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gpfa.f90
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!*********************************************************************
! *
! GPFAPACK - FORTRAN IMPLEMENTATION OF THE SELF-SORTING *
! IN-PLACE GENERALIZED PRIME FACTOR (COMPLEX) FFT [GPFA] *
! *
! WRITTEN BY CLIVE TEMPERTON *
! RECHERCHE EN PREVISION NUMERIQUE / ECMWF *
! *
! THE PACKAGE CONSISTS OF THE SETUP ROUTINE SETGPFA, TOGETHER *
! WITH THE ROUTINES GPFA, GPFA2F, GPFA3F, GPFA5F *
! *
!*********************************************************************
! SUBROUTINE 'SETGPFA'
! SETUP ROUTINE FOR SELF-SORTING IN-PLACE
! GENERALIZED PRIME FACTOR (COMPLEX) FFT [GPFA]
! CALL SETGPFA(TRIGS,N)
! INPUT :
! -----
! N IS THE LENGTH OF THE TRANSFORMS. N MUST BE OF THE FORM:
! -----------------------------------
! N = (2**IP) * (3**IQ) * (5**IR)
! -----------------------------------
! OUTPUT:
! ------
! TRIGS IS A TABLE OF TWIDDLE FACTORS,
! OF LENGTH 2*IPQR (REAL) WORDS, WHERE:
! --------------------------------------
! IPQR = (2**IP) + (3**IQ) + (5**IR)
! --------------------------------------
! WRITTEN BY CLIVE TEMPERTON 1990
!----------------------------------------------------------------------
SUBROUTINE SETGPFA(TRIGS,N)
USE DDPRECISION,ONLY : WP
REAL(WP) :: ANGLE, DEL, TRIGS, TWOPI
DIMENSION TRIGS(*)
DIMENSION NJ(3)
! DECOMPOSE N INTO FACTORS 2,3,5
! ------------------------------
NN = N
IFAC = 2
DO LL = 1, 3
KK = 0
10 CONTINUE
IF (MOD(NN,IFAC)/=0) GO TO 20
KK = KK + 1
NN = NN/IFAC
GO TO 10
20 CONTINUE
NJ(LL) = KK
IFAC = IFAC + LL
END DO
IF (NN/=1) THEN
WRITE (6,40) N
40 FORMAT (' *** WARNING!!!',I10,' IS NOT A LEGAL VALUE OF N ***')
RETURN
END IF
IP = NJ(1)
IQ = NJ(2)
IR = NJ(3)
! COMPUTE LIST OF ROTATED TWIDDLE FACTORS
! ---------------------------------------
NJ(1) = 2**IP
NJ(2) = 3**IQ
NJ(3) = 5**IR
TWOPI = 4.0_WP*ASIN(1.0_WP)
I = 1
DO LL = 1, 3
NI = NJ(LL)
IF (NI==1) GO TO 60
DEL = TWOPI/REAL(NI,KIND=WP)
IROT = N/NI
KINK = MOD(IROT,NI)
KK = 0
DO K = 1, NI
ANGLE = REAL(KK,KIND=WP)*DEL
TRIGS(I) = COS(ANGLE)
TRIGS(I+1) = SIN(ANGLE)
I = I + 2
KK = KK + KINK
IF (KK>NI) KK = KK - NI
END DO
60 END DO
RETURN
END SUBROUTINE SETGPFA
! SUBROUTINE 'GPFA'
! SELF-SORTING IN-PLACE GENERALIZED PRIME FACTOR (COMPLEX) FFT
! *** THIS IS THE ALL-FORTRAN VERSION ***
! -------------------------------
! CALL GPFA(A,B,TRIGS,INC,JUMP,N,LOT,ISIGN)
! A IS FIRST REAL INPUT/OUTPUT VECTOR
! B IS FIRST IMAGINARY INPUT/OUTPUT VECTOR
! TRIGS IS A TABLE OF TWIDDLE FACTORS, PRECALCULATED
! BY CALLING SUBROUTINE 'SETGPFA'
! INC IS THE INCREMENT WITHIN EACH DATA VECTOR
! JUMP IS THE INCREMENT BETWEEN DATA VECTORS
! N IS THE LENGTH OF THE TRANSFORMS:
! -----------------------------------
! N = (2**IP) * (3**IQ) * (5**IR)
! -----------------------------------
! LOT IS THE NUMBER OF TRANSFORMS
! ISIGN = +1 FOR FORWARD TRANSFORM
! = -1 FOR INVERSE TRANSFORM
! WRITTEN BY CLIVE TEMPERTON
! RECHERCHE EN PREVISION NUMERIQUE
! ATMOSPHERIC ENVIRONMENT SERVICE, CANADA
!----------------------------------------------------------------------
! DEFINITION OF TRANSFORM
! -----------------------
! X(J) = SUM(K=0,...,N-1)(C(K)*EXP(ISIGN*2*I*J*K*PI/N))
!---------------------------------------------------------------------
! FOR A MATHEMATICAL DEVELOPMENT OF THE ALGORITHM USED,
! SEE:
! C TEMPERTON : "A GENERALIZED PRIME FACTOR FFT ALGORITHM
! FOR ANY N = (2**P)(3**Q)(5**R)",
! SIAM J. SCI. STAT. COMP., MAY 1992.
