jetzt vollständig auf double umgestellt und überprüfung der Arraylängen

implementiert

5 files changed, 141 insertions, 104 deletions

diff --git a/Physikunit.pas b/Physikunit.pas
index f95dc32..b4b1456 100644
--- a/Physikunit.pas
+++ b/Physikunit.pas
@@ -106,8 +106,9 @@ type
     _aX,_aP:            longint;
     _dX,_dP,iDX:        double;
     ffts:               array of array[0..1,boolean] of fftw_plan_double; // fft-Algorithmen
-    fftTmp:             Pcomplex_double;                         // Zwischenspeicher für ffts
+    fftTmp,lFftTmp:     Pcomplex_double;                         // Zwischenspeicher für ffts
     procedure initialisiereDichte(ort,tlc: longint; breite,n: double); inline;
+    procedure pruefeArrayEnden(fehler: string);
   public
     emFelder:  array[tEMFeldGroesze,boolean] of pDouble;         // EM-Felder und deren Zeitableitungen
                                                                    // dPhiDX und B[xyz] haben keine sinnvolle Ableitung hier!
@@ -585,8 +586,9 @@ begin
   setlength(impulsRaumGradient,length(teilchen));
   for i:=0 to length(impulsRaumGradient)-1 do
     for j:=0 to length(impulsRaumGradient[i])-1 do begin
-      fftw_getmem(impulsRaumGradient[i,j],aP*aX*sizeof(double));
+      fftw_getmem(impulsRaumGradient[i,j],(aP*aX+1)*sizeof(double));
       fillchar(impulsRaumGradient[i,j]^,aP*aX*sizeof(double),#0);
+      (impulsRaumGradient[i,j]+aP*aX)^:=pi;
     end;
   fillchar(iMGamma,sizeof(iMGamma),#0);
   setlength(iMGamma,length(teilchen));
@@ -639,8 +641,13 @@ begin
   lichters[true].grep('^rechts .*');
   lichters[true].subst('^rechts *','');
 
-  fftw_getmem(fftTmp,(aP+1)*(aX+1)*sizeof(complex_double));
-  fillchar(fftTmp^,(aP+1)*(aX+1)*sizeof(complex_double),#0);
+  i:=max((aP div 2 + 1)*aX,(aX div 2 + 1)*aP);
+  fftw_getmem(fftTmp,(i+1)*sizeof(complex_double));
+  fillchar(fftTmp^,(i+1)*sizeof(complex_double),#0);
+  lFftTmp:=fftTmp+i;
+
+  lFftTmp^.re:=pi;
+  lFftTmp^.im:=sqr(pi);
 
   fillchar(ffts,sizeof(ffts),#0);
   setlength(ffts,length(teilchen));
@@ -651,11 +658,14 @@ begin
       fftw_plan_many_dft_c2r(1,@_aX,aP,fftTmp,nil,aP,1,impulsRaumGradient[i,0],nil,aP,1,[fftw_measure]);
 
     ffts[i,1,false]:=  // Planung der Hintransformationen über p
-      fftw_plan_many_dft_r2c(1,@_aP,aX,impulsraum[i,false],nil,1,aP,fftTmp,nil,1,aP,[fftw_preserve_input,fftw_measure]);
+      fftw_plan_many_dft_r2c(1,@_aP,aX,impulsraum[i,false],nil,1,aP,fftTmp,nil,1,aP div 2 + 1,[fftw_preserve_input,fftw_measure]);
     ffts[i,1,true]:=  // Planung der Rücktransformationen über p
-      fftw_plan_many_dft_c2r(1,@_aP,aX,fftTmp,nil,1,aP,impulsRaumGradient[i,1],nil,1,aP,[fftw_measure]);
+      fftw_plan_many_dft_c2r(1,@_aP,aX,fftTmp,nil,1,aP div 2 + 1,impulsRaumGradient[i,1],nil,1,aP,[fftw_measure]);
   end;
-   (*
+
+  pruefeArrayEnden('FFT schreibt beim Planen über das Ende hinaus!');
+
+  (*
      fftw_plan_many_dft_r2c(int rank, const int *n, int howmany,
                                       double *in, const int *inembed,
                                       int istride, int idist,
@@ -729,6 +739,26 @@ begin
     (impulsraum[tlc,false]+i+ort*aP)^:=(impulsraum[tlc,false]+i+ort*aP)^ * ges;
 end;
 
