Add ISO C99 complex support for doubles.

* include/complex.h: New file.
	* mingwex/complex: New directory.
	* mingwex/complex/cabs.c: New file.
	* mingwex/complex/cacos.c: New file.
	* mingwex/complex/cacosh.c: New file.
	* mingwex/complex/casin.c: New file.
	* mingwex/complex/casinh.c: New file.
	* mingwex/complex/catan.c: New file.
	* mingwex/complex/catanh.c: New file.
	* mingwex/complex/ccos.c: New file.
	* mingwex/complex/ccosh.c: New file.
	* mingwex/complex/cexp.c: New file.
	* mingwex/complex/cimag.c: New file.
	* mingwex/complex/clog.c: New file.
	* mingwex/complex/cpow.c: New file.
	* mingwex/complex/cproj.c: New file.
	* mingwex/complex/creal.c: New file.
	* mingwex/complex/csin.c: New file.
	* mingwex/complex/csinh.c: New file.
	* mingwex/complex/csqrt.c: New file.
	* mingwex/complex/ctan.c: New file.
	* mingwex/complex/ctanh.c: New file.
	* mingwex/Makefile.in (COMPLEX_DISTFILES): New list of
	files.
	(dist): Use it.
	(COMPLEX_OBJS): New list of objects.
	(LIB_OBJS): Include it in the library.

winsup/mingw/ChangeLog

@@ -1,3 +1,33 @@
+2003-10-21  Danny Smith  <dannysmith@users.sourceforge.net>
+
+	* include/complex.h: New file.
+	* mingwex/complex: New directory.
+	* mingwex/complex/cabs.c: New file.
+	* mingwex/complex/cacos.c: New file.
+	* mingwex/complex/cacosh.c: New file.
+	* mingwex/complex/casin.c: New file.
+	* mingwex/complex/casinh.c: New file.
+	* mingwex/complex/catan.c: New file.
+	* mingwex/complex/catanh.c: New file.
+	* mingwex/complex/ccos.c: New file.
+	* mingwex/complex/ccosh.c: New file.
+	* mingwex/complex/cexp.c: New file.
+	* mingwex/complex/cimag.c: New file.
+	* mingwex/complex/clog.c: New file.
+	* mingwex/complex/cpow.c: New file.
+	* mingwex/complex/cproj.c: New file.
+	* mingwex/complex/creal.c: New file.
+	* mingwex/complex/csin.c: New file.
+	* mingwex/complex/csinh.c: New file.
+	* mingwex/complex/csqrt.c: New file.
+	* mingwex/complex/ctan.c: New file.
+	* mingwex/complex/ctanh.c: New file.
+	* mingwex/Makefile.in (COMPLEX_DISTFILES): New list of
+	files.
+	(dist): Use it.
+	(COMPLEX_OBJS): New list of objects.
+	(LIB_OBJS): Include it in the library.
+
 2003-10-21  Danny Smith  <dannysmith@users.sourceforge.net>
 
 	* include/math.h (cabs): Remove non-ISO prototype.

