/* origin: FreeBSD /usr/src/lib/msun/src/s_atanl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* See comments in atan.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atanl(long double x)
{
return atan(x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#if LDBL_MANT_DIG == 64
#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | (u.i.m>>55 & 0xff))
static const long double atanhi[] = {
4.63647609000806116202e-01L,
7.85398163397448309628e-01L,
9.82793723247329067960e-01L,
1.57079632679489661926e+00L,
};
static const long double atanlo[] = {
1.18469937025062860669e-20L,
-1.25413940316708300586e-20L,
2.55232234165405176172e-20L,
-2.50827880633416601173e-20L,
};
static const long double aT[] = {
3.33333333333333333017e-01L,
-1.99999999999999632011e-01L,
1.42857142857046531280e-01L,
-1.11111111100562372733e-01L,
9.09090902935647302252e-02L,
-7.69230552476207730353e-02L,
6.66661718042406260546e-02L,
-5.88158892835030888692e-02L,
5.25499891539726639379e-02L,
-4.70119845393155721494e-02L,
4.03539201366454414072e-02L,
-2.91303858419364158725e-02L,
1.24822046299269234080e-02L,
};
static long double T_even(long double x)
{
return aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] +
x * (aT[8] + x * (aT[10] + x * aT[12])))));
}
static long double T_odd(long double x)
{
return aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] +
x * (aT[9] + x * aT[11]))));
}
#elif LDBL_MANT_DIG == 113
#define EXPMAN(u) ((u.i.se & 0x7fff)<<8 | u.i.top>>8)
const long double atanhi[] = {
4.63647609000806116214256231461214397e-01L,
7.85398163397448309615660845819875699e-01L,
9.82793723247329067985710611014666038e-01L,
1.57079632679489661923132169163975140e+00L,
};
const long double atanlo[] = {
4.89509642257333492668618435220297706e-36L,
2.16795253253094525619926100651083806e-35L,
-2.31288434538183565909319952098066272e-35L,
4.33590506506189051239852201302167613e-35L,
};
const long double aT[] = {
3.33333333333333333333333333333333125e-01L,
-1.99999999999999999999999999999180430e-01L,
1.42857142857142857142857142125269827e-01L,
-1.11111111111111111111110834490810169e-01L,
9.09090909090909090908522355708623681e-02L,
-7.69230769230769230696553844935357021e-02L,
6.66666666666666660390096773046256096e-02L,
-5.88235294117646671706582985209643694e-02L,
5.26315789473666478515847092020327506e-02L,
-4.76190476189855517021024424991436144e-02L,
4.34782608678695085948531993458097026e-02L,
-3.99999999632663469330634215991142368e-02L,
3.70370363987423702891250829918659723e-02L,
-3.44827496515048090726669907612335954e-02L,
3.22579620681420149871973710852268528e-02L,
-3.03020767654269261041647570626778067e-02L,
2.85641979882534783223403715930946138e-02L,
-2.69824879726738568189929461383741323e-02L,
2.54194698498808542954187110873675769e-02L,
-2.35083879708189059926183138130183215e-02L,
2.04832358998165364349957325067131428e-02L,
-1.54489555488544397858507248612362957e-02L,
8.64492360989278761493037861575248038e-03L,
-2.58521121597609872727919154569765469e-03L,
};
static long double T_even(long double x)
{
return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * (aT[8] +
x * (aT[10] + x * (aT[12] + x * (aT[14] + x * (aT[16] +
x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
}
static long double T_odd(long double x)
{
return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * (aT[9] +
x * (aT[11] + x * (aT[13] + x * (aT[15] + x * (aT[17] +
x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
}
#endif
long double atanl(long double x)
{
union ldshape u = {x};
long double w, s1, s2, z;
int id;
unsigned e = u.i.se & 0x7fff;
unsigned sign = u.i.se >> 15;
unsigned expman;
if (e >= 0x3fff + LDBL_MANT_DIG + 1) { /* if |x| is large, atan(x)~=pi/2 */
if (isnan(x))
return x;
return sign ? -atanhi[3] : atanhi[3];
}
/* Extract the exponent and the first few bits of the mantissa. */
expman = EXPMAN(u);
if (expman < ((0x3fff - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) { /* if |x| is small, atanl(x)~=x */
/* raise underflow if subnormal */
if (e == 0)
FORCE_EVAL((float)x);
return x;
}
id = -1;
} else {
x = fabsl(x);
if (expman < (0x3fff << 8) + 0x30) { /* |x| < 1.1875 */
if (expman < ((0x3fff - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
id = 0;
x = (2.0*x-1.0)/(2.0+x);
} else { /* 11/16 <= |x| < 19/16 */
id = 1;
x = (x-1.0)/(x+1.0);
}
} else {
if (expman < ((0x3fff + 1) << 8) + 0x38) { /* |x| < 2.4375 */
id = 2;
x = (x-1.5)/(1.0+1.5*x);
} else { /* 2.4375 <= |x| */
id = 3;
x = -1.0/x;
}
}
}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum aT[i]z**(i+1) into odd and even poly */
s1 = z*T_even(w);
s2 = w*T_odd(w);
if (id < 0)
return x - x*(s1+s2);
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return sign ? -z : z;
}
#endif
