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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 QPASSM(A,B,C,D,TRIGS,INC1,INC2,INC3,INC4,LOT,N,IFAC,
* LA,IERR)
DIMENSION A(N),B(N),C(N),D(N),TRIGS(N)
C
C---->
C
C SUBROUTINE 'QPASSM' - PERFORMS ONE PASS THROUGH DATA AS PART
C OF MULTIPLE REAL FFT (FOURIER ANALYSIS) ROUTINE
C
C A IS FIRST REAL INPUT VECTOR
C EQUIVALENCE B(1) WITH A(IFAC*LA*INC1+1)
C C IS FIRST REAL OUTPUT VECTOR
C EQUIVALENCE D(1) WITH C(LA*INC2+1)
C TRIGS IS A PRECALCULATED LIST OF SINES & COSINES
C INC1 IS THE ADDRESSING INCREMENT FOR A
C INC2 IS THE ADDRESSING INCREMENT FOR C
C INC3 IS THE INCREMENT BETWEEN INPUT VECTORS A
C INC4 IS THE INCREMENT BETWEEN OUTPUT VECTORS C
C LOT IS THE NUMBER OF VECTORS
C N IS THE LENGTH OF THE VECTORS
C IFAC IS THE CURRENT FACTOR OF N
C LA = N/(PRODUCT OF FACTORS USED SO FAR)
C IERR IS AN ERROR INDICATOR:
C 0 - PASS COMPLETED WITHOUT ERROR
C 1 - LOT GREATER THAN 64
C 2 - IFAC NOT CATERED FOR
C 3 - IFAC ONLY CATERED FOR IF LA=N/IFAC
C
C-----------------------------------------------------------------------
C----<
C
DATA SIN36/0.587785252292473/,SIN72/0.951056516295154/,
* QRT5/0.559016994374947/,SIN60/0.866025403784437/
C
M=N/IFAC
IINK=LA*INC1
JINK=LA*INC2
IJUMP=(IFAC-1)*IINK
KSTOP=(N-IFAC)/(2*IFAC)
C
IBAD=1
IF (LOT.GT.64) GO TO 910
IBASE=0
JBASE=0
IGO=IFAC-1
IF (IGO.EQ.7) IGO=6
IBAD=2
IF (IGO.LT.1.OR.IGO.GT.6) GO TO 910
GO TO (200,300,400,500,600,800),IGO
C
C CODING FOR FACTOR 2
C -------------------
200 CONTINUE
IA=1
IB=IA+IINK
JA=1
JB=JA+(2*M-LA)*INC2
C
IF (LA.EQ.M) GO TO 290
C
DO 220 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 210 IJK=1,LOT
C(JA+J)=A(IA+I)+A(IB+I)
C(JB+J)=A(IA+I)-A(IB+I)
I=I+INC3
J=J+INC4
210 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
220 CONTINUE
JA=JA+JINK
JINK=2*JINK
JB=JB-JINK
IBASE=IBASE+IJUMP
IJUMP=2*IJUMP+IINK
IF (JA.EQ.JB) GO TO 260
DO 250 K=LA,KSTOP,LA
KB=K+K
C1=TRIGS(KB+1)
S1=TRIGS(KB+2)
JBASE=0
DO 240 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 230 IJK=1,LOT
C(JA+J)=A(IA+I)+(C1*A(IB+I)+S1*B(IB+I))
C(JB+J)=A(IA+I)-(C1*A(IB+I)+S1*B(IB+I))
D(JA+J)=(C1*B(IB+I)-S1*A(IB+I))+B(IA+I)
D(JB+J)=(C1*B(IB+I)-S1*A(IB+I))-B(IA+I)
I=I+INC3
J=J+INC4
230 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
240 CONTINUE
IBASE=IBASE+IJUMP
JA=JA+JINK
JB=JB-JINK
250 CONTINUE
IF (JA.GT.JB) GO TO 900