winsup/mingw/include/complex.h

@@ -0,0 +1,109 @@
+/*
+ * complex.h
+ *
+ * This file is part of the Mingw32 package.
+ *
+ * Contributors:
+ *  Created by Danny Smith <dannysmith@users.sourceforge.net>
+ *
+ *  THIS SOFTWARE IS NOT COPYRIGHTED
+ *
+ *  This source code is offered for use in the public domain. You may
+ *  use, modify or distribute it freely.
+ *
+ *  This code is distributed in the hope that it will be useful but
+ *  WITHOUT ANY WARRANTY. ALL WARRANTIES, EXPRESS OR IMPLIED ARE HEREBY
+ *  DISCLAIMED. This includes but is not limited to warranties of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+ *
+ */
+
+#ifndef _COMPLEX_H_
+#define _COMPLEX_H_
+
+/* All the headers include this file. */
+#include <_mingw.h>
+
+#if (defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L) \
+     || !defined __STRICT_ANSI__ 
+
+/* These macros are specified by C99 standard */
+
+#ifndef __cplusplus
+#define complex _Complex
+#endif
+
+#define _Complex_I  (0.0F +  1.0iF)
+
+/* GCC doesn't support _Imaginary type yet, so we don't
+   define _Imaginary_I */
+
+#define I _Complex_I
+
+#ifdef __cplusplus
+extern "C" {
+#endif 
+
+#ifndef RC_INVOKED
+
+/* TODO: float and long double versions */ 
+double __attribute__ ((const)) creal (double _Complex);
+double __attribute__ ((const)) cimag (double _Complex);
+double __attribute__ ((const)) carg (double _Complex);
+double __attribute__ ((const)) cabs (double _Complex);
+double _Complex __attribute__ ((const)) cconj (double _Complex);
+double _Complex __attribute__ ((const)) cacos (double _Complex);
+double _Complex __attribute__ ((const)) casin (double _Complex);
+double _Complex __attribute__ ((const)) catan (double _Complex);
+double _Complex __attribute__ ((const)) ccos (double _Complex);
+double _Complex __attribute__ ((const)) csin (double _Complex);
+double _Complex __attribute__ ((const)) ctan (double _Complex);
+double _Complex __attribute__ ((const)) cacosh (double _Complex);
+double _Complex __attribute__ ((const)) casinh (double _Complex);
+double _Complex __attribute__ ((const)) catanh (double _Complex);
+double _Complex __attribute__ ((const)) ccosh (double _Complex);
+double _Complex __attribute__ ((const)) csinh (double _Complex);
+double _Complex __attribute__ ((const)) ctanh (double _Complex);
+double _Complex __attribute__ ((const)) cexp (double _Complex);
+double _Complex __attribute__ ((const)) clog (double _Complex);
+double _Complex __attribute__ ((const)) cpow (double _Complex, double _Complex);
+double _Complex __attribute__ ((const)) csqrt (double _Complex);
+double _Complex __attribute__ ((const)) cproj (double _Complex);
+
+#ifdef __GNUC__
+
+__CRT_INLINE double __attribute__ ((const)) creal (double _Complex _Z)
+{
+  return __real__ _Z;
+}
+
+__CRT_INLINE double __attribute__ ((const)) cimag (double _Complex _Z)
+{
+  return __imag__ _Z;
+}
+
+__CRT_INLINE double _Complex __attribute__ ((const)) conj (double _Complex _Z)
+{
+  return __extension__ ~_Z;
+}
+
+__CRT_INLINE  double __attribute__ ((const)) carg (double _Complex _Z)
+{
+  double res;
+  __asm__  ("fpatan;"
+	   : "=t" (res) : "0" (__real__ _Z), "u" (__imag__ _Z) : "st(1)");
+  return res;
+}
+#endif /* __GNUC__ */
+
+
+#endif /* RC_INVOKED */
+
+#ifdef __cplusplus
+}
+#endif 
+
+#endif /* __STDC_VERSION__ >= 199901L */
+
+
+#endif /* _COMPLEX_H */

winsup/mingw/mingwex/Makefile.in

@@ -4,7 +4,7 @@
 # This makefile requires GNU make.
 
 srcdir = @srcdir@
-VPATH = $(srcdir):$(srcdir)/math:$(srcdir)/stdio
+VPATH = $(srcdir):$(srcdir)/math:$(srcdir)/stdio:$(srcdir)/complex
 objdir = .
 
 target_alias = @target_alias@
@@ -65,6 +65,11 @@ STDIO_DISTFILES = \
 	snprintf.c snwprintf.c vsnprintf.c vsnwprintf.c \
 	vfscanf.c vfwscanf.c vscanf.c vsscanf.c vswscanf.c vwscanf.c
 
+COMPLEX_DISTFILES = \
+	cabs.c cacos.c cacosh.c casin.c casinh.c catan.c catanh.c \
+	ccos.c ccosh.c cexp.c cimag.c clog.c cpow.c cproj.c creal.c \
+	csin.c csinh.c csqrt.c ctan.c ctanh.c
+
 CC = @CC@
 # FIXME: Which is it, CC or CC_FOR_TARGET?
 CC_FOR_TARGET = $(CC)
@@ -143,10 +148,14 @@ POSIX_OBJS = \
 	dirent.o wdirent.o getopt.o
 REPLACE_OBJS = \
 	mingw-fseek.o
+COMPLEX_OBJS = \
+	cabs.o cacos.o cacosh.o casin.o casinh.o catan.o catanh.o \
+	ccos.o ccosh.o cexp.o cimag.o clog.o cpow.o cproj.o creal.o \
+	csin.o csinh.o csqrt.o ctan.o ctanh.o
 
