Update.

2001-05-29  Andreas Jaeger  <aj@suse.de>

	* sysdeps/ieee754/ldbl-128/e_acosl.c: New file, contributed by
	Stephen L Moshier <moshier@mediaone.net>.

	* math/libm-test.inc (sinh_test): Add new test case.

	* sysdeps/ieee754/ldbl_96/e_sinhl.c (__ieee754_sinhl): sinhl(x) =
	x when x < 2^-32.
	Patch by Stephen L Moshier <moshier@mediaone.net>.

1 files changed, 311 insertions, 0 deletions

diff --git a/sysdeps/ieee754/ldbl-128/e_acosl.c b/sysdeps/ieee754/ldbl-128/e_acosl.c
new file mode 100644
index 0000000000..745456a3fe
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/e_acosl.c
@@ -0,0 +1,311 @@
+/*
+ * ====================================================
+ * 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_acosl(x)
+ * Method :
+ *      acos(x)  = pi/2 - asin(x)
+ *      acos(-x) = pi/2 + asin(x)
+ * For |x| <= 0.375
+ *      acos(x) = pi/2 - asin(x)
+ * Between .375 and .5 the approximation is
+ *      acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
+ * Between .5 and .625 the approximation is
+ *      acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
+ * For x > 0.625,
+ *      acos(x) = 2 asin(sqrt((1-x)/2))
+ *      computed with an extended precision square root in the leading term.
+ * For x < -0.625
+ *      acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
+ *
+ * Special cases:
+ *      if x is NaN, return x itself;
+ *      if |x|>1, return NaN with invalid signal.
+ *
+ * Functions needed: __ieee754_sqrtl.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const long double
+#else
+static long double
+#endif
+  one = 1.0L,
+  pio2_hi = 1.5707963267948966192313216916397514420986L,
+  pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
+
+  /* acos(0.5625 + x) = acos(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 */
+
+  acosr5625 = 9.7338991014954640492751132535550279812151E-1L,
+  pimacosr5625 = 2.1682027434402468335351320579240000860757E0L,
+
+  /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
+     -0.0625 <= x <= 0.0625
+     peak relative error 2.1e-35  */
+
+  P0 =  2.177690192235413635229046633751390484892E0L,
+  P1 = -2.848698225706605746657192566166142909573E1L,
+  P2 =  1.040076477655245590871244795403659880304E2L,
+  P3 = -1.400087608918906358323551402881238180553E2L,
+  P4 =  2.221047917671449176051896400503615543757E1L,
+  P5 =  9.643714856395587663736110523917499638702E1L,
+  P6 = -5.158406639829833829027457284942389079196E1L,
+  P7 = -1.578651828337585944715290382181219741813E1L,
+  P8 =  1.093632715903802870546857764647931045906E1L,
+  P9 =  5.448925479898460003048760932274085300103E-1L,
+  P10 = -3.315886001095605268470690485170092986337E-1L,
+  Q0 = -1.958219113487162405143608843774587557016E0L,
+  Q1 =  2.614577866876185080678907676023269360520E1L,
+  Q2 = -9.990858606464150981009763389881793660938E1L,
+  Q3 =  1.443958741356995763628660823395334281596E2L,
+  Q4 = -3.206441012484232867657763518369723873129E1L,
+  Q5 = -1.048560885341833443564920145642588991492E2L,
+  Q6 =  6.745883931909770880159915641984874746358E1L,
+  Q7 =  1.806809656342804436118449982647641392951E1L,
+  Q8 = -1.770150690652438294290020775359580915464E1L,
+  Q9 = -5.659156469628629327045433069052560211164E-1L,
+  /* 1.000000000000000000000000000000000000000E0 */
+
+  acosr4375 = 1.1179797320499710475919903296900511518755E0L,
