/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */
/* acos(x)
 * Method :
 *      acos(x)  = pi/2 - asin(x)
 *      acos(-x) = pi/2 + asin(x)
 * For |x|<=0.5
 *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
 * For x>0.5
 *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
 *              = 2asin(sqrt((1-x)/2))
 *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
 *              = 2f + (2c + 2s*z*R(z))
 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
 *     for f so that f+c ~ sqrt(z).
 * For x<-0.5
 *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
 *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
 *
 * Special cases:
 *      if x is NaN, return x itself;
 *      if |x|>1, return NaN with invalid signal.
 *
 * Function needed: sqrt
 */

#include "libm.h"

static const double pio2_hi =
                        1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
    pio2_lo = 6.12323399573676603587e-17,           /* 0x3C91A626, 0x33145C07 */
    pS0 = 1.66666666666666657415e-01,               /* 0x3FC55555, 0x55555555 */
    pS1 = -3.25565818622400915405e-01,              /* 0xBFD4D612, 0x03EB6F7D */
    pS2 = 2.01212532134862925881e-01,               /* 0x3FC9C155, 0x0E884455 */
    pS3 = -4.00555345006794114027e-02,              /* 0xBFA48228, 0xB5688F3B */
    pS4 = 7.91534994289814532176e-04,               /* 0x3F49EFE0, 0x7501B288 */
    pS5 = 3.47933107596021167570e-05,               /* 0x3F023DE1, 0x0DFDF709 */
    qS1 = -2.40339491173441421878e+00,              /* 0xC0033A27, 0x1C8A2D4B */
    qS2 = 2.02094576023350569471e+00,               /* 0x40002AE5, 0x9C598AC8 */
    qS3 = -6.88283971605453293030e-01,              /* 0xBFE6066C, 0x1B8D0159 */
    qS4 = 7.70381505559019352791e-02;               /* 0x3FB3B8C5, 0xB12E9282 */

static double R(double z) {
  double_t p, q;
  p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
  q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
  return p / q;
}

double acos(double x) {
  double z, w, s, c, df;
  uint32_t hx, ix;

  GET_HIGH_WORD(hx, x);
  ix = hx & 0x7fffffff;
  /* |x| >= 1 or nan */
  if (ix >= 0x3ff00000) {
    uint32_t lx;

    GET_LOW_WORD(lx, x);
    if ((ix - 0x3ff00000 | lx) == 0) {
      /* acos(1)=0, acos(-1)=pi */
      if (hx >> 31)
        return 2 * pio2_hi + 0x1p-120f;
      return 0;
    }
    return 0 / (x - x);
  }
  /* |x| < 0.5 */
  if (ix < 0x3fe00000) {
    if (ix <= 0x3c600000) /* |x| < 2**-57 */
      return pio2_hi + 0x1p-120f;
    return pio2_hi - (x - (pio2_lo - x * R(x * x)));
  }
  /* x < -0.5 */
  if (hx >> 31) {
    z = (1.0 + x) * 0.5;
    s = sqrt(z);
    w = R(z) * s - pio2_lo;
    return 2 * (pio2_hi - (s + w));
  }
  /* x > 0.5 */
  z = (1.0 - x) * 0.5;
  s = sqrt(z);
  df = s;
  SET_LOW_WORD(df, 0);
  c = (z - df * df) / (s + df);
  w = R(z) * s + c;
  return 2 * (df + w);
}