Prepare to convert remaining _Complex 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.

6 files changed, 641 insertions, 0 deletions

diff --git a/math/s_cexp_template.c b/math/s_cexp_template.c
new file mode 100644
index 0000000000..3a476bde3c
--- /dev/null
+++ b/math/s_cexp_template.c
@@ -0,0 +1,157 @@
+/* Return value of complex exponential function for double complex 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 <fenv.h>
+#include <math.h>
+#include <math_private.h>
+#include <float.h>
+
+__complex__ double
+__cexp (__complex__ double x)
+{
+  __complex__ double retval;
+  int rcls = fpclassify (__real__ x);
+  int icls = fpclassify (__imag__ x);
+
+  if (__glibc_likely (rcls >= FP_ZERO))
+    {
+      /* Real part is finite.  */
+      if (__glibc_likely (icls >= FP_ZERO))
+	{
+	  /* Imaginary part is finite.  */
+	  const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2);
+	  double sinix, cosix;
+
+	  if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
+	    {
+	      __sincos (__imag__ x, &sinix, &cosix);
+	    }
+	  else
+	    {
+	      sinix = __imag__ x;
+	      cosix = 1.0;
+	    }
+
+	  if (__real__ x > t)
+	    {
+	      double exp_t = __ieee754_exp (t);
+	      __real__ x -= t;
+	      sinix *= exp_t;
+	      cosix *= exp_t;
+	      if (__real__ x > t)
+		{
+		  __real__ x -= t;
+		  sinix *= exp_t;
+		  cosix *= exp_t;
+		}
+	    }
+	  if (__real__ x > t)
+	    {
+	      /* Overflow (original real part of x > 3t).  */
+	      __real__ retval = DBL_MAX * cosix;
+	      __imag__ retval = DBL_MAX * sinix;
+	    }
+	  else
+	    {
+	      double exp_val = __ieee754_exp (__real__ x);
+	      __real__ retval = exp_val * cosix;
+	      __imag__ retval = exp_val * sinix;
+	    }
+	  math_check_force_underflow_complex (retval);
+	}
+      else
+	{
+	  /* If the imaginary part is +-inf or NaN and the real part
+	     is not +-inf the result is NaN + iNaN.  */
+	  __real__ retval = __nan ("");
+	  __imag__ retval = __nan ("");
+
+	  feraiseexcept (FE_INVALID);
+	}
+    }
+  else if (__glibc_likely (rcls == FP_INFINITE))
+    {
+      /* Real part is infinite.  */
+      if (__glibc_likely (icls >= FP_ZERO))
+	{
+	  /* Imaginary part is finite.  */
+	  double value = signbit (__real__ x) ? 0.0 : HUGE_VAL;
+
+	  if (icls == FP_ZERO)
+	    {
+	      /* Imaginary part is 0.0.  */
+	      __real__ retval = value;
+	      __imag__ retval = __imag__ x;
+	    }
+	  else
+	    {
+	      double sinix, cosix;
+
+	      if (__glibc_likely (fabs (__imag__ x) > DBL_MIN))
+		{
+		  __sincos (__imag__ x, &sinix, &cosix);
+		}
+	      else
+		{
+		  sinix = __imag__ x;
+		  cosix = 1.0;
+		}
+
+	      __real__ retval = __copysign (value, cosix);
+	      __imag__ retval = __copysign (value, sinix);
+	    }
+	}
+      else if (signbit (__real__ x) == 0)
+	{
+	  __real__ retval = HUGE_VAL;
+	  __imag__ retval = __nan ("");
+
+	  if (icls == FP_INFINITE)
+	    feraiseexcept (FE_INVALID);
+	}
+      else
+	{
+	  __real__ retval = 0.0;
+	  __imag__ retval = __copysign (0.0, __imag__ x);
+	}
+    }
+  else
+    {
+      /* If the real part is NaN the result is NaN + iNaN unless the
+	 imaginary part is zero.  */
+      __real__ retval = __nan ("");
+      if (icls == FP_ZERO)
+	__imag__ retval = __imag__ x;
+      else
+	{
+	  __imag__ retval = __nan ("");
+
+	  if (rcls != FP_NAN || icls != FP_NAN)
+	    feraiseexcept (FE_INVALID);
+	}
+    }
+
+  return retval;
+}
+weak_alias (__cexp, cexp)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__cexp, __cexpl)
+weak_alias (__cexp, cexpl)
+#endif
diff --git a/math/s_clog10_template.c b/math/s_clog10_template.c
new file mode 100644
index 0000000000..8d9245bac6
--- /dev/null
+++ b/math/s_clog10_template.c
@@ -0,0 +1,124 @@
+/* Compute complex base 10 logarithm.
