1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 "libm.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 3.3333328366e-01,
35 -1.9999158382e-01,
36 1.4253635705e-01,
37 -1.0648017377e-01,
38 6.1687607318e-02,
39 };
40
atanf(float x)41 float atanf(float x)
42 {
43 float_t w,s1,s2,z;
44 uint32_t ix,sign;
45 int id;
46
47 GET_FLOAT_WORD(ix, x);
48 sign = ix>>31;
49 ix &= 0x7fffffff;
50 if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
51 if (isnan(x))
52 return x;
53 z = atanhi[3] + 0x1p-120f;
54 return sign ? -z : z;
55 }
56 if (ix < 0x3ee00000) { /* |x| < 0.4375 */
57 if (ix < 0x39800000) { /* |x| < 2**-12 */
58 if (ix < 0x00800000)
59 /* raise underflow for subnormal x */
60 FORCE_EVAL(x*x);
61 return x;
62 }
63 id = -1;
64 } else {
65 x = fabsf(x);
66 if (ix < 0x3f980000) { /* |x| < 1.1875 */
67 if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */
68 id = 0;
69 x = (2.0f*x - 1.0f)/(2.0f + x);
70 } else { /* 11/16 <= |x| < 19/16 */
71 id = 1;
72 x = (x - 1.0f)/(x + 1.0f);
73 }
74 } else {
75 if (ix < 0x401c0000) { /* |x| < 2.4375 */
76 id = 2;
77 x = (x - 1.5f)/(1.0f + 1.5f*x);
78 } else { /* 2.4375 <= |x| < 2**26 */
79 id = 3;
80 x = -1.0f/x;
81 }
82 }
83 }
84 /* end of argument reduction */
85 z = x*x;
86 w = z*z;
87 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
88 s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
89 s2 = w*(aT[1]+w*aT[3]);
90 if (id < 0)
91 return x - x*(s1+s2);
92 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
93 return sign ? -z : z;
94 }
95