1/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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
17#include "libm.h"
18
19static const float atanhi[] = {
20  4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
21  7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
22  9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
23  1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
24};
25
26static const float atanlo[] = {
27  5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
28  3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
29  3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
30  7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
31};
32
33static const float aT[] = {
34  3.3333328366e-01,
35 -1.9999158382e-01,
36  1.4253635705e-01,
37 -1.0648017377e-01,
38  6.1687607318e-02,
39};
40
41float atanf(float x)
42{
43	float_t w,s1,s2,z;
44	uint32_t ix,sign;
45	int id;
46
47	GET_FLOAT_WORD(ix, x);
48	sign = ix>>31;
49	ix &= 0x7fffffff;
50	if (ix >= 0x4c800000) {  /* if |x| >= 2**26 */
51		if (isnan(x))
52			return x;
53		z = atanhi[3] + 0x1p-120f;
54		return sign ? -z : z;
55	}
56	if (ix < 0x3ee00000) {   /* |x| < 0.4375 */
57		if (ix < 0x39800000) {  /* |x| < 2**-12 */
58			if (ix < 0x00800000)
59				/* raise underflow for subnormal x */
60				FORCE_EVAL(x*x);
61			return x;
62		}
63		id = -1;
64	} else {
65		x = fabsf(x);
66		if (ix < 0x3f980000) {  /* |x| < 1.1875 */
67			if (ix < 0x3f300000) {  /*  7/16 <= |x| < 11/16 */
68				id = 0;
69				x = (2.0f*x - 1.0f)/(2.0f + x);
70			} else {                /* 11/16 <= |x| < 19/16 */
71				id = 1;
72				x = (x - 1.0f)/(x + 1.0f);
73			}
74		} else {
75			if (ix < 0x401c0000) {  /* |x| < 2.4375 */
76				id = 2;
77				x = (x - 1.5f)/(1.0f + 1.5f*x);
78			} else {                /* 2.4375 <= |x| < 2**26 */
79				id = 3;
80				x = -1.0f/x;
81			}
82		}
83	}
84	/* end of argument reduction */
85	z = x*x;
86	w = z*z;
87	/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
88	s1 = z*(aT[0]+w*(aT[2]+w*aT[4]));
89	s2 = w*(aT[1]+w*aT[3]);
90	if (id < 0)
91		return x - x*(s1+s2);
92	z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
93	return sign ? -z : z;
94}
95