!----------------------------------------------------------------------
SUBROUTINE GPFA(A,B,TRIGS,INC,JUMP,N,LOT,ISIGN)
USE DDPRECISION,ONLY : WP
REAL(WP) :: TRIGS, B, A
DIMENSION A(*), B(*), TRIGS(*)
DIMENSION NJ(3)
!*** diagnostic
! write(0,*)'gpfa ckpt 1'
!***
! DECOMPOSE N INTO FACTORS 2,3,5
! ------------------------------
NN = N
IFAC = 2
DO LL = 1, 3
KK = 0
10 CONTINUE
IF (MOD(NN,IFAC)/=0) GO TO 20
KK = KK + 1
NN = NN/IFAC
GO TO 10
20 CONTINUE
NJ(LL) = KK
IFAC = IFAC + LL
END DO
IF (NN/=1) THEN
WRITE (6,40) N
40 FORMAT (' *** WARNING!!!',I10,' IS NOT A LEGAL VALUE OF N ***')
RETURN
END IF
IP = NJ(1)
IQ = NJ(2)
IR = NJ(3)
! COMPUTE THE TRANSFORM
! ---------------------
I = 1
IF (IP>0) THEN
!*** diagnostic
! write(0,*)'in gpfa, about to call gpfa2f'
!***
CALL GPFA2F(A,B,TRIGS,INC,JUMP,N,IP,LOT,ISIGN)
!*** diagnostic
! write(0,*)'returned from gpfa2f'
!***
I = I + 2*(2**IP)
END IF
IF (IQ>0) THEN
!*** diagnostic
! write(0,*)'in gpfa,about to call gpfa3f'
!***
CALL GPFA3F(A,B,TRIGS(I),INC,JUMP,N,IQ,LOT,ISIGN)
!*** diagnostic
! write(0,*)'returned from gpfa3f'
!***
I = I + 2*(3**IQ)
END IF
IF (IR>0) THEN
!*** diagnostic
! write(0,*)'in gpfa, about to call gpfa5f'
!***
CALL GPFA5F(A,B,TRIGS(I),INC,JUMP,N,IR,LOT,ISIGN)
!*** diagnostic
! write(0,*)'returned from gpfa5f'
!***
END IF
RETURN
END SUBROUTINE GPFA
! fortran version of *gpfa2* -
! radix-2 section of self-sorting, in-place, generalized pfa
! central radix-2 and radix-8 passes included
! so that transform length can be any power of 2
!-------------------------------------------------------------------
SUBROUTINE GPFA2F(A,B,TRIGS,INC,JUMP,N,MM,LOT,ISIGN)
USE DDPRECISION, ONLY : WP
REAL (WP) :: SI7, CO7, SI6, CO6, SI5, CO5, SI4, CO4, C3, C2, C1, SI3, &
CO3, SI2, CO2, SI1, CO1, U3, U1, U2, U0, T3, T1, T2, T0, SS, S, B, A, &
TRIGS
DIMENSION A(*), B(*), TRIGS(*)
DATA LVR/64/
! ***************************************************************
! * *
! * N.B. LVR = LENGTH OF VECTOR REGISTERS, SET TO 128 FOR C90. *
! * RESET TO 64 FOR OTHER CRAY MACHINES, OR TO ANY LARGE VALUE *
! * (GREATER THAN OR EQUAL TO LOT) FOR A SCALAR COMPUTER. *
! * *
! ***************************************************************
N2 = 2**MM
INQ = N/N2
JSTEPX = (N2-N)*INC
NINC = N*INC
INK = INC*INQ
M2 = 0
M8 = 0
IF (MOD(MM,2)==0) THEN
