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dfft.c

/* Notes from RFB: 

   Looks like the user-level routines are:

   Real FFT

   void __ogg_fdrffti(int n, double *wsave, int *ifac)
   void __ogg_fdrfftf(int n,double *r,double *wsave,int *ifac)
   void __ogg_fdrfftb(int n, double *r, double *wsave, int *ifac)

     __ogg_fdrffti == initialization
     __ogg_fdrfftf == forward transform
     __ogg_fdrfftb == backward transform

     Parameters are
     n == length of sequence
     r == sequence to be transformed (input)
       == transformed sequence (output)
     wsave == work array of length 2n (allocated by caller)
     ifac == work array of length 15 (allocated by caller)

   Cosine quarter-wave FFT

   void __ogg_fdcosqi(int n, double *wsave, int *ifac)
   void __ogg_fdcosqf(int n,double *x,double *wsave,int *ifac)
   void __ogg_fdcosqb(int n,double *x,double *wsave,int *ifac)
*/

/********************************************************************
 *                                                                  *
 * THIS FILE IS PART OF THE OggSQUISH SOFTWARE CODEC SOURCE CODE.   *
 *                                                                  *
 ********************************************************************

  file: fft.c
  function: Fast discrete Fourier and cosine transforms and inverses
  author: Monty <xiphmont@mit.edu>
  modifications by: Monty
  last modification date: Jul 1 1996

 ********************************************************************/

/* These Fourier routines were originally based on the Fourier
   routines of the same names from the NETLIB bihar and fftpack
   fortran libraries developed by Paul N. Swarztrauber at the National
   Center for Atmospheric Research in Boulder, CO USA.  They have been
   reimplemented in C and optimized in a few ways for OggSquish. */

/* As the original fortran libraries are public domain, the C Fourier
   routines in this file are hereby released to the public domain as
   well.  The C routines here produce output exactly equivalent to the
   original fortran routines.  Of particular interest are the facts
   that (like the original fortran), these routines can work on
   arbitrary length vectors that need not be powers of two in
   length. */

#include <math.h>
#define STIN static

static void drfti1(int n, double *wa, int *ifac){
  static int ntryh[4] = { 4,2,3,5 };
  static double tpi = 6.28318530717958647692528676655900577;
  double arg,argh,argld,fi;
  int ntry=0,i,j=-1;
  int k1, l1, l2, ib;
  int ld, ii, ip, is, nq, nr;
  int ido, ipm, nfm1;
  int nl=n;
  int nf=0;

 L101:
  j++;
  if (j < 4)
    ntry=ntryh[j];
  else
    ntry+=2;

 L104:
  nq=nl/ntry;
  nr=nl-ntry*nq;
  if (nr!=0) goto L101;

  nf++;
  ifac[nf+1]=ntry;
  nl=nq;
  if(ntry!=2)goto L107;
  if(nf==1)goto L107;

  for (i=1;i<nf;i++){
    ib=nf-i+1;
    ifac[ib+1]=ifac[ib];
  }
  ifac[2] = 2;

 L107:
  if(nl!=1)goto L104;
  ifac[0]=n;
  ifac[1]=nf;
  argh=tpi/n;
  is=0;
  nfm1=nf-1;
  l1=1;

  if(nfm1==0)return;

  for (k1=0;k1<nfm1;k1++){
    ip=ifac[k1+2];
    ld=0;
    l2=l1*ip;
    ido=n/l2;
    ipm=ip-1;

    for (j=0;j<ipm;j++){
      ld+=l1;
      i=is;
      argld=(double)ld*argh;
      fi=0.;
      for (ii=2;ii<ido;ii+=2){
      fi+=1.;
      arg=fi*argld;
      wa[i++]=cos(arg);
      wa[i++]=sin(arg);
      }
      is+=ido;
    }
    l1=l2;
  }
}

void __ogg_fdrffti(int n, double *wsave, int *ifac){

  if (n == 1) return;
  drfti1(n, wsave+n, ifac);
}

void __ogg_fdcosqi(int n, double *wsave, int *ifac){
  static double pih = 1.57079632679489661923132169163975;
  static int k;
  static double fk, dt;

  dt=pih/n;
  fk=0.;
  for(k=0;k<n;k++){
    fk+=1.;
    wsave[k] = cos(fk*dt);
  }

