From b43eccd4cffed5bd1017c5821524fb6e49202f78 Mon Sep 17 00:00:00 2001
From: Sandeep Gupta
Date: Sun, 18 Jun 2017 23:55:40 +0530
Subject: First commit

---
 2.3-1/src/c/elementaryFunctions/asin/casins.c | 146 ++++++++++++++++++++++++++
 1 file changed, 146 insertions(+)
 create mode 100644 2.3-1/src/c/elementaryFunctions/asin/casins.c

(limited to '2.3-1/src/c/elementaryFunctions/asin/casins.c')

diff --git a/2.3-1/src/c/elementaryFunctions/asin/casins.c b/2.3-1/src/c/elementaryFunctions/asin/casins.c
new file mode 100644
index 00000000..35a4a8d8
--- /dev/null
+++ b/2.3-1/src/c/elementaryFunctions/asin/casins.c
@@ -0,0 +1,146 @@
+/*
+ *  Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ *  Copyright (C) 2008-2008 - 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"
+
+floatComplex		casins(floatComplex z) {
+  static float sdblPi_2		= 1.5707963267948966192313216f;
+  static float sdblLn2		= 0.6931471805599453094172321f;
+  static float sdblAcross	= 1.5f;
+  static float sdblBcross	= 0.6417f;
+
+  float dblLsup = ssqrts((float) getOverflowThreshold())/ 8.0f;
+  float dblLinf = 4.0f * ssqrts((float) getUnderflowThreshold());
+  float dblEpsm = ssqrts((float) getRelativeMachinePrecision());
+
+  float _dblReal	= creals(z);
+  float _dblImg		= cimags(z);
+
+  float dblAbsReal	= sabss(_dblReal);
+  float dblAbsImg	= sabss(_dblImg);
+  float iSignReal	= _dblReal < 0 ? -1.0f : 1.0f;
+  float iSignImg	= _dblImg < 0 ? -1.0f : 1.0f;
+
+  float dblR = 0, dblS = 0, dblA = 0, dblB = 0;
+
+  float dblTemp = 0;
+
+  float _pdblReal = 0;
+  float _pdblImg = 0;
+
+  if( min(dblAbsReal, dblAbsImg) > dblLinf && max(dblAbsReal, dblAbsImg) <= dblLsup)
+    {
+      /* we are in the safe region */
+      dblR = ssqrts( (dblAbsReal + 1) * (dblAbsReal + 1) + dblAbsImg * dblAbsImg);
+      dblS = ssqrts( (dblAbsReal - 1) * (dblAbsReal - 1) + dblAbsImg * dblAbsImg);
+      dblA = (float) 0.5 * ( dblR + dblS );
+      dblB = dblAbsReal / dblA;
+
+
+      /* compute the real part */
+      if(dblB <= sdblBcross)
+	_pdblReal = sasins(dblB);
+      else if( dblAbsReal <= 1)
+	_pdblReal = satans(dblAbsReal / ssqrts( 0.5f * (dblA + dblAbsReal) * ( (dblAbsImg * dblAbsImg) / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))));
+      else
+	_pdblReal = satans(dblAbsReal / (dblAbsImg * ssqrts( 0.5f * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal-1))))));
+
+      /* compute the imaginary part */
+      if(dblA <= sdblAcross)
+	{
+	  float dblImg1 = 0;
+
+	  if(dblAbsReal < 1)
+	    /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
+	    dblImg1 = 0.5f * (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 = 0.5f * (dblAbsImg * dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (dblAbsReal - 1)));
+	  /* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
+	  dblTemp = dblImg1 + ssqrts(dblImg1 * (dblA + 1));
+	  _pdblImg = slog1ps(dblTemp);
+	}
+      else
+	/* ai = log(A + sqrt(A**2 - 1.d0)) */
+	_pdblImg = slogs(dblA + ssqrts(dblA * dblA - (float) 1.0));
+    }
+  else
+    {
+      /* evaluation in the special regions ... */
+      if(dblAbsImg <= dblEpsm * dabss(dblAbsReal - 1))
+	{
+	  if(dblAbsReal < 1)
+	    {
+	      _pdblReal	= sasins(dblAbsReal);
+	      _pdblImg	= dblAbsImg / ssqrts((1 + dblAbsReal) * (1 - dblAbsReal));
+	    }
+	  else
+	    {
+	      _pdblReal = sdblPi_2;
+	      if(dblAbsReal <= dblLsup)
+		{
+		  dblTemp		= (dblAbsReal - 1) + ssqrts((dblAbsReal - 1) * (dblAbsReal + 1));
+		  _pdblImg	= slog1ps(dblTemp);
+		}
+	      else
+		_pdblImg	= sdblLn2 + slogs(dblAbsReal);
+	    }
+	}
+      else if(dblAbsImg < dblLinf)
+	{
+	  _pdblReal	= sdblPi_2 - ssqrts(dblAbsImg);
+	  _pdblImg	= ssqrts(dblAbsImg);
+	}
+      else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
+	{
+	  _pdblReal	= dblAbsReal * dblAbsImg;
+	  _pdblImg	= sdblLn2 + slogs(dblAbsReal);
+	}
+      else if(dblAbsReal > 1)
+	{
+	  _pdblReal	= satans(dblAbsReal / dblAbsImg);
+	  dblTemp	= (dblAbsReal / dblAbsImg) * (dblAbsReal / dblAbsImg);
+	  _pdblImg	= sdblLn2 + slogs(dblAbsReal) + 0.5f * slog1ps(dblTemp);
+	}
+      else
+	{
+	  float dblTemp2 = ssqrts(1 + dblAbsImg * dblAbsImg);
+	  _pdblReal	= dblAbsReal / dblTemp2;
+	  dblTemp	= 2.0f * dblAbsImg * (dblAbsImg + dblTemp2);
+	  _pdblImg	= 0.5f * slog1ps(dblTemp);
+	}
+    }
+  _pdblReal *= iSignReal;
+  _pdblImg *= iSignImg;
+
+  return (FloatComplex(_pdblReal, _pdblImg));
+}
-- 
cgit