260 CONTINUE
JBASE=0
DO 280 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 270 IJK=1,LOT
C(JA+J)=A(IA+I)
D(JA+J)=-A(IB+I)
I=I+INC3
J=J+INC4
270 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
280 CONTINUE
GO TO 900
C
290 CONTINUE
Z=1.0/FLOAT(N)
DO 294 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 292 IJK=1,LOT
C(JA+J)=Z*(A(IA+I)+A(IB+I))
C(JB+J)=Z*(A(IA+I)-A(IB+I))
I=I+INC3
J=J+INC4
292 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
294 CONTINUE
GO TO 900
C
C CODING FOR FACTOR 3
C -------------------
300 CONTINUE
IA=1
IB=IA+IINK
IC=IB+IINK
JA=1
JB=JA+(2*M-LA)*INC2
JC=JB
C
IF (LA.EQ.M) GO TO 390
C
DO 320 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 310 IJK=1,LOT
C(JA+J)=A(IA+I)+(A(IB+I)+A(IC+I))
C(JB+J)=A(IA+I)-0.5*(A(IB+I)+A(IC+I))
D(JB+J)=SIN60*(A(IC+I)-A(IB+I))
I=I+INC3
J=J+INC4
310 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
320 CONTINUE
JA=JA+JINK
JINK=2*JINK
JB=JB+JINK
JC=JC-JINK
IBASE=IBASE+IJUMP
IJUMP=2*IJUMP+IINK
IF (JA.EQ.JC) GO TO 360
DO 350 K=LA,KSTOP,LA
KB=K+K
KC=KB+KB
C1=TRIGS(KB+1)
S1=TRIGS(KB+2)
C2=TRIGS(KC+1)
S2=TRIGS(KC+2)
JBASE=0
DO 340 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 330 IJK=1,LOT
A1=(C1*A(IB+I)+S1*B(IB+I))+(C2*A(IC+I)+S2*B(IC+I))
B1=(C1*B(IB+I)-S1*A(IB+I))+(C2*B(IC+I)-S2*A(IC+I))
A2=A(IA+I)-0.5*A1
B2=B(IA+I)-0.5*B1
A3=SIN60*((C1*A(IB+I)+S1*B(IB+I))-(C2*A(IC+I)+S2*B(IC+I)))
B3=SIN60*((C1*B(IB+I)-S1*A(IB+I))-(C2*B(IC+I)-S2*A(IC+I)))
C(JA+J)=A(IA+I)+A1
D(JA+J)=B(IA+I)+B1
C(JB+J)=A2+B3
D(JB+J)=B2-A3
C(JC+J)=A2-B3
D(JC+J)=-(B2+A3)
I=I+INC3
J=J+INC4
330 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
340 CONTINUE
IBASE=IBASE+IJUMP
JA=JA+JINK
JB=JB+JINK
JC=JC-JINK
350 CONTINUE
IF (JA.GT.JC) GO TO 900
360 CONTINUE
JBASE=0
DO 380 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 370 IJK=1,LOT
C(JA+J)=A(IA+I)+0.5*(A(IB+I)-A(IC+I))
D(JA+J)=-SIN60*(A(IB+I)+A(IC+I))
C(JB+J)=A(IA+I)-(A(IB+I)-A(IC+I))
I=I+INC3
J=J+INC4
370 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
380 CONTINUE
GO TO 900
C
390 CONTINUE
Z=1.0/FLOAT(N)
ZSIN60=Z*SIN60
DO 394 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 392 IJK=1,LOT
C(JA+J)=Z*(A(IA+I)+(A(IB+I)+A(IC+I)))
C(JB+J)=Z*(A(IA+I)-0.5*(A(IB+I)+A(IC+I)))
D(JB+J)=ZSIN60*(A(IC+I)-A(IB+I))
I=I+INC3
J=J+INC4
392 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
394 CONTINUE
