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
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  3.3333328366e-01,
38 -1.9999158382e-01,
39  1.4253635705e-01,
40 -1.0648017377e-01,
41  6.1687607318e-02,
42};
43
44static const float
45one   = 1.0,
46huge   = 1.0e30;
47
48float
49atanf(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