complex_hss.pas

编译类_Hss VC版_源代码支持表达式的编译执行,速度超快,支持实数和复数,并附带一个复数函数库你还可以同时找到VB和VC版和Delphi版

    tmp:= 1/(sqr(Z1.x) + sqr(Z1.y) + SmallLimit) ;
    result.x:= Z1.x*tmp;
    result.y:=-Z1.y*tmp;
End;

Procedure C_RevV(var Z1: TComplex); {Z1:=1/Z1}
var tmp: CmxFloat;
Begin
    tmp  := 1/(sqr(Z1.x) + sqr(Z1.y) + SmallLimit);
    Z1.x := Z1.x*tmp;
    Z1.y :=-Z1.y*tmp;
End;

Function  C_Chs           (const Z1: TComplex): TComplex;                                 {Z:=-Z1}       {求负}
begin
    result.x:=-Z1.x;
    result.y:=-Z1.y
end;

Procedure C_ChsV          (var Z1: TComplex);                                             {Z1:=-Z1}       {求负}
begin
    Z1.x:=-Z1.x;
    Z1.y:=-Z1.y;
end;

Function  C_Rev2 (const Z1: TComplex;const Z2: TComplex): TComplex; {Z:=1/(Z1-Z2)}
var a,b,tmp: CmxFloat;
Begin
    a:=Z1.x-Z2.x;
    b:=Z2.y-Z1.y;
    tmp:= 1/(sqr(a) + sqr(b) + SmallLimit) ;
    result.x:= a*tmp;
    result.y:= b*tmp;
End;

Procedure C_Rev2V(var Z1: TComplex; const Z2: TComplex); {Z1:=1/(Z1-Z2)}
var a,b,tmp: CmxFloat;
Begin
    a:=Z1.x-Z2.x;
    b:=Z2.y-Z1.y;
    tmp:= 1/(sqr(a) + sqr(b) + SmallLimit) ;
    Z1.x := a*tmp;
    Z1.y := b*tmp;
End;

function  C_Sgn (const Z1: TComplex):TComplex; {Z:=Sgn(Z1)}
begin
    if Z1.x>0 then
        result.x:=1
    else if Z1.x<0 then
        result.x:=-1
    else
        result.x:=0;

    if Z1.y>0 then
        result.y:=1
    else if Z1.y<0 then
        result.y:=-1
    else
        result.y:=0;
end;

Procedure  C_SgnV (var Z1: TComplex); {Z1:=Sgn(Z1)}
begin
    if Z1.x>0 then
        Z1.x:=1
    else if Z1.x<0 then
        Z1.x:=-1
    else
        Z1.x:=0;
        
    if Z1.y>0 then
        Z1.y:=1
    else if Z1.y<0 then
        Z1.y:=-1
    else
        Z1.y:=0;
end;

Procedure C_Xchg (var Z1: TComplex;var Z2: TComplex); {交换值Z1<=>Z2)}
var tmp: CmxFloat;
begin
    tmp:=Z1.x;
    Z1.x:=Z2.x;
    Z2.x:=tmp;

    tmp:=Z1.y;
    Z1.y:=Z2.y;
    Z2.y:=tmp;
end;

Procedure C_Xchg  (var Z1: TComplex);
var
  tmp : CmxFloat;
begin
  tmp:=Z1.x;
  Z1.x:=Z1.y;
  Z1.y:=tmp;
end;

function  C_Max           (const Z1:TComplex;const Z2:TComplex):TComplex; overload;       {由绝对值决定}
begin
  if sqr(Z1.x)+sqr(Z1.y)>sqr(Z2.x)+sqr(Z2.y) then
    result:=Z1
  else
    result:=Z2;
end;

function  C_Min           (const Z1:TComplex;const Z2:TComplex):TComplex; overload;       {由绝对值决定}
begin
  if sqr(Z1.x)+sqr(Z1.y)<sqr(Z2.x)+sqr(Z2.y) then
    result:=Z1
  else
    result:=Z2;
end;

function  C_MaxX          (const Z1:TComplex;const Z2:TComplex):TComplex; overload;       {由实部值决定}
begin
  if Z1.x>Z2.x then
    result:=Z1
  else
    result:=Z2;
end;

function  C_MinX          (const Z1:TComplex;const Z2:TComplex):TComplex; overload;       {由实部值决定}
begin
  if Z1.x<Z2.x then
    result:=Z1
  else
    result:=Z2;
end;

//==============================================================================
//{复数函数_次方}

Function  C_Sqr (const Z1: TComplex): TComplex; {Z:=Z1*Z1}
Begin
    result.x:=(Sqr(Z1.x)-Sqr(Z1.y));
    result.y:= (Z1.x*Z1.y) * 2;
End;