+   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>
+
+/* log_10 (2).  */
+#define M_LOG10_2 0.3010299956639811952137388947244930267682
+
+/* pi * log10 (e).  */
+#define M_PI_LOG10E 1.364376353841841347485783625431355770210
+
+__complex__ double
+__clog10 (__complex__ double x)
+{
+  __complex__ double result;
+  int rcls = fpclassify (__real__ x);
+  int icls = fpclassify (__imag__ x);
+
+  if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
+    {
+      /* Real and imaginary part are 0.0.  */
+      __imag__ result = signbit (__real__ x) ? M_PI_LOG10E : 0.0;
+      __imag__ result = __copysign (__imag__ result, __imag__ x);
+      /* Yes, the following line raises an exception.  */
+      __real__ result = -1.0 / fabs (__real__ x);
+    }
+  else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
+    {
+      /* Neither real nor imaginary part is NaN.  */
+      double absx = fabs (__real__ x), absy = fabs (__imag__ x);
+      int scale = 0;
+
+      if (absx < absy)
+	{
+	  double t = absx;
+	  absx = absy;
+	  absy = t;
+	}
+
+      if (absx > DBL_MAX / 2.0)
+	{
+	  scale = -1;
+	  absx = __scalbn (absx, scale);
+	  absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
+	}
+      else if (absx < DBL_MIN && absy < DBL_MIN)
+	{
+	  scale = DBL_MANT_DIG;
+	  absx = __scalbn (absx, scale);
+	  absy = __scalbn (absy, scale);
+	}
+
+      if (absx == 1.0 && scale == 0)
+	{
+	  __real__ result = __log1p (absy * absy) * (M_LOG10E / 2.0);
+	  math_check_force_underflow_nonneg (__real__ result);
+	}
+      else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
+	{
+	  double d2m1 = (absx - 1.0) * (absx + 1.0);
+	  if (absy >= DBL_EPSILON)
+	    d2m1 += absy * absy;
+	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
+	}
+      else if (absx < 1.0
+	       && absx >= 0.5
+	       && absy < DBL_EPSILON / 2.0
+	       && scale == 0)
+	{
+	  double d2m1 = (absx - 1.0) * (absx + 1.0);
+	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
+	}
+      else if (absx < 1.0
+	       && absx >= 0.5
+	       && scale == 0
+	       && absx * absx + absy * absy >= 0.5)
+	{
+	  double d2m1 = __x2y2m1 (absx, absy);
+	  __real__ result = __log1p (d2m1) * (M_LOG10E / 2.0);
+	}
+      else
+	{
+	  double d = __ieee754_hypot (absx, absy);
+	  __real__ result = __ieee754_log10 (d) - scale * M_LOG10_2;
+	}
+
+      __imag__ result = M_LOG10E * __ieee754_atan2 (__imag__ x, __real__ x);
+    }
+  else
+    {
+      __imag__ result = __nan ("");
+      if (rcls == FP_INFINITE || icls == FP_INFINITE)
+	/* Real or imaginary part is infinite.  */
+	__real__ result = HUGE_VAL;
+      else
+	__real__ result = __nan ("");
+    }
+
+  return result;
+}
+weak_alias (__clog10, clog10)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__clog10, __clog10l)
+weak_alias (__clog10, clog10l)
+#endif
diff --git a/math/s_clog_template.c b/math/s_clog_template.c
new file mode 100644
index 0000000000..b546030313
--- /dev/null
+++ b/math/s_clog_template.c
@@ -0,0 +1,118 @@
+/* Compute complex natural logarithm.
