C     SUBROUTINE COSQF(N,X,WSAVE)                                               
C                                                                               
C     SUBROUTINE COSQF COMPUTES THE FAST FOURIER TRANSFORM OF QUARTER           
C     WAVE DATA. THAT IS , COSQF COMPUTES THE COEFFICIENTS IN A COSINE          
C     SERIES REPRESENTATION WITH ONLY ODD WAVE NUMBERS. THE TRANSFORM           
C     IS DEFINED BELOW AT OUTPUT PARAMETER X                                    
C                                                                               
C     COSQF IS THE UNNORMALIZED INVERSE OF COSQB SINCE A CALL OF COSQF          
C     FOLLOWED BY A CALL OF COSQB WILL MULTIPLY THE INPUT SEQUENCE X            
C     BY 4*N.                                                                   
C                                                                               
C     THE ARRAY WSAVE WHICH IS USED BY SUBROUTINE COSQF MUST BE                 
C     INITIALIZED BY CALLING SUBROUTINE COSQI(N,WSAVE).                         
C                                                                               
C                                                                               
C     INPUT PARAMETERS                                                          
C                                                                               
C     N       THE LENGTH OF THE ARRAY X TO BE TRANSFORMED.  THE METHOD          
C             IS MOST EFFICIENT WHEN N IS A PRODUCT OF SMALL PRIMES.            
C                                                                               
C     X       AN ARRAY WHICH CONTAINS THE SEQUENCE TO BE TRANSFORMED            
C                                                                               
C     WSAVE   A WORK ARRAY WHICH MUST BE DIMENSIONED AT LEAST 3*N+15            
C             IN THE PROGRAM THAT CALLS COSQF. THE WSAVE ARRAY MUST BE          
C             INITIALIZED BY CALLING SUBROUTINE COSQI(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                                                                               
C     OUTPUT PARAMETERS                                                         
C                                                                               
C     X       FOR I=1,...,N                                                     
C                                                                               
C                  X(I) = X(1) PLUS THE SUM FROM K=2 TO K=N OF                  
C                                                                               
C                     2*X(K)*COS((2*I-1)*(K-1)*PI/(2*N))                        
C                                                                               
C                  A CALL OF COSQF FOLLOWED BY A CALL OF                        
C                  COSQB WILL MULTIPLY THE SEQUENCE X BY 4*N.                   
C                  THEREFORE COSQB IS THE UNNORMALIZED INVERSE                  
C                  OF COSQF.                                                    
C                                                                               
C     WSAVE   CONTAINS INITIALIZATION CALCULATIONS WHICH MUST NOT               
C             BE DESTROYED BETWEEN CALLS OF COSQF OR COSQB.                     
C                                                                               
      SUBROUTINE COSQF (N,X,WSAVE)                                              
      DIMENSION       X(*)       ,WSAVE(*)                                      
      DATA SQRT2 /1.4142135623731/                                              
C                                                                               
      IF (N-2) 102,101,103                                                      
  101 TSQX = SQRT2*X(2)                                                         
      X(2) = X(1)-TSQX                                                          
      X(1) = X(1)+TSQX                                                          
  102 RETURN                                                                    
  103 CALL COSQF1 (N,X,WSAVE,WSAVE(N+1))                                        
      RETURN                                                                    
      END