From db464f35f5a10b58d9ed1085e0b462689adee583 Mon Sep 17 00:00:00 2001
From: Siddhesh Wani
Date: Mon, 25 May 2015 14:46:31 +0530
Subject: Original Version

---
 src/c/elementaryFunctions/asin/zasins.c | 146 ++++++++++++++++++++++++++++++++
 1 file changed, 146 insertions(+)
 create mode 100644 src/c/elementaryFunctions/asin/zasins.c

(limited to 'src/c/elementaryFunctions/asin/zasins.c')

diff --git a/src/c/elementaryFunctions/asin/zasins.c b/src/c/elementaryFunctions/asin/zasins.c
new file mode 100644
index 0000000..5bd586a
--- /dev/null
+++ b/src/c/elementaryFunctions/asin/zasins.c
@@ -0,0 +1,146 @@
+/*
+ *  Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ *  Copyright (C) 2007-2008 - 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
+ *
+ */
+
+/*
+ *     REFERENCE
+ *        This is a Fortran-77 translation of an algorithm by
+ *        T.E. Hull, T. F. Fairgrieve and P.T.P. Tang which
+ *        appears in their article :
+ *          "Implementing the Complex Arcsine and Arccosine
+ *           Functions Using Exception Handling", ACM, TOMS,
+ *           Vol 23, No. 3, Sept 1997, p. 299-335
+ *     Thanks to Tom Fairgrieve
+ */
+
+#include "lapack.h"
+#include "asin.h"
+#include "atan.h"
+#include "sqrt.h"
+#include "abs.h"
+#include "log.h"
+#include "log1p.h"
+#include "min.h"
+#include "max.h"
+
+doubleComplex		zasins(doubleComplex z) {
+  static double sdblPi_2	= 1.5707963267948966192313216;
+  static double sdblLn2		= 0.6931471805599453094172321;
+  static double sdblAcross	= 1.5;
+  static double sdblBcross	= 0.6417;
+
+  double dblLsup = dsqrts(getOverflowThreshold())/8.0;
+  double dblLinf = 4 * dsqrts(getUnderflowThreshold());
+  double dblEpsm = dsqrts(getRelativeMachinePrecision());
+
+  double _dblReal	= zreals(z);
+  double _dblImg	= zimags(z);
+
+  double dblAbsReal	= dabss(_dblReal);
+  double dblAbsImg	= dabss(_dblImg);
+  int iSignReal		= _dblReal < 0 ? -1 : 1;
+  int iSignImg		= _dblImg < 0 ? -1 : 1;
+
+  double dblR = 0, dblS = 0, dblA = 0, dblB = 0;
+
+  double dblTemp = 0;
+
+  double _pdblReal = 0;
+  double _pdblImg = 0;
+
+  if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
+    {
+      /* we are in the safe region */
+      dblR = dsqrts( (dblAbsReal + 1) * (dblAbsReal + 1) + dblAbsImg * dblAbsImg);
+      dblS = dsqrts( (dblAbsReal - 1) * (dblAbsReal - 1) + dblAbsImg * dblAbsImg);
+      dblA = 0.5 * ( dblR + dblS );
+      dblB = dblAbsReal / dblA;
+
+
+      /* compute the real part */
+      if(dblB <= sdblBcross)
+	_pdblReal = dasins(dblB);
+      else if( dblAbsReal <= 1)
+	_pdblReal = datans(dblAbsReal / dsqrts( 0.5 * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
+      else
+	_pdblReal = datans(dblAbsReal / (dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
+
+      /* compute the imaginary part */
+      if(dblA <= sdblAcross)
+	{
+	  double dblImg1 = 0;
+
+	  if(dblAbsReal < 1)
+	    /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
+	    dblImg1 = 0.5 * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + dblAbsImg * dblAbsImg / (dblS + (1 - dblAbsReal)));
+	  else
+	    /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(S+(x-1.d0))) */
+	    dblImg1 = 0.5 * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
+	  /* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
+	  dblTemp = dblImg1 + dsqrts(dblImg1 * (dblA + 1));
+	  _pdblImg = dlog1ps(dblTemp);
+	}
+      else
+	/* ai = log(A + sqrt(A**2 - 1.d0)) */
+	_pdblImg = dlogs(dblA + dsqrts(dblA * dblA - 1));
+    }
+  else
+    {
+      /* evaluation in the special regions ... */
+      if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
+	{
+	  if(dblAbsReal < 1)
+	    {
+	      _pdblReal	= dasins(dblAbsReal);
+	      _pdblImg	= dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal));
+	    }
+	  else
+	    {
+	      _pdblReal = sdblPi_2;
+	      if(dblAbsReal <= dblLsup)
+		{
+		  dblTemp		= (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1));
+		  _pdblImg	= dlog1ps(dblTemp);
+		}
+	      else
+		_pdblImg	= sdblLn2 + dlogs(dblAbsReal);
+	    }
+	}
+      else if(dblAbsImg < dblLinf)
+	{
+	  _pdblReal	= sdblPi_2 - dsqrts(dblAbsImg);
+	  _pdblImg	= dsqrts(dblAbsImg);
+	}
+      else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
+	{
+	  _pdblReal	= dblAbsReal * dblAbsImg;
+	  _pdblImg	= sdblLn2 + dlogs(dblAbsReal);
+	}
+      else if(dblAbsReal > 1)
+	{
+	  _pdblReal	= datans(dblAbsReal / dblAbsImg);
+	  dblTemp		= (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
+	  _pdblImg	= sdblLn2 + dlogs(dblAbsReal) + 0.5 * dlog1ps(dblTemp);
+	}
+      else
+	{
+	  double dblTemp2 = dsqrts(1 + dblAbsImg * dblAbsImg);
+	  _pdblReal	= dblAbsReal / dblTemp2;
+	  dblTemp		= 2 * dblAbsImg * (dblAbsImg + dblTemp2);
+	  _pdblImg	= 0.5 * dlog1ps(dblTemp);
+	}
+    }
+  _pdblReal *= iSignReal;
+  _pdblImg *= iSignImg;
+
+  return (DoubleComplex(_pdblReal, _pdblImg));
+}
-- 
cgit