 LIB_OBJS = $(Q8_OBJS) $(STDLIB_OBJS) $(STDLIB_STUB_OBJS) \
 	$(STDIO_OBJS) $(MATH_OBJS)  $(FENV_OBJS) \
-	$(POSIX_OBJS) $(REPLACE_OBJS)
+	$(POSIX_OBJS) $(REPLACE_OBJS) $(COMPLEX_OBJS)
 
 LIBS = $(LIBMINGWEX_A)
 DLLS = 
@@ -216,3 +225,9 @@ dist:
 	@for i in $(STDIO_DISTFILES); do\
 		cp -p $(srcdir)/stdio/$$i $(distdir)/mingwex/stdio/$$i ; \
 	done
+	mkdir $(distdir)/mingwex/complex
+	chmod 755 $(distdir)/mingwex/complex
+	@for i in $(COMPLEX_DISTFILES); do\
+		cp -p $(srcdir)/complex/$$i $(distdir)/mingwex/complex/$$i ; \
+	done
+

winsup/mingw/mingwex/complex/cabs.c

@@ -0,0 +1,7 @@
+#include <math.h>
+#include <complex.h>
+
+double cabs (double complex Z)
+{
+  return _hypot ( __real__ Z,  __imag__ Z);
+}

winsup/mingw/mingwex/complex/cacos.c

@@ -0,0 +1,82 @@
+/*
+   cacos.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+#if 0
+/* cacos (Z) = -I * clog(Z + I * csqrt(1 - Z * Z)) */
+
+double complex cacos (double  complex Z)
+{
+  double complex Res;
+  double x, y;
+
+  x = __real__ Z;
+  y = __imag__ Z;
+
+  if (y == 0.0)
+    {
+      __real__ Res = acos (x);
+      __imag__ Res = 0.0;
+    }
+
+  else
+    {
+      double complex ZZ;
+      /* Z * Z = ((x - y) * (x + y)) + (2.0 * x * y) * I */
+      /* caculate 1 - Z * Z */
+      __real__ ZZ = 1.0 - (x - y) * (x + y);
+      __imag__ ZZ = -2.0 * x * y;
+
+       
+       Res = csqrt(ZZ);
+
+      /* calculate ZZ + I * sqrt (ZZ) */
+    
+      __real__ ZZ = x - __imag__ Res;
+      __imag__ ZZ = y + __real__ Res;
+       
+      ZZ = clog(ZZ);
+
+      /* mult by -I */
+
+      __real__ Res  =  __imag__ ZZ;
+      __imag__ Res = - __real__ ZZ;
+    }
+  return Res;
+}
+
+#else
+
+/* cacos ( Z ) =  pi/2 - casin ( Z ) */
+
+double complex cacos (double complex Z)
+{
+  double complex Res  = casin (Z);
+  __real__ Res = M_PI_2 - __real__ Res;
+  __imag__ Res = - __imag__ Res;
+  return Res;
+}
+#endif
+
+#if 0
+#include <stdio.h>
+int main()
+{
+  double z;
+  double complex bar = 0.7 + 1.2  * I;
+  double complex foo = cacos (bar);
+
+  printf ("%.16e\t%.16e\n", __real__ foo, __imag__ foo);
+
+  foo = cacos (bar);
+  printf ("%.16e\t%.16e\n", __real__ foo, __imag__ foo);
+
+  return 1;
+}
+#endif
+

winsup/mingw/mingwex/complex/cacosh.c

@@ -0,0 +1,37 @@
+/*
+   cacosh.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+#if 0
+/* cacosh (z) = I * cacos (z)  */
+double complex cacosh (double complex Z)
+{
+  double complex Tmp;
+  double complex Res;
+
+  Tmp = cacos (Z);
+  __real__ Res = -__imag__ Tmp;
+  __imag__ Res = __real__ Tmp;
+  return Res;
+}
+
+#else
+
+/* cacosh (z) = I * cacos (z) = I * (pi/2 - casin (z))  */
+
+double complex cacosh (double complex Z)
+{
+  double complex Tmp;
+  double complex Res;
+
+  Tmp = casin (Z);
+  __real__ Res = __imag__ Tmp;
+  __imag__ Res =  M_PI_2 - __real__ Tmp;
+  return Res;
+}
+#endif