+procedure tFelder.pruefeArrayEnden(fehler: string);
+var
+  i,j: longint;
+begin
+  if (abs(lFftTmp^.re-pi)>1e-10) or (abs(lFftTmp^.im-sqr(pi))>1e-10) then begin
+    gitter.prot.schreibe(fehler);
+    gitter.prot.schreibe(floattostr(lFftTmp^.re)+' vs. '+floattostr(pi)+' und '+floattostr(lFftTmp^.im)+' vs. '+floattostr(sqr(pi)));
+    gitter.prot.destroyall;
+    halt(1);
+  end;
+  for i:=0 to length(impulsRaumGradient)-1 do
+    for j:=0 to 1 do
+      if abs((impulsRaumGradient[i,j]+aP*aX)^-pi)>1e-10 then begin
+        gitter.prot.schreibe(fehler);
+        gitter.prot.schreibe(floattostr((impulsRaumGradient[i,j]+aP*aX)^)+' vs. '+floattostr(pi));
+        gitter.prot.destroyall;
+        halt(1);
+      end;
+end;
+
 procedure tFelder.berechneAbleitungen;
 var
   i,j,k:  longint;
@@ -829,26 +859,35 @@ begin
 
   // Gradienten der Phasenraumbesetzungsdichte berechnen
 
+  pruefeArrayEnden('Jemand hat das FFT-Array überschrieben!');
+
   for i:=0 to length(ffts)-1 do begin
-    fftw_execute(ffts[i,0,false]);
-    for j:=0 to aX-1 do
+    fftw_execute(ffts[i,0,false]);     // FFT in x
+    pruefeArrayEnden('Vorwärts-FFT ('+inttostr(i)+',0) schreibt beim Ausführen über das Ende hinaus!');
+
+    for j:=0 to aX div 2 do
       for k:=0 to aP-1 do begin  //    *i*k*2*pi;
-        tmp:=(fftTmp+j+k*aX)^.re;
-        (fftTmp+j+k*aX)^.re:=- 2*pi/dX/aX * j * (fftTmp+j+k*aX)^.im/aX;
-        (fftTmp+j+k*aX)^.im:=  2*pi/dX/aX * j * tmp/aX;
+        tmp:=(fftTmp+j+k*(aX div 2 + 1))^.re;
+        (fftTmp+j+k*(aX div 2 + 1))^.re:=- 2*pi/dX/aX * j * (fftTmp+j+k*(aX div 2 + 1))^.im/aX * byte(2*j<ax);
+        (fftTmp+j+k*(aX div 2 + 1))^.im:=  2*pi/dX/aX * j * tmp/aX                             * byte(2*j<ax);
       end;
 
     fftw_execute(ffts[i,0,true]);
-    fftw_execute(ffts[i,1,false]);
+    pruefeArrayEnden('Rückwärts-FFT ('+inttostr(i)+',0) schreibt beim Ausführen über das Ende hinaus!');
+
+    fftw_execute(ffts[i,1,false]);     // FFT in p
+    pruefeArrayEnden('Vorwärts-FFT ('+inttostr(i)+',1) schreibt beim Ausführen über das Ende hinaus!');
 