M = MM/2
ELSE IF (MOD(MM,4)==1) THEN
M = (MM-1)/2
M2 = 1
ELSE IF (MOD(MM,4)==3) THEN
M = (MM-3)/2
M8 = 1
END IF
MH = (M+1)/2
NBLOX = 1 + (LOT-1)/LVR
LEFT = LOT
S = REAL(ISIGN,KIND=WP)
ISTART = 1
! loop on blocks of lvr transforms
! --------------------------------
DO NB = 1, NBLOX
IF (LEFT<=LVR) THEN
NVEX = LEFT
ELSE IF (LEFT<(2*LVR)) THEN
NVEX = LEFT/2
NVEX = NVEX + MOD(NVEX,2)
ELSE
NVEX = LVR
END IF
LEFT = LEFT - NVEX
LA = 1
! loop on type I radix-4 passes
! -----------------------------
MU = MOD(INQ,4)
IF (ISIGN==-1) MU = 4 - MU
SS = 1.0_WP
IF (MU==3) SS = -1.0_WP
IF (MH==0) GO TO 200
DO IPASS = 1, MH
JSTEP = (N*INC)/(4*LA)
JSTEPL = JSTEP - NINC
! k = 0 loop (no twiddle factors)
! -------------------------------
DO JJJ = 0, (N-1)*INC, 4*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
J = 0
! loop across transforms
! ----------------------
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JC+J)
T2 = A(JA+J) - A(JC+J)
T1 = A(JB+J) + A(JD+J)
T3 = SS*(A(JB+J)-A(JD+J))
U0 = B(JA+J) + B(JC+J)
U2 = B(JA+J) - B(JC+J)
U1 = B(JB+J) + B(JD+J)
U3 = SS*(B(JB+J)-B(JD+J))
A(JA+J) = T0 + T1
A(JC+J) = T0 - T1
B(JA+J) = U0 + U1
B(JC+J) = U0 - U1
A(JB+J) = T2 - U3
A(JD+J) = T2 + U3
B(JB+J) = U2 + T3
B(JD+J) = U2 - T3
J = J + JUMP
END DO
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
! finished if n2 = 4
! ------------------
IF (N2==4) GO TO 490
KK = 2*LA
! loop on nonzero k
! -----------------
DO K = INK, JSTEP - INK, INK
CO1 = TRIGS(KK+1)
SI1 = S*TRIGS(KK+2)
CO2 = TRIGS(2*KK+1)
SI2 = S*TRIGS(2*KK+2)
CO3 = TRIGS(3*KK+1)
SI3 = S*TRIGS(3*KK+2)
! loop along transform
! --------------------
DO JJJ = K, (N-1)*INC, 4*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
J = 0
! loop across transforms
! ----------------------
!dir$ ivdep,shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JC+J)
T2 = A(JA+J) - A(JC+J)
T1 = A(JB+J) + A(JD+J)
T3 = SS*(A(JB+J)-A(JD+J))
U0 = B(JA+J) + B(JC+J)
U2 = B(JA+J) - B(JC+J)
U1 = B(JB+J) + B(JD+J)
U3 = SS*(B(JB+J)-B(JD+J))
A(JA+J) = T0 + T1
B(JA+J) = U0 + U1
A(JB+J) = CO1*(T2-U3) - SI1*(U2+T3)
B(JB+J) = SI1*(T2-U3) + CO1*(U2+T3)
A(JC+J) = CO2*(T0-T1) - SI2*(U0-U1)
B(JC+J) = SI2*(T0-T1) + CO2*(U0-U1)
A(JD+J) = CO3*(T2+U3) - SI3*(U2-T3)
B(JD+J) = SI3*(T2+U3) + CO3*(U2-T3)
J = J + JUMP
END DO
!-----( end of loop across transforms )
