Fix cacos real-part inaccuracy for result real part near 0 (bug 15023).

1 files changed, 92 insertions, 0 deletions

diff --git a/math/k_casinhl.c b/math/k_casinhl.c
new file mode 100644
index 0000000000..6412979755
--- /dev/null
+++ b/math/k_casinhl.c
@@ -0,0 +1,92 @@
+/* Return arc hyperbole sine for long double value, with the imaginary
+   part of the result possibly adjusted for use in computing other
+   functions.
+   Copyright (C) 1997-2013 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C 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.
+
+   The GNU C 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 the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <complex.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+/* To avoid spurious overflows, use this definition to treat IBM long
+   double as approximating an IEEE-style format.  */
+#if LDBL_MANT_DIG == 106
+# undef LDBL_EPSILON
+# define LDBL_EPSILON 0x1p-106L
+#endif
+
+/* Return the complex inverse hyperbolic sine of finite nonzero Z,
+   with the imaginary part of the result subtracted from pi/2 if ADJ
+   is nonzero.  */
+
+__complex__ long double
+__kernel_casinhl (__complex__ long double x, int adj)
+{
+  __complex__ long double res;
+  long double rx, ix;
+  __complex__ long double y;
+
+  /* Avoid cancellation by reducing to the first quadrant.  */
+  rx = fabsl (__real__ x);
+  ix = fabsl (__imag__ x);
+
+  if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_EPSILON)
+    {
+      /* For large x in the first quadrant, x + csqrt (1 + x * x)
+	 is sufficiently close to 2 * x to make no significant
+	 difference to the result; avoid possible overflow from
+	 the squaring and addition.  */
+      __real__ y = rx;
+      __imag__ y = ix;
+
+      if (adj)
+	{
+	  long double t = __real__ y;
+	  __real__ y = __copysignl (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = __clogl (y);
+      __real__ res += M_LN2l;
+    }
+  else
+    {
+      __real__ y = (rx - ix) * (rx + ix) + 1.0;
+      __imag__ y = 2.0 * rx * ix;
+
+      y = __csqrtl (y);
+
+      __real__ y += rx;
+      __imag__ y += ix;
+
+      if (adj)
+	{
+	  long double t = __real__ y;
+	  __real__ y = __copysignl (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = __clogl (y);
+    }
+
+  /* Give results the correct sign for the original argument.  */
+  __real__ res = __copysignl (__real__ res, __real__ x);
+  __imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
+
+  return res;
+}