Add Scilab algorithm emulation

4 files changed, 295 insertions, 19 deletions

diff --git a/src/elementaryFunctions/acos/Makefile.am b/src/elementaryFunctions/acos/Makefile.am
index c6e2a4e4..41c74e4f 100644
--- a/src/elementaryFunctions/acos/Makefile.am
+++ b/src/elementaryFunctions/acos/Makefile.am
@@ -10,8 +10,9 @@
 ##
 ##
 
-libAcos_la_CFLAGS =	-I ../../type \
-			-I ../includes
+libAcos_la_CFLAGS =	-I $(top_builddir)/type \
+			-I $(top_builddir)/elementaryFunctions/includes \
+			-I $(top_builddir)/auxiliaryFunctions/includes
 
 instdir = $(top_builddir)/lib
 
@@ -39,7 +40,13 @@ check_INCLUDES	=	-I $(top_builddir)/elementaryFunctions/includes \
 
 check_LDADD	=	$(top_builddir)/type/libDoubleComplex.la \
 			$(top_builddir)/type/libFloatComplex.la \
+			$(top_builddir)/lib/lapack/libscilapack.la \
 			$(top_builddir)/elementaryFunctions/acos/libAcos.la \
+			$(top_builddir)/elementaryFunctions/atan/libAtan.la \
+			$(top_builddir)/elementaryFunctions/log/libLog.la \
+			$(top_builddir)/elementaryFunctions/log1p/libLog1p.la \
+			$(top_builddir)/elementaryFunctions/sqrt/libSqrt.la \
+			$(top_builddir)/auxiliaryFunctions/abs/libAbs.la \
 			@LIBMATH@
 
 check_PROGRAMS	= 	testFloatAcos testDoubleAcos
diff --git a/src/elementaryFunctions/acos/Makefile.in b/src/elementaryFunctions/acos/Makefile.in
index 77869f41..b797e4b0 100644
--- a/src/elementaryFunctions/acos/Makefile.in
+++ b/src/elementaryFunctions/acos/Makefile.in
@@ -66,7 +66,13 @@ am_testDoubleAcos_OBJECTS = testDoubleAcos-testDoubleAcos.$(OBJEXT)
 testDoubleAcos_OBJECTS = $(am_testDoubleAcos_OBJECTS)
 am__DEPENDENCIES_1 = $(top_builddir)/type/libDoubleComplex.la \
 	$(top_builddir)/type/libFloatComplex.la \
-	$(top_builddir)/elementaryFunctions/acos/libAcos.la
+	$(top_builddir)/lib/lapack/libscilapack.la \
+	$(top_builddir)/elementaryFunctions/acos/libAcos.la \
+	$(top_builddir)/elementaryFunctions/atan/libAtan.la \
+	$(top_builddir)/elementaryFunctions/log/libLog.la \
+	$(top_builddir)/elementaryFunctions/log1p/libLog1p.la \
+	$(top_builddir)/elementaryFunctions/sqrt/libSqrt.la \
+	$(top_builddir)/auxiliaryFunctions/abs/libAbs.la
 testDoubleAcos_DEPENDENCIES = $(am__DEPENDENCIES_1)
 testDoubleAcos_LINK = $(LIBTOOL) --tag=CC $(AM_LIBTOOLFLAGS) \
 	$(LIBTOOLFLAGS) --mode=link $(CCLD) $(testDoubleAcos_CFLAGS) \
@@ -204,8 +210,9 @@ sysconfdir = @sysconfdir@
 target_alias = @target_alias@
 top_builddir = @top_builddir@
 top_srcdir = @top_srcdir@
-libAcos_la_CFLAGS = -I ../../type \
-			-I ../includes
+libAcos_la_CFLAGS = -I $(top_builddir)/type \
+			-I $(top_builddir)/elementaryFunctions/includes \
+			-I $(top_builddir)/auxiliaryFunctions/includes
 
