1 /* $NetBSD: s_atan.c,v 1.13 2024/06/09 13:35:38 riastradh Exp $ */
2
3 /* @(#)s_atan.c 5.1 93/09/24 */
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15 #include <sys/cdefs.h>
16 #if defined(LIBM_SCCS) && !defined(lint)
17 __RCSID("$NetBSD: s_atan.c,v 1.13 2024/06/09 13:35:38 riastradh Exp $");
18 #endif
19
20 /* atan(x)
21 * Method
22 * 1. Reduce x to positive by atan(x) = -atan(-x).
23 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
24 * is further reduced to one of the following intervals and the
25 * arctangent of t is evaluated by the corresponding formula:
26 *
27 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
28 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
29 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
30 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
31 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
32 *
33 * Constants:
34 * The hexadecimal values are the intended ones for the following
35 * constants. The decimal values may be used, provided that the
36 * compiler will convert from decimal to binary accurately enough
37 * to produce the hexadecimal values shown.
38 */
39
40 #include "namespace.h"
41
42 #include "math.h"
43 #include "math_private.h"
44
45 #ifndef __HAVE_LONG_DOUBLE
46 __weak_alias(atanl, _atanl)
47 __strong_alias(_atanl, _atan)
48 #endif
49
50 __weak_alias(atan, _atan)
51
52 static const double atanhi[] = {
53 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
54 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
55 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
56 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
57 };
58
59 static const double atanlo[] = {
60 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
61 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
62 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
63 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
64 };
65
66 static const double aT[] = {
67 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
68 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
69 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
70 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
71 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
72 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
73 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
74 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
75 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
76 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
77 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
78 };
79
80 static const double
81 one = 1.0,
82 huge = 1.0e300;
83
84 double
atan(double x)85 atan(double x)
86 {
87 double w,s1,s2,z;
88 int32_t ix,hx,id;
89
90 GET_HIGH_WORD(hx,x);
91 ix = hx&0x7fffffff;
92 if(ix>=0x44100000) { /* if |x| >= 2^66 */
93 u_int32_t low;
94 GET_LOW_WORD(low,x);
95 if(ix>0x7ff00000||
96 (ix==0x7ff00000&&(low!=0)))
97 return x+x; /* NaN */
98 if(hx>0) return atanhi[3]+atanlo[3];
99 else return -atanhi[3]-atanlo[3];
100 } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
101 if (ix < 0x3e200000) { /* |x| < 2^-29 */
102 if(huge+x>one) return x; /* raise inexact */
103 }
104 id = -1;
105 } else {
106 x = fabs(x);
107 if (ix < 0x3ff30000) { /* |x| < 1.1875 */
108 if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
109 id = 0; x = (2.0*x-one)/(2.0+x);
110 } else { /* 11/16<=|x|< 19/16 */
111 id = 1; x = (x-one)/(x+one);
112 }
113 } else {
114 if (ix < 0x40038000) { /* |x| < 2.4375 */
115 id = 2; x = (x-1.5)/(one+1.5*x);
116 } else { /* 2.4375 <= |x| < 2^66 */
117 id = 3; x = -1.0/x;
118 }
119 }}
120 /* end of argument reduction */
121 z = x*x;
122 w = z*z;
123 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
124 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
125 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
126 if (id<0) return x - x*(s1+s2);
127 else {
128 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
129 return (hx<0)? -z:z;
130 }
131 }
132