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1 /* @(#)s_atan.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
12 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
20 * 1. Reduce x to positive by atan(x) = -atan(-x).
21 * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
22 * is further reduced to one of the following intervals and the
23 * arctangent of t is evaluated by the corresponding formula:
25 * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
26 * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
27 * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
28 * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
29 * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
32 * The hexadecimal values are the intended ones for the following
33 * constants. The decimal values may be used, provided that the
34 * compiler will convert from decimal to binary accurately enough
35 * to produce the hexadecimal values shown.
39 #include "math_private.h"
41 static const double atanhi
[] = {
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 */
48 static const double atanlo
[] = {
49 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
50 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
51 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
52 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
55 static const double aT
[] = {
56 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
57 -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
58 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
59 -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
60 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
61 -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
62 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
63 -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
64 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
65 -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
66 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
81 if(ix
>=0x44100000) { /* if |x| >= 2^66 */
85 (ix
==0x7ff00000&&(low
!=0)))
87 if(hx
>0) return atanhi
[3]+atanlo
[3];
88 else return -atanhi
[3]-atanlo
[3];
89 } if (ix
< 0x3fdc0000) { /* |x| < 0.4375 */
90 if (ix
< 0x3e200000) { /* |x| < 2^-29 */
91 if(huge
+x
>one
) return x
; /* raise inexact */
96 if (ix
< 0x3ff30000) { /* |x| < 1.1875 */
97 if (ix
< 0x3fe60000) { /* 7/16 <=|x|<11/16 */
98 id
= 0; x
= (2.0*x
-one
)/(2.0+x
);
99 } else { /* 11/16<=|x|< 19/16 */
100 id
= 1; x
= (x
-one
)/(x
+one
);
103 if (ix
< 0x40038000) { /* |x| < 2.4375 */
104 id
= 2; x
= (x
-1.5)/(one
+1.5*x
);
105 } else { /* 2.4375 <= |x| < 2^66 */
109 /* end of argument reduction */
112 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
113 s1
= z
*(aT
[0]+w
*(aT
[2]+w
*(aT
[4]+w
*(aT
[6]+w
*(aT
[8]+w
*aT
[10])))));
114 s2
= w
*(aT
[1]+w
*(aT
[3]+w
*(aT
[5]+w
*(aT
[7]+w
*aT
[9]))));
115 if (id
<0) return x
- x
*(s1
+s2
);
117 z
= atanhi
[id
] - ((x
*(s1
+s2
) - atanlo
[id
]) - x
);