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2aa62f2b | 1 | /* @(#)s_atan.c 5.1 93/09/24 */\r |
2 | /*\r | |
3 | * ====================================================\r | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r | |
5 | *\r | |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business.\r | |
7 | * Permission to use, copy, modify, and distribute this\r | |
8 | * software is freely granted, provided that this notice\r | |
9 | * is preserved.\r | |
10 | * ====================================================\r | |
11 | */\r | |
12 | #include <LibConfig.h>\r | |
13 | #include <sys/EfiCdefs.h>\r | |
14 | #if defined(LIBM_SCCS) && !defined(lint)\r | |
15 | __RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");\r | |
16 | #endif\r | |
17 | \r | |
18 | /* atan(x)\r | |
19 | * Method\r | |
20 | * 1. Reduce x to positive by atan(x) = -atan(-x).\r | |
21 | * 2. According to the integer k=4t+0.25 chopped, t=x, the argument\r | |
22 | * is further reduced to one of the following intervals and the\r | |
23 | * arctangent of t is evaluated by the corresponding formula:\r | |
24 | *\r | |
25 | * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)\r | |
26 | * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )\r | |
27 | * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )\r | |
28 | * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )\r | |
29 | * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )\r | |
30 | *\r | |
31 | * Constants:\r | |
32 | * The hexadecimal values are the intended ones for the following\r | |
33 | * constants. The decimal values may be used, provided that the\r | |
34 | * compiler will convert from decimal to binary accurately enough\r | |
35 | * to produce the hexadecimal values shown.\r | |
36 | */\r | |
37 | \r | |
38 | #include "math.h"\r | |
39 | #include "math_private.h"\r | |
40 | \r | |
41 | static const double atanhi[] = {\r | |
42 | 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */\r | |
43 | 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */\r | |
44 | 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */\r | |
45 | 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */\r | |
46 | };\r | |
47 | \r | |
48 | static const double atanlo[] = {\r | |
49 | 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */\r | |
50 | 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */\r | |
51 | 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */\r | |
52 | 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */\r | |
53 | };\r | |
54 | \r | |
55 | static const double aT[] = {\r | |
56 | 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */\r | |
57 | -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */\r | |
58 | 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */\r | |
59 | -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */\r | |
60 | 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */\r | |
61 | -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */\r | |
62 | 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */\r | |
63 | -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */\r | |
64 | 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */\r | |
65 | -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */\r | |
66 | 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */\r | |
67 | };\r | |
68 | \r | |
69 | static const double\r | |
70 | one = 1.0,\r | |
71 | huge = 1.0e300;\r | |
72 | \r | |
73 | double\r | |
74 | atan(double x)\r | |
75 | {\r | |
76 | double w,s1,s2,z;\r | |
77 | int32_t ix,hx,id;\r | |
78 | \r | |
79 | GET_HIGH_WORD(hx,x);\r | |
80 | ix = hx&0x7fffffff;\r | |
81 | if(ix>=0x44100000) { /* if |x| >= 2^66 */\r | |
82 | u_int32_t low;\r | |
83 | GET_LOW_WORD(low,x);\r | |
84 | if(ix>0x7ff00000||\r | |
85 | (ix==0x7ff00000&&(low!=0)))\r | |
86 | return x+x; /* NaN */\r | |
87 | if(hx>0) return atanhi[3]+atanlo[3];\r | |
88 | else return -atanhi[3]-atanlo[3];\r | |
89 | } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */\r | |
90 | if (ix < 0x3e200000) { /* |x| < 2^-29 */\r | |
91 | if(huge+x>one) return x; /* raise inexact */\r | |
92 | }\r | |
93 | id = -1;\r | |
94 | } else {\r | |
95 | x = fabs(x);\r | |
96 | if (ix < 0x3ff30000) { /* |x| < 1.1875 */\r | |
97 | if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */\r | |
98 | id = 0; x = (2.0*x-one)/(2.0+x);\r | |
99 | } else { /* 11/16<=|x|< 19/16 */\r | |
100 | id = 1; x = (x-one)/(x+one);\r | |
101 | }\r | |
102 | } else {\r | |
103 | if (ix < 0x40038000) { /* |x| < 2.4375 */\r | |
104 | id = 2; x = (x-1.5)/(one+1.5*x);\r | |
105 | } else { /* 2.4375 <= |x| < 2^66 */\r | |
106 | id = 3; x = -1.0/x;\r | |
107 | }\r | |
108 | }}\r | |
109 | /* end of argument reduction */\r | |
110 | z = x*x;\r | |
111 | w = z*z;\r | |
112 | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */\r | |
113 | s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));\r | |
114 | s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));\r | |
115 | if (id<0) return x - x*(s1+s2);\r | |
116 | else {\r | |
117 | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);\r | |
118 | return (hx<0)? -z:z;\r | |
119 | }\r | |
120 | }\r |