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
30 long double atanl(long double x)
33 long double w,s1,s2,z;
35 int16_t expsign, expt;
39 expsign = u.xbits.expsign;
40 expt = expsign & 0x7fff;
41 if (expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
42 if (expt == BIAS + LDBL_MAX_EXP &&
43 ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) /* NaN */
46 return atanhi[3]+atanlo[3];
48 return -atanhi[3]-atanlo[3];
50 /* Extract the exponent and the first few bits of the mantissa. */
51 /* XXX There should be a more convenient way to do this. */
52 expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
53 if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
54 if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
62 if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
63 if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
65 x = (2.0*x-one)/(2.0+x);
66 } else { /* 11/16 <= |x| < 19/16 */
71 if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
73 x = (x-1.5)/(one+1.5*x);
74 } else { /* 2.4375 <= |x| < 2^ATAN_CONST */
80 /* end of argument reduction */
83 /* break sum aT[i]z**(i+1) into odd and even poly */
88 z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
89 return expsign < 0 ? -z : z;