winsup/mingw/mingwex/complex/casin.c

@@ -0,0 +1,48 @@
+/*
+   casin.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* casin (Z ) = -I * clog(I * Z + csqrt (1.0 - Z * Z))) */
+
+double complex casin (double complex Z)
+{
+  double complex Res;
+  double x, y;
+
+  x = __real__ Z;
+  y = __imag__ Z;
+
+  if (y == 0.0)
+    {
+      __real__ Res = asin (x);
+      __imag__ Res = 0.0;
+    }
+  else  /* -I * clog(I * Z + csqrt(1.0 - Z * Z))) */
+    {
+      double complex ZZ;
+                                 
+      /* Z * Z = ((x - y) * (x + y)) + (2.0 * x * y) * I */
+      /* calculate 1 - Z * Z */
+      __real__ ZZ = 1.0 - (x - y) * (x + y);
+      __imag__ ZZ = -2.0 * x * y;
+      ZZ = csqrt (ZZ);
+
+
+      /* add  I * Z  to ZZ */
+
+      __real__ ZZ -= y;
+      __imag__ ZZ += x;
+
+      ZZ = clog (ZZ);
+
+      /* mult by -I */
+      __real__ Res = __imag__ ZZ;
+      __imag__ Res = - __real__ ZZ;  
+    }
+  return (Res);
+}

winsup/mingw/mingwex/complex/casinh.c

@@ -0,0 +1,23 @@
+/*
+   casinh.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* casinh (z) = -I casin (I * z) */
+
+double complex casinh (double complex Z)
+{
+  double complex Tmp;
+  double complex Res;
+
+  __real__ Tmp = - __imag__ Z;
+  __imag__ Tmp =   __real__ Z;
+  Tmp = casin (Tmp);
+  __real__ Res =   __imag__ Tmp;
+  __imag__ Res = - __real__ Tmp;
+  return Res;
+}

winsup/mingw/mingwex/complex/catan.c

@@ -0,0 +1,49 @@
+/* catan.c */
+
+/*
+   Contributed by Danny Smith
+   2003-10-17
+
+   FIXME: This needs some serious numerical analysis.
+*/
+
+#include <math.h>
+#include <complex.h>
+#include <errno.h>
+
+/* catan (z) = -I/2 * clog ((I + z) / (I - z)) */ 
+
+double complex 
+catan (double complex Z)
+{
+  double complex Res;
+  double complex Tmp;
+  double x = __real__ Z;
+  double y = __imag__ Z;
+
+  if ( x == 0.0 && (1.0 - fabs (y)) == 0.0)
+    {
+      errno = ERANGE;
+      __real__ Res = HUGE_VAL;
+      __imag__ Res = HUGE_VAL;
+    }
+   else if (isinf (_hypot (x, y)))
+   {
+     __real__ Res = (x > 0 ? M_PI_2 : -M_PI_2);
+     __imag__ Res = 0.0;
+   }
+  else
+    {
+      __real__ Tmp = - x; 
+      __imag__ Tmp = 1.0 - y;
+
+      __real__ Res = x; 
+      __imag__ Res = y + 1.0;
+
+      Tmp = clog (Res/Tmp);	
+      __real__ Res  = - 0.5 * __imag__ Tmp;
+      __imag__ Res =  0.5 * __real__ Tmp;
+    }
+
+   return Res; 
+}

winsup/mingw/mingwex/complex/catanh.c

@@ -0,0 +1,23 @@
+/* catanh.c */
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/*  catanh (z) = -I * catan (I  * z)  */
+
+double complex catanh (double complex Z)
+{
+  double complex Tmp;
+  double complex Res;
+
+  __real__ Tmp = - __imag__ Z;
+  __imag__ Tmp =   __real__ Z;
+  Tmp = catan (Tmp);
+  __real__ Res =  __imag__ Tmp;
+  __imag__ Res = - __real__ Tmp;
+  return Res;
+}

winsup/mingw/mingwex/complex/ccos.c

@@ -0,0 +1,20 @@
+/*
+   ccos.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* ccos (x + I * y) = cos (x) * cosh (y)
+    + I * (sin (x) * sinh (y)) */ 
+
+
+double complex ccos (double complex Z)
+{
+  double complex Res;
+  __real__ Res = cos (__real__ Z) * cosh ( __imag__ Z);
+  __imag__ Res = -sin (__real__ Z) * sinh ( __imag__ Z);
+  return Res;
+}

