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authorZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
committerZack Weinberg <zackw@panix.com>2017-06-08 15:39:03 -0400
commit5046dbb4a7eba5eccfd258f92f4735c9ffc8d069 (patch)
tree4470480d904b65cf14ca524f96f79eca818c3eaf /REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c
parent199fc19d3aaaf57944ef036e15904febe877fc93 (diff)
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Prepare for radical source tree reorganization. zack/build-layout-experiment
All top-level files and directories are moved into a temporary storage
directory, REORG.TODO, except for files that will certainly still
exist in their current form at top level when we're done (COPYING,
COPYING.LIB, LICENSES, NEWS, README), all old ChangeLog files (which
are moved to the new directory OldChangeLogs, instead), and the
generated file INSTALL (which is just deleted; in the new order, there
will be no generated files checked into version control).
Diffstat (limited to 'REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c')
-rw-r--r--REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c166
1 files changed, 166 insertions, 0 deletions
diff --git a/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c
new file mode 100644
index 0000000000..232e00c345
--- /dev/null
+++ b/REORG.TODO/sysdeps/ieee754/ldbl-128ibm/k_tanl.c
@@ -0,0 +1,166 @@
+/*
+ * ====================================================
+ * 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^-57, 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 <float.h>
+#include <math.h>
+#include <math_private.h>
+#include <libc-diag.h>
+
+static const long double
+  one = 1.0L,
+  pio4hi = 7.8539816339744830961566084581987569936977E-1L,
+  pio4lo = 2.1679525325309452561992610065108379921906E-35L,
+
+  /* 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;
+  int32_t ix, sign, hx, lx;
+  double xhi;
+
+  xhi = ldbl_high (x);
+  EXTRACT_WORDS (hx, lx, xhi);
+  ix = hx & 0x7fffffff;
+  if (ix < 0x3c600000)		/* x < 2**-57 */
+    {
+      if ((int) x == 0)		/* generate inexact */
+	{
+	  if ((ix | lx | (iy + 1)) == 0)
+	    return one / fabs (x);
+	  else if (iy == 1)
+	    {
+	      math_check_force_underflow (x);
+	      return x;
+	    }
+	  else
+	    return -one / x;
+	}
+    }
+  if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */
+    {
+      if ((hx & 0x80000000) != 0)
+	{
+	  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 (ix >= 0x3fe59420)
+    {
+      v = (long double) iy;
+      w = (v - 2.0 * (x - (w * w / (w + v) - r)));
+      /* SIGN is set for arguments that reach this code, but not
+	 otherwise, resulting in warnings that it may be used
+	 uninitialized although in the cases where it is used it has
+	 always been set.  */
+      DIAG_PUSH_NEEDS_COMMENT;
+      DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized");
+      if (sign < 0)
+	w = -w;
+      DIAG_POP_NEEDS_COMMENT;
+      return w;
+    }
+  if (iy == 1)
+    return w;
+  else
+    {				/* if allow error up to 2 ulp,
+				   simply return -1.0/(x+r) here */
+      /*  compute -1.0/(x+r) accurately */
+      long double u1, z1;
+
+      u1 = ldbl_high (w);
+      v = r - (u1 - x);		/* u1+v = r+x */
+      z = -1.0 / w;
+      z1 = ldbl_high (z);
+      s = 1.0 + z1 * u1;
+      return z1 + z * (s + z1 * v);
+    }
+}