Procedure C_SqrV(var Z1: TComplex); {Z1:=Z1*Z1}
var tmp: CmxFloat;
Begin
    tmp :=(Sqr(Z1.x)-Sqr(Z1.y));
    Z1.y:= Z1.x*Z1.y * 2;
    Z1.x:=tmp;
End;

Function  C_Sqr3 (const Z1: TComplex): TComplex; {Z:=Z1^3}
Begin
    result.x:=Z1.x*(sqr(Z1.x) - 3*sqr(Z1.y));
    result.y:=Z1.y*(3*sqr(Z1.x) - sqr(Z1.y));
End;

Procedure C_Sqr3V(var Z1: TComplex); {Z1:=Z1^3}
var tmp: CmxFloat;
Begin
    tmp :=Z1.x*(sqr(Z1.x) - 3*sqr(Z1.y));
    Z1.y:=Z1.y*(3*sqr(Z1.x) - sqr(Z1.y));
    Z1.x:=tmp;
End;

Function  C_Sqr4 (const Z1: TComplex): TComplex; {Z:=Z1^4}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
Begin
    tmp1:=(Sqr(Z1.x)-Sqr(Z1.y));
    tmp2:= Z1.x*Z1.y * 2;
    result.x:=(sqr(tmp1)-Sqr(tmp2));
    result.y:= tmp1*tmp2 * 2;
End;

Procedure C_Sqr4V(var Z1: TComplex); {Z1:=Z1^4}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
Begin
    tmp1:=(Sqr(Z1.x)-Sqr(Z1.y));
    tmp2:= Z1.x*Z1.y * 2;
    Z1.x:=(sqr(tmp1)-sqr(tmp2));
    Z1.y:= tmp1*tmp2 * 2;
End;

Function  C_Power (const Z1: TComplex;const Z2: TComplex;const K:integer=0): TComplex; {Z:=Z1^Z2}
var tmph1x: CmxFloat;
    tmph1y: CmxFloat;
    tmph2x: CmxFloat;
    tmph2y: CmxFloat;
    tmpf  : CmxFloat;
    s,c   : CmxFloat;
Begin
    tmph1x:=0.5*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit);    //2003.3.29  Error!!!  sqr(sqr(Z1.y))
    tmph1y:=ArcTan2(Z1.y, Z1.x)+(2*PI)*K;

    tmph2x:=tmph1x*Z2.x-tmph1y*Z2.y;
    tmph2y:=tmph1y*Z2.x+tmph1x*Z2.y;

    tmpf     :=Exp(tmph2x);

    sincos(tmph2y,s,c);
    result.x :=tmpf*c;
    result.y :=tmpf*s;
End;

Procedure C_PowerV(var Z1: TComplex;const Z2: TComplex;const K:integer=0); {Z1:=Z1^Z2}
var tmph1x: CmxFloat;
    tmph1y: CmxFloat;
    tmph2x: CmxFloat;
    tmph2y: CmxFloat;
    tmpf  : CmxFloat;
    s,c   : CmxFloat;
Begin
    tmph1x:=0.5*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit);
    tmph1y:=ArcTan2(Z1.y, Z1.x)+(2*PI)*K;

    tmph2x:=tmph1x*Z2.x-tmph1y*Z2.y;
    tmph2y:=tmph1y*Z2.x+tmph1x*Z2.y;

    tmpf :=Exp(tmph2x);
    sincos(tmph2y,s,c);
    Z1.x :=tmpf*c;
    Z1.y :=tmpf*s;
End;

Function  C_Power (const Z1:TComplex;const x: CmxFloat;const K:integer=0): TComplex; {Z:=Z1^x}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmpf: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp1:=0.5*x*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit);
    tmp2:=x*(ArcTan2(Z1.y,Z1.x)+(2*PI)*K);
    tmpf:=Exp(tmp1);
    sincos(tmp2,s,c);
    result.x:=tmpf*C;
    result.y:=tmpf*S;
End;

Procedure C_PowerV(var Z1: TComplex;const x: CmxFloat;const K:integer=0); {Z1:=Z1^x}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmpf: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp1:=0.5*x*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit);
    tmp2:=x*(ArcTan2(Z1.y,Z1.x)+(2*PI)*K);
    tmpf:=Exp(tmp1);
    sincos(tmp2,s,c);
    Z1.x:=tmpf*C;
    Z1.y:=tmpf*S;
End;

//------------------------------------------------------------------------------

Function  C_Sqrt (const Z1: TComplex;const K:integer=0): TComplex; {Z:=Sqrt(Z1)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    c,s : CmxFloat;
Begin
    With Z1 do
    begin
        tmp1:=Sqrt(Sqrt(sqr(X)+sqr(Y)));
        tmp2:=0.5*(ArcTan2(Y,X)+(2*PI)*K);
        sincos(tmp2,s,c);
        result.x:=tmp1*c;
        result.y:=tmp1*s;
    end;
End;

