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