double fgAtan(double x) {
    double atanhi[4], atanlo[4], aT[11];
    double w,s1,s2,z;
    int32_t ix,hx,id;
 
    atanhi[0] = 4.63647609000806093515e-01; 
                        /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    atanhi[1] = 7.85398163397448278999e-01;
                        /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    atanhi[2] = 9.82793723247329054082e-01;
                        /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    atanhi[3] = 1.57079632679489655800e+00;
                        /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
    atanlo[0] = 2.26987774529616870924e-17; 
                        /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    atanlo[1] = 3.06161699786838301793e-17; 
                        /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    atanlo[2] = 1.39033110312309984516e-17; 
                        /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    atanlo[3] = 6.12323399573676603587e-17; 
                        /* atan(inf)lo 0x3C91A626, 0x33145C07 */
    aT[0] =  3.33333333333329318027e-01; /* 0x3FD55555, 0x5555550D */
    aT[1] = -1.99999999998764832476e-01; /* 0xBFC99999, 0x9998EBC4 */
    aT[2] =  1.42857142725034663711e-01; /* 0x3FC24924, 0x920083FF */
    aT[3] = -1.11111104054623557880e-01; /* 0xBFBC71C6, 0xFE231671 */
    aT[4] =  9.09088713343650656196e-02; /* 0x3FB745CD, 0xC54C206E */
    aT[5] = -7.69187620504482999495e-02; /* 0xBFB3B0F2, 0xAF749A6D */
    aT[6] =  6.66107313738753120669e-02; /* 0x3FB10D66, 0xA0D03D51 */
    aT[7] = -5.83357013379057348645e-02; /* 0xBFADDE2D, 0x52DEFD9A */
    aT[8] =  4.97687799461593236017e-02; /* 0x3FA97B4B, 0x24760DEB */
    aT[9] = -3.65315727442169155270e-02; /* 0xBFA2B444, 0x2C6A6C2F */
    aT[10]=  1.62858201153657823623e-02; /* 0x3F90AD3A, 0xE322DA11 */
 
    GET_HIGH_WORD(hx,x);
    ix = hx&0x7fffffff;
    if(ix>=0x44100000) {    /* if |x| >= 2^66 */
        u_int32_t low;
        GET_LOW_WORD(low,x);
        if(ix>0x7ff00000||
                (ix==0x7ff00000&&(low!=0)))
            return x+x;             /* NaN */
        if(hx>0) return  atanhi[3]+atanlo[3];
        else     return -atanhi[3]-atanlo[3];
    } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
        if (ix < 0x3e200000) {      /* |x| < 2^-29 */
            if(huge+x>one) return x;        /* raise inexact */
        }
        id = -1;
    } else {
        x = __fabs(x);
        if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
            if (ix < 0x3fe60000) {      /* 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 (ix < 0x40038000) {      /* |x| < 2.4375 */
                id = 2; x  = (x-1.5)/(one+1.5*x);
            } else {                    /* 2.4375 <= |x| < 2^66 */
                id = 3; x  = -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;
    }
}