# sint.f

          SUBROUTINE SINT (N, X, WSAVE)
    C***BEGIN PROLOGUE  SINT
    C***PURPOSE  Compute the sine transform of a real, odd sequence.
    C***LIBRARY   SLATEC (FFTPACK)
    C***CATEGORY  J1A3
    C***TYPE      SINGLE PRECISION (SINT-S)
    C***KEYWORDS  FFTPACK, FOURIER TRANSFORM
    C***AUTHOR  Swarztrauber, P. N., (NCAR)
    C***DESCRIPTION
    C
    C  Subroutine SINT computes the discrete Fourier sine transform
    C  of an odd sequence X(I).  The transform is defined below at
    C  output parameter X.
    C
    C  SINT is the unnormalized inverse of itself since a call of SINT
    C  followed by another call of SINT will multiply the input sequence
    C  X by 2*(N+1).
    C
    C  The array WSAVE which is used by subroutine SINT must be
    C  initialized by calling subroutine SINTI(N,WSAVE).
    C
    C  Input Parameters
    C
    C  N       the length of the sequence to be transformed.  The method
    C          is most efficient when N+1 is the product of small primes.
    C
    C  X       an array which contains the sequence to be transformed
    C
    C
    C  WSAVE   a work array with dimension at least INT(3.5*N+16)
    C          in the program that calls SINT.  The WSAVE array must be
    C          initialized by calling subroutine SINTI(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)= the sum from K=1 to K=N
    C
    C                    2*X(K)*SIN(K*I*PI/(N+1))
    C
    C               A call of SINT followed by another call of
    C               SINT will multiply the sequence X by 2*(N+1).
    C               Hence SINT is the unnormalized inverse
    C               of itself.
    C
    C  WSAVE   contains initialization calculations which must not be
    C          destroyed between calls of SINT.
    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           (a) changing dummy array size declarations (1) to (*),
    C           (b) changing definition of variable SQRT3 by using
    C               FORTRAN intrinsic function SQRT instead of a DATA
    C               statement.
    C   881128  Modified by Dick Valent to meet prologue standards.
    C   891009  Removed unreferenced statement label.  (WRB)
    C   891009  REVISION DATE from Version 3.2
    C   891214  Prologue converted to Version 4.0 format.  (BAB)
    C   920501  Reformatted the REFERENCES section.  (WRB)
    C***END PROLOGUE  SINT