+   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
+__clog (__complex__ double x)
+{
+  __complex__ double result;
+  int rcls = fpclassify (__real__ x);
+  int icls = fpclassify (__imag__ x);
+
+  if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
+    {
+      /* Real and imaginary part are 0.0.  */
+      __imag__ result = signbit (__real__ x) ? M_PI : 0.0;
+      __imag__ result = __copysign (__imag__ result, __imag__ x);
+      /* Yes, the following line raises an exception.  */
+      __real__ result = -1.0 / fabs (__real__ x);
+    }
+  else if (__glibc_likely (rcls != FP_NAN && icls != FP_NAN))
+    {
+      /* Neither real nor imaginary part is NaN.  */
+      double absx = fabs (__real__ x), absy = fabs (__imag__ x);
+      int scale = 0;
+
+      if (absx < absy)
+	{
+	  double t = absx;
+	  absx = absy;
+	  absy = t;
+	}
+
+      if (absx > DBL_MAX / 2.0)
+	{
+	  scale = -1;
+	  absx = __scalbn (absx, scale);
+	  absy = (absy >= DBL_MIN * 2.0 ? __scalbn (absy, scale) : 0.0);
+	}
+      else if (absx < DBL_MIN && absy < DBL_MIN)
+	{
+	  scale = DBL_MANT_DIG;
+	  absx = __scalbn (absx, scale);
+	  absy = __scalbn (absy, scale);
+	}
+
+      if (absx == 1.0 && scale == 0)
+	{
+	  __real__ result = __log1p (absy * absy) / 2.0;
+	  math_check_force_underflow_nonneg (__real__ result);
+	}
+      else if (absx > 1.0 && absx < 2.0 && absy < 1.0 && scale == 0)
+	{
+	  double d2m1 = (absx - 1.0) * (absx + 1.0);
+	  if (absy >= DBL_EPSILON)
+	    d2m1 += absy * absy;
+	  __real__ result = __log1p (d2m1) / 2.0;
+	}
+      else if (absx < 1.0
+	       && absx >= 0.5
+	       && absy < DBL_EPSILON / 2.0
+	       && scale == 0)
+	{
+	  double d2m1 = (absx - 1.0) * (absx + 1.0);
+	  __real__ result = __log1p (d2m1) / 2.0;
+	}
+      else if (absx < 1.0
+	       && absx >= 0.5
+	       && scale == 0
+	       && absx * absx + absy * absy >= 0.5)
+	{
+	  double d2m1 = __x2y2m1 (absx, absy);
+	  __real__ result = __log1p (d2m1) / 2.0;
+	}
+      else
+	{
+	  double d = __ieee754_hypot (absx, absy);
+	  __real__ result = __ieee754_log (d) - scale * M_LN2;
+	}
+
+      __imag__ result = __ieee754_atan2 (__imag__ x, __real__ x);
+    }
+  else
+    {
+      __imag__ result = __nan ("");
+      if (rcls == FP_INFINITE || icls == FP_INFINITE)
+	/* Real or imaginary part is infinite.  */
+	__real__ result = HUGE_VAL;
+      else
+	__real__ result = __nan ("");
+    }
+
+  return result;
+}
+weak_alias (__clog, clog)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__clog, __clogl)
+weak_alias (__clog, clogl)
+#endif
diff --git a/math/s_cpow_template.c b/math/s_cpow_template.c
new file mode 100644
index 0000000000..037e575b1a
--- /dev/null
+++ b/math/s_cpow_template.c
@@ -0,0 +1,33 @@
+/* Complex power of double values.
+   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>
+
+
+__complex__ double
+__cpow (__complex__ double x, __complex__ double c)
+{
+  return __cexp (c * __clog (x));
+}
+weak_alias (__cpow, cpow)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__cpow, __cpowl)
+weak_alias (__cpow, cpowl)
+#endif
diff --git a/math/s_cproj_template.c b/math/s_cproj_template.c
new file mode 100644
index 0000000000..d47f009502
--- /dev/null
+++ b/math/s_cproj_template.c
@@ -0,0 +1,44 @@
+/* Compute projection of complex double value to Riemann sphere.
+   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>
+
+
+__complex__ double
+__cproj (__complex__ double x)
+{
+  if (isinf (__real__ x) || isinf (__imag__ x))
+    {
+      __complex__ double res;
+
+      __real__ res = INFINITY;
+      __imag__ res = __copysign (0.0, __imag__ x);
+
+      return res;
+    }
+
+  return x;
+}
+weak_alias (__cproj, cproj)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__cproj, __cprojl)
+weak_alias (__cproj, cprojl)
+#endif
diff --git a/math/s_csqrt_template.c b/math/s_csqrt_template.c
new file mode 100644
index 0000000000..1f073e7f17
--- /dev/null
+++ b/math/s_csqrt_template.c
@@ -0,0 +1,165 @@
+/* Complex square root of double value.