  __ogg_fdrffti(n, wsave+n,ifac);
}

STIN void dradf2(int ido,int l1,double *cc,double *ch,double *wa1){
  int i,k;
  double ti2,tr2;
  int t0,t1,t2,t3,t4,t5,t6;
  
  t1=0;
  t0=(t2=l1*ido);
  t3=ido<<1;
  for(k=0;k<l1;k++){
    ch[t1<<1]=cc[t1]+cc[t2];
    ch[(t1<<1)+t3-1]=cc[t1]-cc[t2];
    t1+=ido;
    t2+=ido;
  }

  if(ido<2)return;
  if(ido==2)goto L105;

  t1=0;
  t2=t0;
  for(k=0;k<l1;k++){
    t3=t2;
    t4=(t1<<1)+(ido<<1);
    t5=t1;
    t6=t1+t1;
    for(i=2;i<ido;i+=2){
      t3+=2;
      t4-=2;
      t5+=2;
      t6+=2;
      tr2=wa1[i-2]*cc[t3-1]+wa1[i-1]*cc[t3];
      ti2=wa1[i-2]*cc[t3]-wa1[i-1]*cc[t3-1];
      ch[t6]=cc[t5]+ti2;
      ch[t4]=ti2-cc[t5];
      ch[t6-1]=cc[t5-1]+tr2;
      ch[t4-1]=cc[t5-1]-tr2;
    }
    t1+=ido;
    t2+=ido;
  }

  if(ido%2==1)return;

 L105:
  t3=(t2=(t1=ido)-1);
  t2+=t0;
  for(k=0;k<l1;k++){
    ch[t1]=-cc[t2];
    ch[t1-1]=cc[t3];
    t1+=ido<<1;
    t2+=ido;
    t3+=ido;
  }
}

STIN void dradf4(int ido,int l1,double *cc,double *ch,double *wa1,
          double *wa2,double *wa3){
  static double hsqt2 = .70710678118654752440084436210485;
  int i,k,t0,t1,t2,t3,t4,t5,t6;
  double ci2,ci3,ci4,cr2,cr3,cr4,ti1,ti2,ti3,ti4,tr1,tr2,tr3,tr4;
  t0=l1*ido;
  
  t1=t0;
  t4=t1<<1;
  t2=t1+(t1<<1);
  t3=0;

  for(k=0;k<l1;k++){
    tr1=cc[t1]+cc[t2];
    tr2=cc[t3]+cc[t4];
    ch[t5=t3<<2]=tr1+tr2;
    ch[(ido<<2)+t5-1]=tr2-tr1;
    ch[(t5+=(ido<<1))-1]=cc[t3]-cc[t4];
    ch[t5]=cc[t2]-cc[t1];

    t1+=ido;
    t2+=ido;
    t3+=ido;
    t4+=ido;
  }

  if(ido<2)return;
  if(ido==2)goto L105;

  t1=0;
  for(k=0;k<l1;k++){
    t2=t1;
    t4=t1<<2;
    t5=(t6=ido<<1)+t4;
    for(i=2;i<ido;i+=2){
      t3=(t2+=2);
      t4+=2;
      t5-=2;

      t3+=t0;
      cr2=wa1[i-2]*cc[t3-1]+wa1[i-1]*cc[t3];
      ci2=wa1[i-2]*cc[t3]-wa1[i-1]*cc[t3-1];
      t3+=t0;
      cr3=wa2[i-2]*cc[t3-1]+wa2[i-1]*cc[t3];
      ci3=wa2[i-2]*cc[t3]-wa2[i-1]*cc[t3-1];
      t3+=t0;
      cr4=wa3[i-2]*cc[t3-1]+wa3[i-1]*cc[t3];
      ci4=wa3[i-2]*cc[t3]-wa3[i-1]*cc[t3-1];

      tr1=cr2+cr4;
      tr4=cr4-cr2;
      ti1=ci2+ci4;
      ti4=ci2-ci4;
      ti2=cc[t2]+ci3;
      ti3=cc[t2]-ci3;
      tr2=cc[t2-1]+cr3;
      tr3=cc[t2-1]-cr3;

      
      ch[t4-1]=tr1+tr2;
      ch[t4]=ti1+ti2;

      ch[t5-1]=tr3-ti4;
      ch[t5]=tr4-ti3;

      ch[t4+t6-1]=ti4+tr3;
      ch[t4+t6]=tr4+ti3;

      ch[t5+t6-1]=tr2-tr1;
      ch[t5+t6]=ti1-ti2;
    }
    t1+=ido;
  }
  if(ido%2==1)return;

 L105:
  
  t2=(t1=t0+ido-1)+(t0<<1);
  t3=ido<<2;
  t4=ido;
  t5=ido<<1;
  t6=ido;

  for(k=0;k<l1;k++){
    ti1=-hsqt2*(cc[t1]+cc[t2]);
    tr1=hsqt2*(cc[t1]-cc[t2]);
    ch[t4-1]=tr1+cc[t6-1];
    ch[t4+t5-1]=cc[t6-1]-tr1;
    ch[t4]=ti1-cc[t1+t0];
    ch[t4+t5]=ti1+cc[t1+t0];
    t1+=ido;
    t2+=ido;
    t4+=t3;
    t6+=ido;
  }
}

