C     SUBROUTINE CFFTF(N,C,WSAVE)                                               
C                                                                               
C     SUBROUTINE CFFTF COMPUTES THE FORWARD COMPLEX DISCRETE FOURIER            
C     TRANSFORM (THE FOURIER ANALYSIS). EQUIVALENTLY , CFFTF COMPUTES           
C     THE FOURIER COEFFICIENTS OF A COMPLEX PERIODIC SEQUENCE.                  
C     THE TRANSFORM IS DEFINED BELOW AT OUTPUT PARAMETER C.                     
C                                                                               
C     THE TRANSFORM IS NOT NORMALIZED. TO OBTAIN A NORMALIZED TRANSFORM         
C     THE OUTPUT MUST BE DIVIDED BY N. OTHERWISE A CALL OF CFFTF                
C     FOLLOWED BY A CALL OF CFFTB WILL MULTIPLY THE SEQUENCE BY N.              
C                                                                               
C     THE ARRAY WSAVE WHICH IS USED BY SUBROUTINE CFFTF MUST BE                 
C     INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE).                         
C                                                                               
C     INPUT PARAMETERS                                                          
C                                                                               
C                                                                               
C     N      THE LENGTH OF THE COMPLEX SEQUENCE C. THE METHOD IS                
C            MORE EFFICIENT WHEN N IS THE PRODUCT OF SMALL PRIMES. N            
C                                                                               
C     C      A COMPLEX ARRAY OF LENGTH N WHICH CONTAINS THE SEQUENCE            
C                                                                               
C     WSAVE   A REAL WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 4N+15        
C             IN THE PROGRAM THAT CALLS CFFTF. THE WSAVE ARRAY MUST BE          
C             INITIALIZED BY CALLING SUBROUTINE CFFTI(N,WSAVE) AND A            
C             DIFFERENT WSAVE ARRAY MUST BE USED FOR EACH DIFFERENT             
C             VALUE OF N. THIS INITIALIZATION DOES NOT HAVE TO BE               
C             REPEATED SO LONG AS N REMAINS UNCHANGED THUS SUBSEQUENT           
C             TRANSFORMS CAN BE OBTAINED FASTER THAN THE FIRST.                 
C             THE SAME WSAVE ARRAY CAN BE USED BY CFFTF AND CFFTB.              
C                                                                               
C     OUTPUT PARAMETERS                                                         
C                                                                               
C     C      FOR J=1,...,N                                                      
C                                                                               
C                C(J)=THE SUM FROM K=1,...,N OF                                 
C                                                                               
C                      C(K)*EXP(-I*(J-1)*(K-1)*2*PI/N)                          
C                                                                               
C                            WHERE I=SQRT(-1)                                   
C                                                                               
C     WSAVE   CONTAINS INITIALIZATION CALCULATIONS WHICH MUST NOT BE            
C             DESTROYED BETWEEN CALLS OF SUBROUTINE CFFTF OR CFFTB              
C                                                                               
      SUBROUTINE CFFTF (N,C,WSAVE)                                              
      DIMENSION       C(*)       ,WSAVE(*)                                      
C                                                                               
      IF (N .EQ. 1) RETURN                                                      
      IW1 = N+N+1                                                               
      IW2 = IW1+N+N                                                             
      CALL CFFTF1 (N,C,WSAVE,WSAVE(IW1),WSAVE(IW2))                             
      RETURN                                                                    
      END