 instdir = $(top_builddir)/lib
 pkglib_LTLIBRARIES = libAcos.la
@@ -229,7 +236,13 @@ check_INCLUDES = -I $(top_builddir)/elementaryFunctions/includes \
 
 check_LDADD = $(top_builddir)/type/libDoubleComplex.la \
 			$(top_builddir)/type/libFloatComplex.la \
+			$(top_builddir)/lib/lapack/libscilapack.la \
 			$(top_builddir)/elementaryFunctions/acos/libAcos.la \
+			$(top_builddir)/elementaryFunctions/atan/libAtan.la \
+			$(top_builddir)/elementaryFunctions/log/libLog.la \
+			$(top_builddir)/elementaryFunctions/log1p/libLog1p.la \
+			$(top_builddir)/elementaryFunctions/sqrt/libSqrt.la \
+			$(top_builddir)/auxiliaryFunctions/abs/libAbs.la \
 			@LIBMATH@
 
 
diff --git a/src/elementaryFunctions/acos/cacoss.c b/src/elementaryFunctions/acos/cacoss.c
index ed174fda..1059c8c3 100644
--- a/src/elementaryFunctions/acos/cacoss.c
+++ b/src/elementaryFunctions/acos/cacoss.c
@@ -1,18 +1,146 @@
 /*
-**  -*- C -*-
-**
-** cacoss.c
-** Made by  Bruno JOFRET <bruno.jofret@inria.fr>
-**
-** Started on  Fri Jan  5 11:29:45 2007 jofret
-** Last update Fri Feb 23 16:37:08 2007 jofret
-**
-** Copyright INRIA 2007
-*/
+ *  Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+ *  Copyright (C) 2007-2008 - INRIA - Bruno JOFRET
+ *
+ *  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
+ *
+ */
+
+/*
+ * This fonction is a translation of fortran wacos write by Bruno Pincon <Bruno.Pincon@iecn.u-nancy.fr>
+ *     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
+ */
 
 #include "acos.h"
+#include "atan.h"
+#include "log.h"
+#include "log1p.h"
+#include "sqrt.h"
+#include "abs.h"
+#include "lapack.h"
+#include "min.h"
+#include "max.h"
+
+#define localSign(x) (x>0 ? 1.0f : -1.0f)
 