     for j:=0 to aX-1 do
-      for k:=0 to aP-1 do begin  //    *i*k*2*pi;
+      for k:=0 to aP div 2 do begin  //    *i*k*2*pi;
         tmp:=(fftTmp+j+k*aX)^.re;
-        (fftTmp+j+k*aX)^.re:=- 2*pi/dP/aP * k * (fftTmp+j+k*aX)^.im/aP;
-        (fftTmp+j+k*aX)^.im:=  2*pi/dP/aP * k * tmp/aP;
+        (fftTmp+j+k*aX)^.re:=- 2*pi/dP/aP * k * (fftTmp+j+k*aX)^.im/aP * byte(2*k < aP);
+        (fftTmp+j+k*aX)^.im:=  2*pi/dP/aP * k * tmp/aP                 * byte(2*k < aP);
       end;
 
     fftw_execute(ffts[i,1,true]);
+    pruefeArrayEnden('Rückwärts-FFT ('+inttostr(i)+',1) schreibt beim Ausführen über das Ende hinaus!');
+
   end;
 
   // Zeitableitung der Phasenraumbesetzungsdichte berechnen
diff --git a/Plasmapropagation.lps b/Plasmapropagation.lps
index d9cdf52..be47378 100644
--- a/Plasmapropagation.lps
+++ b/Plasmapropagation.lps
@@ -3,12 +3,12 @@
   <ProjectSession>
     <Version Value="9"/>
     <BuildModes Active="Default"/>
-    <Units Count="19">
+    <Units Count="20">
       <Unit0>
         <Filename Value="Plasmapropagation.lpr"/>
         <IsPartOfProject Value="True"/>
         <TopLine Value="19"/>
-        <CursorPos Y="46"/>
+        <CursorPos Y="48"/>
         <UsageCount Value="200"/>
         <Loaded Value="True"/>
       </Unit0>
@@ -17,9 +17,9 @@
         <IsPartOfProject Value="True"/>
         <IsVisibleTab Value="True"/>
         <EditorIndex Value="1"/>
-        <TopLine Value="618"/>
-        <CursorPos X="59" Y="643"/>
-        <FoldState Value=" T3lM0{F5 pjdmK0G51214]DWuB0f3]9BkH031 pp4pD0G2 T0!0Pc071F311)"/>
+        <TopLine Value="1039"/>
+        <CursorPos Y="1106"/>
+        <FoldState Value=" T3lN0{F5 pjdmK0G514 pm0s30U3]K2k30f2 T0!dPc071F311Z"/>
         <UsageCount Value="200"/>
         <Loaded Value="True"/>
       </Unit1>
@@ -28,14 +28,14 @@
         <IsPartOfProject Value="True"/>
         <EditorIndex Value="-1"/>
         <CursorPos X="20" Y="8"/>
-        <UsageCount Value="168"/>
+        <UsageCount Value="170"/>
       </Unit2>
       <Unit3>
         <Filename Value="input.plap"/>
         <IsPartOfProject Value="True"/>
         <EditorIndex Value="3"/>
         <CursorPos X="33" Y="23"/>
-        <UsageCount Value="167"/>
+        <UsageCount Value="169"/>
         <Loaded Value="True"/>
         <DefaultSyntaxHighlighter Value="None"/>
       </Unit3>
@@ -43,15 +43,15 @@
         <Filename Value="linearkombination.inc"/>
         <IsPartOfProject Value="True"/>
         <EditorIndex Value="-1"/>
-        <CursorPos X="54" Y="16"/>
-        <UsageCount Value="115"/>
+        <TopLine Value="76"/>
+        <UsageCount Value="117"/>
       </Unit4>
       <Unit5>
         <Filename Value="linearkombinationen.inc"/>
         <IsPartOfProject Value="True"/>
         <EditorIndex Value="-1"/>
-        <CursorPos X="29" Y="16"/>
-        <UsageCount Value="78"/>
+        <TopLine Value="25"/>
+        <UsageCount Value="80"/>
       </Unit5>
       <Unit6>
         <Filename Value="input.epost"/>
@@ -68,7 +68,7 @@
         <TopLine Value="19"/>
         <CursorPos X="66" Y="48"/>
         <FoldState Value=" T3iA05B pj0jV034 piaj60U6 plLmM041p"/>
-        <UsageCount Value="24"/>
+        <UsageCount Value="25"/>
         <Loaded Value="True"/>
       </Unit7>
       <Unit8>
@@ -114,8 +114,8 @@
       <Unit14>
         <Filename Value="rk3_8.inc"/>
         <EditorIndex Value="-1"/>
-        <CursorPos X="41" Y="6"/>
-        <UsageCount Value="9"/>
+        <CursorPos X="71" Y="11"/>
+        <UsageCount Value="10"/>
       </Unit14>
       <Unit15>
         <Filename Value="/usr/lib/fpc/src/rtl/objpas/math.pp"/>
@@ -145,137 +145,135 @@
         <CursorPos X="60" Y="95"/>
         <UsageCount Value="10"/>
       </Unit18>
+      <Unit19>
+        <Filename Value="/usr/lib/fpc/src/rtl/inc/systemh.inc"/>
+        <EditorIndex Value="-1"/>
+        <TopLine Value="295"/>
+        <CursorPos X="3" Y="315"/>
+        <UsageCount Value="10"/>
+      </Unit19>
     </Units>
     <JumpHistory Count="30" HistoryIndex="29">
       <Position1>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="595" TopLine="576"/>
+        <Caret Line="1534" TopLine="1518"/>
       </Position1>
       <Position2>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="597" TopLine="576"/>
