/src/moddable/xs/tools/fdlibm/s_atan.c
Line | Count | Source |
1 | | /* |
2 | | * ==================================================== |
3 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
4 | | * |
5 | | * Developed at SunPro, a Sun Microsystems, Inc. business. |
6 | | * Permission to use, copy, modify, and distribute this |
7 | | * software is freely granted, provided that this notice |
8 | | * is preserved. |
9 | | * ==================================================== |
10 | | */ |
11 | | |
12 | | /* atan(x) |
13 | | * Method |
14 | | * 1. Reduce x to positive by atan(x) = -atan(-x). |
15 | | * 2. According to the integer k=4t+0.25 chopped, t=x, the argument |
16 | | * is further reduced to one of the following intervals and the |
17 | | * arctangent of t is evaluated by the corresponding formula: |
18 | | * |
19 | | * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) |
20 | | * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) |
21 | | * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) |
22 | | * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) |
23 | | * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) |
24 | | * |
25 | | * Constants: |
26 | | * The hexadecimal values are the intended ones for the following |
27 | | * constants. The decimal values may be used, provided that the |
28 | | * compiler will convert from decimal to binary accurately enough |
29 | | * to produce the hexadecimal values shown. |
30 | | */ |
31 | | |
32 | | #include "math_private.h" |
33 | | |
34 | | static const double atanhi[] = { |
35 | | 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ |
36 | | 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ |
37 | | 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ |
38 | | 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ |
39 | | }; |
40 | | |
41 | | static const double atanlo[] = { |
42 | | 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ |
43 | | 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ |
44 | | 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ |
45 | | 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ |
46 | | }; |
47 | | |
48 | | static const double aT[] = { |
49 | | 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ |
50 | | -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ |
51 | | 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ |
52 | | -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ |
53 | | 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ |
54 | | -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ |
55 | | 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ |
56 | | -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ |
57 | | 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ |
58 | | -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ |
59 | | 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ |
60 | | }; |
61 | | |
62 | | static const double |
63 | | one = 1.0, |
64 | | huge = 1.0e300; |
65 | | |
66 | | double |
67 | | s_atan(double x) |
68 | 171k | { |
69 | 171k | double w,s1,s2,z; |
70 | 171k | int32_t ix,hx,id; |
71 | | |
72 | 171k | GET_HIGH_WORD(hx,x); |
73 | 171k | ix = hx&0x7fffffff; |
74 | 171k | if(ix>=0x44100000) { /* if |x| >= 2^66 */ |
75 | 5.03k | u_int32_t low; |
76 | 5.03k | GET_LOW_WORD(low,x); |
77 | 5.03k | if(ix>0x7ff00000|| |
78 | 5.03k | (ix==0x7ff00000&&(low!=0))) |
79 | 1.87k | return x+x; /* NaN */ |
80 | 3.15k | if(hx>0) return atanhi[3]+*(volatile double *)&atanlo[3]; |
81 | 1.78k | else return -atanhi[3]-*(volatile double *)&atanlo[3]; |
82 | 166k | } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ |
83 | 145k | if (ix < 0x3e400000) { /* |x| < 2^-27 */ |
84 | 1.01k | if(huge+x>one) return x; /* raise inexact */ |
85 | 1.01k | } |
86 | 144k | id = -1; |
87 | 144k | } else { |
88 | 20.5k | x = fabs(x); |
89 | 20.5k | if (ix < 0x3ff30000) { /* |x| < 1.1875 */ |
90 | 11.4k | if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ |
91 | 6.54k | id = 0; x = (2.0*x-one)/(2.0+x); |
92 | 6.54k | } else { /* 11/16<=|x|< 19/16 */ |
93 | 4.92k | id = 1; x = (x-one)/(x+one); |
94 | 4.92k | } |
95 | 11.4k | } else { |
96 | 9.03k | if (ix < 0x40038000) { /* |x| < 2.4375 */ |
97 | 4.16k | id = 2; x = (x-1.5)/(one+1.5*x); |
98 | 4.86k | } else { /* 2.4375 <= |x| < 2^66 */ |
99 | 4.86k | id = 3; x = -1.0/x; |
100 | 4.86k | } |
101 | 9.03k | }} |
102 | | /* end of argument reduction */ |
103 | 165k | z = x*x; |
104 | 165k | w = z*z; |
105 | | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ |
106 | 165k | s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); |
107 | 165k | s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); |
108 | 165k | if (id<0) return x - x*(s1+s2); |
109 | 20.5k | else { |
110 | 20.5k | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
111 | 20.5k | return (hx<0)? -z:z; |
112 | 20.5k | } |
113 | 165k | } |