 floatComplex		cacoss(floatComplex z) {
-  /* FIXME: Dummy... */
-  return z;
+	static float sfltPi		= 3.1415926535897932384626433f;
+	static float sfltPi_2		= 1.5707963267948966192313216f;
+	static float sfltLn2		= 0.6931471805599453094172321f;
+	static float sfltAcross	= 1.5f;
+	static float sfltBcross	= 0.6417f;
+
+	float fltLsup = ssqrts((float) getOverflowThreshold())/8.0f;
+	float fltLinf = 4.0f * ssqrts((float) getUnderflowThreshold());
+	float fltEpsm = ssqrts((float) getRelativeMachinePrecision());
+
+	float fltAbsReal	= sabss(creals(z));
+	float fltAbsImg		= sabss(cimags(z));
+	float fltSignReal	= localSign(creals(z));
+	float fltSignImg	= localSign(cimags(z));
+
+	float fltR = 0, fltS = 0, fltA = 0, fltB = 0;
+
+	float fltTemp = 0;
+
+	float _pfltReal = 0;
+	float _pfltImg = 0;
+
+	if( min(fltAbsReal, fltAbsImg) > fltLinf && max(fltAbsReal, fltAbsImg) <= fltLsup)
+	  {/* we are in the safe region */
+		fltR = ssqrts( (fltAbsReal + 1 )*(fltAbsReal + 1 ) + fltAbsImg*fltAbsImg);
+		fltS = ssqrts( (fltAbsReal - 1 )*(fltAbsReal - 1 ) + fltAbsImg*fltAbsImg);
+		fltA = 0.5f * ( fltR + fltS );
+		fltB = fltAbsReal / fltA;
+
+
+		/* compute the real part */
+		if(fltB <= sfltBcross)
+			_pfltReal = sacoss(fltB);
+		else if( fltAbsReal <= 1)
+			_pfltReal = satans(ssqrts(0.5f * (fltA + fltAbsReal) * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + (fltS + (1 - fltAbsReal)))) / fltAbsReal);
+		else
+			_pfltReal = satans((fltAbsImg * ssqrts(0.5f * ((fltA + fltAbsReal) / (fltR + (fltAbsReal + 1)) + (fltA + fltAbsReal) / (fltS + (fltAbsReal - 1))))) / fltAbsReal);
+
+		/* compute the imaginary part */
+		if(fltA <= sfltAcross)
+		{
+			float fltImg1 = 0;
+
+			if(fltAbsReal < 1)
+			  /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(y**2)/(S+(1.d0-x))) */
+				fltImg1 = 0.5f * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + fltAbsImg*fltAbsImg / (fltS + (1 - fltAbsReal)));
+			else
+			  /* Am1 = 0.5d0*((y**2)/(R+(x+1.d0))+(S+(x-1.d0))) */
+				fltImg1 = 0.5f * (fltAbsImg*fltAbsImg / (fltR + (fltAbsReal + 1)) + (fltS + (fltAbsReal - 1)));
+			/* ai = logp1(Am1 + sqrt(Am1*(A+1.d0))) */
+			fltTemp = fltImg1 + ssqrts(fltImg1 *( fltA + 1));
+			_pfltImg = slog1ps(fltTemp);
+		}
+		else
+		  /* ai = log(A + sqrt(A**2 - 1.d0)) */
+			_pfltImg = slogs(fltA + ssqrts(fltA*fltA - 1));
+	}
+	else
+	  {/* evaluation in the special regions ... */
+		if(fltAbsImg <= fltEpsm * sabss(fltAbsReal - 1))
+		{
+			if(fltAbsReal < 1)
+			{
+				_pfltReal	= sacoss(fltAbsReal);
+				_pfltImg	= fltAbsImg / ssqrts((1 + fltAbsReal) * (1 - fltAbsReal));
+			}
+			else
+			{
+				_pfltReal = 0;
+				if(fltAbsReal <= fltLsup)
+				{
+					fltTemp		= (fltAbsReal - 1) + ssqrts((fltAbsReal - 1) * (fltAbsReal + 1));
+					_pfltImg	= slog1ps(fltTemp);
+				}
+				else
+					_pfltImg	= sfltLn2 + slogs(fltAbsReal);
+			}
+		}
+		else if(fltAbsImg < fltLinf)
+		{
+			_pfltReal	= ssqrts(fltAbsImg);
+			_pfltImg	= _pfltReal;
+		}
+		else if((fltEpsm * fltAbsImg - 1 >= fltAbsReal))
+		{
+			_pfltReal	= sfltPi_2;
+			_pfltImg	= sfltLn2 + slogs(fltAbsImg);
+		}
+		else if(fltAbsReal > 1)
+		{
+			_pfltReal	= satans(fltAbsImg / fltAbsReal);
+			fltTemp		= (fltAbsReal / fltAbsImg)*(fltAbsReal / fltAbsImg);
+			_pfltImg	= sfltLn2 + slogs(fltAbsImg) + 0.5f * slog1ps(fltTemp);
+		}
+		else
+		{
+			float fltTemp2 = ssqrts(1 + fltAbsImg*fltAbsImg);
+			_pfltReal	= sfltPi_2;
+			fltTemp		= 2 * fltAbsImg * (fltAbsImg + fltTemp2);
+			_pfltImg	= 0.5f * slog1ps(fltTemp);
+		}
+	}
+	if(fltSignReal < 0)
+		_pfltReal = sfltPi - _pfltReal;
+
+	if(fltAbsImg != 0 || fltSignReal < 0)
+		_pfltImg = - fltSignImg * _pfltImg;
+
+	return FloatComplex(_pfltReal, _pfltImg);
 }
diff --git a/src/elementaryFunctions/acos/zacoss.c b/src/elementaryFunctions/acos/zacoss.c
index 5dfd4b70..7758a932 100644
--- a/src/elementaryFunctions/acos/zacoss.c
+++ b/src/elementaryFunctions/acos/zacoss.c
@@ -10,9 +10,137 @@
  *
  */
 