+        <Caret Line="1070" TopLine="1050"/>
       </Position2>
       <Position3>
         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="1074" TopLine="1050"/>
       </Position3>
       <Position4>
         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="1077" TopLine="1062"/>
       </Position4>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="1079" TopLine="1062"/>
       </Position6>
       <Position7>
-        <Filename Value="Physikunit.pas"/>
-        <Caret Line="609" TopLine="585"/>
+        <Filename Value="Plasmapropagation.lpr"/>
+        <Caret Line="48" TopLine="19"/>
       </Position7>
       <Position8>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="615" TopLine="600"/>
+        <Caret Line="1074" TopLine="1062"/>
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         <Filename Value="Physikunit.pas"/>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="1079" TopLine="91"/>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="109" Column="11" TopLine="85"/>
       </Position13>
       <Position14>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="108" Column="73" TopLine="88"/>
+        <Caret Line="645" Column="21" TopLine="617"/>
       </Position14>
       <Position15>
         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="651" Column="75" TopLine="619"/>
       </Position15>
       <Position16>
         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="653" Column="46" TopLine="621"/>
       </Position16>
       <Position17>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="650" Column="57" TopLine="630"/>
+        <Caret Line="656" Column="75" TopLine="624"/>
       </Position17>
       <Position18>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="112" Column="49" TopLine="83"/>
+        <Caret Line="660" Column="6" TopLine="629"/>
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         <Filename Value="Physikunit.pas"/>
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       </Position19>
       <Position20>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="88" Column="62" TopLine="83"/>
+        <Caret Line="109" Column="95" TopLine="88"/>
       </Position20>
       <Position21>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="936" Column="69" TopLine="486"/>
+        <Caret Line="650" Column="16" TopLine="618"/>
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         <Filename Value="Physikunit.pas"/>
+        <Caret Line="663" Column="22" TopLine="639"/>
       </Position22>
       <Position23>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="108" Column="9" TopLine="93"/>
+        <Caret Line="719" Column="26" TopLine="687"/>
       </Position23>
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         <Filename Value="Physikunit.pas"/>
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       </Position25>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="665" Column="69" TopLine="487"/>
       </Position26>
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         <Filename Value="Physikunit.pas"/>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="112" TopLine="99"/>
       </Position28>
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         <Filename Value="Physikunit.pas"/>
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+        <Caret Line="761" Column="42" TopLine="682"/>
       </Position29>
       <Position30>
         <Filename Value="Physikunit.pas"/>
-        <Caret Line="834" Column="43" TopLine="819"/>
+        <Caret Line="747" Column="36" TopLine="689"/>
       </Position30>
     </JumpHistory>
   </ProjectSession>
-  <Debugging>
-    <BreakPoints Count="1">
-      <Item1>
-        <Kind Value="bpkSource"/>
-        <WatchScope Value="wpsLocal"/>
-        <WatchKind Value="wpkWrite"/>
-        <Source Value="Plasmapropagation.lpr"/>
-        <Line Value="46"/>
-      </Item1>
-    </BreakPoints>
-  </Debugging>
 </CONFIG>
diff --git a/genLikoInc b/genLikoInc
index 6db0770..2c0120f 100755
--- a/genLikoInc
+++ b/genLikoInc
@@ -21,7 +21,7 @@ do
   do
     echo -ne ",fak${j}" >> ${file}
   done
-  echo ": extended); overload; inline;" >> ${file}
+  echo ": double); overload; inline;" >> ${file}
 done
 