GO TO 900
C
C CODING FOR FACTOR 4
C -------------------
400 CONTINUE
IA=1
IB=IA+IINK
IC=IB+IINK
ID=IC+IINK
JA=1
JB=JA+(2*M-LA)*INC2
JC=JB+2*M*INC2
JD=JB
C
IF (LA.EQ.M) GO TO 490
C
DO 420 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 410 IJK=1,LOT
C(JA+J)=(A(IA+I)+A(IC+I))+(A(IB+I)+A(ID+I))
C(JC+J)=(A(IA+I)+A(IC+I))-(A(IB+I)+A(ID+I))
C(JB+J)=A(IA+I)-A(IC+I)
D(JB+J)=A(ID+I)-A(IB+I)
I=I+INC3
J=J+INC4
410 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
420 CONTINUE
JA=JA+JINK
JINK=2*JINK
JB=JB+JINK
JC=JC-JINK
JD=JD-JINK
IBASE=IBASE+IJUMP
IJUMP=2*IJUMP+IINK
IF (JB.EQ.JC) GO TO 460
DO 450 K=LA,KSTOP,LA
KB=K+K
KC=KB+KB
KD=KC+KB
C1=TRIGS(KB+1)
S1=TRIGS(KB+2)
C2=TRIGS(KC+1)
S2=TRIGS(KC+2)
C3=TRIGS(KD+1)
S3=TRIGS(KD+2)
JBASE=0
DO 440 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 430 IJK=1,LOT
A0=A(IA+I)+(C2*A(IC+I)+S2*B(IC+I))
A2=A(IA+I)-(C2*A(IC+I)+S2*B(IC+I))
A1=(C1*A(IB+I)+S1*B(IB+I))+(C3*A(ID+I)+S3*B(ID+I))
A3=(C1*A(IB+I)+S1*B(IB+I))-(C3*A(ID+I)+S3*B(ID+I))
B0=B(IA+I)+(C2*B(IC+I)-S2*A(IC+I))
B2=B(IA+I)-(C2*B(IC+I)-S2*A(IC+I))
B1=(C1*B(IB+I)-S1*A(IB+I))+(C3*B(ID+I)-S3*A(ID+I))
B3=(C1*B(IB+I)-S1*A(IB+I))-(C3*B(ID+I)-S3*A(ID+I))
C(JA+J)=A0+A1
C(JC+J)=A0-A1
D(JA+J)=B0+B1
D(JC+J)=B1-B0
C(JB+J)=A2+B3
C(JD+J)=A2-B3
D(JB+J)=B2-A3
D(JD+J)=-(B2+A3)
I=I+INC3
J=J+INC4
430 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
440 CONTINUE
IBASE=IBASE+IJUMP
JA=JA+JINK
JB=JB+JINK
JC=JC-JINK
JD=JD-JINK
450 CONTINUE
IF (JB.GT.JC) GO TO 900
460 CONTINUE
SIN45=SQRT(0.5)
JBASE=0
DO 480 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 470 IJK=1,LOT
C(JA+J)=A(IA+I)+SIN45*(A(IB+I)-A(ID+I))
C(JB+J)=A(IA+I)-SIN45*(A(IB+I)-A(ID+I))
D(JA+J)=-A(IC+I)-SIN45*(A(IB+I)+A(ID+I))
D(JB+J)=A(IC+I)-SIN45*(A(IB+I)+A(ID+I))
I=I+INC3
J=J+INC4
470 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
480 CONTINUE
GO TO 900
C
490 CONTINUE
Z=1.0/FLOAT(N)
DO 494 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 492 IJK=1,LOT
C(JA+J)=Z*((A(IA+I)+A(IC+I))+(A(IB+I)+A(ID+I)))
C(JC+J)=Z*((A(IA+I)+A(IC+I))-(A(IB+I)+A(ID+I)))
C(JB+J)=Z*(A(IA+I)-A(IC+I))
D(JB+J)=Z*(A(ID+I)-A(IB+I))
I=I+INC3
J=J+INC4
492 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
494 CONTINUE
GO TO 900
C
C CODING FOR FACTOR 5
C -------------------
500 CONTINUE
IA=1
IB=IA+IINK
IC=IB+IINK
ID=IC+IINK
IE=ID+IINK
JA=1
JB=JA+(2*M-LA)*INC2