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
!-----( end of loop along transforms )
KK = KK + 2*LA
END DO
!-----( end of loop on nonzero k )
LA = 4*LA
END DO
!-----( end of loop on type I radix-4 passes)
! central radix-2 pass
! --------------------
200 CONTINUE
IF (M2==0) GO TO 300
JSTEP = (N*INC)/(2*LA)
JSTEPL = JSTEP - NINC
! k=0 loop (no twiddle factors)
! -----------------------------
DO JJJ = 0, (N-1)*INC, 2*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
J = 0
! loop across transforms
! ----------------------
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) - A(JB+J)
A(JA+J) = A(JA+J) + A(JB+J)
A(JB+J) = T0
U0 = B(JA+J) - B(JB+J)
B(JA+J) = B(JA+J) + B(JB+J)
B(JB+J) = U0
J = J + JUMP
END DO
!-----(end of loop across transforms)
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
! finished if n2=2
! ----------------
IF (N2==2) GO TO 490
KK = 2*LA
! loop on nonzero k
! -----------------
DO K = INK, JSTEP - INK, INK
CO1 = TRIGS(KK+1)
SI1 = S*TRIGS(KK+2)
! loop along transforms
! ---------------------
DO JJJ = K, (N-1)*INC, 2*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
J = 0
! loop across transforms
! ----------------------
IF (KK==N2/2) THEN
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = SS*(A(JA+J)-A(JB+J))
A(JA+J) = A(JA+J) + A(JB+J)
A(JB+J) = SS*(B(JB+J)-B(JA+J))
B(JA+J) = B(JA+J) + B(JB+J)
B(JB+J) = T0
J = J + JUMP
END DO
ELSE
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) - A(JB+J)
A(JA+J) = A(JA+J) + A(JB+J)
U0 = B(JA+J) - B(JB+J)
B(JA+J) = B(JA+J) + B(JB+J)
A(JB+J) = CO1*T0 - SI1*U0
B(JB+J) = SI1*T0 + CO1*U0
J = J + JUMP
END DO
END IF
!-----(end of loop across transforms)
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
!-----(end of loop along transforms)
KK = KK + 2*LA
END DO
!-----(end of loop on nonzero k)
!-----(end of radix-2 pass)
LA = 2*LA
GO TO 400
! central radix-8 pass
! --------------------
300 CONTINUE
IF (M8==0) GO TO 400
JSTEP = (N*INC)/(8*LA)
JSTEPL = JSTEP - NINC
MU = MOD(INQ,8)
IF (ISIGN==-1) MU = 8 - MU
C1 = 1.0_WP
IF (MU==3 .OR. MU==7) C1 = -1.0_WP
C2 = SQRT(0.5_WP)
IF (MU==3 .OR. MU==5) C2 = -C2
C3 = C1*C2
! stage 1
! -------
DO K = 0, JSTEP - INK, INK
DO JJJ = K, (N-1)*INC, 8*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
JE = JD + JSTEPL
IF (JE<ISTART) JE = JE + NINC
