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C Copyright 1981-2007 ECMWF
C
C Licensed under the GNU Lesser General Public License which
C incorporates the terms and conditions of version 3 of the GNU
C General Public License.
C See LICENSE and gpl-3.0.txt for details.
C
SUBROUTINE FFT99(A,WORK,TRIGS,IFAX,INC,JUMP,N,LOT,ISIGN)
DIMENSION A(N),WORK(N),TRIGS(N),IFAX(*)
C
C SUBROUTINE 'FFT99' - MULTIPLE FAST REAL PERIODIC TRANSFORM
C SUPERSEDES PREVIOUS ROUTINE 'FFT99'
C
C REAL TRANSFORM OF LENGTH N PERFORMED BY REMOVING REDUNDANT
C OPERATIONS FROM COMPLEX TRANSFORM OF LENGTH N
C
C A IS THE ARRAY CONTAINING INPUT & OUTPUT DATA
C WORK IS AN AREA OF SIZE (N+1)*MIN(LOT,64)
C TRIGS IS A PREVIOUSLY PREPARED LIST OF TRIG FUNCTION VALUES
C IFAX IS A PREVIOUSLY PREPARED LIST OF FACTORS OF N
C INC IS THE INCREMENT WITHIN EACH DATA 'VECTOR'
C (E.G. INC=1 FOR CONSECUTIVELY STORED DATA)
C JUMP IS THE INCREMENT BETWEEN THE START OF EACH DATA VECTOR
C N IS THE LENGTH OF THE DATA VECTORS
C LOT IS THE NUMBER OF DATA VECTORS
C ISIGN = +1 FOR TRANSFORM FROM SPECTRAL TO GRIDPOINT
C = -1 FOR TRANSFORM FROM GRIDPOINT TO SPECTRAL
C
C ORDERING OF COEFFICIENTS:
C A(0),B(0),A(1),B(1),A(2),B(2),...,A(N/2),B(N/2)
C WHERE B(0)=B(N/2)=0; (N+2) LOCATIONS REQUIRED
C
C ORDERING OF DATA:
C X(N-1),X(0),X(1),X(2),...,X(N-1),X(0)
C I.E. EXPLICIT CYCLIC CONTINUITY; (N+2) LOCATIONS REQUIRED
C
C VECTORIZATION IS ACHIEVED ON CRAY BY DOING THE TRANSFORMS
C IN PARALLEL
C
C N MUST BE COMPOSED OF FACTORS 2,3 & 5 BUT DOES NOT HAVE TO BE EVEN
C
C DEFINITION OF TRANSFORMS:
C -------------------------
C
C ISIGN=+1: X(J)=SUM(K=0,...,N-1)(C(K)*EXP(2*I*J*K*PI/N))
C WHERE C(K)=A(K)+I*B(K) AND C(N-K)=A(K)-I*B(K)
C
C ISIGN=-1: A(K)=(1/N)*SUM(J=0,...,N-1)(X(J)*COS(2*J*K*PI/N))
C B(K)=-(1/N)*SUM(J=0,...,N-1)(X(J)*SIN(2*J*K*PI/N))
C
IF(IFAX(10).NE.N) CALL SET99(TRIGS,IFAX,N)
NFAX=IFAX(1)
NX=N+1
IF (MOD(N,2).EQ.1) NX=N
NBLOX=1+(LOT-1)/64
NVEX=LOT-(NBLOX-1)*64
IF (ISIGN.EQ.-1) GO TO 300
C
C ISIGN=+1, SPECTRAL TO GRIDPOINT TRANSFORM
C -----------------------------------------
100 CONTINUE
ISTART=1
DO 220 NB=1,NBLOX
IA=ISTART
I=ISTART
DO 110 J=1,NVEX
A(I+INC)=0.5*A(I)
I=I+JUMP
110 CONTINUE
IF (MOD(N,2).EQ.1) GO TO 130
I=ISTART+N*INC
DO 120 J=1,NVEX
A(I)=0.5*A(I)
I=I+JUMP
120 CONTINUE
130 CONTINUE
IA=ISTART+INC
LA=1
IGO=+1
C
DO 160 K=1,NFAX
IFAC=IFAX(K+1)
IERR=-1
IF (IGO.EQ.-1) GO TO 140
