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 __FBSDID("$FreeBSD$");
18
19 #include "math.h"
20 #include "math_private.h"
21
22 static const float atanhi[] = {
23 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
24 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
25 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
26 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
27 };
28
29 static const float atanlo[] = {
30 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
31 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
32 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
33 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
34 };
35
36 static const float aT[] = {
37 3.3333328366e-01,
38 -1.9999158382e-01,
39 1.4253635705e-01,
40 -1.0648017377e-01,
41 6.1687607318e-02,
42 };
43
44 static const float
45 one = 1.0,
46 huge = 1.0e30;
47
48 float
atanf(float x)49 atanf(float x)
50 {
51 float w,s1,s2,z;
52 int32_t ix,hx,id;
53
54 GET_FLOAT_WORD(hx,x);
55 ix = hx&0x7fffffff;
56 if(ix>=0x4c800000) { /* if |x| >= 2**26 */
57 if(ix>0x7f800000)
58 return x+x; /* NaN */
59 if(hx>0) return atanhi[3]+*(volatile float *)&atanlo[3];
60 else return -atanhi[3]-*(volatile float *)&atanlo[3];
61 } if (ix < 0x3ee00000) { /* |x| < 0.4375 */
62 if (ix < 0x39800000) { /* |x| < 2**-12 */
63 if(huge+x>one) return x; /* raise inexact */
64 }
65 id = -1;
66 } else {
67 x = fabsf(x);
68 if (ix < 0x3f980000) { /* |x| < 1.1875 */
69 if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
70 id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
71 } else { /* 11/16<=|x|< 19/16 */
72 id = 1; x = (x-one)/(x+one);
73 }
74 } else {
75 if (ix < 0x401c0000) { /* |x| < 2.4375 */
76 id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
77 } else { /* 2.4375 <= |x| < 2**26 */
78 id = 3; x = -(float)1.0/x;
79 }
80 }}
81 /* end of argument reduction */
82 z = x*x;
83 w = z*z;
84 /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
85 s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
86 s2 = w*(aT[1]+w*aT[3]);
87 if (id<0) return x - x*(s1+s2);
88 else {
89 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
90 return (hx<0)? -z:z;
91 }
92 }
93