/* s_atanf.c -- float version of s_atan.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
/*
* ====================================================
* 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 <math.h>
#include "math_private.h"
static const float atanhi[] = {
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
};
static const float atanlo[] = {
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
};
static const float aT[] = {
3.3333334327e-01, /* 0x3eaaaaaa */
-2.0000000298e-01, /* 0xbe4ccccd */
1.4285714924e-01, /* 0x3e124925 */
-1.1111110449e-01, /* 0xbde38e38 */
9.0908870101e-02, /* 0x3dba2e6e */
-7.6918758452e-02, /* 0xbd9d8795 */
6.6610731184e-02, /* 0x3d886b35 */
-5.8335702866e-02, /* 0xbd6ef16b */
4.9768779427e-02, /* 0x3d4bda59 */
-3.6531571299e-02, /* 0xbd15a221 */
1.6285819933e-02, /* 0x3c8569d7 */
};
static const float
one = 1.0,
huge = 1.0e30;
float
atanf(float x)
{
float w,s1,s2,z;
int32_t ix,hx,id;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x50800000) { /* if |x| >= 2^34 */
if(ix>0x7f800000)
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x31000000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabsf(x);
if (ix < 0x3f980000) { /* |x| < 1.1875 */
if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -(float)1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}
