lib/asinl.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 #include <config.h>
  13
  14 /* Specification.  */
  15 #include <math.h>
  16
  17 #if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
  18
  19 long double
  20 asinl (long double x)
  21 {
  22   return asin (x);
  23 }
  24
  25 #else
  26
  27 /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_asinl.c.  */
  28
  29 /*
  30   Long double expansions contributed by
  31   Stephen L. Moshier <moshier@na-net.ornl.gov>
  32 */
  33
  34 /* asin(x)
  35  * Method :
  36  *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
  37  *      we approximate asin(x) on [0,0.5] by
  38  *              asin(x) = x + x*x^2*R(x^2)
  39  *      Between .5 and .625 the approximation is
  40  *              asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
  41  *      For x in [0.625,1]
  42  *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
  43  *
  44  * Special cases:
  45  *      if x is NaN, return x itself;
  46  *      if |x|>1, return NaN with invalid signal.
  47  *
  48  */
  49
  50
  51 static const long double
  52   one = 1.0L,
  53   huge = 1.0e+4932L,
  54   pio2_hi = 1.5707963267948966192313216916397514420986L,
  55   pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
  56   pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
  57
  58         /* coefficient for R(x^2) */
  59
  60   /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
  61      0 <= x <= 0.5
  62      peak relative error 1.9e-35  */
  63   pS0 = -8.358099012470680544198472400254596543711E2L,
  64   pS1 =  3.674973957689619490312782828051860366493E3L,
  65   pS2 = -6.730729094812979665807581609853656623219E3L,
  66   pS3 =  6.643843795209060298375552684423454077633E3L,
  67   pS4 = -3.817341990928606692235481812252049415993E3L,
  68   pS5 =  1.284635388402653715636722822195716476156E3L,
  69   pS6 = -2.410736125231549204856567737329112037867E2L,
  70   pS7 =  2.219191969382402856557594215833622156220E1L,
  71   pS8 = -7.249056260830627156600112195061001036533E-1L,
  72   pS9 =  1.055923570937755300061509030361395604448E-3L,
  73
  74   qS0 = -5.014859407482408326519083440151745519205E3L,
  75   qS1 =  2.430653047950480068881028451580393430537E4L,
  76   qS2 = -4.997904737193653607449250593976069726962E4L,
  77   qS3 =  5.675712336110456923807959930107347511086E4L,
  78   qS4 = -3.881523118339661268482937768522572588022E4L,
  79   qS5 =  1.634202194895541569749717032234510811216E4L,
  80   qS6 = -4.151452662440709301601820849901296953752E3L,
  81   qS7 =  5.956050864057192019085175976175695342168E2L,
  82   qS8 = -4.175375777334867025769346564600396877176E1L,
  83   /* 1.000000000000000000000000000000000000000E0 */
  84
  85   /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
  86      -0.0625 <= x <= 0.0625
  87      peak relative error 3.3e-35  */
  88   rS0 = -5.619049346208901520945464704848780243887E0L,
  89   rS1 =  4.460504162777731472539175700169871920352E1L,
  90   rS2 = -1.317669505315409261479577040530751477488E2L,
  91   rS3 =  1.626532582423661989632442410808596009227E2L,
  92   rS4 = -3.144806644195158614904369445440583873264E1L,
  93   rS5 = -9.806674443470740708765165604769099559553E1L,
  94   rS6 =  5.708468492052010816555762842394927806920E1L,
  95   rS7 =  1.396540499232262112248553357962639431922E1L,
  96   rS8 = -1.126243289311910363001762058295832610344E1L,
  97   rS9 = -4.956179821329901954211277873774472383512E-1L,
  98   rS10 =  3.313227657082367169241333738391762525780E-1L,
  99
 100   sS0 = -4.645814742084009935700221277307007679325E0L,
 101   sS1 =  3.879074822457694323970438316317961918430E1L,
 102   sS2 = -1.221986588013474694623973554726201001066E2L,
 103   sS3 =  1.658821150347718105012079876756201905822E2L,
 104   sS4 = -4.804379630977558197953176474426239748977E1L,
 105   sS5 = -1.004296417397316948114344573811562952793E2L,
