/* 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)

static const long double atanhi[] = {
    4.63647609000806116214256231461214397e-01L, 7.85398163397448309615660845819875699e-01L,
    9.82793723247329067985710611014666038e-01L, 1.57079632679489661923132169163975140e+00L,
};

static const long double atanlo[] = {
    4.89509642257333492668618435220297706e-36L, 2.16795253253094525619926100651083806e-35L,
    -2.31288434538183565909319952098066272e-35L, 4.33590506506189051239852201302167613e-35L,
};

static 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