+  pimacosr4375 = 2.0236129215398221908706530535894517323217E0L,
+
+  /* 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 */
+
+#ifdef __STDC__
+long double
+__ieee754_acosl (long double x)
+#else
+long double
+__ieee754_acosl (x)
+     long double x;
+#endif
+{
+  long double z, r, w, p, q, s, t, f2;
+  int32_t ix, sign;
+  ieee854_long_double_shape_type u;
+
+  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)
+	{			/* |x| == 1 */
+	  if (sign & 0x80000000)
+	    return 0.0;		/* acos(1) = 0  */
+	  else
+	    return (2.0 * pio2_hi) + (2.0 * pio2_lo);	/* acos(-1)= pi */
+	}
+      return (x - x) / (x - x);	/* acos(|x| > 1) is NaN */
+    }
+  else if (ix < 0x3ffe0000)	/* |x| < 0.5 */
+    {
+      if (ix < 0x3fc60000)	/* |x| < 2**-57 */
+	return pio2_hi + pio2_lo;
+      if (ix < 0x3ffde000)	/* |x| < .4375 */
+	{
+	  /* Arcsine of x.  */
+	  z = x * x;
+	  p = (((((((((pS9 * z
+		       + pS8) * z
+		      + pS7) * z
+		     + pS6) * z
+		    + pS5) * z
+		   + pS4) * z
+		  + pS3) * z
+		 + pS2) * z
+		+ pS1) * z
+	       + pS0) * z;
+	  q = (((((((( z
+		       + qS8) * z
+		     + qS7) * z
+		    + qS6) * z
+		   + qS5) * z
+		  + qS4) * z
+		 + qS3) * z
+		+ qS2) * z
+	       + qS1) * z
+	    + qS0;
+	  r = x + x * p / q;
+	  z = pio2_hi - (r - pio2_lo);
+	  return z;
+	}
+      /* .4375 <= |x| < .5 */
+      t = u.value - 0.4375L;
+      p = ((((((((((P10 * t
+		    + P9) * t
+		   + P8) * t
+		  + P7) * t
+		 + P6) * t
+		+ P5) * t
+	       + P4) * t
+	      + P3) * t
+	     + P2) * t
+	    + P1) * t
+	   + P0) * t;
+
+      q = (((((((((t
+		   + Q9) * t
+		  + Q8) * t
+		 + Q7) * t
+		+ Q6) * t
+	       + Q5) * t
+	      + Q4) * t
+	     + Q3) * t
+	    + Q2) * t
+	   + Q1) * t
+	+ Q0;
+      r = p / q;
+      if (sign & 0x80000000)
+	r = pimacosr4375 - r;
+      else
+	r = acosr4375 + r;
+      return r;
+    }
+  else if (ix < 0x3ffe4000)	/* |x| < 0.625 */
+    {
+      t = u.value - 0.5625L;
+      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;
+      if (sign & 0x80000000)
+	r = pimacosr5625 - p / q;
+      else
+	r = acosr5625 + p / q;
+      return r;
+    }
+  else
+    {				/* |x| >= .625 */
+      z = (one - u.value) * 0.5;
+      s = __ieee754_sqrtl (z);
+      /* Compute an extended precision square root from
+	 the Newton iteration  s -> 0.5 * (s + z / s).
+         The change w from s to the improved value is
+	    w = 0.5 * (s + z / s) - s  = (s^2 + z)/2s - s = (z - s^2)/2s.
+          Express s = f1 + f2 where f1 * f1 is exactly representable.
+	  w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
+          s + w has extended precision.  */
+      u.value = s;
+      u.parts32.w2 = 0;
+      u.parts32.w3 = 0;
+      f2 = s - u.value;
+      w = z - u.value * u.value;
+      w = w - 2.0 * u.value * f2;
+      w = w - f2 * f2;
+      w = w / (2.0 * s);
+      /* Arcsine of s.  */
+      p = (((((((((pS9 * z
+		   + pS8) * z
+		  + pS7) * z
+		 + pS6) * z
+		+ pS5) * z
+	       + pS4) * z
+	      + pS3) * z
+	     + pS2) * z
+	    + pS1) * z
+	   + pS0) * z;
+      q = (((((((( z
+		   + qS8) * z
+		 + qS7) * z
+		+ qS6) * z
+	       + qS5) * z
+	      + qS4) * z
+	     + qS3) * z
+	    + qS2) * z
+	   + qS1) * z
+	+ qS0;
+      r = s + (w + s * p / q);
+
+      if (sign & 0x80000000)
+	w = pio2_hi + (pio2_lo - r);
+      else
+	w = r;
+      return 2.0 * w;
+    }
+}