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