Arcsine implementation for IEEE 128-bit long double.

1 files changed, 248 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-128/e_asinl.c b/sysdeps/ieee754/ldbl-128/e_asinl.c
new file mode 100644
index 0000000..5d991ac
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/e_asinl.c
@@ -0,0 +1,248 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+  Long double expansions contributed by
+  Stephen L. Moshier <moshier@na-net.ornl.gov>
+*/
+
+/* __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)
+ *      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))
+ *	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"
+long double sqrtl (long double);
+
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+  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;
+
+
+
+#ifdef __STDC__
+long double
+__ieee754_asinl (long double x)
+#else
+double
+__ieee754_asinl (x)
+     long double x;
+#endif
+{
+  long double t, w, p, q, c, r, s;
+  int32_t ix, sign, flag;
+  ieee854_long_double_shape_type u;
+
+  flag = 0;
+  u.value = x;
+  sign = u.parts32.w0;
+  ix = sign & 0x7fffffff;
+  u.parts32.w0 = ix;    /* |x| */
+  if (ix >= 0x3fff0000)	/* |x|>= 1 */
+    {
+      if (ix == 0x3fff0000
+	  && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 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 < 0x3ffe0000) /* |x| < 0.5 */
+    {
+      if (ix < 0x3fc60000) /* |x| < 2**-57 */
+	{
+	  if (huge + x > one)
+	    return x;		/* return x with inexact if x!=0 */
+	}
+      else
+	{
+	  t = x * x;
+	  /* Mark to use pS, qS later on.  */
+	  flag = 1;
+	}
+    }
+  else if (ix < 0x3ffe4000) /* 0.625 */
+    {
+      t = u.value - 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;
+      if ((sign & 0x80000000) == 0)
+	return t;
+      else
+	return -t;
+    }
+  else
+    {
+      /* 1 > |x| >= 0.625 */
+      w = one - u.value;
+      t = w * 0.5;
+    }
+
+  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;
+
+  if (flag) /* 2^-57 < |x| < 0.5 */
+    {
+      w = p / q;
+      return x + x * w;
+    }
+
+  s = __ieee754_sqrtl (t);
+  if (ix >= 0x3ffef333) /* |x| > 0.975 */
+    {
+      w = p / q;
+      t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
+    }
+  else
+    {
+      u.value = s;
+      u.parts32.w3 = 0;
+      u.parts32.w2 = 0;
+      w = u.value;
+      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 ((sign & 0x80000000) == 0)
+    return t;
+  else
+    return -t;
+}