winsup/mingw/mingwex/complex/ccosh.c

@@ -0,0 +1,19 @@
+/*
+   ccosh.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* ccosh (x + I * y) = cosh (x) * cos (y)
+    + I * (sinh (x) * sin (y)) */ 
+
+double complex ccosh (double complex Z)
+{
+  double complex Res;
+  __real__ Res = cosh (__real__ Z) * cos (__imag__ Z);
+  __imag__ Res = sinh (__real__ Z) * sin (__imag__ Z);
+  return Res;
+}

winsup/mingw/mingwex/complex/cexp.c

@@ -0,0 +1,19 @@
+/*
+   cexp.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* cexp (x + I * y) = exp (x) * cos (y) + I * exp (x) * sin (y) */
+
+double complex cexp (double complex Z)
+{
+  double complex  Res;
+  long double rho = exp (__real__ Z);
+  __real__ Res = rho * cos(__imag__ Z);
+  __imag__ Res = rho * sin(__imag__ Z);
+  return Res;
+}

winsup/mingw/mingwex/complex/cimag.c

@@ -0,0 +1,6 @@
+#include <complex.h>
+double __attribute__ ((const)) cimag (double complex _Z)
+{
+  return __imag__ _Z;
+}
+

winsup/mingw/mingwex/complex/clog.c

@@ -0,0 +1,19 @@
+/*
+   clog.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+/* clog (x + I * y) = log (hypot (x, y)) + I * atan2 (y, x) */
+
+#include <math.h>
+#include <complex.h>
+
+double complex clog (double complex Z)
+{
+  double complex Res;
+  __real__ Res = log (_hypot (__real__ Z,  __imag__ Z));
+  __imag__ Res = carg (Z);
+  return Res;
+}
+

winsup/mingw/mingwex/complex/cpow.c

@@ -0,0 +1,48 @@
+/*  cpow.c */
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+/* cpow(X, Y) = cexp(X * clog(Y)) */
+
+#include <math.h>
+#include <complex.h>
+
+/* Use dll version of pow */
+extern double  (*_imp__pow) (double, double);
+#define pow (*_imp__pow)
+
+double complex cpow (double complex X, double complex Y)
+{
+  double complex Res;
+  double i;
+  double r = hypot (__real__ X, __imag__ X);
+  if (r == 0.0)
+    {
+       __real__ Res = __imag__ Res = 0.0;
+    }
+  else
+    {
+      double rho;
+      double theta;
+      i = carg (X);
+      theta = i * __real__ Y;
+ 
+      if (__imag__ Y == 0.0)
+	/* This gives slightly more accurate results in these cases. */
+   	rho = pow (r, __real__ Y);
+      else
+	{
+          r = log (r);
+	  /* rearrangement of cexp(X * clog(Y)) */
+	  theta += r * __imag__ Y;
+	  rho = exp (r * __real__ Y - i * __imag__ Y);
+	}
+
+      __real__ Res = rho * cos (theta);
+      __imag__ Res = rho * sin (theta);
+    }
+  return  Res;
+}
+

winsup/mingw/mingwex/complex/cproj.c

@@ -0,0 +1,22 @@
+/*
+   cproj.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* Return the value of the projection onto the Riemann sphere.*/
+
+double complex cproj (double complex Z)
+{
+  complex double Res = Z;
+  if (isinf (__real__ Z) || isinf (__imag__ Z))
+    {
+      __real__ Res = HUGE_VAL;
+      __imag__ Res = copysign (0.0, __imag__ Z);
+    }
+  return Res;
+}
+

winsup/mingw/mingwex/complex/creal.c

@@ -0,0 +1,6 @@
+#include <complex.h>
+double __attribute__ ((const)) creal (double complex _Z)
+{
+  return __real__ _Z;
+}
+

winsup/mingw/mingwex/complex/csin.c

@@ -0,0 +1,21 @@
+/*  csin.c */
+
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+/* csin (x + I * y) = sin (x) * cosh (y)
+    + I * (cos (x) * sinh (y)) */ 
+
+double complex csin (double complex Z)
+{
+  double complex Res;
+  __real__ Res = sin (__real__ Z) * cosh ( __imag__ Z);
+  __imag__ Res = cos (__real__ Z) * sinh ( __imag__ Z);
+  return Res;
+}
+

