; x  = (x-1.5)/(one+1.5*x);
120:            } else {                    /* 2.4375 <= |x| < 2^66 */
121:                id = 3; x  = -1.0/x;
122:            }
123:        }}
124:     /* end of argument reduction */
125:        z = x*x;
126:        w = z*z;
127:     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
128:        s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
129:        s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
130:        if (id<0) return x - x*(s1+s2);
131:        else {
132:            z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
133:            return (hx<0)? -z:z;
134:        }
135: }
```

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