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fft235.f
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C
C FFTE: A FAST FOURIER TRANSFORM PACKAGE
C
C (C) COPYRIGHT SOFTWARE, 2000-2004, 2008-2014, 2020
C ALL RIGHTS RESERVED
C BY
C DAISUKE TAKAHASHI
C CENTER FOR COMPUTATIONAL SCIENCES
C UNIVERSITY OF TSUKUBA
C 1-1-1 TENNODAI, TSUKUBA, IBARAKI 305-8577, JAPAN
C E-MAIL: [email protected]
C
C
C RADIX-2, 3, 4, 5 AND 8 FFT ROUTINE
C
C FORTRAN77 SOURCE PROGRAM
C
C WRITTEN BY DAISUKE TAKAHASHI
C
SUBROUTINE FFT235(A,B,W,N,IP)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 A(*),B(*),W(*)
DIMENSION IP(*)
C
IF (IP(1) .NE. 1) THEN
KP4=2-MOD(IP(1)+2,3)
KP8=(IP(1)-KP4*2)/3
ELSE
KP4=0
KP8=0
END IF
C
KEY=1
J=1
L=N
M=1
DO 10 K=1,KP8
L=L/8
IF (L .GE. 2) THEN
IF (KEY .GE. 0) THEN
CALL FFT8(A,B,W(J),M,L)
ELSE
CALL FFT8(B,A,W(J),M,L)
END IF
KEY=-KEY
ELSE
IF (KEY .GE. 0) THEN
CALL FFT8(A,A,W(J),M,L)
ELSE
CALL FFT8(B,A,W(J),M,L)
END IF
END IF
M=M*8
J=J+L*7
10 CONTINUE
DO 20 K=1,IP(3)
L=L/5
IF (L .GE. 2) THEN
IF (KEY .GE. 0) THEN
CALL FFT5(A,B,W(J),M,L)
ELSE
CALL FFT5(B,A,W(J),M,L)
END IF
KEY=-KEY
ELSE
IF (KEY .GE. 0) THEN
CALL FFT5(A,A,W(J),M,L)
ELSE
CALL FFT5(B,A,W(J),M,L)
END IF
END IF
M=M*5
J=J+L*4
20 CONTINUE
DO 30 K=1,KP4
L=L/4
IF (L .GE. 2) THEN
IF (KEY .GE. 0) THEN
CALL FFT4(A,B,W(J),M,L)
ELSE
CALL FFT4(B,A,W(J),M,L)
END IF
KEY=-KEY
ELSE
IF (KEY .GE. 0) THEN
CALL FFT4(A,A,W(J),M,L)
ELSE
CALL FFT4(B,A,W(J),M,L)
END IF
END IF
M=M*4
J=J+L*3
30 CONTINUE
DO 40 K=1,IP(2)
L=L/3
IF (L .GE. 2) THEN
IF (KEY .GE. 0) THEN
CALL FFT3(A,B,W(J),M,L)
ELSE
CALL FFT3(B,A,W(J),M,L)
END IF
KEY=-KEY
ELSE
IF (KEY .GE. 0) THEN
CALL FFT3(A,A,W(J),M,L)
ELSE
CALL FFT3(B,A,W(J),M,L)
END IF
END IF
M=M*3
J=J+L*2
40 CONTINUE
IF (IP(1) .EQ. 1) THEN
IF (KEY .GE. 0) THEN
CALL FFT2(A,A,M)
ELSE
CALL FFT2(B,A,M)
END IF
END IF
RETURN
END
SUBROUTINE FFT3(A,B,W,M,L)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 A(*),B(*),W(*)
C
IF (M .EQ. 1) THEN
CALL FFT3A(A,B,W,L)
ELSE
CALL FFT3B(A,B,W,M,L)
END IF
RETURN
END
SUBROUTINE FFT4(A,B,W,M,L)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 A(*),B(*),W(*)
C
IF (M .EQ. 1) THEN
CALL FFT4A(A,B,W,L)
ELSE
CALL FFT4B(A,B,W,M,L)
END IF
RETURN
END
SUBROUTINE FFT5(A,B,W,M,L)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 A(*),B(*),W(*)
C
IF (M .EQ. 1) THEN
CALL FFT5A(A,B,W,L)
ELSE
CALL FFT5B(A,B,W,M,L)
END IF
RETURN
END
SUBROUTINE FFT8(A,B,W,M,L)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 A(*),B(*),W(*)
C
IF (M .EQ. 1) THEN
CALL FFT8A(A,B,W,L)
ELSE
CALL FFT8B(A,B,W,M,L)
END IF
RETURN
END
SUBROUTINE SETTBL(W,N)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 W(*)
DIMENSION IP(3)
C
CALL FACTOR(N,IP)
C
IF (IP(1) .NE. 1) THEN
KP4=2-MOD(IP(1)+2,3)
KP8=(IP(1)-KP4*2)/3
ELSE
KP4=0
KP8=0
END IF
C
J=1
L=N
DO 10 K=1,KP8
L=L/8
CALL SETTBL0(W(J),8,L)
J=J+L*7
10 CONTINUE
DO 20 K=1,IP(3)
L=L/5
CALL SETTBL0(W(J),5,L)
J=J+L*4
20 CONTINUE
DO 30 K=1,KP4
L=L/4
CALL SETTBL0(W(J),4,L)
J=J+L*3
30 CONTINUE
DO 40 K=1,IP(2)
L=L/3
CALL SETTBL0(W(J),3,L)
J=J+L*2
40 CONTINUE
RETURN
END
SUBROUTINE SETTBL0(W,M,L)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 W(M-1,*)
C
PI2=8.0D0*DATAN(1.0D0)
PX=-PI2/(DBLE(M)*DBLE(L))
DO 20 J=1,L
!DIR$ VECTOR ALIGNED
DO 10 I=1,M-1
TEMP=PX*DBLE(I)*DBLE(J-1)
W(I,J)=DCMPLX(DCOS(TEMP),DSIN(TEMP))
10 CONTINUE
20 CONTINUE
RETURN
END
SUBROUTINE SETTBL2(W,NX,NY)
IMPLICIT REAL*8 (A-H,O-Z)
COMPLEX*16 W(NX,*)
C
PI2=8.0D0*DATAN(1.0D0)
PX=-PI2/(DBLE(NX)*DBLE(NY))
!$OMP PARALLEL DO PRIVATE(TEMP)
DO 20 J=1,NY
!DIR$ VECTOR ALIGNED
DO 10 I=1,NX
TEMP=PX*DBLE(I-1)*DBLE(J-1)
W(I,J)=DCMPLX(DCOS(TEMP),DSIN(TEMP))
10 CONTINUE
20 CONTINUE
RETURN
END