KOL merged with Libs

git-svn-id: http://svn.miranda-ng.org/main/trunk@1849 1316c22d-e87f-b044-9b9b-93d7a3e3ba9c

1 files changed, 278 insertions, 0 deletions

diff --git a/plugins/Libs/CplxMath.pas b/plugins/Libs/CplxMath.pas
new file mode 100644
index 0000000000..7cd180af9e
--- /dev/null
+++ b/plugins/Libs/CplxMath.pas
@@ -0,0 +1,278 @@
+unit CplxMath;

+{* This unit contains functins for working with complex numbers. To use with

+   KOL library and its kolmath.pas unit instead of standard math.pas, define

+   synmbol KOL in project options, or uncomment its definition below. }

+

+interface

+

+//{$DEFINE KOL}

+

+{$IFNDEF KOL}

+  {$IFDEF KOL_MCK}

+    {$DEFINE KOL}

+  {$ENDIF}

+{$ENDIF}

+

+uses {$IFDEF KOL} kolmath, kol {$ELSE} math, sysutils {$ENDIF};

+

+type

+  {$IFDEF CPLX_EXTENDED}

+    Double = Extended;

+  {$ENDIF}

+

+  Complex = record Re, Im: double end;

+  {* }

+

+  function CfromReIm( Re, Im: Double ): Complex;

+  {* Re + i * Im }

+

+  function Cadd( const X, Y: Complex ): Complex;

+  {* X + Y }

+

+  function Cneg( const X: Complex ): Complex;

+  {* -X }

+

+  function Csub( const X, Y: Complex ): Complex;

+  {* X - Y }

+

+  function Cmul( const X, Y: Complex ): Complex;

+  {* X * Y }

+

+  function CmulD( const X: Complex; D: Double ): Complex;

+  {* X * D }

+

+  function CmulI( const X: Complex ): Complex;

+  {* i * X }

+

+  function Cdiv( const X, Y: Complex ): Complex;

+  {* X / Y }

+

+  function Cmod( const X: Complex ): Double;

+  {* Q( X.Re^2 + X.Im^2 ) }

+

+  function Carg( const X: Complex ): Double;

+  {* arctg( X.Im / X.Re ) }

+

+  function CfromModArg( R, Arg: Double ): Complex;

+  {* R * ( cos Arg + i * sin Arg ) }

+

+  function Cpow( const X: Complex; Pow: Double ): Complex;

+  {* X ^ Pow }

+

+  function Cpower( const X, Pow: Complex ): Complex;

+  {* X ^ Pow }

+

+  function CIntPower( const X: Complex; Pow: Integer ): Complex;

+  {* X ^ Pow}

+

+  function Csqrt( const X: Complex ): Complex;

+  {* Q( X ) }

+

+  function Cexp( const X: Complex ): Complex;

+  {* exp( X ) }

+

+  function Cln( const X: Complex ): Complex;

+  {* ln( X ) }

+

+  function Ccos( const X: Complex ): Complex;

+  {* cos( X ) }

+

+  function Csin( const X: Complex ): Complex;

+  {* sin( X ) }

+

+  function C2Str( const X: Complex ): String;

+  {* }

+

+  function C2StrEx( const X: Complex ): String;

+  {* experimental }

+

+implementation

+

+  function CfromReIm( Re, Im: Double ): Complex;

+  begin

+    Result.Re := Re;

+    Result.Im := Im;

+  end;

+

+  function Cadd( const X, Y: Complex ): Complex;

+  begin

+    Result.Re := X.Re + Y.Re;

+    Result.Im := X.Im + Y.Im;

+  end;

+

+  function Cneg( const X: Complex ): Complex;

+  begin

+    Result.Re := -X.Re;

+    Result.Im := -X.Im;

+  end;

+

+  function Csub( const X, Y: Complex ): Complex;

+  begin

+    Result := Cadd( X, Cneg( Y ) );

+  end;

+

+  function Cmul( const X, Y: Complex ): Complex;

+  begin

+    Result.Re := X.Re * Y.Re - X.Im * Y.Im;

+    Result.Im := X.Re * Y.Im + X.Im * Y.Re;

+  end;

+

+  function CmulD( const X: Complex; D: Double ): Complex;

+  begin

+    Result.Re := X.Re * D;

+    Result.Im := X.Im * D;

+  end;

+

+  function CmulI( const X: Complex ): Complex;

+  begin

+    Result.Re := -X.Im;

+    Result.Im := X.Re;

+  end;

