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