+/*
+ * This fonction is a translation of fortran wacos write by Bruno Pincon <Bruno.Pincon@iecn.u-nancy.fr>
+ *     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
+ */
+
 #include "acos.h"
+#include "atan.h"
+#include "log.h"
+#include "log1p.h"
+#include "sqrt.h"
+#include "abs.h"
+#include "lapack.h"
+#include "min.h"
+#include "max.h"
+
+#define localSign(x) (x>0 ? 1 : -1)
 
 doubleComplex		zacoss(doubleComplex z) {
-  /* FIXME: Dummy... */
-  return z;
+	static double sdblPi		= 3.1415926535897932384626433;
+	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 = 4.0 * dsqrts(getUnderflowThreshold());
+	double dblEpsm = dsqrts(getRelativeMachinePrecision());
+
+	double dblAbsReal	= dabss(zreals(z));
+	double dblAbsImg	= dabss(zimags(z));
+	double dblSignReal	= localSign(zreals(z));
+	double dblSignImg	= localSign(zimags(z));
+
+	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 = dacoss(dblB);
+		else if( dblAbsReal <= 1)
+			_pdblReal = datans(dsqrts(0.5 * (dblA + dblAbsReal) * (dblAbsImg*dblAbsImg / (dblR + (dblAbsReal + 1)) + (dblS + (1 - dblAbsReal)))) / dblAbsReal);
+		else
+			_pdblReal = datans((dblAbsImg * dsqrts(0.5 * ((dblA + dblAbsReal) / (dblR + (dblAbsReal + 1)) + (dblA + dblAbsReal) / (dblS + (dblAbsReal - 1))))) / dblAbsReal);
+
+		/* 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	= dacoss(dblAbsReal);
+				_pdblImg	= dblAbsImg / dsqrts((1 + dblAbsReal) * (1 - dblAbsReal));
+			}
+			else
+			{
+				_pdblReal = 0;
+				if(dblAbsReal <= dblLsup)
+				{
+					dblTemp		= (dblAbsReal - 1) + dsqrts((dblAbsReal - 1) * (dblAbsReal + 1));
+					_pdblImg	= dlog1ps(dblTemp);
+				}
+				else
+					_pdblImg	= sdblLn2 + dlogs(dblAbsReal);
+			}
+		}
+		else if(dblAbsImg < dblLinf)
+		{
+			_pdblReal	= dsqrts(dblAbsImg);
+			_pdblImg	= _pdblReal;
+		}
+		else if((dblEpsm * dblAbsImg - 1 >= dblAbsReal))
+		{
+			_pdblReal	= sdblPi_2;
+			_pdblImg	= sdblLn2 + dlogs(dblAbsImg);
+		}
+		else if(dblAbsReal > 1)
+		{
+			_pdblReal	= datans(dblAbsImg / dblAbsReal);
+			dblTemp		= (dblAbsReal / dblAbsImg)*(dblAbsReal / dblAbsImg);
+			_pdblImg	= sdblLn2 + dlogs(dblAbsImg) + 0.5 * dlog1ps(dblTemp);
+		}
+		else
+		{
+			double dblTemp2 = dsqrts(1 + dblAbsImg*dblAbsImg);
+			_pdblReal	= sdblPi_2;
+			dblTemp		= 2 * dblAbsImg * (dblAbsImg + dblTemp2);
+			_pdblImg	= 0.5 * dlog1ps(dblTemp);
+		}
+	}
+	if(dblSignReal < 0)
+		_pdblReal = sdblPi - _pdblReal;
+
+	if(dblAbsImg != 0 || dblSignReal < 0)
+		_pdblImg = - dblSignImg * _pdblImg;
+
+	return DoubleComplex(_pdblReal, _pdblImg);
 }