STIN void dradfg(int ido,int ip,int l1,int idl1,double *cc,double *c1,
                    double *c2,double *ch,double *ch2,double *wa){

  static double tpi=6.28318530717958647692528676655900577;
  int idij,ipph,i,j,k,l,ic,ik,is;
  int t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10;
  double dc2,ai1,ai2,ar1,ar2,ds2;
  int nbd;
  double dcp,arg,dsp,ar1h,ar2h;
  int idp2,ipp2;
  
  arg=tpi/(double)ip;
  dcp=cos(arg);
  dsp=sin(arg);
  ipph=(ip+1)>>1;
  ipp2=ip;
  idp2=ido;
  nbd=(ido-1)>>1;
  t0=l1*ido;
  t10=ip*ido;

  if(ido==1)goto L119;
  for(ik=0;ik<idl1;ik++)ch2[ik]=c2[ik];

  t1=0;
  for(j=1;j<ip;j++){
    t1+=t0;
    t2=t1;
    for(k=0;k<l1;k++){
      ch[t2]=c1[t2];
      t2+=ido;
    }
  }

  is=-ido;
  t1=0;
  if(nbd>l1){
    for(j=1;j<ip;j++){
      t1+=t0;
      is+=ido;
      t2= -ido+t1;
      for(k=0;k<l1;k++){
      idij=is-1;
      t2+=ido;
      t3=t2;
      for(i=2;i<ido;i+=2){
        idij+=2;
        t3+=2;
        ch[t3-1]=wa[idij-1]*c1[t3-1]+wa[idij]*c1[t3];
        ch[t3]=wa[idij-1]*c1[t3]-wa[idij]*c1[t3-1];
      }
      }
    }
  }else{

    for(j=1;j<ip;j++){
      is+=ido;
      idij=is-1;
      t1+=t0;
      t2=t1;
      for(i=2;i<ido;i+=2){
      idij+=2;
      t2+=2;
      t3=t2;
      for(k=0;k<l1;k++){
        ch[t3-1]=wa[idij-1]*c1[t3-1]+wa[idij]*c1[t3];
        ch[t3]=wa[idij-1]*c1[t3]-wa[idij]*c1[t3-1];
        t3+=ido;
      }
      }
    }
  }

  t1=0;
  t2=ipp2*t0;
  if(nbd<l1){
    for(j=1;j<ipph;j++){
      t1+=t0;
      t2-=t0;
      t3=t1;
      t4=t2;
      for(i=2;i<ido;i+=2){
      t3+=2;
      t4+=2;
      t5=t3-ido;
      t6=t4-ido;
      for(k=0;k<l1;k++){
        t5+=ido;
        t6+=ido;
        c1[t5-1]=ch[t5-1]+ch[t6-1];
        c1[t6-1]=ch[t5]-ch[t6];
        c1[t5]=ch[t5]+ch[t6];
        c1[t6]=ch[t6-1]-ch[t5-1];
      }
      }
    }
  }else{
    for(j=1;j<ipph;j++){
      t1+=t0;
      t2-=t0;
      t3=t1;
      t4=t2;
      for(k=0;k<l1;k++){
      t5=t3;
      t6=t4;
      for(i=2;i<ido;i+=2){
        t5+=2;
        t6+=2;
        c1[t5-1]=ch[t5-1]+ch[t6-1];
        c1[t6-1]=ch[t5]-ch[t6];
        c1[t5]=ch[t5]+ch[t6];
        c1[t6]=ch[t6-1]-ch[t5-1];
      }
      t3+=ido;
      t4+=ido;
      }
    }
  }

L119:
  for(ik=0;ik<idl1;ik++)c2[ik]=ch2[ik];

  t1=0;
  t2=ipp2*idl1;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1-ido;
    t4=t2-ido;
    for(k=0;k<l1;k++){
      t3+=ido;
      t4+=ido;
      c1[t3]=ch[t3]+ch[t4];
      c1[t4]=ch[t4]-ch[t3];
    }
  }

  ar1=1.;
  ai1=0.;
  t1=0;
  t2=ipp2*idl1;
  t3=(ip-1)*idl1;
  for(l=1;l<ipph;l++){
    t1+=idl1;
    t2-=idl1;
    ar1h=dcp*ar1-dsp*ai1;
    ai1=dcp*ai1+dsp*ar1;
    ar1=ar1h;
    t4=t1;
    t5=t2;
    t6=t3;
    t7=idl1;

    for(ik=0;ik<idl1;ik++){
      ch2[t4++]=c2[ik]+ar1*c2[t7++];
      ch2[t5++]=ai1*c2[t6++];
    }

    dc2=ar1;
    ds2=ai1;
    ar2=ar1;
    ai2=ai1;

    t4=idl1;
    t5=(ipp2-1)*idl1;
    for(j=2;j<ipph;j++){
      t4+=idl1;
      t5-=idl1;

