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 #include <sys/cdefs.h>
17 #if defined(LIBM_SCCS) && !defined(lint)
18 __RCSID("$NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $");
19 #endif
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float atanhi[] = {
25 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
26 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
27 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
28 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
29 };
30
31 static const float atanlo[] = {
32 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
33 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
34 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
35 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
36 };
37
38 static const float aT[] = {
39 3.3333334327e-01, /* 0x3eaaaaaa */
40 -2.0000000298e-01, /* 0xbe4ccccd */
41 1.4285714924e-01, /* 0x3e124925 */
42 -1.1111110449e-01, /* 0xbde38e38 */
43 9.0908870101e-02, /* 0x3dba2e6e */
44 -7.6918758452e-02, /* 0xbd9d8795 */
45 6.6610731184e-02, /* 0x3d886b35 */
46 -5.8335702866e-02, /* 0xbd6ef16b */
47 4.9768779427e-02, /* 0x3d4bda59 */
48 -3.6531571299e-02, /* 0xbd15a221 */
49 1.6285819933e-02, /* 0x3c8569d7 */
50 };
51
52 static const float
53 one = 1.0,
54 huge = 1.0e30;
55
56 float
atanf(float x)57 atanf(float x)
58 {
59 float w,s1,s2,z;
60 int32_t ix,hx,id;
61
62 GET_FLOAT_WORD(hx,x);
63 ix = hx&0x7fffffff;
64 if(ix>=0x50800000) { /* if |x| >= 2^34 */
65 if(ix>0x7f800000)
66 return x+x; /* NaN */
67 if(hx>0) return atanhi[3]+atanlo[3];
68 else return -atanhi[3]-atanlo[3];
69 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
70 if (ix < 0x31000000) { /* |x| < 2^-29 */
71 if(huge+x>one) return x; /* raise inexact */
72 }
73 id = -1;
74 } else {
75 x = fabsf(x);
76 if (ix < 0x3f980000) { /* |x| < 1.1875 */
77 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
78 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
79 } else { /* 11/16<=|x|< 19/16 */
80 id = 1; x = (x-one)/(x+one);
81 }
82 } else {
83 if (ix < 0x401c0000) { /* |x| < 2.4375 */
84 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
85 } else { /* 2.4375 <= |x| < 2^66 */
86 id = 3; x = -(float)1.0/x;
87 }
88 }}
89 /* end of argument reduction */
90 z = x*x;
91 w = z*z;
92 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
93 s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
94 s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
95 if (id<0) return x - x*(s1+s2);
96 else {
97 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
98 return (hx<0)? -z:z;
99 }
100 }
101