86 lines
2.3 KiB
C
86 lines
2.3 KiB
C
/* @(#)s_atan.c 5.1 93/09/24 */
|
|
/* FreeBSD: head/lib/msun/src/s_atan.c 176451 2008-02-22 02:30:36Z das */
|
|
/*
|
|
* ====================================================
|
|
* 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.
|
|
* ====================================================
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
/*
|
|
* See comments in s_atan.c.
|
|
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
|
|
*/
|
|
|
|
#include <float.h>
|
|
|
|
#include "invtrig.h"
|
|
#include "math.h"
|
|
#include "math_private.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)
|
|
return x+x; /* NaN */
|
|
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 */
|
|
if(huge+x>one) return x; /* raise inexact */
|
|
}
|
|
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);
|
|
else {
|
|
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
|
|
return (expsign<0)? -z:z;
|
|
}
|
|
}
|