/* sf_atan.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 "fdlibm.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 (FLT_UWORD_IS_NAN(ix))
            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;
    }
}

_MATH_ALIAS_f_f(atan)