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 */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
11 * ====================================================
14 #include <sys/cdefs.h>
16 * See comments in s_atan.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
24 #include "math_private.h"
26 static const long double
34 long double w,s1,s2,z;
36 int16_t expsign, expt;
40 expsign = u.xbits.expsign;
41 expt = expsign & 0x7fff;
42 if(expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
43 if(expt == BIAS + LDBL_MAX_EXP &&
44 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0)
46 if(expsign>0) return atanhi[3]+atanlo[3];
47 else return -atanhi[3]-atanlo[3];
49 /* Extract the exponent and the first few bits of the mantissa. */
50 /* XXX There should be a more convenient way to do this. */
51 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
52 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
53 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
54 if(huge+x>one) return x; /* raise inexact */
59 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
60 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <=|x|<11/16 */
61 id = 0; x = (2.0*x-one)/(2.0+x);
62 } else { /* 11/16<=|x|< 19/16 */
63 id = 1; x = (x-one)/(x+one);
66 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
67 id = 2; x = (x-1.5)/(one+1.5*x);
68 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */
72 /* end of argument reduction */
75 /* break sum aT[i]z**(i+1) into odd and even poly */
78 if (id<0) return x - x*(s1+s2);
80 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
81 return (expsign<0)? -z:z;