Prepare to convert _Complex tangent 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.

4 files changed, 538 insertions, 0 deletions

diff --git a/math/s_catan_template.c b/math/s_catan_template.c
new file mode 100644
index 0000000000..5ab4c0d635
--- /dev/null
+++ b/math/s_catan_template.c
@@ -0,0 +1,143 @@
+/* Return arc tangent of complex double value.
+   Copyright (C) 1997-2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
+
+   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>
+
+__complex__ double
+__catan (__complex__ double x)
+{
+  __complex__ double res;
+  int rcls = fpclassify (__real__ x);
+  int icls = fpclassify (__imag__ x);
+
+  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
+    {
+      if (rcls == FP_INFINITE)
+	{
+	  __real__ res = __copysign (M_PI_2, __real__ x);
+	  __imag__ res = __copysign (0.0, __imag__ x);
+	}
+      else if (icls == FP_INFINITE)
+	{
+	  if (rcls >= FP_ZERO)
+	    __real__ res = __copysign (M_PI_2, __real__ x);
+	  else
+	    __real__ res = __nan ("");
+	  __imag__ res = __copysign (0.0, __imag__ x);
+	}
+      else if (icls == FP_ZERO || icls == FP_INFINITE)
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __copysign (0.0, __imag__ x);
+	}
+      else
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __nan ("");
+	}
+    }
+  else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
+    {
+      res = x;
+    }
+  else
+    {
+      if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
+	  || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
+	{
+	  __real__ res = __copysign (M_PI_2, __real__ x);
+	  if (fabs (__real__ x) <= 1.0)
+	    __imag__ res = 1.0 / __imag__ x;
+	  else if (fabs (__imag__ x) <= 1.0)
+	    __imag__ res = __imag__ x / __real__ x / __real__ x;
+	  else
+	    {
+	      double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
+	      __imag__ res = __imag__ x / h / h / 4.0;
+	    }
+	}
+      else
+	{
+	  double den, absx, absy;
+
+	  absx = fabs (__real__ x);
+	  absy = fabs (__imag__ x);
+	  if (absx < absy)
+	    {
+	      double t = absx;
+	      absx = absy;
+	      absy = t;
+	    }
+
+	  if (absy < DBL_EPSILON / 2.0)
+	    {
+	      den = (1.0 - absx) * (1.0 + absx);
+	      if (den == -0.0)
+		den = 0.0;
+	    }
+	  else if (absx >= 1.0)
+	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
+	  else if (absx >= 0.75 || absy >= 0.5)
+	    den = -__x2y2m1 (absx, absy);
+	  else
+	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
+
+	  __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den);
+
+	  if (fabs (__imag__ x) == 1.0
+	      && fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON)
+	    __imag__ res = (__copysign (0.5, __imag__ x)
+			    * (M_LN2 - __ieee754_log (fabs (__real__ x))));
+	  else
+	    {
+	      double r2 = 0.0, num, f;
+
+	      if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON)
+		r2 = __real__ x * __real__ x;
+
+	      num = __imag__ x + 1.0;
+	      num = r2 + num * num;
+
+	      den = __imag__ x - 1.0;
+	      den = r2 + den * den;
+
+	      f = num / den;
+	      if (f < 0.5)
+		__imag__ res = 0.25 * __ieee754_log (f);
+	      else
+		{
+		  num = 4.0 * __imag__ x;
+		  __imag__ res = 0.25 * __log1p (num / den);
+		}
+	    }
+	}
+
+      math_check_force_underflow_complex (res);
+    }
+
+  return res;
+}
+weak_alias (__catan, catan)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__catan, __catanl)
+weak_alias (__catan, catanl)
+#endif
diff --git a/math/s_catanh_template.c b/math/s_catanh_template.c
new file mode 100644
index 0000000000..11ea06246e
--- /dev/null
+++ b/math/s_catanh_template.c
@@ -0,0 +1,137 @@
+/* Return arc hyperbole tangent for double value.