winsup/mingw/mingwex/complex/csinh.c

@@ -0,0 +1,21 @@
+/* csinh.c */
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+
+#include <math.h>
+#include <complex.h>
+
+/* csinh (x + I * y) = sinh (x) * cos (y)
+    + I * (cosh (x) * sin (y)) */ 
+
+
+double complex csinh (double complex Z)
+{
+  double complex Res;
+  __real__ Res = sinh (__real__ Z) * cos (__imag__ Z);
+  __imag__ Res = cosh (__real__ Z) * sin (__imag__ Z);
+  return Res;
+}

winsup/mingw/mingwex/complex/csqrt.c

@@ -0,0 +1,55 @@
+/*
+   csqrt.c
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+
+double complex  csqrt (double complex Z)
+{
+  double complex Res;
+  double t;
+  double x = __real__ Z;
+  double y = __imag__ Z;
+
+  if (y == 0.0)
+    {
+      if (x < 0.0)
+        {
+ 	  __real__ Res = 0.0;
+	  __imag__ Res = sqrt (-x);
+        }
+      else
+        {
+ 	  __real__ Res = sqrt (x);
+	  __imag__ Res = 0.0;
+        }
+    }
+
+  else if (x == 0.0)
+    {
+      t = sqrt(0.5 * fabs (y));
+      __real__ Res = y > 0 ? t : -t;
+      __imag__ Res = t;
+    }
+
+  else
+    {
+      t = sqrt (2.0  * (_hypot (x, y) + fabs (x)));
+      if ( x > 0.0)
+        {	
+          __real__ Res = 0.5 * t;
+          __imag__ Res = y / t;
+        }
+      else
+        {
+	  __real__ Res = fabs ( y / t);
+	  __imag__ Res = (y < 0.0 ? -0.5 : 0.5) * t;
+        }
+    }
+
+  return Res;
+}
+

winsup/mingw/mingwex/complex/ctan.c

@@ -0,0 +1,41 @@
+/* ctan.c */
+
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+#include <math.h>
+#include <complex.h>
+#include <errno.h>
+
+
+/* ctan (x + I * y) = (sin (2 * x)  +  I * sinh(2 * y))
+		      / (cos (2 * x)  +  cosh (2 * y)) */
+
+double complex ctan (double complex Z)
+{
+  double complex Res;
+  double two_I = 2.0 * __imag__ Z;
+  double two_R = 2.0 * __real__ Z;
+  double denom = cos (two_R) + cosh (two_I);
+  if (denom == 0.0)
+    {
+      errno = ERANGE;
+      __real__ Res = HUGE_VAL;
+      __imag__ Res = HUGE_VAL;
+    }
+  else if (isinf (denom))
+    {
+      errno = ERANGE;
+      __real__ Res = 0.0;
+      __imag__ Res = two_I > 0 ? 1.0 : -1.0;
+    }
+  else
+    {
+      __real__ Res = sin (two_R) / denom;
+      __imag__ Res = sinh (two_I) / denom;
+    }
+  return Res;
+}
+

winsup/mingw/mingwex/complex/ctanh.c

@@ -0,0 +1,44 @@
+/*  ctanh.c */
+
+/*
+   Contributed by Danny Smith
+   2003-10-20
+*/
+
+
+#include <math.h>
+#include <complex.h>
+#include <errno.h>
+
+/*
+  ctanh (x + I * y) = (sinh (2 * x)  +  sin (2 * y) * I )
+		     / (cosh (2 * x) + cos (2 * y)) .
+*/
+
+double complex
+ctanh (double complex Z)
+{
+  double complex Res;
+  double two_R = 2.0 * __real__ Z;
+  double two_I = 2.0 * __imag__ Z;
+  double denom = cosh (two_R) + cos (two_I);
+
+  if (denom == 0.0)
+    {
+      errno = ERANGE;
+      __real__ Res = HUGE_VAL;
+      __imag__ Res = HUGE_VAL;
+    }
+  else if ( isinf (denom))
+    {
+      errno = ERANGE;
+      __real__ Res = two_R > 0 ? 1.0 : -1.0;
+      __imag__ Res = 0.0;
+    }
+  else
+    {
+      __real__ Res = sinh (two_R) / denom;
+      __imag__ Res = sin (two_I) / denom;
+    }
+  return Res;
+}