# source:trunk/sys/libm/s_atan.c@1

Last change on this file since 1 was 1, checked in by alain, 5 years ago

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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 <libm/fdlibm.h>
36
37#ifdef __STDC__
38static const double atanhi[] = {
39#else
40static 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__
49static const double atanlo[] = {
50#else
51static 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__
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 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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