void fourew(NRvector<fstream*> &file, Int &na, Int &nb, Int &nc, Int &nd) {
	Int i;
	for (i=0;i<4;i++) (*file[i]).seekp(0);
	for (i=0;i<4;i++) (*file[i]).seekg(0);
	SWAP(file[1],file[3]);
	SWAP(file[0],file[2]);
	na=2;
	nb=3;
	nc=0;
	nd=1;
}
void fourfs(NRvector<fstream*> &file, VecInt_I &nn, const Int isign) {
	const Int KBF=128;
	static Int mate[4]={1,0,3,2};
	Int cc,cc0,j,j12,jk,k,kk,n=1,mm,kc=0,kd,ks,kr,na,nb,nc,nd,nr,ns,nv;
	Doub tempr,tempi,wr,wi,wpr,wpi,wtemp,theta;
	VecDoub afa(KBF),afb(KBF),afc(KBF);
	Int ndim=nn.size();
	for (j=0;j<ndim;j++) {
		n *= nn[j];
		if (nn[j] <= 1) throw("invalid Doub or wrong ndim in fourfs");
	}
	nv=0;
	jk=nn[nv];
	mm=n;
	ns=n/KBF;
	nr=ns >> 1;
	kd=KBF >> 1;
	ks=n;
	fourew(file,na,nb,nc,nd);
	for (;;) {
		theta=isign*3.141592653589793/(n/mm);
		wtemp=sin(0.5*theta);
		wpr = -2.0*wtemp*wtemp;
		wpi=sin(theta);
		wr=1.0;
		wi=0.0;
		mm >>= 1;
		for (j12=0;j12<2;j12++) {
			kr=0;
			do {
				cc0=(*file[na]).tellg()/sizeof(Doub);
				(*file[na]).read((char *) &afa[0],KBF*sizeof(Doub));
				cc=(*file[na]).tellg()/sizeof(Doub);
				if ((cc-cc0) != KBF) throw("read error 1 in fourfs");
				cc0=(*file[nb]).tellg()/sizeof(Doub);
				(*file[nb]).read((char *) &afb[0],KBF*sizeof(Doub));
				cc=(*file[nb]).tellg()/sizeof(Doub);
				if ((cc-cc0) != KBF) throw("read error 2 in fourfs");
				for (j=0;j<KBF;j+=2) {
					tempr=wr*afb[j]-wi*afb[j+1];
					tempi=wi*afb[j]+wr*afb[j+1];
					afb[j]=afa[j]-tempr;
					afa[j] += tempr;
					afb[j+1]=afa[j+1]-tempi;
					afa[j+1] += tempi;
				}
				kc += kd;
				if (kc == mm) {
					kc=0;
					wr=(wtemp=wr)*wpr-wi*wpi+wr;
					wi=wi*wpr+wtemp*wpi+wi;
				}
				cc0=(*file[nc]).tellp()/sizeof(Doub);
				(*file[nc]).write((char *) &afa[0],KBF*sizeof(Doub));
				cc=(*file[nc]).tellp()/sizeof(Doub);
				if ((cc-cc0) != KBF) throw("write error 1 in fourfs");
				cc0=(*file[nd]).tellp()/sizeof(Doub);
				(*file[nd]).write((char *) &afb[0],KBF*sizeof(Doub));
				cc=(*file[nd]).tellp()/sizeof(Doub);
				if ((cc-cc0) != KBF) throw("write error 2 in fourfs");
			} while (++kr < nr);
			if (j12 == 0 && ks != n && ks == KBF) {
				na=mate[na];
				nb=na;
			}
			if (nr == 0) break;
		}
		fourew(file,na,nb,nc,nd);
		jk >>= 1;
		while (jk == 1) {
			mm=n;
			jk=nn[++nv];
		}
		ks >>= 1;
		if (ks > KBF) {
			for (j12=0;j12<2;j12++) {
				for (kr=0;kr<ns;kr+=ks/KBF) {
					for (k=0;k<ks;k+=KBF) {
						cc0=(*file[na]).tellg()/sizeof(Doub);
						(*file[na]).read((char *) &afa[0],KBF*sizeof(Doub));
						cc=(*file[na]).tellg()/sizeof(Doub);
						if ((cc-cc0) != KBF) throw("read error 3 in fourfs");
						cc0=(*file[nc]).tellp()/sizeof(Doub);
						(*file[nc]).write((char *) &afa[0],KBF*sizeof(Doub));
						cc=(*file[nc]).tellp()/sizeof(Doub);
						if ((cc-cc0) != KBF) throw("write error 3 in fourfs");
					}
					nc=mate[nc];
				}
				na=mate[na];
			}
			fourew(file,na,nb,nc,nd);
		} else if (ks == KBF) nb=na;
		else break;
	}
	j=0;
	for (;;) {
		theta=isign*3.141592653589793/(n/mm);
		wtemp=sin(0.5*theta);
		wpr = -2.0*wtemp*wtemp;
		wpi=sin(theta);
		wr=1.0;
		wi=0.0;
		mm >>= 1;
		ks=kd;
		kd >>= 1;
		for (j12=0;j12<2;j12++) {
			for (kr=0;kr<ns;kr++) {
				cc0=(*file[na]).tellg()/sizeof(Doub);
				(*file[na]).read((char *) &afc[0],KBF*sizeof(Doub));
				cc=(*file[na]).tellg()/sizeof(Doub);
				if ((cc-cc0) != KBF) throw("read error 4 in fourfs");
				kk=0;
				k=ks;
				for (;;) {
					tempr=wr*afc[kk+ks]-wi*afc[kk+ks+1];
					tempi=wi*afc[kk+ks]+wr*afc[kk+ks+1];
					afa[j]=afc[kk]+tempr;
					afb[j]=afc[kk]-tempr;
					afa[++j]=afc[++kk]+tempi;
					afb[j++]=afc[kk++]-tempi;
					if (kk < k) continue;
					kc += kd;
					if (kc == mm) {
						kc=0;
						wr=(wtemp=wr)*wpr-wi*wpi+wr;
						wi=wi*wpr+wtemp*wpi+wi;
					}
					kk += ks;
					if (kk > KBF-1) break;
					else k=kk+ks;
				}
				if (j > KBF-1) {
					cc0=(*file[nc]).tellp()/sizeof(Doub);
					(*file[nc]).write((char *) &afa[0],KBF*sizeof(Doub));
					cc=(*file[nc]).tellp()/sizeof(Doub);
					if ((cc-cc0) != KBF) throw("write error 4 in fourfs");
					cc0=(*file[nd]).tellp()/sizeof(Doub);
					(*file[nd]).write((char *) &afb[0],KBF*sizeof(Doub));
					cc=(*file[nd]).tellp()/sizeof(Doub);
					if ((cc-cc0) != KBF) throw("write error 5 in fourfs");
					j=0;
				}
			}
			na=mate[na];
		}
		fourew(file,na,nb,nc,nd);
		jk >>= 1;
		if (jk > 1) continue;
		mm=n;
		do {
			if (nv < ndim-1) jk=nn[++nv];
			else return;
		} while (jk == 1);
	}
}