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b34b60bc 1/* @(#)s_atan.c 5.1 93/09/24 */
6ff43c94 2/* \$FreeBSD: head/lib/msun/src/s_atan.c 218509 2011-02-10 07:37:50Z das \$ */
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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 * ====================================================
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12 */
13
14/* atan(x)
15 * Method
16 * 1. Reduce x to positive by atan(x) = -atan(-x).
17 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
18 * is further reduced to one of the following intervals and the
19 * arctangent of t is evaluated by the corresponding formula:
20 *
21 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
22 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
23 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
24 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
25 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
26 *
27 * Constants:
28 * The hexadecimal values are the intended ones for the following
29 * constants. The decimal values may be used, provided that the
30 * compiler will convert from decimal to binary accurately enough
31 * to produce the hexadecimal values shown.
32 */
33
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34#include <float.h>
35
36#include "math.h"
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37#include "math_private.h"
38
39static const double atanhi[] = {
40 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
41 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
42 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
43 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
44};
45
46static const double atanlo[] = {
47 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
48 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
49 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
50 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
51};
52
53static const double aT[] = {
54 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
55 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
56 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
57 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
58 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
59 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
60 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
61 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
62 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
63 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
64 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
65};
66
67 static const double
68one = 1.0,
69huge = 1.0e300;
70
71double
72atan(double x)
73{
74 double w,s1,s2,z;
75 int32_t ix,hx,id;
76
77 GET_HIGH_WORD(hx,x);
78 ix = hx&0x7fffffff;
79 if(ix>=0x44100000) { /* if |x| >= 2^66 */
80 u_int32_t low;
81 GET_LOW_WORD(low,x);
82 if(ix>0x7ff00000||
83 (ix==0x7ff00000&&(low!=0)))
84 return x+x; /* NaN */
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85 if(hx>0) return atanhi[3]+*(volatile double *)&atanlo[3];
86 else return -atanhi[3]-*(volatile double *)&atanlo[3];
b34b60bc 87 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
6ff43c94 88 if (ix < 0x3e400000) { /* |x| < 2^-27 */
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89 if(huge+x>one) return x; /* raise inexact */
90 }
91 id = -1;
92 } else {
93 x = fabs(x);
94 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
95 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
96 id = 0; x = (2.0*x-one)/(2.0+x);
97 } else { /* 11/16<=|x|< 19/16 */
98 id = 1; x = (x-one)/(x+one);
99 }
100 } else {
101 if (ix < 0x40038000) { /* |x| < 2.4375 */
102 id = 2; x = (x-1.5)/(one+1.5*x);
103 } else { /* 2.4375 <= |x| < 2^66 */
104 id = 3; x = -1.0/x;
105 }
106 }}
107 /* end of argument reduction */
108 z = x*x;
109 w = z*z;
110 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
111 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
112 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
113 if (id<0) return x - x*(s1+s2);
114 else {
115 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
116 return (hx<0)? -z:z;
117 }
118}
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119
120#if LDBL_MANT_DIG == 53
121__weak_reference(atan, atanl);
122#endif