1 /* sf_atan.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
17 #include "fdlibm.h"
18
19 static const float atanhi[] = {
20 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
21 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
22 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
23 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
24 };
25
26 static const float atanlo[] = {
27 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
28 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
29 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
30 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
31 };
32
33 static const float aT[] = {
34 3.3333334327e-01, /* 0x3eaaaaaa */
35 -2.0000000298e-01, /* 0xbe4ccccd */
36 1.4285714924e-01, /* 0x3e124925 */
37 -1.1111110449e-01, /* 0xbde38e38 */
38 9.0908870101e-02, /* 0x3dba2e6e */
39 -7.6918758452e-02, /* 0xbd9d8795 */
40 6.6610731184e-02, /* 0x3d886b35 */
41 -5.8335702866e-02, /* 0xbd6ef16b */
42 4.9768779427e-02, /* 0x3d4bda59 */
43 -3.6531571299e-02, /* 0xbd15a221 */
44 1.6285819933e-02, /* 0x3c8569d7 */
45 };
46
47 static const float one = 1.0, huge = 1.0e30;
48
49 float
atanf(float x)50 atanf(float x)
51 {
52 float w, s1, s2, z;
53 __int32_t ix, hx, id;
54
55 GET_FLOAT_WORD(hx, x);
56 ix = hx & 0x7fffffff;
57 if (ix >= 0x50800000) { /* if |x| >= 2^34 */
58 if (FLT_UWORD_IS_NAN(ix))
59 return x + x; /* NaN */
60 if (hx > 0)
61 return atanhi[3] + atanlo[3];
62 else
63 return -atanhi[3] - atanlo[3];
64 }
65 if (ix < 0x3ee00000) { /* |x| < 0.4375 */
66 if (ix < 0x31000000) { /* |x| < 2^-29 */
67 if (huge + x > one)
68 return x; /* raise inexact */
69 }
70 id = -1;
71 } else {
72 x = fabsf(x);
73 if (ix < 0x3f980000) { /* |x| < 1.1875 */
74 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
75 id = 0;
76 x = ((float)2.0 * x - one) / ((float)2.0 + x);
77 } else { /* 11/16<=|x|< 19/16 */
78 id = 1;
79 x = (x - one) / (x + one);
80 }
81 } else {
82 if (ix < 0x401c0000) { /* |x| < 2.4375 */
83 id = 2;
84 x = (x - (float)1.5) / (one + (float)1.5 * x);
85 } else { /* 2.4375 <= |x| < 2^66 */
86 id = 3;
87 x = -(float)1.0 / x;
88 }
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 *
96 (aT[0] +
97 w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10])))));
98 s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9]))));
99 if (id < 0)
100 return x - x * (s1 + s2);
101 else {
102 z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
103 return (hx < 0) ? -z : z;
104 }
105 }
106
107 _MATH_ALIAS_f_f(atan)
108
