/* origin: FreeBSD /usr/src/lib/msun/src/s_atan.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.
 * ====================================================
 */
/* atan(x)
 * Method
 *   1. Reduce x to positive by atan(x) = -atan(-x).
 *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
 *      is further reduced to one of the following intervals and the
 *      arctangent of t is evaluated by the corresponding formula:
 *
 *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
 *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
 *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
 *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
 *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "libm.h"

static const double atanhi[] = {
    4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
    7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
    9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
    1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
};

static const double atanlo[] = {
    2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
    3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
    1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
    6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
};

static const double aT[] = {
    3.33333333333329318027e-01,  /* 0x3FD55555, 0x5555550D */
    -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
    1.42857142725034663711e-01,  /* 0x3FC24924, 0x920083FF */
    -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
    9.09088713343650656196e-02,  /* 0x3FB745CD, 0xC54C206E */
    -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
    6.66107313738753120669e-02,  /* 0x3FB10D66, 0xA0D03D51 */
    -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
    4.97687799461593236017e-02,  /* 0x3FA97B4B, 0x24760DEB */
    -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
    1.62858201153657823623e-02,  /* 0x3F90AD3A, 0xE322DA11 */
};

double atan(double x) {
  double_t w, s1, s2, z;
  uint32_t ix, sign;
  int id;

  GET_HIGH_WORD(ix, x);
  sign = ix >> 31;
  ix &= 0x7fffffff;
  if (ix >= 0x44100000) { /* if |x| >= 2^66 */
    if (isnan(x))
      return x;
    z = atanhi[3] + 0x1p-120f;
    return sign ? -z : z;
  }
  if (ix < 0x3fdc0000) {   /* |x| < 0.4375 */
    if (ix < 0x3e400000) { /* |x| < 2^-27 */
      if (ix < 0x00100000)
        /* raise underflow for subnormal x */
        FORCE_EVAL((float)x);
      return x;
    }
    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 - 1.0) / (2.0 + x);
      } else { /* 11/16 <= |x| < 19/16 */
        id = 1;
        x = (x - 1.0) / (x + 1.0);
      }
    } else {
      if (ix < 0x40038000) { /* |x| < 2.4375 */
        id = 2;
        x = (x - 1.5) / (1.0 + 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);
  z = atanhi[id] - (x * (s1 + s2) - atanlo[id] - x);
  return sign ? -z : z;
}