 echo "{\$ENDIF}" >> ${file}
@@ -60,7 +60,7 @@ for ((i=3; i<=maximum; i++))
 do
   echo -ne "\n{\$IFDEF lkA${i}},fak${i}{\$ENDIF}" >> ${file}
 done
-echo ": extended);" >> ${file}
+echo ": double);" >> ${file}
 echo "var" >> ${file}
 echo "  i,j: longint;" >> ${file}
 echo "  emF: tEMFeldGroesze;" >> ${file}
diff --git a/linearkombination.inc b/linearkombination.inc
index 8fca2c0..5727f04 100644
--- a/linearkombination.inc
+++ b/linearkombination.inc
@@ -62,7 +62,7 @@ fak2
 {$IFDEF lkA29},fak29{$ENDIF}
 {$IFDEF lkA30},fak30{$ENDIF}
 {$IFDEF lkA31},fak31{$ENDIF}
-{$IFDEF lkA32},fak32{$ENDIF}: extended);
+{$IFDEF lkA32},fak32{$ENDIF}: double);
 var
   i,j: longint;
   emF: tEMFeldGroesze;
diff --git a/linearkombinationen.inc b/linearkombinationen.inc
index 5862886..1d11858 100644
--- a/linearkombinationen.inc
+++ b/linearkombinationen.inc
@@ -3,37 +3,37 @@
 
 {$IFDEF LiKoInterface}
 // Werte werden auf (in1 + \sum_i faki * ini') gesetzt
-procedure liKo(in1,in2: tFelder; fak2: extended); overload; inline;
-procedure liKo(in1,in2,in3: tFelder; fak2,fak3: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4: tFelder; fak2,fak3,fak4: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5: tFelder; fak2,fak3,fak4,fak5: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6: tFelder; fak2,fak3,fak4,fak5,fak6: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7: tFelder; fak2,fak3,fak4,fak5,fak6,fak7: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30,in31: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30,fak31: extended); overload; inline;
-procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30,in31,in32: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30,fak31,fak32: extended); overload; inline;
+procedure liKo(in1,in2: tFelder; fak2: double); overload; inline;
+procedure liKo(in1,in2,in3: tFelder; fak2,fak3: double); overload; inline;
+procedure liKo(in1,in2,in3,in4: tFelder; fak2,fak3,fak4: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5: tFelder; fak2,fak3,fak4,fak5: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6: tFelder; fak2,fak3,fak4,fak5,fak6: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7: tFelder; fak2,fak3,fak4,fak5,fak6,fak7: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30,in31: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30,fak31: double); overload; inline;
+procedure liKo(in1,in2,in3,in4,in5,in6,in7,in8,in9,in10,in11,in12,in13,in14,in15,in16,in17,in18,in19,in20,in21,in22,in23,in24,in25,in26,in27,in28,in29,in30,in31,in32: tFelder; fak2,fak3,fak4,fak5,fak6,fak7,fak8,fak9,fak10,fak11,fak12,fak13,fak14,fak15,fak16,fak17,fak18,fak19,fak20,fak21,fak22,fak23,fak24,fak25,fak26,fak27,fak28,fak29,fak30,fak31,fak32: double); overload; inline;
 {$ENDIF}
 
 // implementation **************************************************************