+

+  function Cdiv( const X, Y: Complex ): Complex;

+  var Z: Double;

+  begin

+    Z := 1.0 / ( Y.Re * Y.Re + Y.Im * Y.Im );

+    Result.Re := (X.Re * Y.Re + X.Im * Y.Im ) * Z;

+    Result.Im := (X.Im * Y.Re - X.Re * Y.Im ) * Z;

+  end;

+

+  function Cmod( const X: Complex ): Double;

+  begin

+    Result := sqrt( X.Re * X.Re + X.Im * X.Im );

+  end;

+

+  function Carg( const X: Complex ): Double;

+  begin

+    Result := ArcTan2( X.Im, X.Re );

+  end;

+

+  function CfromModArg( R, Arg: Double ): Complex;

+  begin

+    Result.Re := R * cos( Arg );

+    Result.Im := R * sin( Arg );

+  end;

+

+  function Cpow( const X: Complex; Pow: Double ): Complex;

+  var R, A: Double;

+  begin

+    R := power( Cmod( X ), Pow );

+    A := Pow * Carg( X );

+    Result := CfromModArg( R, A );

+  end;

+

+  function Cpower( const X, Pow: Complex ): Complex;

+  begin

+    Result := Cexp( Cmul( X, Cln( Pow ) ) );

+  end;

+

+  function CIntPower( const X: Complex; Pow: Integer ): Complex;

+  begin

+    if (Pow < 0) or (Pow > 100) then Result := Cpow( X, Pow )

+    else if Pow = 0 then

+    begin

+      Result.Re := 1;

+      Result.Im := 0;

+    end

+      else

+    begin

+      Result := X;

+      while Pow > 1 do

+      begin

+        Result := Cmul( Result, X );

+        dec( Pow );

+      end;

+    end;

+  end;

+

+  function Csqrt( const X: Complex ): Complex;

+  begin

+    Result := Cpow( X, 0.5 );

+  end;

+

+  function Cexp( const X: Complex ): Complex;

+  var Z: Double;

+  begin

+    Z := exp( X.Re );

+    Result.Re := Z * cos( X.Im );

+    Result.Im := Z * sin( X.Im );

+  end;

+

+  function Cln( const X: Complex ): Complex;

+  begin

+    Result := CfromModArg( ln( Cmod( X ) ), Carg( X ) );

+  end;

+

+  function Ccos( const X: Complex ): Complex;

+  begin

+    Result := CmulI( X );

+    Result := CmulD( Cadd( Cexp( Result ), Cexp( Cneg( Result ) ) ),

+                     0.5 );

+  end;

+

+  function Csin( const X: Complex ): Complex;

+  begin

+    Result := CmulI( X );

+    Result := CmulD( Csub( Cexp(Result), Cexp( Cneg(Result) ) ),

+                     0.5 );

+  end;

+

+  {$IFDEF KOL}

+  function Abs( X: Double ): Double;

+  begin

+    Result := EAbs( X );

+  end;

+  {$ENDIF}

+

+  {$IFNDEF KOL}

+  function Double2Str( D: Double ): String;

+  begin

+    Result := DoubleToStr( D );

+  end;

+  {$ENDIF}

+

+  function C2Str( const X: Complex ): String;

+  begin

+    if Abs( X.Im ) < 1e-307 then

+    begin

+      Result := Double2Str( X.Re );

+    end

+      else

+    begin

+      Result := '';

+      if Abs( X.Re ) > 1e-307 then

+      begin

+        Result := Double2Str( X.Re );

+        if X.Im > 0.0 then

+          Result := Result + ' + ';

+      end;

+      if X.Im < 0.0 then

+        Result := Result + '- i * ' + Double2Str( -X.Im )

+      else

+        Result := Result + 'i * ' + Double2Str( X.Im );

+    end;

+  end;

+

+  function C2StrEx( const X: Complex ): String;

+  begin

+    if Abs( X.Im ) < 1e-307 then

+    begin

+      Result := Double2StrEx( X.Re );

+    end

+      else

+    begin

+      Result := '';

+      if Abs( X.Re ) > 1e-307 then

+      begin

+        Result := Double2StrEx( X.Re );

+        if X.Im > 0.0 then

+          Result := Result + ' + ';

+      end;

+      if X.Im < 0.0 then

+        Result := Result + '- i * ' + Double2StrEx( -X.Im )

+      else

+        Result := Result + 'i * ' + Double2StrEx( X.Im );

+    end;

+  end;

+

+end.