/* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.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 "libm.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[] = {
    3.3333328366e-01,  -1.9999158382e-01, 1.4253635705e-01,
    -1.0648017377e-01, 6.1687607318e-02,
};

float atanf(float x) {
  float_t w, s1, s2, z;
  uint32_t ix, sign;
  int id;

  GET_FLOAT_WORD(ix, x);
  sign = ix >> 31;
  ix &= 0x7fffffff;
  if (ix >= 0x4c800000) { /* if |x| >= 2**26 */
    if (isnan(x))
      return x;
    z = atanhi[3] + 0x1p-120f;
    return sign ? -z : z;
  }
  if (ix < 0x3ee00000) {   /* |x| < 0.4375 */
    if (ix < 0x39800000) { /* |x| < 2**-12 */
      if (ix < 0x00800000)
        /* raise underflow for subnormal x */
        FORCE_EVAL(x * x);
      return x;
    }
    id = -1;
  } else {
    x = fabsf(x);
    if (ix < 0x3f980000) {   /* |x| < 1.1875 */
      if (ix < 0x3f300000) { /*  7/16 <= |x| < 11/16 */
        id = 0;
        x = (2.0f * x - 1.0f) / (2.0f + x);
      } else { /* 11/16 <= |x| < 19/16 */
        id = 1;
        x = (x - 1.0f) / (x + 1.0f);
      }
    } else {
      if (ix < 0x401c0000) { /* |x| < 2.4375 */
        id = 2;
        x = (x - 1.5f) / (1.0f + 1.5f * x);
      } else { /* 2.4375 <= |x| < 2**26 */
        id = 3;
        x = -1.0f / 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]));
  s2 = w * (aT[1] + w * aT[3]);
  if (id < 0)
    return x - x * (s1 + s2);
  z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x);
  return sign ? -z : z;
}