1 | /* s_atanf.c -- float version of s_atan.c. |
2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
3 | */ |
4 | |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | #if defined(LIBM_SCCS) && !defined(lint) |
17 | static char rcsid[] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $" ; |
18 | #endif |
19 | |
20 | #include <float.h> |
21 | #include <math.h> |
22 | #include <math_private.h> |
23 | #include <math-underflow.h> |
24 | #include <libm-alias-float.h> |
25 | |
26 | static const float atanhi[] = { |
27 | 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ |
28 | 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ |
29 | 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ |
30 | 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ |
31 | }; |
32 | |
33 | static const float atanlo[] = { |
34 | 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ |
35 | 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ |
36 | 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ |
37 | 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ |
38 | }; |
39 | |
40 | static const float aT[] = { |
41 | 3.3333334327e-01, /* 0x3eaaaaaa */ |
42 | -2.0000000298e-01, /* 0xbe4ccccd */ |
43 | 1.4285714924e-01, /* 0x3e124925 */ |
44 | -1.1111110449e-01, /* 0xbde38e38 */ |
45 | 9.0908870101e-02, /* 0x3dba2e6e */ |
46 | -7.6918758452e-02, /* 0xbd9d8795 */ |
47 | 6.6610731184e-02, /* 0x3d886b35 */ |
48 | -5.8335702866e-02, /* 0xbd6ef16b */ |
49 | 4.9768779427e-02, /* 0x3d4bda59 */ |
50 | -3.6531571299e-02, /* 0xbd15a221 */ |
51 | 1.6285819933e-02, /* 0x3c8569d7 */ |
52 | }; |
53 | |
54 | static const float |
55 | one = 1.0, |
56 | huge = 1.0e30; |
57 | |
58 | float __atanf(float x) |
59 | { |
60 | float w,s1,s2,z; |
61 | int32_t ix,hx,id; |
62 | |
63 | GET_FLOAT_WORD(hx,x); |
64 | ix = hx&0x7fffffff; |
65 | if(ix>=0x4c000000) { /* if |x| >= 2^25 */ |
66 | if(ix>0x7f800000) |
67 | return x+x; /* NaN */ |
68 | if(hx>0) return atanhi[3]+atanlo[3]; |
69 | else return -atanhi[3]-atanlo[3]; |
70 | } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ |
71 | if (ix < 0x31000000) { /* |x| < 2^-29 */ |
72 | math_check_force_underflow (x); |
73 | if(huge+x>one) return x; /* raise inexact */ |
74 | } |
75 | id = -1; |
76 | } else { |
77 | x = fabsf(x); |
78 | if (ix < 0x3f980000) { /* |x| < 1.1875 */ |
79 | if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ |
80 | id = 0; x = ((float)2.0*x-one)/((float)2.0+x); |
81 | } else { /* 11/16<=|x|< 19/16 */ |
82 | id = 1; x = (x-one)/(x+one); |
83 | } |
84 | } else { |
85 | if (ix < 0x401c0000) { /* |x| < 2.4375 */ |
86 | id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); |
87 | } else { /* 2.4375 <= |x| < 2^66 */ |
88 | id = 3; x = -(float)1.0/x; |
89 | } |
90 | }} |
91 | /* end of argument reduction */ |
92 | z = x*x; |
93 | w = z*z; |
94 | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ |
95 | s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); |
96 | s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); |
97 | if (id<0) return x - x*(s1+s2); |
98 | else { |
99 | z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); |
100 | return (hx<0)? -z:z; |
101 | } |
102 | } |
103 | libm_alias_float (__atan, atan) |
104 | |