JF = JE + JSTEPL
IF (JF<ISTART) JF = JF + NINC
JG = JF + JSTEPL
IF (JG<ISTART) JG = JG + NINC
JH = JG + JSTEPL
IF (JH<ISTART) JH = JH + NINC
J = 0
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) - A(JE+J)
A(JA+J) = A(JA+J) + A(JE+J)
T1 = C1*(A(JC+J)-A(JG+J))
A(JE+J) = A(JC+J) + A(JG+J)
T2 = A(JB+J) - A(JF+J)
A(JC+J) = A(JB+J) + A(JF+J)
T3 = A(JD+J) - A(JH+J)
A(JG+J) = A(JD+J) + A(JH+J)
A(JB+J) = T0
A(JF+J) = T1
A(JD+J) = C2*(T2-T3)
A(JH+J) = C3*(T2+T3)
U0 = B(JA+J) - B(JE+J)
B(JA+J) = B(JA+J) + B(JE+J)
U1 = C1*(B(JC+J)-B(JG+J))
B(JE+J) = B(JC+J) + B(JG+J)
U2 = B(JB+J) - B(JF+J)
B(JC+J) = B(JB+J) + B(JF+J)
U3 = B(JD+J) - B(JH+J)
B(JG+J) = B(JD+J) + B(JH+J)
B(JB+J) = U0
B(JF+J) = U1
B(JD+J) = C2*(U2-U3)
B(JH+J) = C3*(U2+U3)
J = J + JUMP
END DO
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
END DO
! stage 2
! -------
! k=0 (no twiddle factors)
! ------------------------
DO JJJ = 0, (N-1)*INC, 8*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
JE = JD + JSTEPL
IF (JE<ISTART) JE = JE + NINC
JF = JE + JSTEPL
IF (JF<ISTART) JF = JF + NINC
JG = JF + JSTEPL
IF (JG<ISTART) JG = JG + NINC
JH = JG + JSTEPL
IF (JH<ISTART) JH = JH + NINC
J = 0
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JE+J)
T2 = A(JA+J) - A(JE+J)
T1 = A(JC+J) + A(JG+J)
T3 = C1*(A(JC+J)-A(JG+J))
U0 = B(JA+J) + B(JE+J)
U2 = B(JA+J) - B(JE+J)
U1 = B(JC+J) + B(JG+J)
U3 = C1*(B(JC+J)-B(JG+J))
A(JA+J) = T0 + T1
A(JE+J) = T0 - T1
B(JA+J) = U0 + U1
B(JE+J) = U0 - U1
A(JC+J) = T2 - U3
A(JG+J) = T2 + U3
B(JC+J) = U2 + T3
B(JG+J) = U2 - T3
T0 = A(JB+J) + A(JD+J)
T2 = A(JB+J) - A(JD+J)
T1 = A(JF+J) - A(JH+J)
T3 = A(JF+J) + A(JH+J)
U0 = B(JB+J) + B(JD+J)
U2 = B(JB+J) - B(JD+J)
U1 = B(JF+J) - B(JH+J)
U3 = B(JF+J) + B(JH+J)
A(JB+J) = T0 - U3
A(JH+J) = T0 + U3
B(JB+J) = U0 + T3
B(JH+J) = U0 - T3
A(JD+J) = T2 + U1
A(JF+J) = T2 - U1
B(JD+J) = U2 - T1
B(JF+J) = U2 + T1
J = J + JUMP
END DO
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
IF (N2==8) GO TO 490
! loop on nonzero k
! -----------------
KK = 2*LA
DO K = INK, JSTEP - INK, INK
CO1 = TRIGS(KK+1)
SI1 = S*TRIGS(KK+2)
CO2 = TRIGS(2*KK+1)
SI2 = S*TRIGS(2*KK+2)
CO3 = TRIGS(3*KK+1)
SI3 = S*TRIGS(3*KK+2)
CO4 = TRIGS(4*KK+1)
SI4 = S*TRIGS(4*KK+2)
CO5 = TRIGS(5*KK+1)
SI5 = S*TRIGS(5*KK+2)
CO6 = TRIGS(6*KK+1)
SI6 = S*TRIGS(6*KK+2)
