Numeric Programs

				Procedure FOUR1(var DATA:array of real; NN, ISIGN:integer);
				var
				    N,J,JJ,I,M,II,MM,ISTEP,MMAX:integer;
				    THETA,WR,WI,WPR,SUM,WTEMP,Y1,Y2,TEMPR,TEMPI,WPI:real;
				begin
				    N:=2 * NN;
				    J:=1;
				    For II:=1 To NN do
				    begin
				        I:= II * 2 - 1;
				        If J > I Then
				        begin
				            TEMPR:=DATA[J];
				            TEMPI:=DATA[J + 1];
				            DATA[J]:=DATA[I];
				            DATA[J + 1]:=DATA[I + 1];
				            DATA[I]:=TEMPR;
				            DATA[I + 1]:=TEMPI;
				        end; 
				        M:=N div 2;
				        While (M >= 2) And (J > M) do
				        begin
				            J:=J - M;
				            M:=M div 2;
				        end;
				        J:=J + M;
				    end; 
				    MMAX:=2;
				    While N > MMAX do
				    begin
				        ISTEP:=2 * MMAX;
				        THETA:=6.28318530717959 / (ISIGN * MMAX);
				        WPR:=-2 * Sqr(Sin(0.5 * THETA));
				        WPI:=Sin(THETA);
				        WR:=1;
				        WI:=0;
				        For II:=1 To (MMAX div 2) do
				        begin
				            M:= II * 2 - 1;
				            For JJ:=0 To ((N-M) div ISTEP) do
				            begin
				                I:= M + JJ*ISTEP ;
				                J:=I + MMAX;
				                TEMPR:=WR * DATA[J] - WI * DATA[J + 1];
				                TEMPI:=WR * DATA[J + 1] + WI * DATA[J];
				                DATA[J]:=DATA[I] - TEMPR;
				                DATA[J + 1]:=DATA[I + 1] - TEMPI;
				                DATA[I]:=DATA[I] + TEMPR;
				                DATA[I + 1]:=DATA[I + 1] + TEMPI;
				            end; 
				            WTEMP:=WR;
				            WR:=WR * WPR - WI * WPI + WR;
				            WI:=WI * WPR + WTEMP * WPI + WI;
				        end; 
				        MMAX:=ISTEP;
				    end;
				end;