s_atanf.c revision 176451 
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: head/lib/msun/src/s_atanf.c 176451 2008-02-22 02:30:36Z das $");
18
19#include "math.h"
20#include "math_private.h"
21
22static 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
29static 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
36static 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
51one   = 1.0,
52huge   = 1.0e30;
53
54float
55atanf(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