Prepare to convert _Complex sine functions

This patch has no function changes, except to
ensure the git history correctly tracks the
changes to convert the double version of these
functions into a templated version.

1 files changed, 210 insertions, 0 deletions

diff --git a/math/k_casinh_template.c b/math/k_casinh_template.c
new file mode 100644
index 0000000000..354dde1f3e
--- /dev/null
+++ b/math/k_casinh_template.c
@@ -0,0 +1,210 @@
+/* Return arc hyperbole sine for double value, with the imaginary part
+   of the result possibly adjusted for use in computing other
+   functions.
+   Copyright (C) 1997-2016 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>
+
+/* 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__ double
+__kernel_casinh (__complex__ double x, int adj)
+{
+  __complex__ double res;
+  double rx, ix;
+  __complex__ double y;
+
+  /* Avoid cancellation by reducing to the first quadrant.  */
+  rx = fabs (__real__ x);
+  ix = fabs (__imag__ x);
+
+  if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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)
+	{
+	  double t = __real__ y;
+	  __real__ y = __copysign (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = __clog (y);
+      __real__ res += M_LN2;
+    }
+  else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
+    {
+      double s = __ieee754_hypot (1.0, rx);
+
+      __real__ res = __ieee754_log (rx + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2 (s, __imag__ x);
+      else
+	__imag__ res = __ieee754_atan2 (ix, s);
+    }
+  else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
+    {
+      double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
+
+      __real__ res = __ieee754_log (ix + s);
+      if (adj)
+	__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
+      else
+	__imag__ res = __ieee754_atan2 (s, rx);
+    }
+  else if (ix > 1.0 && ix < 1.5 && rx < 0.5)
+    {
+      if (rx < DBL_EPSILON * DBL_EPSILON)
+	{
+	  double ix2m1 = (ix + 1.0) * (ix - 1.0);
+	  double s = __ieee754_sqrt (ix2m1);
+
+	  __real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2 (s, rx);
+	}
+      else
+	{
+	  double ix2m1 = (ix + 1.0) * (ix - 1.0);
+	  double rx2 = rx * rx;
+	  double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
+	  double d = __ieee754_sqrt (ix2m1 * ix2m1 + f);
+	  double dp = d + ix2m1;
+	  double dm = f / dp;
+	  double r1 = __ieee754_sqrt ((dm + rx2) / 2.0);
+	  double r2 = rx * ix / r1;
+
+	  __real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2,
+								 __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
+	}
+    }
+  else if (ix == 1.0 && rx < 0.5)
+    {
+      if (rx < DBL_EPSILON / 8.0)
+	{
+	  __real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx),
+					    __copysign (1.0, __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx));
+	}
+      else
+	{
+	  double d = rx * __ieee754_sqrt (4.0 + rx * rx);
+	  double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0);
+	  double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0);
+
+	  __real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2,
+								 __imag__ x));
+	  else
+	    __imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1);
+	}
+    }
+  else if (ix < 1.0 && rx < 0.5)
+    {
+      if (ix >= DBL_EPSILON)
+	{
+	  if (rx < DBL_EPSILON * DBL_EPSILON)
+	    {
+	      double onemix2 = (1.0 + ix) * (1.0 - ix);
+	      double s = __ieee754_sqrt (onemix2);
+
+	      __real__ res = __log1p (2.0 * rx / s) / 2.0;
+	      if (adj)
+		__imag__ res = __ieee754_atan2 (s, __imag__ x);
+	      else
+		__imag__ res = __ieee754_atan2 (ix, s);
+	    }
+	  else
+	    {
+	      double onemix2 = (1.0 + ix) * (1.0 - ix);
+	      double rx2 = rx * rx;
+	      double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix);
+	      double d = __ieee754_sqrt (onemix2 * onemix2 + f);
+	      double dp = d + onemix2;
+	      double dm = f / dp;
+	      double r1 = __ieee754_sqrt ((dp + rx2) / 2.0);
+	      double r2 = rx * ix / r1;
+
+	      __real__ res
+		= __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0;
+	      if (adj)
+		__imag__ res = __ieee754_atan2 (rx + r1,
+						__copysign (ix + r2,
+							    __imag__ x));
+	      else
+		__imag__ res = __ieee754_atan2 (ix + r2, rx + r1);
+	    }
+	}
+      else
+	{
+	  double s = __ieee754_hypot (1.0, rx);
+
+	  __real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0;
+	  if (adj)
+	    __imag__ res = __ieee754_atan2 (s, __imag__ x);
+	  else
+	    __imag__ res = __ieee754_atan2 (ix, s);
+	}
+      math_check_force_underflow_nonneg (__real__ res);
+    }
+  else
+    {
+      __real__ y = (rx - ix) * (rx + ix) + 1.0;
+      __imag__ y = 2.0 * rx * ix;
+
+      y = __csqrt (y);
+
+      __real__ y += rx;
+      __imag__ y += ix;
+
+      if (adj)
+	{
+	  double t = __real__ y;
+	  __real__ y = __copysign (__imag__ y, __imag__ x);
+	  __imag__ y = t;
+	}
+
+      res = __clog (y);
+    }
+
+  /* Give results the correct sign for the original argument.  */
+  __real__ res = __copysign (__real__ res, __real__ x);
+  __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
+
+  return res;
+}