1/* @(#)s_atan.c 5.1 93/09/24 */
2/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14#include <sys/cdefs.h>
15__FBSDID("$FreeBSD$");
16
17/*
18 * See comments in s_atan.c.
19 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
20 */
21
22#include <float.h>
23
24#include "invtrig.h"
25#include "math.h"
26#include "math_private.h"
27
28static const long double
29one   = 1.0,
30huge   = 1.0e300;
31
32long double
33atanl(long double x)
34{
35	union IEEEl2bits u;
36	long double w,s1,s2,z;
37	int id;
38	int16_t expsign, expt;
39	int32_t expman;
40
41	u.e = x;
42	expsign = u.xbits.expsign;
43	expt = expsign & 0x7fff;
44	if(expt >= ATAN_CONST) {	/* if |x| is large, atan(x)~=pi/2 */
45	    if(expt == BIAS + LDBL_MAX_EXP &&
46	       ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
47		return x+x;		/* NaN */
48	    if(expsign>0) return  atanhi[3]+atanlo[3];
49	    else     return -atanhi[3]-atanlo[3];
50	}
51	/* Extract the exponent and the first few bits of the mantissa. */
52	/* XXX There should be a more convenient way to do this. */
53	expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
54	if (expman < ((BIAS - 2) << 8) + 0xc0) {	/* |x| < 0.4375 */
55	    if (expt < ATAN_LINEAR) {	/* if |x| is small, atanl(x)~=x */
56		if(huge+x>one) return x;	/* raise inexact */
57	    }
58	    id = -1;
59	} else {
60	x = fabsl(x);
61	if (expman < (BIAS << 8) + 0x30) {		/* |x| < 1.1875 */
62	    if (expman < ((BIAS - 1) << 8) + 0x60) {	/* 7/16 <=|x|<11/16 */
63		id = 0; x = (2.0*x-one)/(2.0+x);
64	    } else {			/* 11/16<=|x|< 19/16 */
65		id = 1; x  = (x-one)/(x+one);
66	    }
67	} else {
68	    if (expman < ((BIAS + 1) << 8) + 0x38) {	/* |x| < 2.4375 */
69		id = 2; x  = (x-1.5)/(one+1.5*x);
70	    } else {			/* 2.4375 <= |x| < 2^ATAN_CONST */
71		id = 3; x  = -1.0/x;
72	    }
73	}}
74    /* end of argument reduction */
75	z = x*x;
76	w = z*z;
77    /* break sum aT[i]z**(i+1) into odd and even poly */
78	s1 = z*T_even(w);
79	s2 = w*T_odd(w);
80	if (id<0) return x - x*(s1+s2);
81	else {
82	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
83	    return (expsign<0)? -z:z;
84	}
85}
86