# cost.f

          SUBROUTINE COST (N, X, WSAVE)
    C***BEGIN PROLOGUE  COST
    C***PURPOSE  Compute the cosine transform of a real, even sequence.
    C***LIBRARY   SLATEC (FFTPACK)
    C***CATEGORY  J1A3
    C***TYPE      SINGLE PRECISION (COST-S)
    C***KEYWORDS  COSINE FOURIER TRANSFORM, FFTPACK
    C***AUTHOR  Swarztrauber, P. N., (NCAR)
    C***DESCRIPTION
    C
    C  Subroutine COST computes the discrete Fourier cosine transform
    C  of an even sequence X(I).  The transform is defined below at output
    C  parameter X.
    C
    C  COST is the unnormalized inverse of itself since a call of COST
    C  followed by another call of COST will multiply the input sequence
    C  X by 2*(N-1).  The transform is defined below at output parameter X.
    C
    C  The array WSAVE which is used by subroutine COST must be
    C  initialized by calling subroutine COSTI(N,WSAVE).
    C
    C  Input Parameters
    C
    C  N       the length of the sequence X.  N must be greater than 1.
    C          The method is most efficient when N-1 is a product of
    C          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 COST.  The WSAVE array must be
    C          initialized by calling subroutine COSTI(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)+(-1)**(I-1)*X(N)
    C
    C               + the sum from K=2 to K=N-1
    C
    C                 2*X(K)*COS((K-1)*(I-1)*PI/(N-1))
    C
    C               A call of COST followed by another call of
    C               COST will multiply the sequence X by 2*(N-1).
    C               Hence COST is the unnormalized inverse
    C               of itself.
    C
    C  WSAVE   contains initialization calculations which must not be
    C          destroyed between calls of COST.
    C
    C***REFERENCES  P. N. Swarztrauber, Vectorizing the FFTs, in Parallel
    C                 Computations (G. Rodrigue, ed.), Academic Press,
    C                 1982, pp. 51-83.
    C***ROUTINES CALLED  RFFTF
    C***REVISION HISTORY  (YYMMDD)
    C   790601  DATE WRITTEN
    C   830401  Modified to use SLATEC library source file format.
    C   860115  Modified by Ron Boisvert to adhere to Fortran 77 by
    C           changing dummy array size declarations (1) to (*)
    C   861211  REVISION DATE from Version 3.2
    C   881128  Modified by Dick Valent to meet prologue standards.
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  COST