Procedure C_SqrtV(var Z1: TComplex;const K:integer=0); {Z1:=Sqrt(Z1)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    c,s : CmxFloat;
Begin
    With Z1 do
    begin
        tmp1:=Sqrt(Sqrt(sqr(X)+sqr(Y)));
        tmp2:=0.5*(ArcTan2(Y,X)+(2*PI)*K);
        sincos(tmp2,s,c);
        X:=tmp1*c;
        Y:=tmp1*s;
    end;
End;

Procedure C_Sqrt(const Z1:TComplex;var Z:array of TComplex);{Z(i):=Sqrt(Z1)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    c,s : CmxFloat;
Begin
    With Z1 do
    begin
        tmp1:=Sqrt(Sqrt(sqr(X)+sqr(Y)));
        tmp2:=0.5*(ArcTan2(Y,X));
        sincos(tmp2,s,c);
        Z[0].x:=tmp1*c;
        z[0].y:=tmp1*s;
        tmp2:=tmp2+PI;
        sincos(tmp2,s,c);
        Z[1].x:=tmp1*c;
        z[1].y:=tmp1*s;
    end;
End;

Function  C_SqrtN (const Z1: TComplex;const N:CmxFloat;const K:integer=0): TComplex; {Z:=Z1^(1/N)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmpf: CmxFloat;
    c,s : CmxFloat;
Begin
    tmpf:=N;
    if tmpf=0 then tmpf:=SmallLimit;
    tmpf:=1.0/tmpf;
    tmp1:=0.5*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit)*tmpf;
    tmp2:=(ArcTan2(Z1.y,Z1.x)+(2*PI)*K)*tmpf;
    tmpf:=Exp(tmp1);
    sincos(tmp2,s,c);
    result.x:=tmpf*C;
    result.y:=tmpf*S;
end;

Procedure C_SqrtNV(var Z1: TComplex;const N:CmxFloat;const K:integer=0); {Z1:=Sqrt(Z1)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmpf: CmxFloat;
    tmpN: CmxFloat;
    c,s : CmxFloat;
Begin
    tmpN:=N;
    if tmpN=0 then tmpN:=SmallLimit;
    tmpN:=1/tmpN;
    tmp1:=0.5*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit)*tmpN;
    tmp2:=(ArcTan2(Z1.y,Z1.x)+(2*PI)*K)*tmpN;
    tmpf:=Exp(tmp1);
    sincos(tmp2,s,c);
    Z1.x:=tmpf*C;
    Z1.y:=tmpf*S;
end;

Procedure C_SqrtN (const Z1:TComplex;const N:integer;var Z:array of TComplex);overload;{Z(i):=Z1^(1/N)}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmpf: CmxFloat; 
    tmpN: CmxFloat;
    tmpd: CmxFloat;
    i   : integer;
    c,s : CmxFloat;
Begin
    tmpN:=N;
    if tmpN=0 then tmpN:=SmallLimit;
    tmpN:=1.0/tmpN;
    tmp1:=0.5*Ln(sqr(Z1.x)+sqr(Z1.y) + SmallLimit)*tmpN;
    tmp2:=ArcTan2(Z1.y,Z1.x)*tmpN;
    tmpd:=2*PI*tmpN;
    tmpf:=Exp(tmp1);
    for i:=0 to N-1 do
    begin
        tmp2:=tmp2+i*tmpd;
        sincos(tmp2,s,c);
        Z[i].x:=tmpf*C;
        Z[i].y:=tmpf*S;
    end;
end;

Function  C_Exp  (const Z1: TComplex): TComplex; {Z:=Exp(Z1)}
var tmp: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp :=Exp(Z1.x);
    sincos(Z1.y,s,c);
    result.x:=tmp*C;
    result.y:=tmp*S;
End;

Procedure C_ExpV (var Z1: TComplex); {Z1:=Exp(Z1)}
var tmp: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp :=Exp(Z1.x);
    sincos(Z1.y,s,c);
    Z1.x:=tmp*C;
    Z1.y:=tmp*S;
End;

Function  C_Power (const xBase: CmxFloat;const Z1: TComplex): TComplex;{Z:=x^Z1}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmp3: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp1:=Ln(xBase);
    tmp2:=Exp(Z1.x*tmp1);
    tmp3:=Z1.y*tmp1;
    sincos(tmp3,s,c);
    result.x:=tmp2*C;
    result.y:=tmp2*S;
End;

Procedure C_PowerV(const xBase: CmxFloat;var Z1: TComplex);{Z1:=x^Z1}
var tmp1: CmxFloat;
    tmp2: CmxFloat;
    tmp3: CmxFloat;
    c,s : CmxFloat;
Begin
    tmp1:=Ln(xBase);
    tmp2:=Exp(Z1.x*tmp1);
    tmp3:=Z1.y*tmp1;
    sincos(tmp3,s,c);
    Z1.x:=tmp2*C;
    Z1.y:=tmp2*S;
End;