1 /* $NetBSD: s_atanf.c,v 1.9 2024/06/09 13:35:38 riastradh Exp $ */
2
3 /*
4 * s_atanf.c -- float version of s_atan.c.
5 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 */
7
8 /*
9 * ====================================================
10 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
11 *
12 * Developed at SunPro, a Sun Microsystems, Inc. business.
13 * Permission to use, copy, modify, and distribute this
14 * software is freely granted, provided that this notice
15 * is preserved.
16 * ====================================================
17 */
18
19 #include <sys/cdefs.h>
20 #if defined(LIBM_SCCS) && !defined(lint)
21 __RCSID("$NetBSD: s_atanf.c,v 1.9 2024/06/09 13:35:38 riastradh Exp $");
22 #endif
23
24 #include "namespace.h"
25
26 #include "math.h"
27 #include "math_private.h"
28
29 __weak_alias(atanf, _atanf)
30
31 static const float atanhi[] = {
32 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
33 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
34 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
35 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
36 };
37
38 static const float atanlo[] = {
39 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
40 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
41 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
42 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
43 };
44
45 static const float aT[] = {
46 3.3333334327e-01, /* 0x3eaaaaaa */
47 -2.0000000298e-01, /* 0xbe4ccccd */
48 1.4285714924e-01, /* 0x3e124925 */
49 -1.1111110449e-01, /* 0xbde38e38 */
50 9.0908870101e-02, /* 0x3dba2e6e */
51 -7.6918758452e-02, /* 0xbd9d8795 */
52 6.6610731184e-02, /* 0x3d886b35 */
53 -5.8335702866e-02, /* 0xbd6ef16b */
54 4.9768779427e-02, /* 0x3d4bda59 */
55 -3.6531571299e-02, /* 0xbd15a221 */
56 1.6285819933e-02, /* 0x3c8569d7 */
57 };
58
59 static const float
60 one = 1.0,
61 huge = 1.0e30;
62
63 float
atanf(float x)64 atanf(float x)
65 {
66 float w,s1,s2,z;
67 int32_t ix,hx,id;
68
69 GET_FLOAT_WORD(hx,x);
70 ix = hx&0x7fffffff;
71 if(ix>=0x50800000) { /* if |x| >= 2^34 */
72 if(ix>0x7f800000)
73 return x+x; /* NaN */
74 if(hx>0) return atanhi[3]+atanlo[3];
75 else return -atanhi[3]-atanlo[3];
76 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
77 if (ix < 0x31000000) { /* |x| < 2^-29 */
78 if(huge+x>one) return x; /* raise inexact */
79 }
80 id = -1;
81 } else {
82 x = fabsf(x);
83 if (ix < 0x3f980000) { /* |x| < 1.1875 */
84 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
85 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
86 } else { /* 11/16<=|x|< 19/16 */
87 id = 1; x = (x-one)/(x+one);
88 }
89 } else {
90 if (ix < 0x401c0000) { /* |x| < 2.4375 */
91 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
92 } else { /* 2.4375 <= |x| < 2^66 */
93 id = 3; x = -(float)1.0/x;
94 }
95 }}
96 /* end of argument reduction */
97 z = x*x;
98 w = z*z;
99 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
100 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
101 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
102 if (id<0) return x - x*(s1+s2);
103 else {
104 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
105 return (hx<0)? -z:z;
106 }
107 }
108