CO7 = TRIGS(7*KK+1)
SI7 = S*TRIGS(7*KK+2)
DO JJJ = K, (N-1)*INC, 8*JSTEP
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
JE = JD + JSTEPL
IF (JE<ISTART) JE = JE + NINC
JF = JE + JSTEPL
IF (JF<ISTART) JF = JF + NINC
JG = JF + JSTEPL
IF (JG<ISTART) JG = JG + NINC
JH = JG + JSTEPL
IF (JH<ISTART) JH = JH + NINC
J = 0
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JE+J)
T2 = A(JA+J) - A(JE+J)
T1 = A(JC+J) + A(JG+J)
T3 = C1*(A(JC+J)-A(JG+J))
U0 = B(JA+J) + B(JE+J)
U2 = B(JA+J) - B(JE+J)
U1 = B(JC+J) + B(JG+J)
U3 = C1*(B(JC+J)-B(JG+J))
A(JA+J) = T0 + T1
B(JA+J) = U0 + U1
A(JE+J) = CO4*(T0-T1) - SI4*(U0-U1)
B(JE+J) = SI4*(T0-T1) + CO4*(U0-U1)
A(JC+J) = CO2*(T2-U3) - SI2*(U2+T3)
B(JC+J) = SI2*(T2-U3) + CO2*(U2+T3)
A(JG+J) = CO6*(T2+U3) - SI6*(U2-T3)
B(JG+J) = SI6*(T2+U3) + CO6*(U2-T3)
T0 = A(JB+J) + A(JD+J)
T2 = A(JB+J) - A(JD+J)
T1 = A(JF+J) - A(JH+J)
T3 = A(JF+J) + A(JH+J)
U0 = B(JB+J) + B(JD+J)
U2 = B(JB+J) - B(JD+J)
U1 = B(JF+J) - B(JH+J)
U3 = B(JF+J) + B(JH+J)
A(JB+J) = CO1*(T0-U3) - SI1*(U0+T3)
B(JB+J) = SI1*(T0-U3) + CO1*(U0+T3)
A(JH+J) = CO7*(T0+U3) - SI7*(U0-T3)
B(JH+J) = SI7*(T0+U3) + CO7*(U0-T3)
A(JD+J) = CO3*(T2+U1) - SI3*(U2-T1)
B(JD+J) = SI3*(T2+U1) + CO3*(U2-T1)
A(JF+J) = CO5*(T2-U1) - SI5*(U2+T1)
B(JF+J) = SI5*(T2-U1) + CO5*(U2+T1)
J = J + JUMP
END DO
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
KK = KK + 2*LA
END DO
LA = 8*LA
! loop on type II radix-4 passes
! ------------------------------
400 CONTINUE
MU = MOD(INQ,4)
IF (ISIGN==-1) MU = 4 - MU
SS = 1.0_WP
IF (MU==3) SS = -1.0_WP
DO IPASS = MH + 1, M
JSTEP = (N*INC)/(4*LA)
JSTEPL = JSTEP - NINC
LAINCL = LA*INK - NINC
! k=0 loop (no twiddle factors)
! -----------------------------
DO LL = 0, (LA-1)*INK, 4*JSTEP
DO JJJ = LL, (N-1)*INC, 4*LA*INK
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
JE = JA + LAINCL
IF (JE<ISTART) JE = JE + NINC
JF = JE + JSTEPL
IF (JF<ISTART) JF = JF + NINC
JG = JF + JSTEPL
IF (JG<ISTART) JG = JG + NINC
JH = JG + JSTEPL
IF (JH<ISTART) JH = JH + NINC
JI = JE + LAINCL
IF (JI<ISTART) JI = JI + NINC
JJ = JI + JSTEPL
IF (JJ<ISTART) JJ = JJ + NINC
JK = JJ + JSTEPL
IF (JK<ISTART) JK = JK + NINC
JL = JK + JSTEPL
IF (JL<ISTART) JL = JL + NINC
JM = JI + LAINCL
IF (JM<ISTART) JM = JM + NINC
JN = JM + JSTEPL
IF (JN<ISTART) JN = JN + NINC
JO = JN + JSTEPL
