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s_atan.c (4126B)
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1 /* @(#)s_atan.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 */
12
13 #ifndef lint
14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_atan.c,v 1.9 2003/07/23 04:53:46 peter Exp $";
15 #endif
16
17 /* atan(x)
18 * Method
19 * 1. Reduce x to positive by atan(x) = -atan(-x).
20 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
21 * is further reduced to one of the following intervals and the
22 * arctangent of t is evaluated by the corresponding formula:
23 *
24 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
25 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
26 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
27 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
28 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
29 *
30 * Constants:
31 * The hexadecimal values are the intended ones for the following
32 * constants. The decimal values may be used, provided that the
33 * compiler will convert from decimal to binary accurately enough
34 * to produce the hexadecimal values shown.
35 */
36
37 #include "math.h"
38 #include "math_private.h"
39
40 static const double atanhi[] = {
41 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
42 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
43 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
44 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
45 };
46
47 static const double atanlo[] = {
48 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
49 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
50 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
51 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
52 };
53
54 static const double aT[] = {
55 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
56 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
57 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
58 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
59 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
60 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
61 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
62 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
63 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
64 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
65 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
66 };
67
68 static const double
69 one = 1.0,
70 huge = 1.0e300;
71
72 double
73 atan(double x)
74 {
75 double w,s1,s2,z;
76 int32_t ix,hx,id;
77
78 GET_HIGH_WORD(hx,x);
79 ix = hx&0x7fffffff;
80 if(ix>=0x44100000) { /* if |x| >= 2^66 */
81 u_int32_t low;
82 GET_LOW_WORD(low,x);
83 if(ix>0x7ff00000||
84 (ix==0x7ff00000&&(low!=0)))
85 return x+x; /* NaN */
86 if(hx>0) return atanhi[3]+atanlo[3];
87 else return -atanhi[3]-atanlo[3];
88 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
89 if (ix < 0x3e200000) { /* |x| < 2^-29 */
90 if(huge+x>one) return x; /* raise inexact */
91 }
92 id = -1;
93 } else {
94 x = fabs(x);
95 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
96 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
97 id = 0; x = (2.0*x-one)/(2.0+x);
98 } else { /* 11/16<=|x|< 19/16 */
99 id = 1; x = (x-one)/(x+one);
100 }
101 } else {
102 if (ix < 0x40038000) { /* |x| < 2.4375 */
103 id = 2; x = (x-1.5)/(one+1.5*x);
104 } else { /* 2.4375 <= |x| < 2^66 */
105 id = 3; x = -1.0/x;
106 }
107 }}
108 /* end of argument reduction */
109 z = x*x;
110 w = z*z;
111 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
112 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
113 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
114 if (id<0) return x - x*(s1+s2);
115 else {
116 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
117 return (hx<0)? -z:z;
118 }
119 }