1 /* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
13 * See comments in atan.c.
14 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
19 #if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
20 long double atanl(long double x)
24 #elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
25 #include "__invtrigl.h"
26 static const long double huge = 1.0e300;
28 long double atanl(long double x)
31 long double w,s1,s2,z;
33 int16_t expsign, expt;
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) /* NaN */
44 return atanhi[3]+atanlo[3];
46 return -atanhi[3]-atanlo[3];
48 /* Extract the exponent and the first few bits of the mantissa. */
49 /* XXX There should be a more convenient way to do this. */
50 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
51 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
52 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
60 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
61 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
63 x = (2.0*x-1.0)/(2.0+x);
64 } else { /* 11/16 <= |x| < 19/16 */
69 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
71 x = (x-1.5)/(1.0+1.5*x);
72 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */
78 /* end of argument reduction */
81 /* break sum aT[i]z**(i+1) into odd and even poly */
86 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
87 return expsign < 0 ? -z : z;