 106   sS6 =  7.530281592861320234941101403870010111138E1L,
 107   sS7 =  1.270735595411673647119592092304357226607E1L,
 108   sS8 = -1.815144839646376500705105967064792930282E1L,
 109   sS9 = -7.821597334910963922204235247786840828217E-2L,
 110   /*  1.000000000000000000000000000000000000000E0 */
 111
 112  asinr5625 =  5.9740641664535021430381036628424864397707E-1L;
 113
 114
 115 long double
 116 asinl (long double x)
 117 {
 118   long double y, t, p, q;
 119   int sign;
 120
 121   sign = 1;
 122   y = x;
 123   if (x < 0.0L)
 124     {
 125       sign = -1;
 126       y = -x;
 127     }
 128
 129   if (y >= 1.0L)        /* |x|>= 1 */
 130     {
 131       if (y == 1.0L)
 132         /* asin(1)=+-pi/2 with inexact */
 133         return x * pio2_hi + x * pio2_lo;
 134
 135       return (x - x) / (x - x); /* asin(|x|>1) is NaN */
 136     }
 137   else if (y < 0.5L) /* |x| < 0.5 */
 138     {
 139       if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
 140         if (huge + y > one)
 141           return y;             /* return x with inexact if x!=0 */
 142
 143       t = x * x;
 144       p = (((((((((pS9 * t
 145                    + pS8) * t
 146                   + pS7) * t
 147                  + pS6) * t
 148                 + pS5) * t
 149                + pS4) * t
 150               + pS3) * t
 151              + pS2) * t
 152             + pS1) * t
 153            + pS0) * t;
 154
 155       q = (((((((( t
 156                   + qS8) * t
 157                  + qS7) * t
 158                 + qS6) * t
 159                + qS5) * t
 160               + qS4) * t
 161              + qS3) * t
 162             + qS2) * t
 163            + qS1) * t
 164         + qS0;
 165
 166       return x + x * (p / q);
 167     }
 168
 169   else if (y < 0.625) /* 0.625 */
 170     {
 171       t = y - 0.5625;
 172       p = ((((((((((rS10 * t
 173                     + rS9) * t
 174                    + rS8) * t
 175                   + rS7) * t
 176                  + rS6) * t
 177                 + rS5) * t
 178                + rS4) * t
 179               + rS3) * t
 180              + rS2) * t
 181             + rS1) * t
 182            + rS0) * t;
 183
 184       q = ((((((((( t
 185                     + sS9) * t
 186                   + sS8) * t
 187                  + sS7) * t
 188                 + sS6) * t
 189                + sS5) * t
 190               + sS4) * t
 191              + sS3) * t
 192             + sS2) * t
 193            + sS1) * t
 194         + sS0;
 195       t = asinr5625 + p / q;
 196     }
 197   else
 198     t = pio2_hi + pio2_lo - 2 * asinl (sqrtl ((1 - y) / 2));
 199
 200   return t * sign;
 201 }
 202
 203 #endif
 204
 205 #if 0
 206 int
 207 main (void)
 208 {
 209   printf ("%.18Lg %.18Lg\n",
 210           asinl (1.0L),
 211           1.5707963267948966192313216916397514420984L);
 212   printf ("%.18Lg %.18Lg\n",
 213           asinl (0.7071067811865475244008443621048490392848L),
 214           0.7853981633974483096156608458198757210492L);
 215   printf ("%.18Lg %.18Lg\n",
 216           asinl (0.5L),
 217           0.5235987755982988730771072305465838140328L);
 218   printf ("%.18Lg %.18Lg\n",
 219           asinl (0.3090169943749474241022934171828190588600L),
 220           0.3141592653589793238462643383279502884196L);
 221   printf ("%.18Lg %.18Lg\n",
 222           asinl (-1.0L),
 223           -1.5707963267948966192313216916397514420984L);
 224   printf ("%.18Lg %.18Lg\n",
 225           asinl (-0.7071067811865475244008443621048490392848L),
 226           -0.7853981633974483096156608458198757210492L);
 227   printf ("%.18Lg %.18Lg\n",
 228           asinl (-0.5L),
 229           -0.5235987755982988730771072305465838140328L);
 230   printf ("%.18Lg %.18Lg\n",
 231           asinl (-0.3090169943749474241022934171828190588600L),
 232           -0.3141592653589793238462643383279502884196L);
 233 }
 234 #endif