1/*	$OpenBSD: s_atanl.c,v 1.2 2016/09/12 19:47:02 guenther Exp $	*/
2/* @(#)s_atan.c 5.1 93/09/24 */
3/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15/*
16 * See comments in s_atan.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18 * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
19 */
20
21#include <float.h>
22#include <math.h>
23
24#include "invtrig.h"
25#include "math_private.h"
26
27#ifdef EXT_IMPLICIT_NBIT
28#define	LDBL_NBIT	0
29#else /* EXT_IMPLICIT_NBIT */
30#define	LDBL_NBIT	0x80000000
31#endif /* EXT_IMPLICIT_NBIT */
32
33static const long double
34one   = 1.0,
35huge   = 1.0e300;
36
37long double
38atanl(long double x)
39{
40	union {
41		long double e;
42		struct ieee_ext bits;
43	} u;
44	long double w,s1,s2,z;
45	int id;
46	int16_t expsign, expt;
47	int32_t expman;
48
49	u.e = x;
50	expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
51	expt = expsign & 0x7fff;
52	if(expt >= ATAN_CONST) {	/* if |x| is large, atan(x)~=pi/2 */
53	    if(expt == BIAS + LDBL_MAX_EXP &&
54	       ((u.bits.ext_frach&~LDBL_NBIT)
55#ifdef EXT_FRACHMBITS
56		| u.bits.ext_frachm
57#endif /* EXT_FRACHMBITS */
58#ifdef EXT_FRACLMBITS
59		| u.bits.ext_fraclm
60#endif /* EXT_FRACLMBITS */
61		| u.bits.ext_fracl)!=0)
62		return x+x;		/* NaN */
63	    if(expsign>0) return  atanhi[3]+atanlo[3];
64	    else     return -atanhi[3]-atanlo[3];
65	}
66	/* Extract the exponent and the first few bits of the mantissa. */
67	/* XXX There should be a more convenient way to do this. */
68	expman = (expt << 8) |
69		((u.bits.ext_frach >> (EXT_FRACHBITS - 9)) & 0xff);
70	if (expman < ((BIAS - 2) << 8) + 0xc0) {	/* |x| < 0.4375 */
71	    if (expt < ATAN_LINEAR) {	/* if |x| is small, atanl(x)~=x */
72		if(huge+x>one) return x;	/* raise inexact */
73	    }
74	    id = -1;
75	} else {
76	x = fabsl(x);
77	if (expman < (BIAS << 8) + 0x30) {		/* |x| < 1.1875 */
78	    if (expman < ((BIAS - 1) << 8) + 0x60) {	/* 7/16 <=|x|<11/16 */
79		id = 0; x = (2.0*x-one)/(2.0+x);
80	    } else {			/* 11/16<=|x|< 19/16 */
81		id = 1; x  = (x-one)/(x+one);
82	    }
83	} else {
84	    if (expman < ((BIAS + 1) << 8) + 0x38) {	/* |x| < 2.4375 */
85		id = 2; x  = (x-1.5)/(one+1.5*x);
86	    } else {			/* 2.4375 <= |x| < 2^ATAN_CONST */
87		id = 3; x  = -1.0/x;
88	    }
89	}}
90    /* end of argument reduction */
91	z = x*x;
92	w = z*z;
93    /* break sum aT[i]z**(i+1) into odd and even poly */
94	s1 = z*T_even(w);
95	s2 = w*T_odd(w);
96	if (id<0) return x - x*(s1+s2);
97	else {
98	    z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
99	    return (expsign<0)? -z:z;
100	}
101}
102DEF_STD(atanl);
103