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)
17static 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
26static 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
33static 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
40static 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
54static const float
55one = 1.0,
56huge = 1.0e30;
57
58float __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}
103libm_alias_float (__atan, atan)
104