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/* 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
#include "__invtrigl.h"
static const long double
one = 1.0,
huge = 1.0e300;
long double atanl(long double x)
{
union IEEEl2bits u;
long double w,s1,s2,z;
int id;
int16_t expsign, expt;
int32_t expman;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if (expt >= ATAN_CONST) { /* if |x| is large, atan(x)~=pi/2 */
if (expt == BIAS + LDBL_MAX_EXP &&
((u.bits.manh&~LDBL_NBIT)|u.bits.manl)!=0) /* NaN */
return x+x;
if (expsign > 0)
return atanhi[3]+atanlo[3];
else
return -atanhi[3]-atanlo[3];
}
/* Extract the exponent and the first few bits of the mantissa. */
/* XXX There should be a more convenient way to do this. */
expman = (expt << 8) | ((u.bits.manh >> (MANH_SIZE - 9)) & 0xff);
if (expman < ((BIAS - 2) << 8) + 0xc0) { /* |x| < 0.4375 */
if (expt < ATAN_LINEAR) { /* if |x| is small, atanl(x)~=x */
/* raise inexact */
if (huge+x > one)
return x;
}
id = -1;
} else {
x = fabsl(x);
if (expman < (BIAS << 8) + 0x30) { /* |x| < 1.1875 */
if (expman < ((BIAS - 1) << 8) + 0x60) { /* 7/16 <= |x| < 11/16 */
id = 0;
x = (2.0*x-one)/(2.0+x);
} else { /* 11/16 <= |x| < 19/16 */
id = 1;
x = (x-one)/(x+one);
}
} else {
if (expman < ((BIAS + 1) << 8) + 0x38) { /* |x| < 2.4375 */
id = 2;
x = (x-1.5)/(one+1.5*x);
} else { /* 2.4375 <= |x| < 2^ATAN_CONST */
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 expsign < 0 ? -z : z;
}
#endif
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