+   Copyright (C) 1997-2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+   Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
+   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
+__csqrt (__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 = HUGE_VAL;
+	  __imag__ res = __imag__ x;
+	}
+      else if (rcls == FP_INFINITE)
+	{
+	  if (__real__ x < 0.0)
+	    {
+	      __real__ res = icls == FP_NAN ? __nan ("") : 0;
+	      __imag__ res = __copysign (HUGE_VAL, __imag__ x);
+	    }
+	  else
+	    {
+	      __real__ res = __real__ x;
+	      __imag__ res = (icls == FP_NAN
+			      ? __nan ("") : __copysign (0.0, __imag__ x));
+	    }
+	}
+      else
+	{
+	  __real__ res = __nan ("");
+	  __imag__ res = __nan ("");
+	}
+    }
+  else
+    {
+      if (__glibc_unlikely (icls == FP_ZERO))
+	{
+	  if (__real__ x < 0.0)
+	    {
+	      __real__ res = 0.0;
+	      __imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
+					 __imag__ x);
+	    }
+	  else
+	    {
+	      __real__ res = fabs (__ieee754_sqrt (__real__ x));
+	      __imag__ res = __copysign (0.0, __imag__ x);
+	    }
+	}
+      else if (__glibc_unlikely (rcls == FP_ZERO))
+	{
+	  double r;
+	  if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
+	    r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
+	  else
+	    r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
+
+	  __real__ res = r;
+	  __imag__ res = __copysign (r, __imag__ x);
+	}
+      else
+	{
+	  double d, r, s;
+	  int scale = 0;
+
+	  if (fabs (__real__ x) > DBL_MAX / 4.0)
+	    {
+	      scale = 1;
+	      __real__ x = __scalbn (__real__ x, -2 * scale);
+	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
+	    }
+	  else if (fabs (__imag__ x) > DBL_MAX / 4.0)
+	    {
+	      scale = 1;
+	      if (fabs (__real__ x) >= 4.0 * DBL_MIN)
+		__real__ x = __scalbn (__real__ x, -2 * scale);
+	      else
+		__real__ x = 0.0;
+	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
+	    }
+	  else if (fabs (__real__ x) < 2.0 * DBL_MIN
+		   && fabs (__imag__ x) < 2.0 * DBL_MIN)
+	    {
+	      scale = -((DBL_MANT_DIG + 1) / 2);
+	      __real__ x = __scalbn (__real__ x, -2 * scale);
+	      __imag__ x = __scalbn (__imag__ x, -2 * scale);
+	    }
+
+	  d = __ieee754_hypot (__real__ x, __imag__ x);
+	  /* Use the identity   2  Re res  Im res = Im x
+	     to avoid cancellation error in  d +/- Re x.  */
+	  if (__real__ x > 0)
+	    {
+	      r = __ieee754_sqrt (0.5 * (d + __real__ x));
+	      if (scale == 1 && fabs (__imag__ x) < 1.0)
+		{
+		  /* Avoid possible intermediate underflow.  */
+		  s = __imag__ x / r;
+		  r = __scalbn (r, scale);
+		  scale = 0;
+		}
+	      else
+		s = 0.5 * (__imag__ x / r);
+	    }
+	  else
+	    {
+	      s = __ieee754_sqrt (0.5 * (d - __real__ x));
+	      if (scale == 1 && fabs (__imag__ x) < 1.0)
+		{
+		  /* Avoid possible intermediate underflow.  */
+		  r = fabs (__imag__ x / s);
+		  s = __scalbn (s, scale);
+		  scale = 0;
+		}
+	      else
+		r = fabs (0.5 * (__imag__ x / s));
+	    }
+
+	  if (scale)
+	    {
+	      r = __scalbn (r, scale);
+	      s = __scalbn (s, scale);
+	    }
+
+	  math_check_force_underflow (r);
+	  math_check_force_underflow (s);
+
+	  __real__ res = r;
+	  __imag__ res = __copysign (s, __imag__ x);
+	}
+    }
+
+  return res;
+}
+weak_alias (__csqrt, csqrt)
+#ifdef NO_LONG_DOUBLE
+strong_alias (__csqrt, __csqrtl)
+weak_alias (__csqrt, csqrtl)
+#endif