text: /* @(#)e_acos.c 1.3 95/01/18 */
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* __ieee754_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 "fdlibm.h"
  
  #ifdef __STDC__
  static const double
  #else
  static double
  #endif
          one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
          pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
          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 */
  
  #ifdef __STDC__
  void __ieee754_acos(double x, double* result)
  #else
  void __ieee754_acos(x, result)
          double x; double result;
  #endif
  {
      double z, p, q, r, w, s, c, df;
      int hx, ix;
      hx = __HI(x);
      ix = hx & 0x7fffffff;
      if (ix >= 0x3ff00000) {    /* |x| >= 1 */
          if (((ix - 0x3ff00000) | __LO(x)) == 0) {    /* |x|==1 */
              if (hx > 0) {
                  *result = 0.0;        /* acos(1) = 0  */
                  return;
              }
              else {
                  *result = pi + 2.0 * pio2_lo;    /* acos(-1)= pi */
                  return;
              }
          }
          *result = (x - x) / (x - x);        /* acos(|x|>1) is NaN */
          return;
      }
      if (ix < 0x3fe00000) {    /* |x| < 0.5 */
          if (ix <= 0x3c600000) {
              *result = pio2_hi + pio2_lo;/*if|x|<2**-57*/
              return;
          }
          z = x * x;
          p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
          q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
          r = p / q;
          *result = pio2_hi - (x - (pio2_lo - x * r));
          return;
      }
      else if (hx < 0) {        /* x < -0.5 */
          z = (one + x) * 0.5;
          p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
          q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
          sqrt(z, &s);
          r = p / q;
          w = r * s - pio2_lo;
          *result = pi - 2.0 * (s + w);
          return;
      }
      else {            /* x > 0.5 */
          z = (one - x) * 0.5;
          sqrt(z, &s);
          df = s;
          __LO(df) = 0;
          c = (z - df * df) / (s + df);
          p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
          q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
          r = p / q;
          w = r * s + c;
          *result = 2.0 * (df + w);
          return;
      }
  }
  