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+/*
+ *  Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ *  Copyright (C) 2006-2008 - INRIA - Bruno JOFRET
+ *  Copyright (C) Bruno Pincon
+ *
+ *  This file must be used under the terms of the CeCILL.
+ *  This source file is licensed as described in the file COPYING, which
+ *  you should have received as part of this distribution.  The terms
+ *  are also available at
+ *  http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
+ *
+ */
+
+/*
+  ALGORITHM
+   based on the formula :
+
+                    0.5 sin(2 xr) +  i 0.5 sinh(2 xi)
+   tan(xr + i xi) = ---------------------------------
+                        cos(xr)^2  + sinh(xi)^2
+
+   noting  d = cos(xr)^2 + sinh(xi)^2, we have :
+
+           yr = 0.5 * sin(2 * xr) / d       (1)
+
+           yi = 0.5 * sinh(2 * xi) / d      (2)
+
+   to avoid spurious overflows in computing yi with
+   formula (2) (which results in NaN for yi)
+   we use also the following formula :
+
+           yi = sign(xi)   when |xi| > LIM  (3)
+
+   Explanations for (3) :
+
+   we have d = sinh(xi)^2 ( 1 + (cos(xr)/sinh(xi))^2 ),
+   so when :
+
+      (cos(xr)/sinh(xi))^2 < epsm   ( epsm = max relative error
+                                     for coding a real in a f.p.
+                                     number set F(b,p,emin,emax)
+                                        epsm = 0.5 b^(1-p) )
+   which is forced  when :
+
+       1/sinh(xi)^2 < epsm   (4)
+   <=> |xi| > asinh(1/sqrt(epsm)) (= 19.06... in ieee 754 double)
+
+   sinh(xi)^2 is a good approximation for d (relative to the f.p.
+   arithmetic used) and then yr may be approximate with :
+
+    yr = cosh(xi)/sinh(xi)
+       = sign(xi) (1 + exp(-2 |xi|))/(1 - exp(-2|xi|))
+       = sign(xi) (1 + 2 u + 2 u^2 + 2 u^3 + ...)
+
+   with u = exp(-2 |xi|)). Now when :
+
+       2 exp(-2|xi|) < epsm  (2)
+   <=> |xi| > 0.5 * log(2/epsm) (= 18.71... in ieee 754 double)
+
+   sign(xi)  is a good approximation for yr.
+
+   Constraint (1) is stronger than (2) and we take finaly
+
+   LIM = 1 + log(2/sqrt(epsm))
+
+   (log(2/sqrt(epsm)) being very near asinh(1/sqrt(epsm))
+
+AUTHOR
+   Bruno Pincon <Bruno.Pincon@iecn.u-nancy.fr>
+*/
+
+#include <math.h>
+#include "lapack.h"
+#include "tan.h"
+#include "sqrt.h"
+#include "cos.h"
+#include "sinh.h"
+#include "sin.h"
+#include "log.h"
+#include "abs.h"
+
+#define localSign(x) x >= 0 ? 1.0 : -1.0
+
+doubleComplex		ztans(doubleComplex z) {
+  double Temp = 0;
+  double Lim = 1 + dlogs(2.0 / dsqrts( getRelativeMachinePrecision()));
+  double RealIn = zreals(z);
+  double ImagIn = zimags(z);
+  double RealOut = 0;
+  double ImagOut = 0;
+
+  Temp = pow(dcoss(RealIn), 2) + pow(dsinhs(ImagIn), 2);
+  RealOut = 0.5 * dsins(2 * RealIn) / Temp;
+  if(dabss(ImagIn) < Lim)
+    {
+      ImagOut = 0.5 * dsinhs(2 * ImagIn) / Temp;
+    }
+  else
+    {
+      ImagOut = localSign(ImagIn);
+    }
+
+  return DoubleComplex(RealOut, ImagOut);
+}