Fix tan, tanl for large inputs.

2 files changed, 145 insertions, 3 deletions

diff --git a/sysdeps/ieee754/ldbl-96/k_tanl.c b/sysdeps/ieee754/ldbl-96/k_tanl.c
new file mode 100644
index 0000000000..31cd236aa2
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/k_tanl.c
@@ -0,0 +1,137 @@
+/*
+ * ====================================================
+ * 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 are
+  Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
+  and are incorporated herein by permission of the author.  The author
+  reserves the right to distribute this material elsewhere under different
+  copying permissions.  These modifications are distributed here under
+  the following terms:
+
+    This library is free software; you can redistribute it and/or
+    modify it under the terms of the GNU Lesser General Public
+    License as published by the Free Software Foundation; either
+    version 2.1 of the License, or (at your option) any later version.
+
+    This library is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+    Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public
+    License along with this library; if not, see
+    <http://www.gnu.org/licenses/>.  */
+
+/* __kernel_tanl( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ *	2. if x < 2^-33, return x with inexact if x!=0.
+ *	3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
+ *          on [0,0.67433].
+ *
+ *	   Note: tan(x+y) = tan(x) + tan'(x)*y
+ *		          ~ tan(x) + (1+x*x)*y
+ *	   Therefore, for better accuracy in computing tan(x+y), let
+ *		r = x^3 * R(x^2)
+ *	   then
+ *		tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
+ *
+ *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then
+ *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include <math.h>
+#include <math_private.h>
+static const long double
+  one = 1.0L,
+  pio4hi = 0xc.90fdaa22168c235p-4L,
+  pio4lo = -0x3.b399d747f23e32ecp-68L,
+
+  /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
+     0 <= x <= 0.6743316650390625
+     Peak relative error 8.0e-36  */
+ TH =  3.333333333333333333333333333333333333333E-1L,
+ T0 = -1.813014711743583437742363284336855889393E7L,
+ T1 =  1.320767960008972224312740075083259247618E6L,
+ T2 = -2.626775478255838182468651821863299023956E4L,
+ T3 =  1.764573356488504935415411383687150199315E2L,
+ T4 = -3.333267763822178690794678978979803526092E-1L,
+
+ U0 = -1.359761033807687578306772463253710042010E8L,
+ U1 =  6.494370630656893175666729313065113194784E7L,
+ U2 = -4.180787672237927475505536849168729386782E6L,
+ U3 =  8.031643765106170040139966622980914621521E4L,
+ U4 = -5.323131271912475695157127875560667378597E2L;
+  /* 1.000000000000000000000000000000000000000E0 */
+
+
+long double
+__kernel_tanl (long double x, long double y, int iy)
+{
+  long double z, r, v, w, s;
+  long double absx = fabsl (x);
+  int sign;
+
+  if (absx < 0x1p-33)
+    {
+      if ((int) x == 0)
+	{			/* generate inexact */
+	  if (x == 0 && iy == -1)
+	    return one / fabsl (x);
+	  else
+	    return (iy == 1) ? x : -one / x;
+	}
+    }
+  if (absx >= 0.6743316650390625L)
+    {
+      if (signbit (x))
+	{
+	  x = -x;
+	  y = -y;
+	  sign = -1;
+	}
+      else
+	sign = 1;
+      z = pio4hi - x;
+      w = pio4lo - y;
+      x = z + w;
+      y = 0.0;
+    }
+  z = x * x;
+  r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
+  v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
+  r = r / v;
+
+  s = z * x;
+  r = y + z * (s * r + y);
+  r += TH * s;
+  w = x + r;
+  if (absx >= 0.6743316650390625L)
+    {
+      v = (long double) iy;
+      w = (v - 2.0 * (x - (w * w / (w + v) - r)));
+      if (sign < 0)
+	w = -w;
+      return w;
+    }
+  if (iy == 1)
+    return w;
+  else
+    return -1.0 / (x + r);
+}
diff --git a/sysdeps/ieee754/ldbl-96/s_tanl.c b/sysdeps/ieee754/ldbl-96/s_tanl.c
index 3054601a50..3fbe4a8f6b 100644
--- a/sysdeps/ieee754/ldbl-96/s_tanl.c
+++ b/sysdeps/ieee754/ldbl-96/s_tanl.c
@@ -48,23 +48,28 @@ static char rcsid[] = "$NetBSD: $";
  *	TRIG(x) returns trig(x) nearly rounded
  */
 
+#include <errno.h>
 #include <math.h>
 #include <math_private.h>
 
 long double __tanl(long double x)
 {
 	long double y[2],z=0.0;
-	int32_t n, se;
+	int32_t n, se, i0, i1;
 
     /* High word of x. */
-	GET_LDOUBLE_EXP(se,x);
+	GET_LDOUBLE_WORDS(se,i0,i1,x);
 
     /* |x| ~< pi/4 */
 	se &= 0x7fff;
 	if(se <= 0x3ffe) return __kernel_tanl(x,z,1);
 
     /* tan(Inf or NaN) is NaN */
-	else if (se==0x7fff) return x-x;		/* NaN */
+	else if (se==0x7fff) {
+	  if (i1 == 0 && i0 == 0x80000000)
+	    __set_errno (EDOM);
+	  return x-x;
+	}
 
     /* argument reduction needed */
 	else {