JC=JB+2*M*INC2
JD=JC
JE=JB
C
IF (LA.EQ.M) GO TO 590
C
DO 520 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 510 IJK=1,LOT
A1=A(IB+I)+A(IE+I)
A3=A(IB+I)-A(IE+I)
A2=A(IC+I)+A(ID+I)
A4=A(IC+I)-A(ID+I)
A5=A(IA+I)-0.25*(A1+A2)
A6=QRT5*(A1-A2)
C(JA+J)=A(IA+I)+(A1+A2)
C(JB+J)=A5+A6
C(JC+J)=A5-A6
D(JB+J)=-SIN72*A3-SIN36*A4
D(JC+J)=-SIN36*A3+SIN72*A4
I=I+INC3
J=J+INC4
510 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
520 CONTINUE
JA=JA+JINK
JINK=2*JINK
JB=JB+JINK
JC=JC+JINK
JD=JD-JINK
JE=JE-JINK
IBASE=IBASE+IJUMP
IJUMP=2*IJUMP+IINK
IF (JB.EQ.JD) GO TO 560
DO 550 K=LA,KSTOP,LA
KB=K+K
KC=KB+KB
KD=KC+KB
KE=KD+KB
C1=TRIGS(KB+1)
S1=TRIGS(KB+2)
C2=TRIGS(KC+1)
S2=TRIGS(KC+2)
C3=TRIGS(KD+1)
S3=TRIGS(KD+2)
C4=TRIGS(KE+1)
S4=TRIGS(KE+2)
JBASE=0
DO 540 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 530 IJK=1,LOT
A1=(C1*A(IB+I)+S1*B(IB+I))+(C4*A(IE+I)+S4*B(IE+I))
A3=(C1*A(IB+I)+S1*B(IB+I))-(C4*A(IE+I)+S4*B(IE+I))
A2=(C2*A(IC+I)+S2*B(IC+I))+(C3*A(ID+I)+S3*B(ID+I))
A4=(C2*A(IC+I)+S2*B(IC+I))-(C3*A(ID+I)+S3*B(ID+I))
B1=(C1*B(IB+I)-S1*A(IB+I))+(C4*B(IE+I)-S4*A(IE+I))
B3=(C1*B(IB+I)-S1*A(IB+I))-(C4*B(IE+I)-S4*A(IE+I))
B2=(C2*B(IC+I)-S2*A(IC+I))+(C3*B(ID+I)-S3*A(ID+I))
B4=(C2*B(IC+I)-S2*A(IC+I))-(C3*B(ID+I)-S3*A(ID+I))
A5=A(IA+I)-0.25*(A1+A2)
A6=QRT5*(A1-A2)
B5=B(IA+I)-0.25*(B1+B2)
B6=QRT5*(B1-B2)
A10=A5+A6
A20=A5-A6
B10=B5+B6
B20=B5-B6
A11=SIN72*B3+SIN36*B4
A21=SIN36*B3-SIN72*B4
B11=SIN72*A3+SIN36*A4
B21=SIN36*A3-SIN72*A4
C(JA+J)=A(IA+I)+(A1+A2)
C(JB+J)=A10+A11
C(JE+J)=A10-A11
C(JC+J)=A20+A21
C(JD+J)=A20-A21
D(JA+J)=B(IA+I)+(B1+B2)
D(JB+J)=B10-B11
D(JE+J)=-(B10+B11)
D(JC+J)=B20-B21
D(JD+J)=-(B20+B21)
I=I+INC3
J=J+INC4
530 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
540 CONTINUE
IBASE=IBASE+IJUMP
JA=JA+JINK
JB=JB+JINK
JC=JC+JINK
JD=JD-JINK
JE=JE-JINK
550 CONTINUE
IF (JB.GT.JD) GO TO 900
560 CONTINUE
JBASE=0
DO 580 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 570 IJK=1,LOT
A1=A(IB+I)+A(IE+I)
A3=A(IB+I)-A(IE+I)
A2=A(IC+I)+A(ID+I)
A4=A(IC+I)-A(ID+I)
A5=A(IA+I)+0.25*(A3-A4)
A6=QRT5*(A3+A4)
C(JA+J)=A5+A6
C(JB+J)=A5-A6
C(JC+J)=A(IA+I)-(A3-A4)
D(JA+J)=-SIN36*A1-SIN72*A2
D(JB+J)=-SIN72*A1+SIN36*A2
I=I+INC3
J=J+INC4
570 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
580 CONTINUE
GO TO 900
C
590 CONTINUE
Z=1.0/FLOAT(N)
ZQRT5=Z*QRT5
ZSIN36=Z*SIN36
ZSIN72=Z*SIN72