CALL RPASSM(A(IA),A(IA+LA*INC),WORK(1),WORK(IFAC*LA+1),TRIGS,
* INC,1,JUMP,NX,NVEX,N,IFAC,LA,IERR)
GO TO 150
140 CONTINUE
CALL RPASSM(WORK(1),WORK(LA+1),A(IA),A(IA+IFAC*LA*INC),TRIGS,
* 1,INC,NX,JUMP,NVEX,N,IFAC,LA,IERR)
150 CONTINUE
IF (IERR.NE.0) GO TO 500
LA=IFAC*LA
IGO=-IGO
IA=ISTART+INC
160 CONTINUE
C
C IF NECESSARY, COPY RESULTS BACK TO A
C ------------------------------------
IF (MOD(NFAX,2).EQ.0) GO TO 190
IBASE=1
JBASE=IA
DO 180 JJ=1,NVEX
I=IBASE
J=JBASE
DO 170 II=1,N
A(J)=WORK(I)
I=I+1
J=J+INC
170 CONTINUE
IBASE=IBASE+NX
JBASE=JBASE+JUMP
180 CONTINUE
190 CONTINUE
C
C FILL IN CYCLIC BOUNDARY VALUES
C ------------------------------
IX=ISTART
IZ=ISTART+N*INC
CDIR$ IVDEP
DO 200 J=1,NVEX
A(IX)=A(IZ)
A(IZ+INC)=A(IX+INC)
IX=IX+JUMP
IZ=IZ+JUMP
200 CONTINUE
C
ISTART=ISTART+NVEX*JUMP
NVEX=64
220 CONTINUE
RETURN
C
C ISIGN=-1, GRIDPOINT TO SPECTRAL TRANSFORM
C -----------------------------------------
300 CONTINUE
ISTART=1
DO 410 NB=1,NBLOX
IA=ISTART+INC
LA=N
IGO=+1
C
DO 340 K=1,NFAX
IFAC=IFAX(NFAX+2-K)
LA=LA/IFAC
IERR=-1
IF (IGO.EQ.-1) GO TO 320
CALL QPASSM(A(IA),A(IA+IFAC*LA*INC),WORK(1),WORK(LA+1),TRIGS,
* INC,1,JUMP,NX,NVEX,N,IFAC,LA,IERR)
GO TO 330
320 CONTINUE
CALL QPASSM(WORK(1),WORK(IFAC*LA+1),A(IA),A(IA+LA*INC),TRIGS,
* 1,INC,NX,JUMP,NVEX,N,IFAC,LA,IERR)
330 CONTINUE
IF (IERR.NE.0) GO TO 500
IGO=-IGO
IA=ISTART+INC
340 CONTINUE
C
C IF NECESSARY, COPY RESULTS BACK TO A
C ------------------------------------
IF (MOD(NFAX,2).EQ.0) GO TO 370
IBASE=1
JBASE=IA
DO 360 JJ=1,NVEX
I=IBASE
J=JBASE
DO 350 II=1,N
A(J)=WORK(I)
I=I+1
J=J+INC
350 CONTINUE
IBASE=IBASE+NX
JBASE=JBASE+JUMP
360 CONTINUE
370 CONTINUE
C
C SHIFT A(0) & FILL IN ZERO IMAG PARTS
C ------------------------------------
IX=ISTART
DO 380 J=1,NVEX
A(IX)=A(IX+INC)
A(IX+INC)=0.0
IX=IX+JUMP
380 CONTINUE
IF (MOD(N,2).EQ.1) GO TO 400
IZ=ISTART+(N+1)*INC
DO 390 J=1,NVEX
A(IZ)=0.0
IZ=IZ+JUMP
390 CONTINUE
400 CONTINUE
C
ISTART=ISTART+NVEX*JUMP
NVEX=64
410 CONTINUE
RETURN
C
C ERROR MESSAGES
C --------------
500 CONTINUE
GO TO (510,530,550) IERR
510 CONTINUE
WRITE(6,520) NVEX
520 FORMAT('1VECTOR LENGTH =',I4,', GREATER THAN 64')
GO TO 570
530 CONTINUE
WRITE(6,540) IFAC
540 FORMAT( '1FACTOR =',I3,', NOT CATERED FOR')
GO TO 570
550 CONTINUE
WRITE(6,560) IFAC
560 FORMAT('1FACTOR =',I3,', ONLY CATERED FOR IF LA*IFAC=N')
570 CONTINUE
RETURN
END
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