IF (JO<ISTART) JO = JO + NINC
JP = JO + JSTEPL
IF (JP<ISTART) JP = JP + NINC
J = 0
! loop across transforms
! ----------------------
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JC+J)
T2 = A(JA+J) - A(JC+J)
T1 = A(JB+J) + A(JD+J)
T3 = SS*(A(JB+J)-A(JD+J))
A(JC+J) = A(JI+J)
U0 = B(JA+J) + B(JC+J)
U2 = B(JA+J) - B(JC+J)
U1 = B(JB+J) + B(JD+J)
U3 = SS*(B(JB+J)-B(JD+J))
A(JB+J) = A(JE+J)
A(JA+J) = T0 + T1
A(JI+J) = T0 - T1
B(JA+J) = U0 + U1
B(JC+J) = U0 - U1
B(JD+J) = B(JM+J)
A(JE+J) = T2 - U3
A(JD+J) = T2 + U3
B(JB+J) = U2 + T3
B(JM+J) = U2 - T3
!----------------------
T0 = A(JB+J) + A(JG+J)
T2 = A(JB+J) - A(JG+J)
T1 = A(JF+J) + A(JH+J)
T3 = SS*(A(JF+J)-A(JH+J))
A(JG+J) = A(JJ+J)
U0 = B(JE+J) + B(JG+J)
U2 = B(JE+J) - B(JG+J)
U1 = B(JF+J) + B(JH+J)
U3 = SS*(B(JF+J)-B(JH+J))
B(JE+J) = B(JB+J)
A(JB+J) = T0 + T1
A(JJ+J) = T0 - T1
B(JG+J) = B(JJ+J)
B(JB+J) = U0 + U1
B(JJ+J) = U0 - U1
A(JF+J) = T2 - U3
A(JH+J) = T2 + U3
B(JF+J) = U2 + T3
B(JH+J) = U2 - T3
!----------------------
T0 = A(JC+J) + A(JK+J)
T2 = A(JC+J) - A(JK+J)
T1 = A(JG+J) + A(JL+J)
T3 = SS*(A(JG+J)-A(JL+J))
U0 = B(JI+J) + B(JK+J)
U2 = B(JI+J) - B(JK+J)
A(JL+J) = A(JO+J)
U1 = B(JG+J) + B(JL+J)
U3 = SS*(B(JG+J)-B(JL+J))
B(JI+J) = B(JC+J)
A(JC+J) = T0 + T1
A(JK+J) = T0 - T1
B(JL+J) = B(JO+J)
B(JC+J) = U0 + U1
B(JK+J) = U0 - U1
A(JG+J) = T2 - U3
A(JO+J) = T2 + U3
B(JG+J) = U2 + T3
B(JO+J) = U2 - T3
!----------------------
T0 = A(JM+J) + A(JL+J)
T2 = A(JM+J) - A(JL+J)
T1 = A(JN+J) + A(JP+J)
T3 = SS*(A(JN+J)-A(JP+J))
A(JM+J) = A(JD+J)
U0 = B(JD+J) + B(JL+J)
U2 = B(JD+J) - B(JL+J)
U1 = B(JN+J) + B(JP+J)
U3 = SS*(B(JN+J)-B(JP+J))
A(JN+J) = A(JH+J)
A(JD+J) = T0 + T1
A(JL+J) = T0 - T1
B(JD+J) = U0 + U1
B(JL+J) = U0 - U1
B(JN+J) = B(JH+J)
A(JH+J) = T2 - U3
A(JP+J) = T2 + U3
B(JH+J) = U2 + T3
B(JP+J) = U2 - T3
J = J + JUMP
END DO
!-----( end of loop across transforms )
JA = JA + JSTEPX
IF (JA<ISTART) JA = JA + NINC
END DO
END DO
END DO
!-----( end of double loop for k=0 )
! finished if last pass
! ---------------------
IF (IPASS==M) GO TO 490
KK = 2*LA
! loop on nonzero k
! -----------------
DO K = INK, JSTEP - INK, INK
CO1 = TRIGS(KK+1)
SI1 = S*TRIGS(KK+2)
CO2 = TRIGS(2*KK+1)
SI2 = S*TRIGS(2*KK+2)
CO3 = TRIGS(3*KK+1)
SI3 = S*TRIGS(3*KK+2)
! double loop along first transform in block
! ------------------------------------------