DO 594 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 592 IJK=1,LOT
A1=A(IB+I)+A(IE+I)
A3=A(IB+I)-A(IE+I)
A2=A(IC+I)+A(ID+I)
A4=A(IC+I)-A(ID+I)
A5=Z*(A(IA+I)-0.25*(A1+A2))
A6=ZQRT5*(A1-A2)
C(JA+J)=Z*(A(IA+I)+(A1+A2))
C(JB+J)=A5+A6
C(JC+J)=A5-A6
D(JB+J)=-ZSIN72*A3-ZSIN36*A4
D(JC+J)=-ZSIN36*A3+ZSIN72*A4
I=I+INC3
J=J+INC4
592 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
594 CONTINUE
GO TO 900
C
C CODING FOR FACTOR 6
C -------------------
600 CONTINUE
IA=1
IB=IA+IINK
IC=IB+IINK
ID=IC+IINK
IE=ID+IINK
IF=IE+IINK
JA=1
JB=JA+(2*M-LA)*INC2
JC=JB+2*M*INC2
JD=JC+2*M*INC2
JE=JC
JF=JB
C
IF (LA.EQ.M) GO TO 690
C
DO 620 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 610 IJK=1,LOT
A11=(A(IC+I)+A(IF+I))+(A(IB+I)+A(IE+I))
C(JA+J)=(A(IA+I)+A(ID+I))+A11
C(JC+J)=(A(IA+I)+A(ID+I)-0.5*A11)
D(JC+J)=SIN60*((A(IC+I)+A(IF+I))-(A(IB+I)+A(IE+I)))
A11=(A(IC+I)-A(IF+I))+(A(IE+I)-A(IB+I))
C(JB+J)=(A(IA+I)-A(ID+I))-0.5*A11
D(JB+J)=SIN60*((A(IE+I)-A(IB+I))-(A(IC+I)-A(IF+I)))
C(JD+J)=(A(IA+I)-A(ID+I))+A11
I=I+INC3
J=J+INC4
610 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
620 CONTINUE
JA=JA+JINK
JINK=2*JINK
JB=JB+JINK
JC=JC+JINK
JD=JD-JINK
JE=JE-JINK
JF=JF-JINK
IBASE=IBASE+IJUMP
IJUMP=2*IJUMP+IINK
IF (JC.EQ.JD) GO TO 660
DO 650 K=LA,KSTOP,LA
KB=K+K
KC=KB+KB
KD=KC+KB
KE=KD+KB
KF=KE+KB
C1=TRIGS(KB+1)
S1=TRIGS(KB+2)
C2=TRIGS(KC+1)
S2=TRIGS(KC+2)
C3=TRIGS(KD+1)
S3=TRIGS(KD+2)
C4=TRIGS(KE+1)
S4=TRIGS(KE+2)
C5=TRIGS(KF+1)
S5=TRIGS(KF+2)
JBASE=0
DO 640 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 630 IJK=1,LOT
A1=C1*A(IB+I)+S1*B(IB+I)
B1=C1*B(IB+I)-S1*A(IB+I)
A2=C2*A(IC+I)+S2*B(IC+I)
B2=C2*B(IC+I)-S2*A(IC+I)
A3=C3*A(ID+I)+S3*B(ID+I)
B3=C3*B(ID+I)-S3*A(ID+I)
A4=C4*A(IE+I)+S4*B(IE+I)
B4=C4*B(IE+I)-S4*A(IE+I)
A5=C5*A(IF+I)+S5*B(IF+I)
B5=C5*B(IF+I)-S5*A(IF+I)
A11=(A2+A5)+(A1+A4)
A20=(A(IA+I)+A3)-0.5*A11
A21=SIN60*((A2+A5)-(A1+A4))
B11=(B2+B5)+(B1+B4)
B20=(B(IA+I)+B3)-0.5*B11
B21=SIN60*((B2+B5)-(B1+B4))
C(JA+J)=(A(IA+I)+A3)+A11
D(JA+J)=(B(IA+I)+B3)+B11
C(JC+J)=A20-B21
D(JC+J)=A21+B20
C(JE+J)=A20+B21
D(JE+J)=A21-B20
A11=(A2-A5)+(A4-A1)
A20=(A(IA+I)-A3)-0.5*A11
A21=SIN60*((A4-A1)-(A2-A5))
B11=(B5-B2)-(B4-B1)
B20=(B3-B(IA+I))-0.5*B11
B21=SIN60*((B5-B2)+(B4-B1))
C(JB+J)=A20-B21
D(JB+J)=A21-B20
C(JD+J)=A11+(A(IA+I)-A3)
D(JD+J)=B11+(B3-B(IA+I))
C(JF+J)=A20+B21
D(JF+J)=A21+B20
I=I+INC3
J=J+INC4
630 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
