xref: /freebsd/lib/msun/src/s_atanf.c (revision 2be1a816b9ff69588e55be0a84cbe2a31efc0f2f)
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   3.3333334327e-01, /* 0x3eaaaaaa */
38  -2.0000000298e-01, /* 0xbe4ccccd */
39   1.4285714924e-01, /* 0x3e124925 */
40  -1.1111110449e-01, /* 0xbde38e38 */
41   9.0908870101e-02, /* 0x3dba2e6e */
42  -7.6918758452e-02, /* 0xbd9d8795 */
43   6.6610731184e-02, /* 0x3d886b35 */
44  -5.8335702866e-02, /* 0xbd6ef16b */
45   4.9768779427e-02, /* 0x3d4bda59 */
46  -3.6531571299e-02, /* 0xbd15a221 */
47   1.6285819933e-02, /* 0x3c8569d7 */
48 };
49 
50 	static const float
51 one   = 1.0,
52 huge   = 1.0e30;
53 
54 float
55 atanf(float x)
56 {
57 	float w,s1,s2,z;
58 	int32_t ix,hx,id;
59 
60 	GET_FLOAT_WORD(hx,x);
61 	ix = hx&0x7fffffff;
62 	if(ix>=0x50800000) {	/* if |x| >= 2^34 */
63 	    if(ix>0x7f800000)
64 		return x+x;		/* NaN */
65 	    if(hx>0) return  atanhi[3]+atanlo[3];
66 	    else     return -atanhi[3]-atanlo[3];
67 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
68 	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
69 		if(huge+x>one) return x;	/* raise inexact */
70 	    }
71 	    id = -1;
72 	} else {
73 	x = fabsf(x);
74 	if (ix < 0x3f980000) {		/* |x| < 1.1875 */
75 	    if (ix < 0x3f300000) {	/* 7/16 <=|x|<11/16 */
76 		id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
77 	    } else {			/* 11/16<=|x|< 19/16 */
78 		id = 1; x  = (x-one)/(x+one);
79 	    }
80 	} else {
81 	    if (ix < 0x401c0000) {	/* |x| < 2.4375 */
82 		id = 2; x  = (x-(float)1.5)/(one+(float)1.5*x);
83 	    } else {			/* 2.4375 <= |x| < 2^66 */
84 		id = 3; x  = -(float)1.0/x;
85 	    }
86 	}}
87     /* end of argument reduction */
88 	z = x*x;
89 	w = z*z;
90     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
91 	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
92 	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
93 	if (id<0) return x - x*(s1+s2);
94 	else {
95 	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
96 	    return (hx<0)? -z:z;
97 	}
98 }
99