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
28 static const long double
29 one = 1.0,
30 huge = 1.0e300;
31
32 long double
atanl(long double x)33 atanl(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