SUBROUTINE REALFT(DATA,N,ISIGN)
      REAL*8 WR,WI,WPR,WPI,WTEMP,THETA
      DIMENSION DATA(*)
      THETA=6.28318530717959D0/2.0D0/DBLE(N)
      C1=0.5
      IF (ISIGN.EQ.1) THEN
        C2=-0.5
        CALL FOUR1(DATA,N,+1)
      ELSE
        C2=0.5
        THETA=-THETA
      ENDIF
      WPR=-2.0D0*DSIN(0.5D0*THETA)**2
      WPI=DSIN(THETA)
      WR=1.0D0+WPR
      WI=WPI
      N2P3=2*N+3
      DO 11 I=2,N/2+1
        I1=2*I-1
        I2=I1+1
        I3=N2P3-I2
        I4=I3+1
        WRS=SNGL(WR)
        WIS=SNGL(WI)
        H1R=C1*(DATA(I1)+DATA(I3))
        H1I=C1*(DATA(I2)-DATA(I4))
        H2R=-C2*(DATA(I2)+DATA(I4))
        H2I=C2*(DATA(I1)-DATA(I3))
        DATA(I1)=H1R+WRS*H2R-WIS*H2I
        DATA(I2)=H1I+WRS*H2I+WIS*H2R
        DATA(I3)=H1R-WRS*H2R+WIS*H2I
        DATA(I4)=-H1I+WRS*H2I+WIS*H2R
        WTEMP=WR
        WR=WR*WPR-WI*WPI+WR
        WI=WI*WPR+WTEMP*WPI+WI
11    CONTINUE
      IF (ISIGN.EQ.1) THEN
        H1R=DATA(1)
        DATA(1)=H1R+DATA(2)
        DATA(2)=H1R-DATA(2)
      ELSE
        H1R=DATA(1)
        DATA(1)=C1*(H1R+DATA(2))
        DATA(2)=C1*(H1R-DATA(2))
        CALL FOUR1(DATA,N,-1)
      ENDIF
      RETURN
      END