640 CONTINUE
IBASE=IBASE+IJUMP
JA=JA+JINK
JB=JB+JINK
JC=JC+JINK
JD=JD-JINK
JE=JE-JINK
JF=JF-JINK
650 CONTINUE
IF (JC.GT.JD) GO TO 900
660 CONTINUE
JBASE=0
DO 680 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 670 IJK=1,LOT
C(JA+J)=(A(IA+I)+0.5*(A(IC+I)-A(IE+I)))+ SIN60*(A(IB+I)-A(IF+I))
D(JA+J)=-(A(ID+I)+0.5*(A(IB+I)+A(IF+I)))-SIN60*(A(IC+I)+A(IE+I))
C(JB+J)=A(IA+I)-(A(IC+I)-A(IE+I))
D(JB+J)=A(ID+I)-(A(IB+I)+A(IF+I))
C(JC+J)=(A(IA+I)+0.5*(A(IC+I)-A(IE+I)))-SIN60*(A(IB+I)-A(IF+I))
D(JC+J)=-(A(ID+I)+0.5*(A(IB+I)+A(IF+I)))+SIN60*(A(IC+I)+A(IE+I))
I=I+INC3
J=J+INC4
670 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
680 CONTINUE
GO TO 900
C
690 CONTINUE
Z=1.0/FLOAT(N)
ZSIN60=Z*SIN60
DO 694 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 692 IJK=1,LOT
A11=(A(IC+I)+A(IF+I))+(A(IB+I)+A(IE+I))
C(JA+J)=Z*((A(IA+I)+A(ID+I))+A11)
C(JC+J)=Z*((A(IA+I)+A(ID+I))-0.5*A11)
D(JC+J)=ZSIN60*((A(IC+I)+A(IF+I))-(A(IB+I)+A(IE+I)))
A11=(A(IC+I)-A(IF+I))+(A(IE+I)-A(IB+I))
C(JB+J)=Z*((A(IA+I)-A(ID+I))-0.5*A11)
D(JB+J)=ZSIN60*((A(IE+I)-A(IB+I))-(A(IC+I)-A(IF+I)))
C(JD+J)=Z*((A(IA+I)-A(ID+I))+A11)
I=I+INC3
J=J+INC4
692 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
694 CONTINUE
GO TO 900
C
C CODING FOR FACTOR 8
C -------------------
800 CONTINUE
IBAD=3
IF (LA.NE.M) GO TO 910
IA=1
IB=IA+IINK
IC=IB+IINK
ID=IC+IINK
IE=ID+IINK
IF=IE+IINK
IG=IF+IINK
IH=IG+IINK
JA=1
JB=JA+LA*INC2
JC=JB+2*M*INC2
JD=JC+2*M*INC2
JE=JD+2*M*INC2
Z=1.0/FLOAT(N)
ZSIN45=Z*SQRT(0.5)
C
DO 820 L=1,LA
I=IBASE
J=JBASE
CDIR$ IVDEP
DO 810 IJK=1,LOT
C(JA+J)=Z*(((A(IA+I)+A(IE+I))+(A(IC+I)+A(IG+I)))+
* ((A(ID+I)+A(IH+I))+(A(IB+I)+A(IF+I))))
C(JE+J)=Z*(((A(IA+I)+A(IE+I))+(A(IC+I)+A(IG+I)))-
* ((A(ID+I)+A(IH+I))+(A(IB+I)+A(IF+I))))
C(JC+J)=Z*((A(IA+I)+A(IE+I))-(A(IC+I)+A(IG+I)))
D(JC+J)=Z*((A(ID+I)+A(IH+I))-(A(IB+I)+A(IF+I)))
C(JB+J)=Z*(A(IA+I)-A(IE+I))
* +ZSIN45*((A(IH+I)-A(ID+I))-(A(IF+I)-A(IB+I)))
C(JD+J)=Z*(A(IA+I)-A(IE+I))
* -ZSIN45*((A(IH+I)-A(ID+I))-(A(IF+I)-A(IB+I)))
D(JB+J)=ZSIN45*((A(IH+I)-A(ID+I))+(A(IF+I)-A(IB+I)))
* +Z*(A(IG+I)-A(IC+I))
D(JD+J)=ZSIN45*((A(IH+I)-A(ID+I))+(A(IF+I)-A(IB+I)))
* -Z*(A(IG+I)-A(IC+I))
I=I+INC3
J=J+INC4
810 CONTINUE
IBASE=IBASE+INC1
JBASE=JBASE+INC2
820 CONTINUE
C
C RETURN
C ------
900 CONTINUE
IBAD=0
910 CONTINUE
IERR=IBAD
RETURN
END
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