+   Copyright (C) 1997-2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
+
+   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>
+
+__complex__ double
+__catanh (__complex__ double x)
+{
+  __complex__ double res;
+  int rcls = fpclassify (__real__ x);
+  int icls = fpclassify (__imag__ x);
+
+  if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
+    {
+      if (icls == FP_INFINITE)
+	{
+	  __real__ res = __copysign (0.0, __real__ x);
+	  __imag__ res = __copysign (M_PI_2, __imag__ x);
+	}
+      else if (rcls == FP_INFINITE || rcls == FP_ZERO)
+	{
+	  __real__ res = __copysign (0.0, __real__ x);
+	  if (icls >= FP_ZERO)
+	    __imag__ res = __copysign (M_PI_2, __imag__ x);
+	  else
+	    __imag__ res = __nan ("");
+	}
+      else
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __nan ("");
+	}
+    }
+  else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
+    {
+      res = x;
+    }
+  else
+    {
+      if (fabs (__real__ x) >= 16.0 / DBL_EPSILON
+	  || fabs (__imag__ x) >= 16.0 / DBL_EPSILON)
+	{
+	  __imag__ res = __copysign (M_PI_2, __imag__ x);
+	  if (fabs (__imag__ x) <= 1.0)
+	    __real__ res = 1.0 / __real__ x;
+	  else if (fabs (__real__ x) <= 1.0)
+	    __real__ res = __real__ x / __imag__ x / __imag__ x;
+	  else
+	    {
+	      double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0);
+	      __real__ res = __real__ x / h / h / 4.0;
+	    }
+	}
+      else
+	{
+	  if (fabs (__real__ x) == 1.0
+	      && fabs (__imag__ x) < DBL_EPSILON * DBL_EPSILON)
+	    __real__ res = (__copysign (0.5, __real__ x)
+			    * (M_LN2 - __ieee754_log (fabs (__imag__ x))));
+	  else
+	    {
+	      double i2 = 0.0;
+	      if (fabs (__imag__ x) >= DBL_EPSILON * DBL_EPSILON)
+		i2 = __imag__ x * __imag__ x;
+
+	      double num = 1.0 + __real__ x;
+	      num = i2 + num * num;
+
+	      double den = 1.0 - __real__ x;
+	      den = i2 + den * den;
+
+	      double f = num / den;
+	      if (f < 0.5)
+		__real__ res = 0.25 * __ieee754_log (f);
+	      else
+		{
+		  num = 4.0 * __real__ x;
+		  __real__ res = 0.25 * __log1p (num / den);
+		}
+	    }
+
+	  double absx, absy, den;
+
+	  absx = fabs (__real__ x);
+	  absy = fabs (__imag__ x);
+	  if (absx < absy)
+	    {
+	      double t = absx;
+	      absx = absy;
+	      absy = t;
+	    }
+
+	  if (absy < DBL_EPSILON / 2.0)
+	    {
+	      den = (1.0 - absx) * (1.0 + absx);
+	      if (den == -0.0)
+		den = 0.0;
+	    }
+	  else if (absx >= 1.0)
+	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
+	  else if (absx >= 0.75 || absy >= 0.5)
+	    den = -__x2y2m1 (absx, absy);
+	  else
+	    den = (1.0 - absx) * (1.0 + absx) - absy * absy;
+
+	  __imag__ res = 0.5 * __ieee754_atan2 (2.0 * __imag__ x, den);
+	}
+
+      math_check_force_underflow_complex (res);
+    }
+
+  return res;
+}
+weak_alias (__catanh, catanh)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__catanh, __catanhl)
+weak_alias (__catanh, catanhl)
+#endif
diff --git a/math/s_ctan_template.c b/math/s_ctan_template.c
new file mode 100644
index 0000000000..8e8bf2ee2b
--- /dev/null
+++ b/math/s_ctan_template.c
@@ -0,0 +1,129 @@
+/* Complex tangent function for double.
+   Copyright (C) 1997-2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
+
+   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 <fenv.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+__complex__ double
+__ctan (__complex__ double x)
+{
+  __complex__ double res;
+
+  if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
+    {
+      if (isinf (__imag__ x))
+	{
+	  if (isfinite (__real__ x) && fabs (__real__ x) > 1.0)
+	    {
+	      double sinrx, cosrx;
+	      __sincos (__real__ x, &sinrx, &cosrx);
+	      __real__ res = __copysign (0.0, sinrx * cosrx);
+	    }
+	  else
+	    __real__ res = __copysign (0.0, __real__ x);
+	  __imag__ res = __copysign (1.0, __imag__ x);
+	}
+      else if (__real__ x == 0.0)
+	{
+	  res = x;
+	}
+      else
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __nan ("");
+
+	  if (isinf (__real__ x))
+	    feraiseexcept (FE_INVALID);
+	}
+    }
+  else
+    {
+      double sinrx, cosrx;
+      double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
+
+      /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
+	 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
+
+      if (__glibc_likely (fabs (__real__ x) > DBL_MIN))
+	{
+	  __sincos (__real__ x, &sinrx, &cosrx);
+	}
+      else
+	{
+	  sinrx = __real__ x;
