text: /* @(#)e_asin.c 5.1 93/09/24 */
  /*
   * ====================================================
   * 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  <LibConfig.h>
  #include  <sys/EfiCdefs.h>
  #if defined(LIBM_SCCS) && !defined(lint)
  __RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
  #endif
  
  #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  // C4723: potential divide by zero.
  #pragma warning ( disable : 4723 )
  #endif
  
  /* __ieee754_asin(x)
   * Method :
   *  Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
   *  we approximate asin(x) on [0,0.5] by
   *    asin(x) = x + x*x^2*R(x^2)
   *  where
   *    R(x^2) is a rational approximation of (asin(x)-x)/x^3
   *  and its remez error is bounded by
   *    |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
   *
   *  For x in [0.5,1]
   *    asin(x) = pi/2-2*asin(sqrt((1-x)/2))
   *  Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
   *  then for x>0.98
   *    asin(x) = pi/2 - 2*(s+s*z*R(z))
   *      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
   *  For x<=0.98, let pio4_hi = pio2_hi/2, then
   *    f = hi part of s;
   *    c = sqrt(z) - f = (z-f*f)/(s+f)   ...f+c=sqrt(z)
   *  and
   *    asin(x) = pi/2 - 2*(s+s*z*R(z))
   *      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
   *      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
   *
   * Special cases:
   *  if x is NaN, return x itself;
   *  if |x|>1, return NaN with invalid signal.
   *
   */
  
  
  #include "math.h"
  #include "math_private.h"
  
  static const double
  one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  huge =  1.000e+300,
  pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
  pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
  pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
    /* coefficient for R(x^2) */
  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 */
  
  double
  __ieee754_asin(double x)
  {
    double t,w,p,q,c,r,s;
    int32_t hx,ix;
  
    t = 0;
    GET_HIGH_WORD(hx,x);
    ix = hx&0x7fffffff;
    if(ix>= 0x3ff00000) {   /* |x|>= 1 */
        u_int32_t lx;
        GET_LOW_WORD(lx,x);
        if(((ix-0x3ff00000)|lx)==0)
          /* asin(1)=+-pi/2 with inexact */
      return x*pio2_hi+x*pio2_lo;
        return (x-x)/(x-x);   /* asin(|x|>1) is NaN */
    } else if (ix<0x3fe00000) { /* |x|<0.5 */
        if(ix<0x3e400000) {   /* if |x| < 2**-27 */
      if(huge+x>one) return x;/* return x with inexact if x!=0*/
        } else
      t = x*x;
      p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
      q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
      w = p/q;
      return x+x*w;
    }
    /* 1> |x|>= 0.5 */
    w = one-fabs(x);
    t = w*0.5;
    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
    s = __ieee754_sqrt(t);
    if(ix>=0x3FEF3333) {  /* if |x| > 0.975 */
        w = p/q;
        t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
    } else {
        w  = s;
        SET_LOW_WORD(w,0);
        c  = (t-w*w)/(s+w);
        r  = p/q;
        p  = 2.0*s*r-(pio2_lo-2.0*c);
        q  = pio4_hi-2.0*w;
        t  = pio4_hi-(p-q);
    }
    if(hx>0) return t; else return -t;
  }
  