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 //__FBSDID("$FreeBSD: src/lib/msun/src/s_atanl.c,v 1.1 2008/07/31 22:41:26 das Exp $");
15
16 /*
17 * See comments in s_atan.c.
18 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
19 */
20
21 #include "invtrig.h"
22
23 static const long double
24 one = 1.0l,
25 huge = 1.0e300l;
26
27 long double
atanl(long double x)28 atanl(long double x)
29 {
30 union IEEEl2bits u;
31 long double w,s1,s2,z;
32 int id;
33 int16_t expsign, expt;
34 int32_t expman;
35
36 u.e = x;
37 expsign = u.xbits.expsign;
38 expt = expsign & 0x7fff;
39 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
40 if(expt == BIAS + LDBL_MAX_EXP &&
41 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
42 return x+x; /* NaN */
43 if(expsign>0) return atanhi[3]+atanlo[3];
44 else return -atanhi[3]-atanlo[3];
45 }
46 /* Extract the exponent and the first few bits of the mantissa. */
47 /* XXX There should be a more convenient way to do this. */
48 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
49 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
50 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
51 if(huge+x>one) return x; /* raise inexact */
52 }
53 id = -1;
54 } else {
55 x = fabsl(x);
56 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
57 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */
58 id = 0; x = (2.0l*x-one)/(2.0l+x);
59 } else { /* 11/16<=|x|< 19/16 */
60 id = 1; x = (x-one)/(x+one);
61 }
62 } else {
63 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
64 id = 2; x = (x-1.5l)/(one+1.5l*x);
65 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */
66 id = 3; x = -1.0l/x;
67 }
68 }}
69 /* end of argument reduction */
70 z = x*x;
71 w = z*z;
72 /* break sum aT[i]z**(i+1) into odd and even poly */
73 s1 = z*T_even(w);
74 s2 = w*T_odd(w);
75 if (id<0) return x - x*(s1+s2);
76 else {
77 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
78 return (expsign<0)? -z:z;
79 }
80 }
81