DO LL = K, (LA-1)*INK, 4*JSTEP
DO JJJ = LL, (N-1)*INC, 4*LA*INK
JA = ISTART + JJJ
! "transverse" loop
! -----------------
DO NU = 1, INQ
JB = JA + JSTEPL
IF (JB<ISTART) JB = JB + NINC
JC = JB + JSTEPL
IF (JC<ISTART) JC = JC + NINC
JD = JC + JSTEPL
IF (JD<ISTART) JD = JD + NINC
JE = JA + LAINCL
IF (JE<ISTART) JE = JE + NINC
JF = JE + JSTEPL
IF (JF<ISTART) JF = JF + NINC
JG = JF + JSTEPL
IF (JG<ISTART) JG = JG + NINC
JH = JG + JSTEPL
IF (JH<ISTART) JH = JH + NINC
JI = JE + LAINCL
IF (JI<ISTART) JI = JI + NINC
JJ = JI + JSTEPL
IF (JJ<ISTART) JJ = JJ + NINC
JK = JJ + JSTEPL
IF (JK<ISTART) JK = JK + NINC
JL = JK + JSTEPL
IF (JL<ISTART) JL = JL + NINC
JM = JI + LAINCL
IF (JM<ISTART) JM = JM + NINC
JN = JM + JSTEPL
IF (JN<ISTART) JN = JN + NINC
JO = JN + JSTEPL
IF (JO<ISTART) JO = JO + NINC
JP = JO + JSTEPL
IF (JP<ISTART) JP = JP + NINC
J = 0
! loop across transforms
! ----------------------
!dir$ ivdep, shortloop
DO L = 1, NVEX
T0 = A(JA+J) + A(JC+J)
T2 = A(JA+J) - A(JC+J)
T1 = A(JB+J) + A(JD+J)
T3 = SS*(A(JB+J)-A(JD+J))
A(JC+J) = A(JI+J)
U0 = B(JA+J) + B(JC+J)
U2 = B(JA+J) - B(JC+J)
U1 = B(JB+J) + B(JD+J)
U3 = SS*(B(JB+J)-B(JD+J))
A(JB+J) = A(JE+J)
A(JA+J) = T0 + T1
B(JA+J) = U0 + U1
A(JE+J) = CO1*(T2-U3) - SI1*(U2+T3)
B(JB+J) = SI1*(T2-U3) + CO1*(U2+T3)
B(JD+J) = B(JM+J)
A(JI+J) = CO2*(T0-T1) - SI2*(U0-U1)
B(JC+J) = SI2*(T0-T1) + CO2*(U0-U1)
A(JD+J) = CO3*(T2+U3) - SI3*(U2-T3)
B(JM+J) = SI3*(T2+U3) + CO3*(U2-T3)
!----------------------------------------
T0 = A(JB+J) + A(JG+J)
T2 = A(JB+J) - A(JG+J)
T1 = A(JF+J) + A(JH+J)
T3 = SS*(A(JF+J)-A(JH+J))
A(JG+J) = A(JJ+J)
U0 = B(JE+J) + B(JG+J)
U2 = B(JE+J) - B(JG+J)
U1 = B(JF+J) + B(JH+J)
U3 = SS*(B(JF+J)-B(JH+J))
B(JE+J) = B(JB+J)
A(JB+J) = T0 + T1
B(JB+J) = U0 + U1
B(JG+J) = B(JJ+J)
A(JF+J) = CO1*(T2-U3) - SI1*(U2+T3)
B(JF+J) = SI1*(T2-U3) + CO1*(U2+T3)
A(JJ+J) = CO2*(T0-T1) - SI2*(U0-U1)
B(JJ+J) = SI2*(T0-T1) + CO2*(U0-U1)
A(JH+J) = CO3*(T2+U3) - SI3*(U2-T3)
B(JH+J) = SI3*(T2+U3) + CO3*(U2-T3)
!----------------------------------------
T0 = A(JC+J) + A(JK+J)
T2 = A(JC+J) - A(JK+J)
T1 = A(JG+J) + A(JL+J)
T3 = SS*(A(JG+J)-A(JL+J))
U0 = B(JI+J) + B(JK+J)
U2 = B(JI+J) - B(JK+J)
A(JL+J) = A(JO+J)
U1 = B(JG+J) + B(JL+J)
U3 = SS*(B(JG+J)-B(JL+J))
B(JI+J) = B(JC+J)
A(JC+J) = T0 + T1
B(JC+J) = U0 + U1
B(JL+J) = B(JO+J)