text: /*
   * ====================================================
   * 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 <config.h>
  
  /* Specification.  */
  #include <math.h>
  
  /*
    Long double expansions contributed by
    Stephen L. Moshier <moshier@na-net.ornl.gov>
  */
  
  /* 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)
   *      Between .5 and .625 the approximation is
   *              asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
   *      For x in [0.625,1]
   *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
   *
   * Special cases:
   *      if x is NaN, return x itself;
   *      if |x|>1, return NaN with invalid signal.
   *
   */
  
  
  static const long double
    one = 1.0L,
    huge = 1.0e+4932L,
    pio2_hi = 1.5707963267948966192313216916397514420986L,
    pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
    pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
  
          /* coefficient for R(x^2) */
  
    /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
       0 <= x <= 0.5
       peak relative error 1.9e-35  */
    pS0 = -8.358099012470680544198472400254596543711E2L,
    pS1 =  3.674973957689619490312782828051860366493E3L,
    pS2 = -6.730729094812979665807581609853656623219E3L,
    pS3 =  6.643843795209060298375552684423454077633E3L,
    pS4 = -3.817341990928606692235481812252049415993E3L,
    pS5 =  1.284635388402653715636722822195716476156E3L,
    pS6 = -2.410736125231549204856567737329112037867E2L,
    pS7 =  2.219191969382402856557594215833622156220E1L,
    pS8 = -7.249056260830627156600112195061001036533E-1L,
    pS9 =  1.055923570937755300061509030361395604448E-3L,
  
    qS0 = -5.014859407482408326519083440151745519205E3L,
    qS1 =  2.430653047950480068881028451580393430537E4L,
    qS2 = -4.997904737193653607449250593976069726962E4L,
    qS3 =  5.675712336110456923807959930107347511086E4L,
    qS4 = -3.881523118339661268482937768522572588022E4L,
    qS5 =  1.634202194895541569749717032234510811216E4L,
    qS6 = -4.151452662440709301601820849901296953752E3L,
    qS7 =  5.956050864057192019085175976175695342168E2L,
    qS8 = -4.175375777334867025769346564600396877176E1L,
    /* 1.000000000000000000000000000000000000000E0 */
  
    /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
       -0.0625 <= x <= 0.0625
       peak relative error 3.3e-35  */
    rS0 = -5.619049346208901520945464704848780243887E0L,
    rS1 =  4.460504162777731472539175700169871920352E1L,
    rS2 = -1.317669505315409261479577040530751477488E2L,
    rS3 =  1.626532582423661989632442410808596009227E2L,
    rS4 = -3.144806644195158614904369445440583873264E1L,
    rS5 = -9.806674443470740708765165604769099559553E1L,
    rS6 =  5.708468492052010816555762842394927806920E1L,
    rS7 =  1.396540499232262112248553357962639431922E1L,
    rS8 = -1.126243289311910363001762058295832610344E1L,
    rS9 = -4.956179821329901954211277873774472383512E-1L,
    rS10 =  3.313227657082367169241333738391762525780E-1L,
  
    sS0 = -4.645814742084009935700221277307007679325E0L,
    sS1 =  3.879074822457694323970438316317961918430E1L,
    sS2 = -1.221986588013474694623973554726201001066E2L,
    sS3 =  1.658821150347718105012079876756201905822E2L,
    sS4 = -4.804379630977558197953176474426239748977E1L,
    sS5 = -1.004296417397316948114344573811562952793E2L,
    sS6 =  7.530281592861320234941101403870010111138E1L,
    sS7 =  1.270735595411673647119592092304357226607E1L,
    sS8 = -1.815144839646376500705105967064792930282E1L,
    sS9 = -7.821597334910963922204235247786840828217E-2L,
    /*  1.000000000000000000000000000000000000000E0 */
  
   asinr5625 =  5.9740641664535021430381036628424864397707E-1L;
  
  
  long double
  asinl (long double x)
  {
    long double y, t, p, q;
    int sign;
  
    sign = 1;
    y = x;
    if (x < 0.0L)
      {
        sign = -1;
        y = -x;
      }
  
    if (y >= 1.0L)        /* |x|>= 1 */
      {
        if (y == 1.0L)
          /* 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 (y < 0.5L) /* |x| < 0.5 */
      {
        if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
          if (huge + y > one)
            return y;             /* return x with inexact if x!=0 */
  
        t = x * x;
        p = (((((((((pS9 * t
                     + pS8) * t
                    + pS7) * t
                   + pS6) * t
                  + pS5) * t
                 + pS4) * t
                + pS3) * t
               + pS2) * t
              + pS1) * t
             + pS0) * t;
  
        q = (((((((( t
                    + qS8) * t
                   + qS7) * t
                  + qS6) * t
                 + qS5) * t
                + qS4) * t
               + qS3) * t
              + qS2) * t
             + qS1) * t
          + qS0;
  
        return x + x * (p / q);
      }
  
    else if (y < 0.625) /* 0.625 */
      {
        t = y - 0.5625;
        p = ((((((((((rS10 * t
                      + rS9) * t
                     + rS8) * t
                    + rS7) * t
                   + rS6) * t
                  + rS5) * t
                 + rS4) * t
                + rS3) * t
               + rS2) * t
              + rS1) * t
             + rS0) * t;
  
        q = ((((((((( t
                      + sS9) * t
                    + sS8) * t
                   + sS7) * t
                  + sS6) * t
                 + sS5) * t
                + sS4) * t
               + sS3) * t
              + sS2) * t
             + sS1) * t
          + sS0;
        t = asinr5625 + p / q;
      }
    else
      t = pio2_hi + pio2_lo - 2 * asinl (sqrtl ((1 - y) / 2));
  
    return t * sign;
  }
  
  #if 0
  int
  main (void)
  {
    printf ("%.18Lg %.18Lg\n",
            asinl (1.0L),
            1.5707963267948966192313216916397514420984L);
    printf ("%.18Lg %.18Lg\n",
            asinl (0.7071067811865475244008443621048490392848L),
            0.7853981633974483096156608458198757210492L);
    printf ("%.18Lg %.18Lg\n",
            asinl (0.5L),
            0.5235987755982988730771072305465838140328L);
    printf ("%.18Lg %.18Lg\n",
            asinl (0.3090169943749474241022934171828190588600L),
            0.3141592653589793238462643383279502884196L);
    printf ("%.18Lg %.18Lg\n",
            asinl (-1.0L),
            -1.5707963267948966192313216916397514420984L);
    printf ("%.18Lg %.18Lg\n",
            asinl (-0.7071067811865475244008443621048490392848L),
            -0.7853981633974483096156608458198757210492L);
    printf ("%.18Lg %.18Lg\n",
            asinl (-0.5L),
            -0.5235987755982988730771072305465838140328L);
    printf ("%.18Lg %.18Lg\n",
            asinl (-0.3090169943749474241022934171828190588600L),
            -0.3141592653589793238462643383279502884196L);
  }
  #endif
  