+	  cosrx = 1.0;
+	}
+
+      if (fabs (__imag__ x) > t)
+	{
+	  /* Avoid intermediate overflow when the real part of the
+	     result may be subnormal.  Ignoring negligible terms, the
+	     imaginary part is +/- 1, the real part is
+	     sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y).  */
+	  double exp_2t = __ieee754_exp (2 * t);
+
+	  __imag__ res = __copysign (1.0, __imag__ x);
+	  __real__ res = 4 * sinrx * cosrx;
+	  __imag__ x = fabs (__imag__ x);
+	  __imag__ x -= t;
+	  __real__ res /= exp_2t;
+	  if (__imag__ x > t)
+	    {
+	      /* Underflow (original imaginary part of x has absolute
+		 value > 2t).  */
+	      __real__ res /= exp_2t;
+	    }
+	  else
+	    __real__ res /= __ieee754_exp (2 * __imag__ x);
+	}
+      else
+	{
+	  double sinhix, coshix;
+	  if (fabs (__imag__ x) > DBL_MIN)
+	    {
+	      sinhix = __ieee754_sinh (__imag__ x);
+	      coshix = __ieee754_cosh (__imag__ x);
+	    }
+	  else
+	    {
+	      sinhix = __imag__ x;
+	      coshix = 1.0;
+	    }
+
+	  if (fabs (sinhix) > fabs (cosrx) * DBL_EPSILON)
+	    den = cosrx * cosrx + sinhix * sinhix;
+	  else
+	    den = cosrx * cosrx;
+	  __real__ res = sinrx * cosrx / den;
+	  __imag__ res = sinhix * coshix / den;
+	}
+      math_check_force_underflow_complex (res);
+    }
+
+  return res;
+}
+weak_alias (__ctan, ctan)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__ctan, __ctanl)
+weak_alias (__ctan, ctanl)
+#endif
diff --git a/math/s_ctanh_template.c b/math/s_ctanh_template.c
new file mode 100644
index 0000000000..2d18875c70
--- /dev/null
+++ b/math/s_ctanh_template.c
@@ -0,0 +1,129 @@
+/* Complex hyperbole tangent for double.
+   Copyright (C) 1997-2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
+
+   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 <fenv.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+__complex__ double
+__ctanh (__complex__ double x)
+{
+  __complex__ double res;
+
+  if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
+    {
+      if (isinf (__real__ x))
+	{
+	  __real__ res = __copysign (1.0, __real__ x);
+	  if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0)
+	    {
+	      double sinix, cosix;
+	      __sincos (__imag__ x, &sinix, &cosix);
+	      __imag__ res = __copysign (0.0, sinix * cosix);
+	    }
+	  else
+	    __imag__ res = __copysign (0.0, __imag__ x);
+	}
+      else if (__imag__ x == 0.0)
+	{
+	  res = x;
+	}
+      else
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __nan ("");
+
+	  if (isinf (__imag__ x))
+	    feraiseexcept (FE_INVALID);
+	}
+    }
+  else
+    {
+      double sinix, cosix;
+      double den;
+      const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2);
+
+      /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y))
+	 = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2).  */
+
+      if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
+	{
+	  __sincos (__imag__ x, &sinix, &cosix);
+	}
+      else
+	{
+	  sinix = __imag__ x;
+	  cosix = 1.0;
+	}
+
+      if (fabs (__real__ x) > t)
+	{
+	  /* Avoid intermediate overflow when the imaginary part of
+	     the result may be subnormal.  Ignoring negligible terms,
+	     the real part is +/- 1, the imaginary part is
+	     sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x).  */
+	  double exp_2t = __ieee754_exp (2 * t);
+
+	  __real__ res = __copysign (1.0, __real__ x);
+	  __imag__ res = 4 * sinix * cosix;
+	  __real__ x = fabs (__real__ x);
+	  __real__ x -= t;
+	  __imag__ res /= exp_2t;
+	  if (__real__ x > t)
+	    {
+	      /* Underflow (original real part of x has absolute value
+		 > 2t).  */
+	      __imag__ res /= exp_2t;
+	    }
+	  else
+	    __imag__ res /= __ieee754_exp (2 * __real__ x);
+	}
+      else
+	{
+	  double sinhrx, coshrx;
+	  if (fabs (__real__ x) > DBL_MIN)
+	    {
+	      sinhrx = __ieee754_sinh (__real__ x);
+	      coshrx = __ieee754_cosh (__real__ x);
+	    }
+	  else
+	    {
+	      sinhrx = __real__ x;
+	      coshrx = 1.0;
+	    }
+
+	  if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON)
+	    den = sinhrx * sinhrx + cosix * cosix;
+	  else
+	    den = cosix * cosix;
+	  __real__ res = sinhrx * coshrx / den;
+	  __imag__ res = sinix * cosix / den;
+	}
+      math_check_force_underflow_complex (res);
+    }
+
+  return res;
+}
+weak_alias (__ctanh, ctanh)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__ctanh, __ctanhl)
+weak_alias (__ctanh, ctanhl)
+#endif