diff options
Diffstat (limited to '2.3-1/src/c/elementaryFunctions/acos')
17 files changed, 3068 insertions, 0 deletions
diff --git a/2.3-1/src/c/elementaryFunctions/acos/Makefile.am b/2.3-1/src/c/elementaryFunctions/acos/Makefile.am new file mode 100644 index 00000000..24935987 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/Makefile.am @@ -0,0 +1,73 @@ +## +## 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 +## +## + +libAcos_la_CFLAGS = -I $(top_builddir)/src/c/type \ + -I $(top_builddir)/src/c/elementaryFunctions/includes \ + -I $(top_builddir)/src/c/auxiliaryFunctions/includes + +instdir = $(top_builddir)/lib + +pkglib_LTLIBRARIES = libAcos.la + +libAcos_la_SOURCES = $(HEAD) $(SRC) + +SRC = sacoss.c \ + dacoss.c \ + cacoss.c \ + zacoss.c \ + sacosa.c \ + dacosa.c \ + cacosa.c \ + zacosa.c + +HEAD = ../includes/acos.h \ + ../../auxiliaryFunctions/includes/min.h \ + ../../auxiliaryFunctions/includes/max.h + +#### +# Checking Part +#### + +check_INCLUDES = -I $(top_builddir)/src/c/elementaryFunctions/includes \ + -I $(top_builddir)/includes \ + -I $(top_builddir)/src/c/type + +check_LDADD = $(top_builddir)/src/c/type/libDoubleComplex.la \ + $(top_builddir)/src/c/type/libFloatComplex.la \ + $(top_builddir)/src/c/operations/addition/libAddition.la \ + $(top_builddir)/src/fortran/lapack/libscilapack.la \ + $(top_builddir)/src/c/elementaryFunctions/acos/libAcos.la \ + $(top_builddir)/src/c/elementaryFunctions/atan/libAtan.la \ + $(top_builddir)/src/c/elementaryFunctions/log/libLog.la \ + $(top_builddir)/src/c/elementaryFunctions/log1p/libLog1p.la \ + $(top_builddir)/src/c/elementaryFunctions/sqrt/libSqrt.la \ + $(top_builddir)/src/c/elementaryFunctions/lnp1m1/libLnp1m1.la \ + $(top_builddir)/src/c/auxiliaryFunctions/abs/libAbs.la \ + $(top_builddir)/src/c/auxiliaryFunctions/pythag/libPythag.la \ + $(top_builddir)/src/c/operations/multiplication/libMultiplication.la \ + @LIBMATH@ + +check_PROGRAMS = testRealsAcos testCplxAcos + +TESTS = testRealsAcos testCplxAcos + +# +# -*- Acosine Tests -*- +# +testRealsAcos_SOURCES = testAcos.h testRealsAcos.c +testRealsAcos_CFLAGS = $(check_INCLUDES) +testRealsAcos_LDADD = $(check_LDADD) + +testCplxAcos_SOURCES = testAcos.h testCplxAcos.c +testCplxAcos_CFLAGS = $(check_INCLUDES) +testCplxAcos_LDADD = $(check_LDADD) + diff --git a/2.3-1/src/c/elementaryFunctions/acos/Makefile.in b/2.3-1/src/c/elementaryFunctions/acos/Makefile.in new file mode 100644 index 00000000..504e3d15 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/Makefile.in @@ -0,0 +1,813 @@ +# Makefile.in generated by automake 1.11.1 from Makefile.am. +# @configure_input@ + +# Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, +# 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, +# Inc. +# This Makefile.in is free software; the Free Software Foundation +# gives unlimited permission to copy and/or distribute it, +# with or without modifications, as long as this notice is preserved. + +# This program is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY, to the extent permitted by law; without +# even the implied warranty of MERCHANTABILITY or FITNESS FOR A +# PARTICULAR PURPOSE. + +@SET_MAKE@ + +VPATH = @srcdir@ +pkgdatadir = $(datadir)/@PACKAGE@ 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dvi-am html html-am info info-am install install-am \ + install-data install-data-am install-dvi install-dvi-am \ + install-exec install-exec-am install-html install-html-am \ + install-info install-info-am install-man install-pdf \ + install-pdf-am install-pkglibLTLIBRARIES install-ps \ + install-ps-am install-strip installcheck installcheck-am \ + installdirs maintainer-clean maintainer-clean-generic \ + mostlyclean mostlyclean-compile mostlyclean-generic \ + mostlyclean-libtool pdf pdf-am ps ps-am tags uninstall \ + uninstall-am uninstall-pkglibLTLIBRARIES + + +# Tell versions [3.59,3.63) of GNU make to not export all variables. +# Otherwise a system limit (for SysV at least) may be exceeded. +.NOEXPORT: diff --git a/2.3-1/src/c/elementaryFunctions/acos/cacosa.c b/2.3-1/src/c/elementaryFunctions/acos/cacosa.c new file mode 100644 index 00000000..da7e2e0f --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/cacosa.c @@ -0,0 +1,20 @@ +/* + * 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 + * + */ + +#include "acos.h" + +void cacosa(floatComplex* x, int size, floatComplex* y) { + int i = 0; + for (i = 0; i < size; ++i) { + y[i] = cacoss(x[i]); + } +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/cacoss.c b/2.3-1/src/c/elementaryFunctions/acos/cacoss.c new file mode 100644 index 00000000..97420313 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/cacoss.c @@ -0,0 +1,147 @@ +/*
+ * 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
+ *
+ */
+
+/*
+ * 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) {
+ 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/2.3-1/src/c/elementaryFunctions/acos/dacosa.c b/2.3-1/src/c/elementaryFunctions/acos/dacosa.c new file mode 100644 index 00000000..62626a7c --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/dacosa.c @@ -0,0 +1,20 @@ +/* + * 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 + * + */ + +#include "acos.h" + +void dacosa(double* x, int size, double* y) { + int i = 0; + for (i = 0; i < size; ++i) { + y[i] = dacoss(x[i]); + } +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/dacoss.c b/2.3-1/src/c/elementaryFunctions/acos/dacoss.c new file mode 100644 index 00000000..1c5eab24 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/dacoss.c @@ -0,0 +1,19 @@ +/* + * 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 + * + */ + + +#include <math.h> +#include "acos.h" + +double dacoss(double x) { + return (acos(x)); +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/sacosa.c b/2.3-1/src/c/elementaryFunctions/acos/sacosa.c new file mode 100644 index 00000000..6035130b --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/sacosa.c @@ -0,0 +1,20 @@ +/* + * 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 + * + */ + +#include "acos.h" + +void sacosa(float* x, int size, float* y) { + int i = 0; + for (i = 0; i < size; ++i) { + y[i] = sacoss(x[i]); + } +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/sacoss.c b/2.3-1/src/c/elementaryFunctions/acos/sacoss.c new file mode 100644 index 00000000..733c8afe --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/sacoss.c @@ -0,0 +1,18 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008-2008 - 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 + * + */ + +#include <math.h> +#include "acos.h" + +float sacoss(float x) { + return (acosf(x)); +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/testAcos.h b/2.3-1/src/c/elementaryFunctions/acos/testAcos.h new file mode 100644 index 00000000..781c9cb9 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/testAcos.h @@ -0,0 +1,38 @@ +/* + * 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 + * + */ + +#ifndef _TESTACOS_H_ +#define _TESTACOS_H_ + +#include <stdio.h> +#include <assert.h> +#include "acos.h" + +void sacossTest(void); + +void dacossTest(void); + +void cacossTest(void); + +void zacossTest(void); + +void sacosaTest(void); + +void dacosaTest(void); + +void cacosaTest(void); + +void zacosaTest(void); + +int testAcos(void); + +#endif /* ! _TESTACOS_H_ */ diff --git a/2.3-1/src/c/elementaryFunctions/acos/testCplxAcos.c b/2.3-1/src/c/elementaryFunctions/acos/testCplxAcos.c new file mode 100644 index 00000000..f1b235db --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/testCplxAcos.c @@ -0,0 +1,681 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008-2008 - INRIA - Arnaud TORSET + * + * 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 + * + */ + +#include "testAcos.h" +#include <math.h> +#include <stdio.h> +#include <assert.h> + + +#define InRF {0.4424391170032322406769f,0.6678683990612626075745f,0.3319660718552768230438f, \ +0.9546736516058444976807f,0.0156700448133051395416f,0.8749210601672530174255f, \ +0.4522444806061685085297f,0.5117330569773912429810f,0.0253186416812241077423f, \ +0.0014351801946759223938f,0.9977079438976943492889f,0.2380047738552093505859f, \ +0.9923671730794012546539f,0.8377430764958262443542f,0.3201149418018758296967f, \ +0.8609968703240156173706f,0.2300571207888424396515f,0.0514277378097176551819f, \ +0.7738713542930781841278f,0.7888738475739955902100f,0.3247241438366472721100f, \ +0.4342710664495825767517f,0.2505763596855103969574f,0.1493970695883035659790f, \ +0.1849924144335091114044f,0.4753739954903721809387f,0.1413027080707252025604f, \ 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+0.7590293344110250473022f,0.8550809700973331928253f,0.6527025634422898292542f, \ +0.7750031943432986736298f,0.3234997726976871490479f,0.0574064985848963260651f, \ +0.5859434073790907859802f,0.3590891859494149684906f,0.146858902648091316223f, \ +0.2846125257201492786407f,0.7778714792802929878235f,0.6364495265297591686249f, \ +0.2102845311164855957031f,0.3402740904130041599274f,0.46986890118569135666f, \ +0.3029589070938527584076f,0.8358892183750867843628f,0.2167098228819668292999f, \ +0.372365341521799564362f,0.4379987935535609722137f,0.9151138328015804290771f, \ +0.9195669055916368961334f,0.3805362572893500328064f,0.1327533251605927944183f, \ +0.1664179805666208267212f,0.3607654091902077198029f,0.1161730112507939338684f, \ +0.0462395879440009593964f,0.8910173103213310241699f,0.4135520034469664096832f, \ +0.5144748641178011894226f,0.7328222631476819515228f,0.1954176928848028182983f, \ +0.7234130431897938251495f,0.1745128417387604713440f,0.0849626506678760051727f, \ 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+0.6740669626742601394653f,0.1436607432551681995392f,0.9407137231901288032532f, \ +0.9242008137516677379608f,0.9963994324207305908203f,0.0636921771802008152008f, \ +0.7568332878872752189636f,0.1861553504131734371185f,0.6694165151566267014f, \ +0.6417399053461849689484f,0.2864959994331002235413f,0.1503058592788875102997f, \ +0.036585446447134017944f,0.8965126336552202701569f,0.2470208695158362388611f, \ +0.4511714405380189418793f,0.8758140746504068374634f,0.8369763311930000782013f, \ +0.6116396905854344367981f,0.8594635161571204662323f,0.8739381656050682067871f, \ +0.8611579411663115024567f,0.6650390280410647392273f,0.7033504783175885677338f, \ +0.0680055823177099227905f,0.4108084668405354022980f,0.3225740874186158180237f, \ +0.9049567128531634807587f,0.7221073396503925323486f,0.9756754324771463871002f, \ +0.931904456578195095062f,0.4758459976874291896820f,0.6085055340081453323364f, \ +0.0411347192712128162384f,0.27580172289162874222f,0.8152392762713134288788f, \ +0.1618081480264663696289f,0.0729317762888967990875f,0.9948789654299616813660f, \ +0.6547168060205876827240f,0.4749407302588224411011f,0.1327822064049541950226f, \ +0.1489921221509575843811f,0.9931546817533671855927f,0.605664949864149093628f, \ +0.2185817272402346134186f,0.1360632320865988731384f,0.8656457341276109218597f, \ +0.1623940262943506240845f,0.9229755070991814136505f,0.6870755525305867195129f, \ +0.2901548030786216259003f,0.6380550339818000793457f,0.5040368759073317050934f, \ +0.1559905512258410453796f,0.2356583862565457820892f,0.4607480820268392562866f, \ +0.9618054111488163471222f,0.8233367735520005226135f,0.9555186624638736248016f, \ +0.2299523688852787017822f,0.2144343988038599491119f,0.4322205847129225730896f, \ +0.5298418900929391384125f,0.1070291120558977127075f} + +#define InIF {0.9676976692862808704376f,0.6755087869241833686829f,0.9605711805634200572968f, \ +0.8287713527679443359375f,0.3716058083809912204742f,0.8529331116005778312683f, \ +0.6630636467598378658295f,0.3127506356686353683472f,0.0578817431814968585968f, \ +.4168665865436196327209f,0.6979019264690577983856f,0.3232105635106563568115f, \ +0.6520457030273973941803f,0.6255217781290411949158f,0.5866900808177888393402f, \ +0.1662572268396615982056f,0.3538595554418861865997f,0.0223209084942936897278f, \ +0.0555838677100837230682f,0.8830965086817741394043f,0.6798805170692503452301f, \ +0.9601878477260470390320f,0.5503053902648389339447f,0.9100682642310857772827f, \ +0.9618742396123707294464f,0.8895119810476899147034f,0.8663921202532947063446f, \ +0.6742273755371570587158f,0.6948372707702219486237f,0.6285339510068297386169f, \ +0.7384302965365350246429f,0.0932216811925172805786f,0.3283788901753723621368f, \ +0.3349032746627926826477f,0.7320226985029876232147f,0.4482167810201644897461f, \ +0.5952123203314840793610f,0.3971578357741236686707f,0.2822407945059239864349f, \ +0.5986177157610654830933f,0.9705053125508129596710f,0.9648752519860863685608f, \ +0.2223112653009593486786f,0.0073375217616558074951f,0.3558401078917086124420f, \ +0.3362461170181632041931f,0.6462869024835526943207f,0.5453626606613397598267f, \ +0.5815327730961143970490f,0.9218191178515553474426f,0.4494518819265067577362f, \ +0.5443653240799903869629f,0.8210619115270674228668f,0.0031680269166827201843f, \ +0.3902114122174680233002f,0.0661126133054494857788f,0.5113567491061985492706f, \ +0.0052305692806839942932f,0.0172157580964267253876f,0.8574225939810276031494f, \ +0.872694595251232385635f,0.5010691648349165916443f,0.3054686388932168483734f, \ +0.9594172257930040359497f,0.6219576788134872913361f,0.6678035454824566841125f, \ +0.3451700019650161266327f,0.439822167158126831055f,0.9729993590153753757477f, \ +0.4124652473255991935730f,0.9270431711338460445404f,0.2170634549111127853394f, \ +0.5178697113879024982452f,0.8865239778533577919006f,0.3678963701240718364716f, \ +0.4449110589921474456787f,0.0826504887081682682037f,0.6078358581289649009705f, \ +0.4201686209999024868011f,0.4264193121343851089478f,0.1516494569368660449982f, \ +0.9087635399773716926575f,0.6092100176028907299042f,0.5259142145514488220215f, \ +0.9537041061557829380035f,0.9292181981727480888367f,0.8420463739894330501556f, \ +0.0477776136249303817749f,0.8043447365052998065948f,0.8733733976259827613831f, \ +0.6313782478682696819305f,0.5507782585918903350830f,0.7975669191218912601471f, \ +0.7488008355721831321716f,0.7785643390379846096039f,0.5666997302323579788208f, \ +0.4409633320756256580353f,0.3067779587581753730774f,0.8593392628245055675507f, \ +0.1920152455568313598633f,0.3279649713076651096344f,0.4025174556300044059753f, \ +0.3560156985186040401459f,0.5213593374937772750854f,0.4409417365677654743195f, \ +0.4940686235204339027405f,0.7799209128133952617645f,0.3915464095771312713623f, \ +0.1789123923517763614655f,0.4986406108364462852478f,0.6278176582418382167816f, \ +0.4048861656337976455688f,0.7036139038391411304474f,0.7250975342467427253723f, \ +0.5160594466142356395721f,0.7005459144711494445801f,0.6976801478303968906403f, \ +0.1013754708692431449890f,0.3362301974557340145111f,0.4427097495645284652710f, \ +0.1286799986846745014191f,0.4155713254585862159729f,0.7760182614438235759735f, \ +0.4942846037447452545166f,0.1127647892571985721588f,0.7894535725936293601990f, \ +0.0490748188458383083344f,0.2449031788855791091919f,0.4716751468367874622345f, \ +0.1031448738649487495422f,0.1776066529564559459686f,0.0619737505912780761719f, \ +0.0768572040833532810211f,0.5897265700623393058777f,0.6714532985351979732513f, \ +0.3335268478840589523315f,0.5744381849654018878937f,0.3185150483623147010803f, \ +0.9473985652439296245575f,0.57160880789160728455f,0.5848113656975328922272f, \ +0.7857599845156073570251f,0.3324664360843598842621f,0.5449722055345773696899f, \ +0.9705804106779396533966f,0.3315144600346684455872f,0.9949513408355414867401f, \ +0.9098131582140922546387f,0.2666130834259092807770f,0.6014269543811678886414f, \ +0.6469328044913709163666f,0.3073055054992437362671f,0.8659543325193226337433f, \ +0.7722052121534943580627f,0.3620244706980884075165f,0.3966818638145923614502f, \ +0.0553487525321543216705f,0.7595019852742552757263f,0.3521075001917779445648f, \ +0.7926115561276674270630f,0.4941224199719727039337f,0.1269726501777768135071f, \ +0.0467983442358672618866f,0.3756254166364669799805f,0.2301741042174398899078f, \ +0.9152546999976038932800f,0.3194008930586278438568f,0.9443374704569578170776f, \ +0.8468258534558117389679f,0.1096191117540001869202f,0.2030929992906749248505f, \ +0.6782134883105754852295f,0.8342829556204378604889f,0.9650435885414481163025f, \ +0.9410973764024674892426f,0.3796364162117242813110f,0.7794532743282616138458f, \ +0.9074576767161488533020f,0.7145868721418082714081f,0.9640186801552772521973f, \ +0.4678759598173201084137f,0.2299097580835223197937f,0.8920741169713437557220f, \ +0.1667113658040761947632f,0.4915095348842442035675f,0.3024059170857071876526f, \ +0.1440355475060641765594f,0.9354602731764316558838f,0.4561293558217585086823f, \ +0.5141706829890608787537f,0.2665198049508035182953f,0.4771588463336229324341f, \ +0.3820844483561813831329f,0.6670796470716595649719f,0.0574905085377395153046f, \ +0.4276479780673980712891f,0.3921637185849249362946f,0.0390139548107981681824f, \ +0.0896534039638936519623f,0.1133126895874738693237f} + +#define ResRF {1.255529833022194452496f,1.0200026717383132712769f,1.3324589639215225211899f, \ +0.8677406156444121831939f,1.5561073447625946020167f,0.9286968935379427136922f, \ +1.1937226600193293624130f,1.067915927099262640709f,1.545517326047555650703f, \ +1.5694716389035829884335f,0.7825751983710025339036f,1.3429338762216549429951f, \ +0.7639188473405255086490f,0.8664584310401818312286f,1.2939802433811951054565f, \ +0.5990898407849659657032f,1.3527841901085291276274f,1.5193587499057941148095f, \ +0.6904789613904125378241f,0.9961995980090498914450f,1.3021994564088539281244f, \ +1.26004387047876331707f,1.3507596621653372714889f,1.4603873397973008430029f, \ +1.4376480261770669955013f,1.2185152537606129818926f,1.4640602217743992063959f, \ +0.894854807527207585238f,0.9591997301055474878240f,1.164221222913740527716f, \ +1.1146461656150485897143f,1.0887716288036126677241f,0.5830870294869971992568f, \ +0.6121373513947664379842f,1.3737517861001466989990f,0.7178494362155037888940f, \ +1.4830224178312794158785f,1.15302764511686950399f,0.7870894488597584004452f, \ +1.5273165827155432694440f,0.9046421279509564428167f,1.1098998065332701390417f, \ +0.8178369263058140603562f,1.0104814656927540994502f,1.2625532917342228156343f, \ +0.6793632590344759192291f,1.1798090506359553142346f,1.2887180301097407308930f, \ +1.0105656841969548054294f,1.0915011675220371856199f,0.7542427310988851774098f, \ +1.0653686177891663611206f,0.8900627912448225709241f,0.7149348217487093704037f, \ +0.7102600249699384526991f,0.6960735527765307129044f,1.088533305867128486710f, \ +1.388790211991853373874f,1.2713337729965381583952f,1.088577004770347134155f, \ +1.0451133763707507462470f,1.028861647762511877f,1.0500108990334240388620f, \ +1.0388362590565514143037f,0.8513413455225736781173f,1.0298997364083655181588f, \ +0.7980374938553029817712f,1.272512010082343492101f,1.5296574807566454268226f, \ +1.0155756589776196996411f,1.3087404816635104243261f,1.4268507232054599143112f, \ +1.3171287563927265296115f,1.0046812403038571925862f,0.9520223764784513376114f, \ +1.3780800950311928865233f,1.2249760089920562755594f,1.1679630143718853219070f, \ +1.2895295822531129825705f,0.7757074400337321540277f,1.3549804577387012383127f, \ +1.2966028029732796778006f,1.1956170559024092980849f,0.7573690728750529510549f, \ +0.9358060876311721232312f,1.2935811029700821084276f,1.4692924940131448785507f, \ +1.403798205397557063989f,1.2904936439816625526333f,1.4833304573509458190728f, \ +1.5316962881883187108656f,0.7896852637031629429387f,1.2487229023268595629048f, \ +1.1608910658948932148604f,1.0024005845134518200013f,1.4005673415801471737296f, \ +0.8902696237675791213206f,1.4033814016250207856729f,1.5063701881984010721993f, \ +1.4235075164410782022628f,1.2154417216544426416647f,0.9067832509325496337382f, \ +0.8451361326845713284328f,0.8105760364528488137736f,0.6677149293012821784643f, \ +0.9376824522142382933865f,0.9834531063046333398958f,0.7435234402945338771929f, \ +1.2692770995801996303243f,0.8506643591613352040071f,1.1209388788239313949902f, \ +0.6577834067257107841797f,1.4685347852910790589220f,1.4304586887418837548580f, \ +1.5216097729687187989356f,0.9508172376200363373755f,1.4718437723337385314437f, \ +1.5147598813826532726523f,0.9228342692416234838149f,1.463425399368290413804f, \ +0.7595378867190821781108f,0.8934128848181713822285f,1.3234788454526924539323f, \ +1.0022503118871550764624f,0.4807627355715887174092f,1.3509123886799738745168f, \ +0.9845326329544197285770f,1.0135326383159133367684f,1.2959003688929946473962f, \ +1.4493071459819437674099f,1.393898839191649585700f,1.2489929355782913856f, \ +1.4543809570962817900863f,0.8282434492927793767691f,0.979974070275603015290f, \ +0.9016529084751209177639f,1.4461450567069793482489f,0.6070295384428338048011f, \ +0.9308147234333767894299f,0.7189471755291521049003f,1.5158092773905904593335f, \ +0.9872214614683698652442f,1.3935021592326080064339f,0.9771853998510096062091f, \ +1.1193192900537867195965f,1.296487096062820532083f,1.4643457982927459148925f, \ +1.5437362050733878238162f,0.6187847061723403818689f,1.3588173690830449569233f, \ +1.1915339871130086191187f,0.6686084978144331003591f,0.9583842322663218560308f, \ +1.0912664509894050013372f,0.7181625782359223331142f,0.7233140240221890282513f, \ +0.5428178535441999796873f,1.0471999339904087822362f,0.8769816861755428405445f, \ +1.5175053601847408035752f,1.1993783088315406182289f,1.2453663926230837954989f, \ +0.4514953581289469219939f,0.8662667007384096118372f,0.4974730247398895799371f, \ +0.9147617192703559885203f,1.1061521220724712666339f,1.1357238908175482094975f, \ +1.5394063571165421677733f,1.2932180862175921554069f,0.6824933434976203638911f, \ +1.43686302401783927429f,1.5148015609296603400935f,0.8950325309450218869145f, \ +1.1033723890979516557564f,1.1179316393641773874634f,1.4660961587943455164407f, \ +1.4605422546022659435749f,0.7934640514556516865952f,1.1421515306768439401708f, \ +1.3722266762337298473540f,1.4378608786974975686235f,0.9484918901540384528204f, \ +1.409977666065525436778f,0.7322918733552260528441f,0.8770810468745882104713f, \ +1.2797762559830598849686f,1.113354965599829160539f,1.1052282890851641283803f, \ +1.4319057784002142685864f,1.3414927111991592489915f,1.150175091750528233447f, \ +0.6311676673228704403940f,0.8947310349200747747744f,0.3427408557056949023334f, \ +1.3585307702603606205827f,1.3703718078359574672476f,1.1242902219788122319954f, \ +1.0158255484348914787773f,1.4642540410581941223711f} + +#define ResIF {-0.89394934684766447219f,-0.7269960621148598978181f,-0.873228865930417708086f, \ +-0.9411580369058477613109f,-0.3635823360806625381692f,-0.9266296361203899545345f, \ +-0.6634195150572302912551f,-0.3497653794429004814326f,-0.0578679396761476172451f, \ +-0.4056499805826500049122f,-0.8741287625997348209594f,-0.3259826010316183575455f, \ +-0.8401934298465025818814f,-0.7488675904074600930826f,-0.5773032354998757220699f, \ +-0.2907264701768227377343f,-0.3549390003452199127132f,-0.0223486092632642734113f, \ +-0.0871612243254889368371f,-0.9176985409654165870563f,-0.6568925683359604361655f, \ +-0.8873647393225528867688f,-0.5376252047526711708159f,-0.8204495329467825781578f, \ +-0.8603334854615410920431f,-0.8439135541376909799283f,-0.7874200016694758996749f, \ +-0.7820668187587638264802f,-0.7702271668977674901058f,-0.6397730584800335185136f, \ +-0.7501646240735952986256f,-0.1050163064317838901296f,-0.5657338500383883861389f, \ +-0.5540440668540072000070f,-0.6903185807895677594814f,-0.6373808782648936466231f, \ +-0.5666907482042378152443f,-0.4219005724672658108609f,-0.3886193868474250856515f, \ +-0.5681250599967884173935f,-1.0378225966102092581167f,-0.9349807842842002836292f, \ +-0.3001473873644374679159f,-0.0086619472523597629970f,-0.3652645919168465704630f, \ +-0.5124455823851000735303f,-0.6518809665531226649193f,-0.5410207144441225857179f, \ +-0.6415487649665978509006f,-0.9086003711350160161331f,-0.6165709440100644034288f, \ +-0.5877295308593559752808f,-0.9208050182698661600966f,-0.0048324714164703318209f, \ +-0.5674999297524496721934f,-0.1029242691026374945107f,-0.5491640506289516832084f, \ +-0.0053183908272447745144f,-0.0180166547854653871785f,-0.8584065847628071788122f, \ +-0.8876649204332747178370f,-0.5558116272697392057367f,-0.3452541277977640987729f, \ +-0.9592322323801306671598f,-0.7535283497855133072463f,-0.7161931212080890896132f, \ +-0.4651350655885536089507f,-0.4452798781006889750067f,-0.8627422069241995616906f, \ +-0.4680940627922438035391f,-0.8526687741435754475106f,-0.2176103156742132949120f, \ +-0.5122870446551318623918f,-0.9165631260315680872708f,-0.4375389900682862820425f, \ +-0.4390596706521518455268f,-0.0877388848995636905226f,-0.6201939230056620067089f, \ +-0.4244909451374946907087f,-0.5765081340409458077190f,-0.1546339715387441970940f, \ +-0.8412371149638495637646f,-0.6152054338449556292190f,-0.7055085618375696032700f, \ +-1.0060843012853948330587f,-0.8572003556218193986993f,-0.7684942188683597796839f, \ +-0.0484327267220403465120f,-0.7613094946055299905296f,-0.7914662562103550458303f, \ +-0.5959529832580606756309f,-0.7135015962341314521566f,-0.7642115760119819745100f, \ +-0.7454508488281011979737f,-0.8264682151161963918895f,-0.5472791982347332551129f, \ +-0.5406217977943502672744f,-0.3063151633155380415552f,-0.7796913689590335705404f, \ +-0.1929181474134157303624f,-0.3430522750956541133682f,-0.4911328183727812768389f, \ +-0.459568916168811014700f,-0.6685113226304408851064f,-0.6625697799772538587604f, \ +-0.5798078060087921148380f,-0.8360708027394485597483f,-0.5502607336825936501512f, \ +-0.1862858035907569154155f,-0.6223700777366898417853f,-0.6503554622010890851058f, \ +-0.6214803763548166770647f,-0.658644048866955045263f,-0.6789244719569749175747f, \ +-0.4960847336430311282918f,-0.7793968717468962026373f,-0.6535755489490102654315f, \ +-0.1013611882342874415119f,-0.4101097128485187148783f,-0.4317360856761057741338f, \ +-0.1858046514491050738016f,-0.5108140928015871828904f,-0.7329583102689192219970f, \ +-0.5572655332532194805140f,-0.2414852833474282756132f,-0.7396265276752447270781f, \ +-0.0588783609986792688673f,-0.2846992688951475170001f,-0.4723177842872927079121f, \ +-0.1037246805315373693324f,-0.1794574611552203768916f,-0.0652808430937008854489f, \ +-0.0773039499491101622652f,-0.7330187724544895422341f,-0.7392992415079050472215f,\ +-0.4133533124652354895368f,-0.5506738102468112794341f,-0.5328074192235940920170f, \ +-1.0038415897821586497685f,-0.7848345170731062525604f,-0.5565211946593774383629f, \ +-0.8394668443345630892694f,-0.3316478088740031915371f,-0.6174546571080481438543f, \ +-0.9359141759808927707454f,-0.3379222154458279558931f,-0.8818086263290126902703f, \ +-0.8163896696778171202524f,-0.4448261056193882900800f,-0.5818126677407939872921f, \ +-0.6497328441864358428148f,-0.4773967451595543809439f,-0.9219910445529124753961f, \ +-0.7866824847635498496601f,-0.5256445971902782288154f,-0.5682526122395586964942f, \ +-0.1069466527081457118964f,-0.7916702346016932789752f,-0.4433240253515259299277f, \ +-0.7277712730096503879196f,-0.508130072062960125301f,-0.1336083189147964367383f,\ +-0.1070544087071799849165f,-0.4749428955148710107537f,-0.4653576600823912667870f, \ +-0.9868535311953914312966f,-0.3500843154048065564155f,-0.9103124176740465811619f, \ +-0.7691355099915161419588f,-0.1137367567447675059666f,-0.3166772504537387900037f, \ +-0.6397920481545310567029f,-0.7602207727265776204817f,-1.0393654015282784985885f, \ +-0.9191682984673771317219f,-0.4105629424946563021948f,-0.7199249389558314282667f, \ +-0.8184995123883722634162f,-0.8831578283865785250484f,-0.9231074927684407294137f, \ +-0.4607753273118053716217f,-0.2299250742000491787298f,-0.9489247717923485758718f, \ +-0.1680978688129062259549f,-0.6812321574150533853853f,-0.3838159223290327215494f, \ +-0.1497969931648169827909f,-0.9112200478501172318246f,-0.4905472078299850102745f, \ +-0.4982920949193456183757f,-0.2703771635876200951643f,-0.501441786599973071681f,\ +-0.6091306446866900925485f,-0.7751834725402599879374f,-0.1702436202720564450974f, \ +-0.4245933471268953929290f,-0.3901971933403464709578f,-0.0432410994613097177108f, \ +-0.1052903868471218307157f,-0.1137136398834104750177f} + + + +#define InRD {0.9181839306838810443878,0.0884356433525681495667,0.4926414485089480876923, \ +0.8834870792925357818604,0.6802056566812098026276,0.0268530314788222312927, \ +0.7203164598904550075531,0.4598560053855180740356,0.4730282914824783802032, \ +0.0919386046007275581360,0.7707213866524398326874,0.2658544182777404785156, \ +0.0074534364975988864899,0.9752697972580790519714,0.7235199823044240474701, \ +0.5191026907414197921753,0.6986512844450771808624,0.0405965903773903846741, \ +0.1825077752582728862762,0.3346745036542415618896,0.7407455802895128726959, \ +0.2895397534593939781189,0.1539079672656953334808,0.2327872756868600845337, \ +0.249757957179099321365,0.1534609617665410041809,0.8524017068557441234589, \ +0.1445394679903984069824,0.5686616473831236362457,0.3302547885105013847351, \ +0.2786427377723157405853,0.8844447638839483261108,0.3282945682294666767120, \ +0.3848125720396637916565,0.9120064224116504192352,0.5585131235420703887939, \ +0.3578817830421030521393,0.3319081580266356468201,0.3623231402598321437836, \ +0.8766287136822938919067,0.0389173370786011219025,0.9202555166557431221008, \ +0.3243460613302886486053,0.8379747122526168823242,0.1961554684676229953766, \ +0.836488234810531139374,0.6787032946012914180756,0.7582549881190061569214, \ +0.1194611941464245319366,0.5478108832612633705139,0.0830844114534556865692, \ +0.1074626557528972625732,0.8102702707983553409576,0.0020722588524222373962, \ +0.8974113441072404384613,0.1269455049186944961548,0.0464085307903587818146, \ +0.9040105016902089118958,0.7867436590604484081268,0.6945183053612709045410, \ +0.3590205931104719638824,0.7864200873300433158875,0.8456682055257260799408, \ +0.4063719864934682846069,0.5153579493053257465363,0.5949906939640641212463, \ +0.5879231388680636882782,0.3445296920835971832275,0.6011764244176447391510, \ +0.0055679446086287498474,0.6450063190422952175140,0.4985997099429368972778, \ +0.2964930129237473011017,0.1925860242918133735657,0.5175180840305984020233, \ +0.3105752766132354736328,0.4384520896710455417633,0.2674221722409129142761, \ +0.2229883982799947261810,0.3114312570542097091675,0.465050995815545320511, \ +0.1054230490699410438538,0.1839383761398494243622,0.3182676993310451507568, \ +0.8334749997593462467194,0.7803529789671301841736,0.1999261802993714809418, \ +0.1607502643018960952759,0.0067916330881416797638,0.3250140668824315071106, \ +0.8473272952251136302948,0.4055975303053855895996,0.1027544015087187290192, \ +0.0367881907150149345398,0.1505991755984723567963,0.0478651728481054306030, \ +0.7984658707864582538605,0.0468508685007691383362,0.8687802697531878948212, \ +0.6377770192921161651611,0.5846501276828348636627,0.3718070005998015403748, \ +0.2409734181128442287445,0.8118529785424470901489,0.9632846158929169178009, \ +0.1664984868839383125305,0.5345636266283690929413,0.6970838457345962524414, \ +0.6823413469828665256500,0.3967337189242243766785,0.2399202152155339717865, \ +0.1569029819220304489136,0.6013874863274395465851,0.6506889471784234046936, \ +0.2553333411924540996552,0.3477048687636852264404,0.2817953140474855899811, \ +0.3077315231785178184509,0.9059348977170884609222,0.5546605382114648818970, \ +0.8953115609474480152130,0.7834150167182087898254,0.1403537872247397899628, \ +0.7755798771977424621582,0.5447361194528639316559,0.0693962080404162406921, \ +0.7488555698655545711517,0.0215708073228597640991,0.5904601295478641986847, \ +0.2870239550247788429260,0.9467164869420230388641,0.8032453395426273345947, \ +0.0766134397126734256744,0.4733499353751540184021,0.1665818593464791774750, \ +0.7712225038558244705200,0.8505714428611099720001,0.3183112638071179389954, \ +0.4035588609986007213593,0.9796781539916992187500,0.4695712872780859470367, \ +0.0718349842354655265808,0.9567936672829091548920,0.7416916470974683761597, \ +0.4881874625571072101593,0.3396144369617104530334,0.9112829784862697124481, \ +0.5451393984258174896240,0.2204167605377733707428,0.9863075008615851402283, \ +0.2036699182353913784027,0.9978853110224008560181,0.5701226112432777881622, \ +0.8649067105725407600403,0.6157743069343268871307,0.2710180804133415222168, \ +0.0235887938179075717926,0.5910312486812472343445,0.5396073102019727230072, \ +0.0088853742927312850952,0.3979325224645435810089,0.0808908129110932350159, \ +0.8576204623095691204071,0.1746748872101306915283,0.4391269073821604251862, \ +0.0716713583096861839294,0.7819390646182000637054,0.8002922702580690383911, \ +0.8633827907033264636993,0.3430927144363522529602,0.9963299590162932872772, \ +0.1092859357595443725586,0.9356399574317038059235,0.8588880775496363639832, \ +0.9446536763571202754974,0.9815687369555234909058,0.1789177213795483112335, \ +0.5469553777948021888733,0.6095509598962962627411,0.2286865226924419403076, \ +0.3082748861052095890045,0.9369305213913321495056,0.6251136637292802333832, \ +0.6483835671097040176392,0.9831290808506309986115,0.3739325078204274177551, \ +0.0672900262288749217987,0.327214874327182769775,0.4716854714788496494293, \ +0.0272304220125079154968,0.7657743184827268123627,0.1599553581327199935913, \ +0.8212248464114964008331,0.4125823015347123146057,0.4811308677308261394501, \ +0.0545558966696262359619,0.6280010775662958621979,0.6469958787783980369568, \ +0.7909024558030068874359,0.7913962621241807937622} + + +#define InID {0.0004979562945663928986,0.1546611981466412544250,0.0284530925564467906952, \ +0.0055849254131317138672,0.8097954043187201023102,0.0428051082417368888855, \ +0.1182951643131673336029,0.2610557358711957931519,0.8207950596697628498077, \ +0.8662176290526986122131,0.6516509572975337505341,0.6852114759385585784912, \ +0.7980552376247942447662,0.9992001941427588462830,0.0459985560737550258636, \ +0.1328642908483743667603,0.1799852666445076465607,0.3336857678368687629700, \ +0.1323521169833838939667,0.3482229933142662048340,0.4151491993106901645660, \ +0.5222808374091982841492,0.0140265165828168392181,0.0936772432178258895874, \ +0.554428898263722658157,0.4849792802706360816956,0.5406363750807940959930, \ +0.7141286022961139678955,0.1927964971400797367096,0.3982981061562895774841, \ +0.2410794547758996486664,0.1056184638291597366333,0.3544462365098297595978, \ +0.8855850743129849433899,0.0592544334940612316132,0.5570028573274612426758, \ +0.4150356748141348361969,0.6272481856867671012878,0.7362630530260503292084, \ +0.4334241282194852828979,0.6547862743027508258820,0.1096570501103997230530, \ +0.1828466425649821758270,0.1703294925391674041748,0.5361933619715273380280, \ +0.7314661284908652305603,0.6858070171438157558441,0.5467864666134119033813, \ +0.3000954654999077320099,0.9861098499968647956848,0.2921617510728538036346, \ +0.7068451717495918273926,0.9738530241884291172028,0.9392196042463183403015, \ +0.2147838263772428035736,0.8976975139230489730835,0.3853864748962223529816, \ +0.7197126084938645362854,0.6032756562344729900360,0.3933832384645938873291, \ +0.2768237129785120487213,0.2433026498183608055115,0.5238274834118783473969, \ +0.5727928597480058670044,0.1115069282241165637970,0.8871827023103833198547, \ +0.4918101537041366100311,0.620717465877532958984,0.6681088157929480075836, \ +0.3346294192597270011902,0.4008522643707692623138,0.8206953983753919601440, \ +0.0156081621535122394562,0.3082795003429055213928,0.1921516875736415386200, \ +0.9084058068692684173584,0.9628748060204088687897,0.4108279338106513023376, \ +0.1077714688144624233246,0.4543590787798166275024,0.5766139742918312549591, \ +0.7918981136754155158997,0.8716701003722846508026,0.7446341440081596374512, \ +0.8614199929870665073395,0.8598338318988680839539,0.6422161697410047054291, \ +0.1284126546233892440796,0.1956893731839954853058,0.7571631455793976783752, \ +0.0799373830668628215790,0.3010600395500659942627,0.61714327195659279823, \ +0.8184841191396117210388,0.3742539635859429836273,0.4915034342557191848755, \ +0.5517093283124268054962,0.7295224415138363838196,0.5729464250616729259491, \ +0.0226564854383468627930,0.0795128741301596164703,0.6061109183356165885925, \ +0.0581077202223241329193,0.2136410307139158248901,0.3317275200970470905304, \ +0.7118408391252160072327,0.5123297641985118389130,0.0925556533038616180420, \ +0.1120351166464388370514,0.0331352194771170616150,0.2188743329606950283051, \ +0.8885411117225885391235,0.3364450898952782154083,0.4304939182475209236145, \ +0.0395783367566764354706,0.7718926444649696350098,0.3852231525816023349762, \ +0.584660629741847515106,0.9142434685491025447845,0.8109691496938467025757, \ +0.9606793900020420551300,0.4564617509022355079651,0.2252602274529635906219, \ +0.6146492399275302886963,0.5445657209493219852448,0.4790671234950423240662, \ +0.8712163171730935573578,0.6290841717272996902466,0.0488327336497604846954, \ +0.2014226512983441352844,0.3932394194416701793671,0.5574976503849029541016, \ +0.7534958967007696628571,0.6016047922894358634949,0.9978243424557149410248, \ +0.871782509610056877136,0.1253611450083553791046,0.7888469258323311805725, \ +0.8198945443145930767059,0.8846442662179470062256,0.6113598407246172428131, \ +0.3129875948652625083923,0.2698480314575135707855,0.3510415498167276382446, \ +0.0002431091852486133575,0.8000906230881810188293,0.8083376321010291576385, \ +0.0676734074950218200684,0.4463855498470366001129,0.1329871071502566337585, \ +0.9925356446765363216400,0.4392634835094213485718,0.7494483222253620624542, \ +0.8954892838373780250549,0.1376328612677752971649,0.4803910739719867706299, \ +0.9836516068316996097565,0.2990262722596526145935,0.4373219660483300685883, \ +0.2216190565377473831177,0.0704064411111176013947,0.3104516910389065742493, \ +0.8870153087191283702850,0.9886686950922012329102,0.3880559303797781467438, \ +0.1997731504961848258972,0.8535470529459416866302,0.5233913194388151168823, \ +0.0124758337624371051788,0.2265536198392510414124,0.6351096997968852519989, \ +0.4152868799865245819092,0.6822845251299440860748,0.6837346693500876426697, \ +0.8551749861799180507660,0.8123193774372339248657,0.0824123290367424488068, \ +0.0176315875723958015442,0.0341491582803428173065,0.8797791674733161926270, \ +0.5397802316583693027496,0.2428503734990954399109,0.1825126199983060359955, \ +0.9759421404451131820679,0.7248379667289555072784,0.3708766037598252296448, \ +0.7591939563862979412079,0.0132757760584354400635,0.4527114764787256717682, \ +0.0710861748084425926208,0.8389283320866525173187,0.9739420730620622634888, \ +0.1777097475714981555939,0.2829279201105237007141,0.8323502647690474987030, \ +0.0483473539352416992188,0.2749410220421850681305,0.9980281023308634757996, \ +0.6025707735680043697357,0.3654889445751905441284} + +#define ResRD {0.4073265521222889096187,1.4832960157658940936187,1.0559760538030802390352, \ +0.4876757408319799536,1.0503603238676473274893,1.543964660923583975816, \ +0.7807960353449081569721,1.113475122068019684818,1.2074148700721019089599, \ +1.5013200231227292746894,0.9297840505433454527662,1.3514532021448848464473, \ +1.5649706537079166590587,0.9184476769025181619455,0.7642136963785024494911, \ +1.0321272581534788326252,0.8249731824697179582984,1.5322804352205618982907, \ +1.3889179161647142723979,1.2511777469647082927651,0.8631362880453896657684, \ +1.3132001390852299227419,1.4162898618562522745634,1.336955652419456130886, \ +1.3518798690760625014207,1.432530814961507692473,0.8166991767829372417253, \ +1.4531763459288651318957,0.9836350291388685773697,1.2611871109235879284682, \ +1.2970941054870110953345,0.5247972514595955484396,1.2580817851890182534902, \ +1.284150657350121349509,0.4431164578699607337064,1.0790628231962844374436, \ +1.2369697766373111136318,1.2891801931155641991467,1.279426005626910445301, \ +0.7411469003274002709247,1.5382371539791293013621,0.4648284998100537523946, \ +1.2466755478200817197632,0.6344745057664578080647,1.3976472343104680007286, \ +0.9101343728052767589887,1.0145238645542766775520,0.8998398574208711364619, \ +1.4561881086142904884184,1.18618251793282958317,1.4909812525527503801470, \ +1.483042965312622918361,1.0101711671842434903112,1.5692858337560215975515, \ +0.581296448133323040430,1.4763786358343300442186,1.5274840435675274274985, \ +0.8570040265906480048130,0.8982361671454072160614,0.9010874927564332947938, \ +1.2192362807008756409033,0.7383467259694986850604,0.8144931489593250084624, \ +1.2166243834118397604271,1.03436100179767165308,1.131906113417643577890, \ +1.0351962467792186206594,1.2775309074990219837531,1.071918673883956119042, \ +1.565516150270076733975,0.9534817223618026194032,1.18808795707930903163, \ +1.2698193301194886650762,1.3859852741821954147383,1.0412417743580970608264, \ +1.3416868735639895238165,1.2575402806037097036551,1.3220218864013655313272, \ +1.3473014979095856435976,1.285468609148218810390,1.1658747858778166772709, \ +1.488164159422029397817,1.4322756049582612281057,1.3158102253315304697168, \ +0.9591789810942366045765,0.9946060566652682455313,1.4024848311652073906686, \ +1.4107060249666192319751,1.5641310708030540244096,1.3120464909736666569984, \ +0.5765266085251754546448,1.174948768778458774165,1.4833345055395814604537, \ +1.542328840440976067683,1.4294563291509121416567,1.5278339217974101771347, \ +0.8672708709861330911295,1.5329472698613195724704,0.8183477500293765416473, \ +0.8795454275343114192154,0.9497631085851768739658,1.2520159281840994580648, \ +1.3278713297298554429915,0.6921693745176561440857,0.5940515258646017482391, \ +1.4351615904003474089023,1.0896179081737702443178,0.8073262505844599479232, \ +0.8303525589696477693380,1.1631217540254512599063,1.3345425852020198487224, \ +1.4535942378139874442411,0.9795882485013941431973,0.9572655323242533764727, \ +1.3128248243665050498663,1.2961023348938622845594,1.3059941497461620141252, \ +1.304483982989253165741,0.9305437394849996879387,1.1438076057366068916110, \ +0.9529804506540070496712,0.8395036014732552009932,1.4335056151860767759132, \ +0.9118181357873784698143,1.088227104950570067743,1.5081933427510285650186, \ +1.0197527081918582592124,1.5525377607896333476134,0.9404998007389445691118, \ +1.286060244811547681465,0.6524446466111782916286,0.8656706311155134558888, \ +1.5096117736353744653854,1.1637012525123178185993,1.4530145530183353752562, \ +1.0046068631631419609818,0.5919009089776723353538,1.3213581010685828687201, \ +1.2600188980179465314535,0.8740394919467842083094,1.1689296619753437589395, \ +1.5022014467298512307991,0.5528837279866596343680,0.8359949109724567062329, \ +1.0607846432300507277802,1.3062568171740265299263,0.8879559287204453754683, \ +0.9963420783593853746751,1.3688496242545662440193,0.3803570908643706949270, \ +1.4264926442838912201694,0.6382023556059207569646,1.117517041236663288828, \ +0.9501387596985741978983,0.9188351614160777947049,1.3254743353137110606355, \ +1.55398001104990246546,0.9810746826810110565731,1.0669910119329548692235, \ +1.5621213392572059763808,1.162804162098360238886,1.4934861287145768660167, \ +0.9519686104540553417408,1.4467374415079707894449,1.154639180917391483305, \ +1.500462431806032004289,0.9915094174043252994721,0.8535439676775620210236, \ +0.5293817691790781987393,1.23068211775509039896,0.7526195369457671091595, \ +1.4697720678086412249286,0.8182121412746224953239,0.8746692343808056824273, \ +0.8844573970963010012269,0.8439197222579799539943,1.391544468064010775521, \ +0.9922180869468192332405,0.9160137371548995322001,1.3993728411492449836828, \ +1.2985217508033519706601,0.5536816066461542895638,0.9157598470345392760450, \ +1.1161566883090805468726,0.8048708844349877766788,1.2156607775224024248217, \ +1.5172042703120385276350,1.2374758085060872936367,1.1351487844726630971337, \ +1.5436311555741579759626,0.9980288444492946275943,1.4563247763642750420843, \ +0.6617790067192217406955,1.1654713730545154248830,1.2035174317997594517493, \ +1.5162772650111728811595,0.9344765112644882742998,1.1223294698972574590101, \ +0.8945516347671441659273,0.7901547616106909810441} + +#define ResID {-0.0012569697886744767793,-0.1546381133029076926366,-0.0326845596217153130936, \ +-0.0119187043920920034135,-0.8334668693395566041460,-0.0428074462389216731095, \ +-0.1672885154101033944318,-0.2869984863074300229790,-0.7925278559645111409182, \ +-0.7851274769100758943452,-0.7428250726131904180249,-0.6543302407510473983621, \ +-0.7311595163178985501418,-1.052203053002093824375,-0.0664259655312470775890, \ +-0.1541712629474439599786,-0.2426466544194012253666,-0.3280193987403173250250, \ +-0.1341688909762420167660,-0.3590358673724926563686,-0.5222636224036150132122, \ +-0.5167890418406643204818,-0.0141951437273657391641,-0.0961499124903888030547, \ +-0.5411789866531571124852,-0.4719374206382114245173,-0.6865145475966729637918, \ +-0.6682412786135066840032,-0.229561178131867382746,-0.4068630429518135804834, \ +-0.2478546467124292662643,-0.2092687177409224830171,-0.3643943961998056257912, \ +-0.8260533990387732838911,-0.1377643146197947143783,-0.5959599853289488935459, \ +-0.4262600844346774997540,-0.6137130366455740837495,-0.7080093721711945287112, \ +-0.6044893440702200360093,-0.6155234120386735563457,-0.2422467665254410262854, \ +-0.1917136851747310299920,-0.2835381480340813942220,-0.5205087419896101685879, \ +-0.8283554785369232620340,-0.7385639097367507899250,-0.6511255066138333935655, \ +-0.2976620683491659202780,-0.9257955504050334738508,-0.2890528438121037768660, \ +-0.6604934892243505828446,-0.9834822614680237551354,-0.8377366271338905212573, \ +-0.3818062735980304323036,-0.8101402379111779517018,-0.3767706089539061276028, \ +-0.8471279280465069394523,-0.7100416511121218077207,-0.4827879396812622680990, \ +-0.2907446603933081519244,-0.3540413099584073797210,-0.6691029908570297335402, \ +-0.5779752710357292100340,-0.1293680641651104301637,-0.8672105047323137583248, \ +-0.5445780680276932628203,-0.6098830976698420558435,-0.701796561463252421831, \ +-0.3286839097690721356315,-0.4736684460520745321155,-0.7974492297316398969897, \ +-0.0163420882574338011128,-0.3086940489965586675858,-0.2208475495159677448598, \ +-0.8330345833509705810727,-0.8899247395553587791639,-0.4121122816452804649145, \ +-0.110296470108896760287,-0.4573875737589336853972,-0.5921314598231492976055, \ +-0.7284533656063938433789,-0.7940022333816690869313,-0.7086861369245996966626, \ +-0.9177754728271111384075,-0.8992125494626673765097,-0.6124156802640610131050, \ +-0.1297119059766182191940,-0.1944657181402436596507,-0.7195246660784752057438, \ +-0.1461225286840270864985,-0.3207633116621479985042,-0.5854835047639634915129, \ +-0.7472936554211552229177,-0.3695542509299474809303,-0.4740067448468703315001, \ +-0.6718044057588442585782,-0.67710691385219745619,-0.7207858066458165957613, \ +-0.0294026163397106028718,-0.0976133299331403969656,-0.6013612638349056238596, \ +-0.0598297565651504936746,-0.328794773496815184721,-0.5625239033097394480976, \ +-0.6677071141299576462202,-0.5498312284204850408642,-0.1277672590472646030335, \ +-0.1511975528780685473773,-0.0360853980890413067462,-0.2232684445667622585852, \ +-0.8049065446736692885921,-0.3948819631358797543896,-0.5048059213328937033793, \ +-0.0409214035081632079849,-0.7341976462547471493636,-0.3892323418939396262317, \ +-0.5739837580671862671267,-0.9770097106672435138819,-0.8021342946497018733254, \ +-1.0021601470891579044320,-0.5801678547205166847078,-0.2254843767325802050827, \ +-0.7149457311090813282917,-0.5814477978791194878738,-0.4632588121589609753137, \ +-0.8972503262100923748790,-0.5936926452425980160754,-0.0604108143246592510511, \ +-0.2083620749723606169201,-0.6092960412140594472774,-0.6787459939901434591292, \ +-0.6970693351773428192431,-0.6155344865687581989988,-0.8847535831035618913987, \ +-0.9045009940161035100203,-0.2228370896879496854126,-0.7435945044006587734131, \ +-0.7797072997435431362945,-0.9858551830709869623348,-0.6231594490146994402835, \ +-0.3087944685075739159608,-0.4935703580252177591348,-0.4570457045425700415286, \ +-0.0002785589239395412880,-0.7550970319205865255441,-0.9107367125371321758820, \ +-0.0805255675456537367563,-0.4411921852011919109593,-0.3509629581295168887500, \ +-0.8834651688371163436031,-0.6829765945613543998149,-0.7587154857028519661100, \ +-0.9508788895131682350481,-0.1722922072289033157411,-0.4769308753189193672561, \ +-0.8698653140140508721601,-0.3524550030910831299735,-0.48064598279368742073, \ +-0.2198520225955942486440,-0.0766272000705114642027,-0.3065575707631173485446, \ +-0.9428944463643879059234,-0.8787732160663290770231,-0.4124717822835545222304, \ +-0.198953189056428669801,-0.8954090767834280706339,-0.6481614554957403351310, \ +-0.0247021173339000768565,-0.2380648741688522473936,-0.8303628800121001241052, \ +-0.4061558941427557689607,-0.8344614350167003369307,-0.8022035151889936877012, \ +-0.9540346088196560714323,-0.9416233317955250425868,-0.0836566823356919425647, \ +-0.0210575991644249005397,-0.0430401703581563405132,-0.8035548300562509460576, \ +-0.5345951582358715592491,-0.4468307121957418859282,-0.2281623925724436396933, \ +-0.9410916791444350337770,-0.8853872018362433093941,-0.3859095350986695427409, \ +-0.7013552814699581805513,-0.0140485558911140305527,-0.4806326207619357471224, \ +-0.0710526121402196841892,-0.8801311527599792183807,-0.8674163434334025701844, \ +-0.2852979580229001999037,-0.3032063540671979806618,-0.8027805094234632399264, \ +-0.0484003958010784038346,-0.3355136589916887235319,-0.9554164532781582730436, \ +-0.7111271555138466426982,-0.4940883791858934337426} + + + + + + +void cacossTest(void){ + int i=0; + float tInR[]=InRF; + float tInI[]=InIF; + float tResR[]=ResRF; + float tResI[]=ResIF; + floatComplex tIn[200]; + floatComplex tRes[200]; + floatComplex out[200]; + + for (i=0;i<200;i++){ + tIn[i]=FloatComplex(tInR[i],tInI[i]); + tRes[i]=FloatComplex(tResR[i],tResI[i]); + out[i]=cacoss(tIn[i]); + } + + + for (i=0;i<200;i++){ + assert ( ( fabs(creals(out[i]) - creals(tRes[i])) / fabs(creals(out[i])) ) < 1e-6); + assert ( ( fabs(cimags(out[i]) - cimags(tRes[i])) / fabs(cimags(out[i])) ) < 1e-6); + } +} + + + +void zacossTest(void){ + int i=0; + double tInR[]=InRD; + double tInI[]=InID; + double tResR[]=ResRD; + double tResI[]=ResID; + doubleComplex tIn[200]; + doubleComplex tRes[200]; + doubleComplex out[200]; + + for (i=0;i<200;i++){ + tIn[i]=DoubleComplex(tInR[i],tInI[i]); + tRes[i]=DoubleComplex(tResR[i],tResI[i]); + out[i]=zacoss(tIn[i]); + } + + + for (i=0;i<200;i++){ + assert ( ( fabs(zreals(out[i]) - zreals(tRes[i])) / fabs(zreals(out[i])) ) < 3e-15); + assert ( ( fabs(zimags(out[i]) - zimags(tRes[i])) / fabs(zimags(out[i])) ) < 3e-15); + } + + out[0]=zacoss(DoubleComplex(0.2,0.1)); + printf ("%1.20f + %1.20f *i\n",zreals(out[0]),zimags(out[0])); + assert ( ( fabs(zreals(out[0]) - 1.3704927556955963652285) / fabs(zreals(out[0])) ) < 3e-16); + assert ( ( fabs(zimags(out[0]) - (- 0.1018639159801242727310)) / fabs(zimags(out[0])) ) < 3e-16); +} + + +void cacosaTest(void){ + int i=0; + float tInR[]=InRF; + float tInI[]=InIF; + float tResR[]=ResRF; + float tResI[]=ResIF; + floatComplex tIn[200]; + floatComplex tRes[200]; + floatComplex out[200]; + + for (i=0;i<200;i++){ + tIn[i]=FloatComplex(tInR[i],tInI[i]); + tRes[i]=FloatComplex(tResR[i],tResI[i]); + } + cacosa(tIn,200,out); + for (i=0;i<200;i++){ + assert ( ( fabs(creals(out[i]) - creals(tRes[i])) / fabs(creals(out[i])) ) < 1e-6); + assert ( ( fabs(cimags(out[i]) - cimags(tRes[i])) / fabs(cimags(out[i])) ) < 1e-6); + } +} + + +void zacosaTest(void){ + int i=0; + double tInR[]=InRD; + double tInI[]=InID; + double tResR[]=ResRD; + double tResI[]=ResID; + doubleComplex tIn[200]; + doubleComplex tRes[200]; + doubleComplex out[200]; + + for (i=0;i<200;i++){ + tIn[i]=DoubleComplex(tInR[i],tInI[i]); + tRes[i]=DoubleComplex(tResR[i],tResI[i]); + } + zacosa(tIn,200,out); + for (i=0;i<200;i++){ + assert ( ( fabs(zreals(out[i]) - zreals(tRes[i])) / fabs(zreals(out[i])) ) < 3e-15); + assert ( ( fabs(zimags(out[i]) - zimags(tRes[i])) / fabs(zimags(out[i])) ) < 3e-15); + } +} + + +int testAcos(void) { + printf("\n>>>> Complex ArcCosine Tests\n"); + cacossTest(); + zacossTest(); + cacosaTest(); + zacosaTest(); + return 0; +} + +int main(void) { + assert(testAcos() == 0); + return 0; +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/testRealsAcos.c b/2.3-1/src/c/elementaryFunctions/acos/testRealsAcos.c new file mode 100644 index 00000000..0609a7c2 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/testRealsAcos.c @@ -0,0 +1,647 @@ +/* + * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab + * Copyright (C) 2008-2008 - INRIA - Arnaud TORSET + * + * 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 + * + */ + +#include "testAcos.h" +#include <math.h> +#include <stdio.h> +#include <assert.h> + + +#define InRF {0.2146485899575054645538f,0.0151845822110772132874f,0.0480025182478129863739f, \ +0.2151292376220226287842f,0.3335768491961061954498f,0.4239571234211325645447f, \ +0.8191771185956895351410f,0.1142293009907007217407f,0.2984248069114983081818f, \ +0.7708469005301594734192f,0.9841971280984580516815f,0.4902752116322517395020f, \ +0.1607228242792189121246f,0.4278817875310778617859f,0.3875273256562650203705f, \ +0.9808397348970174789429f,0.9092800100333988666534f,0.482719236053526401520f, \ +0.665830671321600675583f,0.2464372254908084869385f,0.7713316814042627811432f, \ +0.8996570175513625144958f,0.9153267047367990016937f,0.9860265571624040603638f, \ +0.2070462000556290149689f,0.6318158404901623725891f,0.9118843185715377330780f, \ +0.5755609273910522460938f,0.6911411830224096775055f,0.9032438425347208976746f, \ +0.7275989069603383541107f,0.2983345370739698410034f,0.8753590886481106281281f, \ +0.3796929577365517616272f,0.0876038889400660991669f,0.6358761452138423919678f, \ +0.2255521775223314762115f,0.446817158721387386322f,0.3108666068874299526215f, \ +0.5881394986063241958618f,0.7271268484182655811310f,0.3145425738766789436340f, \ +0.1787185999564826488495f,0.4917406365275382995605f,0.7525973492302000522614f, \ +0.1663594795390963554382f,0.5748702525161206722260f,0.3049920704215764999390f, \ +0.6849988629110157489777f,0.0722861671820282936096f,0.2406598175875842571259f, \ +0.8284838385879993438721f,0.3909099684096872806549f,0.8842546856030821800232f, \ +0.4892868152819573879242f,0.8299614358693361282349f,0.1368344766087830066681f, \ +0.8326684581115841865540f,0.2227798062376677989960f,0.5422506183385848999023f, \ +0.0426926412619650363922f,0.0428817747160792350769f,0.0954485400579869747162f, \ +0.5029790829867124557495f,0.6661717449314892292023f,0.6903511593118309974670f, \ +0.1675704787485301494598f,0.2048450224101543426514f,0.8116860599257051944733f, \ +0.0132086118683218955994f,0.8930616951547563076019f,0.5251825544983148574829f, \ +0.1576961842365562915802f,0.9010067256167531013489f,0.7848821463994681835175f, \ +0.4035740271210670471191f,0.7961377524770796298981f,0.2783856792375445365906f, \ +0.6019253223203122615814f,0.7362591978162527084351f,0.2777095218189060688019f, \ +0.0024121040478348731995f,0.4011422689072787761688f,0.9560912884771823883057f, \ +0.2567708329297602176666f,0.4923398261889815330505f,0.2986499867402017116547f, \ +0.2667899150401353836060f,0.3295984459109604358673f,0.8105424838140606880188f, \ +0.2835742044262588024139f,0.0002408921718597412109f,0.1597527512349188327789f, \ +0.4133680192753672599792f,0.9283765270374715328217f,0.0655929129570722579956f, \ +0.4843033556826412677765f,0.2906650463119149208069f,0.3394159595482051372528f, \ +0.9589011035859584808350f,0.0946640432812273502350f,0.7127310922369360923767f, \ +0.1914948052726686000824f,0.3020674530416727066040f,0.3857871112413704395294f, \ +0.303432715125381946564f,0.1901389393024146556854f,0.3798281177878379821777f, \ +0.5674670808948576450348f,0.6582474960014224052429f,0.8053624569438397884369f, \ +0.6435376014560461044312f,0.1315037836320698261261f,0.2259779060259461402893f, \ +0.6206666971556842327118f,0.6504998095333576202393f,0.6684748218394815921783f, \ +0.6728870486840605735779f,0.1410236409865319728851f,0.4075959790498018264771f, \ +0.627867404837161302567f,0.4480062769725918769836f,0.4035936850123107433319f, \ +0.5879594832658767700195f,0.1153195598162710666656f,0.7683646855875849723816f, \ +0.2349277897737920284271f,0.5894475113600492477417f,0.3207207177765667438507f, \ +0.7428904781118035316467f,0.4984040032140910625458f,0.9036596231162548065186f, \ +0.6709216744638979434967f,0.8537342092022299766541f,0.1756483591161668300629f, \ +0.7642531786113977432251f,0.3008039263077080249786f,0.5137639017775654792786f, \ +0.6256901505403220653534f,0.5433056429028511047363f,0.9364583813585340976715f, \ +0.9189820392057299613953f,0.8656015782617032527924f,0.8644737657159566879272f, \ +0.7842234452255070209503f,0.9146144324913620948792f,0.2163717742078006267548f, \ +0.9016996361315250396729f,0.5193324820138514041901f,0.0936209624633193016052f, \ +0.1577651998959481716156f,0.8322136122733354568481f,0.9679206502623856067657f, \ +0.8463781969621777534485f,0.7359144198708236217499f,0.9125841259956359863281f, \ +0.5761411138810217380524f,0.5802838830277323722839f,0.3673972501419484615326f, \ +0.1465643625706434249878f,0.2601406280882656574249f,0.8280333140864968299866f, \ +0.3835482816211879253387f,0.0134858153760433197021f,0.7306445003487169742584f, \ +0.4633175721392035484314f,0.1587547785602509975433f,0.2259487155824899673462f, \ +0.8859009263105690479279f,0.7426936449483036994934f,0.1664869519881904125214f, \ +0.9855593368411064147949f,0.3667347007431089878082f,0.3923764182254672050476f, \ +0.8068126081489026546478f,0.7054641749709844589233f,0.8674603034742176532745f, \ +0.4587025428190827369690f,0.34914617193862795830f,0.6684310026466846466064f, \ +0.2964043603278696537018f,0.1410161769017577171326f,0.8339820853434503078461f, \ +0.5892267990857362747192f,0.3797874790616333484650f,0.3257266031578183174133f, \ +0.277362580876797437668f,0.5500425547361373901367f,0.8027154603041708469391f, \ +0.0402877209708094596863f,0.0218298300169408321381f,0.2777149509638547897339f, \ +0.4810298834927380084991f,0.5458494136109948158264f,0.5776124666444957256317f, \ +0.2314949147403240203857f,0.0577680678106844425201f,0.2873307904228568077087f, \ +0.7977964854799211025238f,0.4701130483299493789673f} + + +#define InIF {0.0394321014173328876495f,0.3370208526030182838440f,0.6783407176844775676727f, \ +0.2560503073036670684814f,0.5241241441108286380768f,0.9488922869786620140076f, \ +0.3087073317728936672211f,0.7950635720044374465942f,0.9224105221219360828400f, \ +0.4595228182151913642883f,0.7807972389273345470428f,0.226513788104057312012f, \ +0.9408814110793173313141f,0.6131632206961512565613f,0.4430119856260716915131f, \ +0.2909095119684934616089f,0.8606127654202282428741f,0.8565102526918053627014f, \ +0.9051895807497203350067f,0.6799235455691814422607f,0.5336262793280184268951f, \ +0.7887798985466361045837f,0.7137753940187394618988f,0.4034583661705255508423f, \ +0.1977087226696312427521f,0.1879524858668446540833f,0.7047274294309318065643f, \ +0.4047584310173988342285f,0.2033406519331037998199f,0.8319396777078509330750f, \ +0.8779059736989438533783f,0.3923193570226430892944f,0.2464844961650669574738f, \ +0.8334233397617936134338f,0.1366976196877658367157f,0.3573439754545688629150f, \ +0.2009820179082453250885f,0.7071162825450301170349f,0.7366236648522317409515f, \ +0.7454952616244554519653f,0.1443111491389572620392f,0.8881948785856366157532f, \ +0.7866828846745193004608f,0.751696139574050903f,0.6704522022046148777008f, \ +0.9206535546109080314636f,0.6471786811016499996185f,0.7067261617630720138550f, \ +0.0836134557612240314484f,0.0343311587348580360413f,0.5677806059829890727997f, \ +0.0243650637567043304443f,0.5665661157108843326569f,0.3293592026457190513611f, \ +0.4095702595077455043793f,0.6778331939131021499634f,0.9173386511392891407013f, \ +0.2867819787934422492981f,0.7948215636424720287323f,0.6742788180708885192871f, \ +0.9480205052532255649567f,0.8240985525771975517273f,0.5282654105685651302338f, \ +0.4960622992366552352905f,0.1394251813180744647980f,0.6144766295328736305237f, \ +0.6335886861197650432587f,0.9775871522724628448486f,0.6453627035953104496002f, \ +0.8883882975205779075623f,0.8489176682196557521820f,0.5864279735833406448364f, \ +0.240271453280001878738f,0.4364176439121365547180f,0.925035800319164991379f, \ +0.5775052458047866821289f,0.3039593794383108615875f,0.0319902477785944938660f, \ +0.5700858398340642452240f,0.9890570174902677536011f,0.4372045849449932575226f, \ +0.9927745470777153968811f,0.3845063815824687480927f,0.9491574577987194061279f, \ +0.8019652874208986759186f,0.0995050808414816856384f,0.6299527562223374843597f, \ +0.2615322861820459365845f,0.7799491551704704761505f,0.5909776063635945320129f, \ +0.1759523036889731884003f,0.7394210770726203918457f,0.0432920181192457675934f, \ +0.4539660913869738578796f,0.4680440216325223445892f,0.2562364395707845687866f, \ +0.6310959537513554096222f,0.7268115812912583351135f,0.8611525888554751873016f, \ +0.9817700721323490142822f,0.125576748047024011612f,0.0354329412803053855896f, \ +0.1619467637501657009125f,0.7726956922560930252075f,0.5215707314200699329376f, \ +0.0805094735696911811829f,0.7239321577362716197968f,0.1861188411712646484375f, \ +0.8831509896554052829742f,0.2945854095742106437683f,0.9390283836983144283295f, \ +0.0849235635250806808472f,0.3811029498465359210968f,0.3878462770953774452209f, \ +0.4693805794231593608856f,0.3036659620702266693115f,0.8050093413330614566803f, \ +0.0013171425089240074158f,0.0631553060375154018402f,0.3437646273523569107056f, \ +0.1436945316381752490997f,0.1862327279523015022278f,0.2980708214454352855682f, \ +0.5667379423975944519043f,0.3277782374061644077301f,0.9283294035121798515320f, \ +0.0964117287658154964447f,0.8542382624000310897827f,0.7280886103399097919464f, \ +0.4358090544119477272034f,0.3552779997698962688446f,0.2036329694092273712158f, \ +0.5036846981383860111237f,0.4097248231992125511169f,0.5358183733187615871429f, \ +0.2278824020177125930786f,0.3932382804341614246368f,0.0155387269333004951477f, \ +0.5551981288008391857147f,0.0284646600484848022461f,0.0435250797308981418610f, \ +0.7746011493727564811707f,0.8250512345694005489349f,0.4100972842425107955933f, \ +0.4687753473408520221710f,0.0943022081628441810608f,0.7801668713800609111786f, \ +0.9060058109462261199951f,0.7346338243223726749420f,0.6556449970230460166931f, \ +0.7411603308282792568207f,0.5824892017990350723267f,0.4604790774174034595490f, \ +0.3769907029345631599426f,0.4548782887868583202362f,0.0915321484208106994629f, \ +0.2338522099889814853668f,0.1727255983278155326843f,0.1562884538434445858002f, \ +0.9402142520993947982788f,0.5307449479587376117706f,0.2255999082699418067932f, \ +0.495603590738028287888f,0.4456660784780979156494f,0.2354971007443964481354f, \ +0.9914885526522994041443f,0.1743899188004434108734f,0.3443220872431993484497f, \ +0.354053397197276353836f,0.6553237633779644966125f,0.6344098853878676891327f, \ +0.5242204368114471435547f,0.0143296965397894382477f,0.2569495765492320060730f, \ +0.6429493143223226070404f,0.8490996640175580978394f,0.3474385743029415607452f, \ +0.2056481996551156044006f,0.1183789293281733989716f,0.5430422388017177581787f, \ +0.3435242832638323307037f,0.4020882537588477134705f,0.0397002524696290493011f, \ +0.1044149938970804214478f,0.2759570893831551074982f,0.6864448906853795051575f, \ +0.7838258775882422924042f,0.217856429517269134521f,0.7876369827426970005035f, \ +0.8314417852088809013367f,0.7343441187404096126556f,0.6330608930438756942749f, \ +0.2331567634828388690948f,0.79906500224024057388f,0.5055180336348712444305f, \ +0.4791096337139606475830f,0.3705745027400553226471f,0.4796987390145659446716f, \ +0.6252688220702111721039f,0.9830987323075532913208f} + + +#define ResRF {1.3544643076000049131125f,1.555611161001190234643f,1.5227753545043396510295f, \ +1.3539721626852589953f,1.2307011179667750599975f,1.132986233674521114878f, \ +0.6108215211136103217626f,1.4563171387342028761935f,1.26775449603837397916f, \ +0.6906267709340139226981f,0.1780149993077420056409f,1.0583908356731808186879f, \ +1.4093733723685308856233f,1.1286484374252463425137f,1.1728485230904668323859f, \ +0.1960702202025065843394f,0.4292455238079518897720f,1.0670393141498673017509f, \ +0.8421897142243505163250f,1.3217939513349721281088f,0.6898654070878095234676f, \ +0.4518130294310849226491f,0.4144778912738525944448f,0.1673685006122558327490f, \ +1.3622415598200958708475f,0.886902683876586550582f,0.4229445354426950576254f, \ +0.9575064117084541859271f,0.8077294519947597617460f,0.4435267853313298869189f, \ +0.7559810258252398496026f,1.2678490741689776299950f,0.5046182820452449480086f, \ +1.1813319501282872892034f,1.4830799972889596727299f,0.8816531266139947531357f, \ +1.3432865448676185593513f,1.107591898499146854107f,1.2546916476714633503775f, \ +0.9420398538652174913466f,0.7566689041304636154095f,1.2508215962260114118010f, \ +1.3911123978681665391832f,1.0567086722755880678903f,0.7187986332601904448936f, \ +1.4036597839870441628563f,0.9583507556750017197800f,1.260866223812947772842f, \ +0.8161941887163420839002f,1.49844705842773628923f,1.327750735837211149004f, \ +0.5944014578559909667277f,1.1691763062196611766552f,0.4859006803898779369710f, \ +1.0595245187218389482098f,0.5917577795331790957434f,1.4335312043991983443902f, \ +0.5868872597311183270108f,1.3461313138241890463576f,0.9976829092544128307907f, \ +1.5280907058444337387471f,1.5279013990243792697754f,1.4752022598870020431150f, \ +1.0437541728877690605515f,0.8417324807407642328627f,0.8088220073687144573427f, \ +1.4024315436728629347130f,1.3644909573371579725176f,0.6237633497149321915032f, \ +1.5575873308176619858045f,0.4666916888200717261626f,1.0178667076465526264428f, \ +1.4124391178254291911998f,0.4487116894768009012218f,0.6682904180063654608901f, \ +1.1553765634714785459636f,0.6499108421939678859047f,1.2886833903313061888696f, \ +0.9248863868474237470707f,0.7432707317726728879492f,1.2893873050266133617470f, \ +1.5683842204080198357019f,1.1580328237052455175871f,0.297435226780083439291f, \ +1.3111168037999454405451f,1.0560204013836156367034f,1.267518556897496040392f, \ +1.300735649674872540515f,1.2349181037163743379637f,0.6257185580692986581752f, \ +1.2832770556580765930477f,1.5705554346207071247932f,1.4103561444004117930717f, \ 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+0.7334183218187529940124f,1.049039471207045437495f,0.4425568980368907445744f, \ +0.8353452979806201827984f,0.5476812518090538040028f,1.3942319989111211508970f, \ +0.7009138051156860171886f,1.2652608172154014010147f,1.0312300888962582234853f, \ +0.8947803803621411367075f,0.9964267421930456114509f,0.3584025169927071985398f, \ +0.4053053537674792816681f,0.52444580540694141213f,0.5266937610818180903749f, \ +0.6693527332761076698020f,0.4162430398171838019650f,1.3526996566064570792776f, \ +0.4471117451927261177147f,1.0247266752134434053545f,1.4770380592585463652711f, \ +1.4123692272878969333760f,0.5877081129044480212187f,0.2539777406414896465670f, \ +0.5616486929670342354015f,0.7437800898892800161022f,0.4212363058629264855881f, \ +0.9567967508657543307393f,0.9517191061460341661160f,1.1945873210943909192849f, \ +1.4237020985347941248733f,1.307628484293123394266f,0.5952054691773595029858f, \ +1.1771609573131449621997f,1.5573101026141118463642f,0.7515308864404272037874f, \ +1.08906115052591578873f,1.4113670182151965004635f,1.3428794989819419214427f, \ +0.4823637262878405218558f,0.7337123123270111735295f,1.403530508718869640461f, \ +0.1701502458411716656173f,1.1952995905474013138559f,1.1675825417504139824842f, \ +0.632059235534878305351f,0.7877184695580223827704f,0.5207218041934291719031f, \ +1.0942618099823884225685f,1.2141365475300021081750f,0.8386990520942673166260f, \ +1.2698707048803585806240f,1.4293085531739009308438f,0.5845108665288674121285f, \ +0.9406947904242937141817f,1.1812297752030191944073f,1.2390161854573771282872f, \ +1.2897484327948283144849f,0.9883811343629644863285f,0.6389615878853852626307f, \ +1.5304976993530934326060f,1.5489647626028015814370f,1.2893816535780269205702f, \ +1.0689672707047077615528f,0.9933937851799321538948f,0.9549954566636918995570f, \ +1.337182267875798302725f,1.5129960805231705833762f,1.2793573801230322395384f, \ +0.6471646932978184496577f,1.0813774684738581832733f} + +#define ResIF {1.5313539994534084431876f,1.2270454945240594213374f,0.8252943559980340237914f, \ +1.3118622512767883492302f,1.0191099717030900340120f,0.3210890168818836265530f, \ +1.2569626427487261555171f,0.6516839411893488032135f,0.3965201754844740467121f, \ +1.0933384694570118522705f,0.6748555027471666578620f,1.3422993862285261812417f, \ +0.3455732962500616678447f,0.9107376302950138668990f,1.1118407738194451273017f, \ +1.2756190002512473036234f,0.534324627989826939078f,0.5423264441023638582351f, \ +0.4389707532009931023609f,0.8231379603724421345490f,1.0079137337479666669537f, \ +0.6619748165277959950359f,0.7759222830602500176056f,1.1555029726809751267069f, \ +1.3717763753859233410992f,1.3817192645680580476153f,0.7887574388774107880806f, \ +1.154081687844786152652f,1.3660276734930973940862f,0.5882019906981408308155f, \ +0.4993250010048232434556f,1.1676445771431656073247f,1.3217451760779403979740f, \ +0.5855226957110959418173f,1.4336693595120120203745f,1.205373778014949381898f, \ +1.3684360354595728193061f,0.7853847263571438475083f,0.7427319788503217168341f, \ +0.7295187281370371090716f,1.425979527467823082532f,0.4773949303589768988765f, \ +0.6653789652250786668120f,0.7201661840055592067600f,0.8359782312775623225320f, \ +0.4010449856231582121957f,0.8669186056114237537429f,0.7859362957809750138694f, \ +1.4870851367060453629421f,1.536458420533861612967f,0.9669891090554120216538f, \ +1.5464288516482158630794f,0.9684637239770992334087f,1.2351714956359907127137f, \ +1.1488133772379154340371f,0.8259848817840680368363f,0.4094531852851721054343f, \ +1.2799303040161731370716f,0.6520828442366262134300f,0.8308086408007220313721f, \ +0.3238399424616983379721f,0.6021873821209878796523f,1.0142399690964163383455f, \ +1.0517384795139694819710f,1.4309154243829336206062f,0.9090739203715231253611f, \ +0.8846133529122768290875f,0.2121182423802339123142f,0.8692983189363326923527f, \ +0.47697379514371801568f,0.5568622476164218904060f,0.9441544643774535394698f, \ +1.3281508401476103120586f,1.1191830432760909719292f,0.3896665024665909582424f, \ +0.9551267985697193818595f,1.2619503910172775729137f,1.5388006201603028344493f, \ +0.9641859946151247751089f,0.1480742995944135109720f,1.1183082300559199495638f, \ +0.1202844206176664348940f,1.1761232908094509941321f,0.3202477413820724594373f, \ +0.6402184399260194558323f,1.4711263056909940072359f,0.8893039482321445365898f, \ +1.3061869235485943363528f,0.6762117558368399006241f,0.9385261464846976764420f, \ +1.3939232457675478915604f,0.7385862765729950263349f,1.5274907742828045531525f, \ +1.0995848226997599894617f,1.0837202329455530858127f,1.3116696951046082908476f, \ +0.8878310767922412694020f,0.7571280287683522791653f,0.5332636611081145172619f, \ +0.1912359123928325799202f,1.44488716691460328256f,1.5353559670190242147925f, \ +1.4081331860416281820392f,0.6877194039437647399282f,1.02210543863474323523f, \ +1.4901996245029442977881f,0.7613110787878502039305f,1.3835858489414398775352f, \ +0.4882587676373527640905f,1.2717746792548134671108f,0.3510027969902725919482f, \ +1.48577035226708975557f,1.1798073422108839025668f,1.1725025103978652385450f, \ +1.082207178445642403730f,1.262258365804196147408f,0.6351051130420296564338f, \ +1.5694791839051283055539f,1.5075989617580312085465f,1.2198734065895773248656f, \ +1.4266026395050115383f,1.3834699355835038403484f,1.2681253600974256023903f, \ +0.9682551856135412915449f,1.2368453959617209392263f,0.3809027641084558046813f, \ +1.4742346083993373984100f,0.5467124691036475692130f,0.7552669049014355540095f, \ +1.1198593352029904135492f,1.2075848742491721576897f,1.3657291093636882983731f, \ +1.0429375766976551886955f,1.1486439448135470353662f,1.0053196235121615309538f, \ +1.3408940198345395966584f,1.166645348645906299367f,1.555256974484105159107f, \ +0.9821951633092294020599f,1.5423278214913895833860f,1.5272574927805724342988f, \ +0.6847121192620346796787f,0.6005034615094222427700f,1.1482356007343721415737f, \ +1.0828924838534597085982f,1.4763537862006439471685f,0.6758638036045827579557f, \ +0.4370463027476746975530f,0.7456695165395208491077f,0.8557598004935614843802f, \ +0.7359992024987982439654f,0.9490086268240732758628f,1.0922615019568577832132f, \ +1.184251206507022535774f,1.098560786595480287531f,1.4791358826505083268188f, \ +1.334758450002002438950f,1.3972001359840415801727f,1.4138645236300337870716f, \ +0.3475374929910621246698f,1.0113170412320249269555f,1.3432375513394290145186f, \ +1.0522666912154046148231f,1.1088781475531621634190f,1.3330663041014356728908f, \ +0.1305645353871486558095f,1.3955101678176036195111f,1.2192797033375830650925f, \ +1.2088946193116594240990f,0.8561851579342378837367f,0.8835514575659523250906f, \ +1.0189969006408940987995f,1.5564661397993202474055f,1.3109318548790835912143f, \ +0.8724535168872261658990f,0.5565178057806303701938f,1.215958206971465838109f, \ +1.3636703086937589368688f,1.4521391539839998419126f,0.9967404603545287899991f, \ +1.2201293368773795666726f,1.1569998731124000457271f,1.5310856382606727876805f, \ +1.4661906653829819280332f,1.2912110119575965772043f,0.8142075135673421115712f, \ +0.6699932176804166417128f,1.3511787210901111677686f,0.6638319846196626405899f, \ +0.5890987081162550875746f,0.7460964201464012068854f,0.8852953565042832595466f, \ +1.3354736682149619397819f,0.6450578234482783335224f,1.0408140682934756693356f, \ +1.0711562631188329408616f,1.1911688411902121575991f,1.0704849901046198379362f, \ +0.8953203785098390321551f,0.1841145960893279809323f} + + +#define InRD {0.3596746218390762805939,0.9327730434015393257141,0.6520409691147506237030, \ +0.4466360807418823242188,0.5597501345910131931305,0.1586764482781291007996, \ +0.1349689974449574947357,0.5309285502880811691284,0.7984495465643703937531, \ +0.5877699116244912147522,0.5329149584285914897919,0.3033532761037349700928, \ +0.0826407433487474918365,0.2014105310663580894470,0.2214868194423615932465, \ +0.5626921299844980239868,0.594995748717337846756,0.3364775599911808967590, \ +0.9449067446403205394745,0.2256392762064933776855,0.0615444355644285678864, \ +0.3346643997356295585632,0.9560257433913648128510,0.1118353512138128280640, \ +0.875087611842900514603,0.9554424667730927467346,0.2715726937167346477509, \ +0.6644485183060169219971,0.0682194815017282962799,0.7714469349011778831482, \ +0.8863877407275140285492,0.5750523973256349563599,0.7297094804234802722931, \ +0.2650343524292111396790,0.2903900700621306896210,0.7815508693456649780273, \ +0.9579934873618185520172,0.8447621343657374382019,0.1320300563238561153412, \ +0.8078997563570737838745,0.9455244098789989948273,0.500539929606020450592, \ +0.3719757865183055400848,0.9143753759562969207764,0.2877321452833712100983, \ +0.3162028631195425987244,0.7707839584909379482269,0.0271399710327386856079, \ +0.1103429165668785572052,0.5582566531375050544739,0.0543051543645560741425, \ +0.9158540144562721252441,0.1088079833425581455231,0.5595446033403277397156, \ +0.6005734889768064022064,0.5880853887647390365601,0.0935917277820408344269, \ +0.1165864700451493263245,0.9919306333176791667938,0.3692654408514499664307, \ +0.1350691155530512332916,0.6193392043933272361755,0.2761342129670083522797, \ +0.6369419116526842117310,0.9017825317569077014923,0.6321295695379376411438, \ +0.2802005815319716930389,0.6780787408351898193359,0.2858079918660223484039, \ +0.1445086328312754631042,0.8207319690845906734467,0.6381527464836835861206, \ +0.9089807276614010334015,0.2107781330123543739319,0.1544780055992305278778, \ +0.0307971797883510589600,0.6037301481701433658600,0.1969387223944067955017, \ +0.5128816193901002407074,0.7767421547323465347290,0.4622741756029427051544, \ +0.3538100840523838996887,0.0643593105487525463104,0.2408019527792930603027, \ +0.54792295629158616066,0.9350729240104556083679,0.148065799381583929062, \ +0.2356592025607824325562,0.8622419466264545917511,0.5789828384295105934143, \ +0.1228930498473346233368,0.4611959345638751983643,0.6618243739940226078033, \ +0.1725060557946562767029,0.6754536679945886135101,0.3481215108186006546021, \ +0.7184230727143585681915,0.9166270541027188301086,0.9307986753992736339569, \ +0.7746474295854568481445,0.6161916949786245822906,0.8115780530497431755066, \ +0.2096196576021611690521,0.6249590050429105758667,0.6797852967865765094757, \ +0.2807403812184929847717,0.7756852875463664531708,0.6582339219748973846436, \ +0.6270702988840639591217,0.1519677182659506797791,0.4172622240148484706879, \ +0.6569576654583215713501,0.5401938227005302906036,0.7150812121108174324036, \ +0.2062703850679099559784,0.3232858255505561828613,0.2487624012865126132965, \ +0.0742864711210131645203,0.2789225964806973934174,0.8922032769769430160522, \ +0.7188800652511417865753,0.5142624313011765480042,0.9815986151807010173798, \ +0.9302302338182926177979,0.5417958036996424198151,0.0986720984801650047302, \ +0.2257035276852548122406,0.2884251791983842849731,0.1159104001708328723907, \ +0.2198451654985547065735,0.3952605235390365123749,0.6784346699714660644531, \ +0.6158926435746252536774,0.3183825043961405754089,0.6509880437515676021576, \ +0.8403400164097547531128,0.3426549141295254230499,0.4914325335994362831116, \ +0.9746113042347133159637,0.7710508368909358978271,0.5479381443001329898834, \ +0.2083894601091742515564,0.7971581942401826381683,0.98199548758566379547, \ +0.327256154734641313553,0.8527633966878056526184,0.5549895497970283031464, \ +0.2548583671450614929199,0.6749493652023375034332,0.3089723540470004081726, \ +0.0173138021491467952728,0.8641140963882207870483,0.2950978805311024188995, \ +0.3128061080351471900940,0.7289360011927783489227,0.7351085729897022247314, \ +0.2620439515449106693268,0.7843119418248534202576,0.4119912139140069484711, \ +0.5064369011670351028442,0.1242738110013306140900,0.8618522631004452705383, \ +0.6704122978262603282928,0.9653681963682174682617,0.5454088845290243625641, \ +0.8560840962454676628113,0.8408820494078099727631,0.8250672649592161178589, \ +0.0760563765652477741241,0.8426104495301842689514,0.3340197275392711162567, \ +0.3123631589114665985107,0.1502692312933504581451,0.1120535572990775108337, \ +0.3095519519411027431488,0.5348146054893732070923,0.9003654685802757740021, \ +0.1962999971583485603333,0.0292179766111075878143,0.0958223119378089904785, \ +0.8838568949140608310699,0.6896676821634173393250,0.7311593382619321346283, \ +0.926538145169615745544,0.3162371893413364887238,0.5837447280064225196838, \ +0.3695438797585666179657,0.8033211864531040191650,0.9033793644048273563385, \ +0.3346501952037215232849,0.0631741485558450222015,0.5194906610995531082153, \ +0.8672926020808517932892,0.3814667062833905220032,0.5968301701359450817108, \ +0.1801257431507110595703,0.2589884647168219089508,0.3345949379727244377136, \ +0.8190965964458882808685,0.5886622350662946701050} + + +#define InID {0.9229331132955849170685,0.3624883117154240608215,0.4197423788718879222870, \ +0.1054803654551506042480,0.9433643990196287631989,0.2429116321727633476257, \ +0.5323819159530103206635,0.6621514465659856796265,0.3330680062063038349152, \ +0.5687411213293671607971,0.8901842678897082805634,0.3511209674179553985596, \ +0.0435834513045847415924,0.3901510154828429222107,0.6022473922930657863617, \ +0.1305641103535890579224,0.7857504826970398426056,0.3076619254425168037415, \ +0.1008732873015105724335,0.4706113189458847045898,0.23320029163733124733, \ +0.7386203287169337272644,0.0550201400183141231537,0.9430699776858091354370, \ +0.3567060981877148151398,0.8223499367013573646545,0.7739888499490916728973, \ +0.6216929666697978973389,0.9831431121565401554108,0.1827249368652701377869, \ 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+0.5864494233392179012299,0.1381675656884908676147,0.6646229107864201068878, \ +0.8385901385918259620667,0.3738613124005496501923,0.9116719700396060943604, \ +0.9028714434243738651276,0.0236200755462050437927,0.9373822710476815700531, \ +0.8237647730857133865356,0.3227997911162674427032,0.1873689787462353706360, \ +0.4784183013252913951874,0.4933190941810607910156,0.5492720552720129489899, \ +0.1542267827317118644714,0.0531956567429006099701,0.0832678060978651046753, \ +0.5365209286101162433624,0.5457559684291481971741,0.8670723657123744487762, \ +0.7789970897138118743896,0.6427326560951769351959,0.7463898053392767906189, \ +0.1528341299854218959808,0.2960368636995553970337,0.772991370875388383865, \ +0.6953024687245488166809,0.9767245980910956859589,0.8857980892062187194824, \ +0.6843328052200376987457,0.7232010317966341972351,0.8159600137732923030853, \ +0.8081069495528936386108,0.0466573764570057392120,0.1527893329039216041565, \ +0.2514782394282519817352,0.7392859049141407012939,0.3532526479102671146393, \ +0.8816537177190184593201,0.6196721545420587062836,0.0845316220074892044067, \ +0.2746751648373901844025,0.6663206564262509346008,0.9668574291281402111053, \ +0.6633397787809371948242,0.5497416653670370578766,0.32623623590916395187, \ +0.1502246721647679805756,0.7367267441004514694214,0.0073796664364635944366, \ +0.5864175269380211830139,0.4290259550325572490692,0.8449981324374675750732, \ +0.8130874247290194034576,0.7775258263573050498962,0.3897457099519670009613, \ +0.4248142335563898086548,0.533753272611647844315,0.1121117742732167243958, \ +0.5490060034207999706268,0.6743023172020912170410,0.1145843290723860263824, \ +0.7557823462411761283875,0.4779561846517026424408,0.6349658127874135971069, \ +0.3618945856578648090363,0.4120397204533219337463,0.7918969090096652507782, \ +0.9591403640806674957275,0.0255023674108088016510,0.6395420199260115623474, \ +0.8488885364495217800140,0.3317467588931322097778,0.0744871688075363636017, \ +0.6205359296873211860657,0.5010939049534499645233,0.0150907337665557861328, \ +0.2600558646954596042633,0.5992111889645457267761,0.7426054789684712886810, \ +0.48545965366065502167,0.5592682962305843830109,0.7087269583716988563538, \ +0.5975068728439509868622,0.6302660666406154632568,0.5933722318150103092194, \ +0.4056600620970129966736,0.0919187492690980434418,0.4744881335645914077759, \ +0.6144977030344307422638,0.2306251050904393196106,0.6537790927104651927948, \ +0.9051569327712059020996,0.1544607155956327915192,0.1138164652511477470398, \ +0.7841078578494489192963,0.3626406397670507431030} + + +#define ResRD {1.2028771717397248597337,0.3687655164040291033700,0.8605230767316590645422, \ +1.1077942947750605284796,0.9767120864552386594326,1.4114463541323842843411, \ +1.4354141532486464072349,1.0111003946929904007135,0.6460807643012056455945, \ +0.942496758054768402069,1.0087545936051280914825,1.262586531900748765267, \ +1.4880612274536648698131,1.3679985766801496804845,1.3474574320651662162618, \ +0.9731575131888534624380,0.9335359675538464907518,1.2276224867355149950043, \ +0.3334867299422681341525,1.3431971414533188102780,1.5092129727018919194137, \ +1.2295472552241557551156,0.2976587959346745915212,1.4587265301529550587389, \ +0.5051795104327043706149,0.2996411780017103065887,1.2957695643431932364109, \ +0.8440406830828603990113,1.50252381975481164034,0.6896842944166139410811, \ +0.4813132194495245430588,0.9581281339053301371322,0.7528993595207621458698, \ +1.3025567781811444589835,1.2761618784887454047805,0.6736483673578720354769, \ +0.2908743485069323897463,0.5646758064966191925649,1.438379639941827381477, \ +0.6302168108311377858755,0.3315946371104716572376,1.0465739819013770706135, \ +1.1896596872617526408078,0.4168338903307298726197,1.2789383292392024760176, \ 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+1.2526503588977928593806,0.7540298966945283565266,0.7449695106054331494860, \ +1.3056567692434561944737,0.6692100940463061586883,1.1461580467200653821180, \ +1.0397487722058409431725,1.4462003916605226105929,0.5318856797809271563793, \ +0.8360320128831254526958,0.2639453129802519226743,0.9939194594428718554369, \ +0.5431515558502996166013,0.5718854142758250658218,0.6004750914590427646189, \ +1.494666433096084601218,0.5686839111974200111632,1.2302312925591223358168, \ +1.253116675176039196415,1.4199557361545380729240,1.4585069438499760341443, \ +1.2560745223234066614282,1.0065080046249368361799,0.4501876422711190706138, \ +1.37321326022231460229,1.541574191402776516924,1.474826766905839248167, \ +0.4867517858084012272180,0.8097662970595214115832,0.7507765257710836692695, \ +0.3856924750031833770691,1.249035839325627783580,0.9474631507713823230787, \ +1.1922782211545606134706,0.6379451906902231517194,0.4432108724859483706027, \ +1.2295623289060186866806,1.5075800815380702157853,1.0245415674248141701952, \ +0.5210587890871913874236,1.1794138612822491207766,0.9312516456662516262099, \ +1.3896820429875444968815,1.3088215387819075452569,1.2296209664609143441538, \ +0.6109619018903345022409,0.9413933583319856746030} + +#define ResID {0.3951648575239898320000,1.1998599191854182333117,1.1376348605752844012073, \ +1.465119377848908444051,0.3381668921842964636859,1.3254300655944222242510, \ +1.0093844168860410803745,0.8471101875532934810664,1.2312408252616013903946, \ +0.9658218036234816894492,0.4730468665045839404826,1.2120282989381994109834, \ +1.5271990657633036647667,1.1700007263913658750454,0.9244830082340818044884, \ +1.4398583874714105945714,0.6668878269832446692433,1.2580615360595837071145, \ +1.469751180044867489016,1.0808128388866473645891,1.3354289061467599086797, \ +0.7397748903744012505257,1.5157483892532124247765,0.3390532325241176758723, \ 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( fabs(sacoss(tIn1[i]) - tRes1[i]) / fabs(sacoss(tIn1[i])) ) < 1e-6); + assert ( ( fabs(sacoss(tIn2[i]) - tRes2[i]) / fabs(sacoss(tIn2[i])) ) < 3e-6); + } +} + + +void dacossTest(void) { + int i=0; + double tIn1[]=InRD; + double tRes1[]=ResRD; + double tIn2[]=InID; + double tRes2[]=ResID; + + for(i=0;i<200;i++){ + assert ( ( (fabs(dacoss(tIn1[i])) - tRes1[i]) / fabs(dacoss(tIn1[i])) ) < 3e-15); + assert ( ( (fabs(dacoss(tIn2[i])) - tRes2[i]) / fabs(dacoss(tIn2[i])) ) < 3e-15); + } +} + + +void sacosaTest(void){ + int i=0; + float tIn1[]=InRF; + float tRes1[]=ResRF; + float tIn2[]=InIF; + float tRes2[]=ResIF; + float out1[200]; + float out2[200]; + sacosa(tIn1,200,out1); + sacosa(tIn2,200,out2); + for(i=0;i<200;i++){ + assert( (fabs(out1[i]-tRes1[i])/fabs(out1[i])) <1e-6); + assert( (fabs(out2[i]-tRes2[i])/fabs(out2[i])) <3e-6); + } +} + +void dacosaTest(void){ + int i=0; + double tIn1[]=InRD; + double tRes1[]=ResRD; + double tIn2[]=InID; + double tRes2[]=ResID; + double out1[200]; + 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\ No newline at end of file diff --git a/2.3-1/src/c/elementaryFunctions/acos/zacosa.c b/2.3-1/src/c/elementaryFunctions/acos/zacosa.c new file mode 100644 index 00000000..812c1405 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/zacosa.c @@ -0,0 +1,20 @@ +/* + * 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 + * + */ + +#include "acos.h" + +void zacosa(doubleComplex* x, int size, doubleComplex* y) { + int i = 0; + for (i = 0; i < size; ++i) { + y[i] = zacoss(x[i]); + } +} diff --git a/2.3-1/src/c/elementaryFunctions/acos/zacoss.c b/2.3-1/src/c/elementaryFunctions/acos/zacoss.c new file mode 100644 index 00000000..de6f3fe9 --- /dev/null +++ b/2.3-1/src/c/elementaryFunctions/acos/zacoss.c @@ -0,0 +1,147 @@ +/*
+ * 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
+ *
+ */
+
+/*
+ * 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) {
+ 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);
+}
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