      ar2h=dc2*ar2-ds2*ai2;
      ai2=dc2*ai2+ds2*ar2;
      ar2=ar2h;

      t6=t1;
      t7=t2;
      t8=t4;
      t9=t5;
      for(ik=0;ik<idl1;ik++){
      ch2[t6++]+=ar2*c2[t8++];
      ch2[t7++]+=ai2*c2[t9++];
      }
    }
  }

  t1=0;
  for(j=1;j<ipph;j++){
    t1+=idl1;
    t2=t1;
    for(ik=0;ik<idl1;ik++)ch2[ik]+=c2[t2++];
  }

  if(ido<l1)goto L132;

  t1=0;
  t2=0;
  for(k=0;k<l1;k++){
    t3=t1;
    t4=t2;
    for(i=0;i<ido;i++)cc[t4++]=ch[t3++];
    t1+=ido;
    t2+=t10;
  }

  goto L135;

 L132:
  for(i=0;i<ido;i++){
    t1=i;
    t2=i;
    for(k=0;k<l1;k++){
      cc[t2]=ch[t1];
      t1+=ido;
      t2+=t10;
    }
  }

 L135:
  t1=0;
  t2=ido<<1;
  t3=0;
  t4=ipp2*t0;
  for(j=1;j<ipph;j++){

    t1+=t2;
    t3+=t0;
    t4-=t0;

    t5=t1;
    t6=t3;
    t7=t4;

    for(k=0;k<l1;k++){
      cc[t5-1]=ch[t6];
      cc[t5]=ch[t7];
      t5+=t10;
      t6+=ido;
      t7+=ido;
    }
  }

  if(ido==1)return;
  if(nbd<l1)goto L141;

  t1=-ido;
  t3=0;
  t4=0;
  t5=ipp2*t0;
  for(j=1;j<ipph;j++){
    t1+=t2;
    t3+=t2;
    t4+=t0;
    t5-=t0;
    t6=t1;
    t7=t3;
    t8=t4;
    t9=t5;
    for(k=0;k<l1;k++){
      for(i=2;i<ido;i+=2){
      ic=idp2-i;
      cc[i+t7-1]=ch[i+t8-1]+ch[i+t9-1];
      cc[ic+t6-1]=ch[i+t8-1]-ch[i+t9-1];
      cc[i+t7]=ch[i+t8]+ch[i+t9];
      cc[ic+t6]=ch[i+t9]-ch[i+t8];
      }
      t6+=t10;
      t7+=t10;
      t8+=ido;
      t9+=ido;
    }
  }
  return;

 L141:

  t1=-ido;
  t3=0;
  t4=0;
  t5=ipp2*t0;
  for(j=1;j<ipph;j++){
    t1+=t2;
    t3+=t2;
    t4+=t0;
    t5-=t0;
    for(i=2;i<ido;i+=2){
      t6=idp2+t1-i;
      t7=i+t3;
      t8=i+t4;
      t9=i+t5;
      for(k=0;k<l1;k++){
      cc[t7-1]=ch[t8-1]+ch[t9-1];
      cc[t6-1]=ch[t8-1]-ch[t9-1];
      cc[t7]=ch[t8]+ch[t9];
      cc[t6]=ch[t9]-ch[t8];
      t6+=t10;
      t7+=t10;
      t8+=ido;
      t9+=ido;
      }
    }
  }
}

STIN void drftf1(int n,double *c,double *ch,double *wa,int *ifac){
  int i,k1,l1,l2;
  int na,kh,nf;
  int ip,iw,ido,idl1,ix2,ix3;

  nf=ifac[1];
  na=1;
  l2=n;
  iw=n;

  for(k1=0;k1<nf;k1++){
    kh=nf-k1;
    ip=ifac[kh+1];
    l1=l2/ip;
    ido=n/l2;
    idl1=ido*l1;
    iw-=(ip-1)*ido;
    na=1-na;

    if(ip!=4)goto L102;

    ix2=iw+ido;
    ix3=ix2+ido;
    if(na!=0)
      dradf4(ido,l1,ch,c,wa+iw-1,wa+ix2-1,wa+ix3-1);
    else
      dradf4(ido,l1,c,ch,wa+iw-1,wa+ix2-1,wa+ix3-1);
    goto L110;

 L102:
    if(ip!=2)goto L104;
    if(na!=0)goto L103;

    dradf2(ido,l1,c,ch,wa+iw-1);
    goto L110;

  L103:
    dradf2(ido,l1,ch,c,wa+iw-1);
    goto L110;

  L104:
    if(ido==1)na=1-na;
    if(na!=0)goto L109;

    dradfg(ido,ip,l1,idl1,c,c,c,ch,ch,wa+iw-1);
    na=1;
    goto L110;

  L109:
    dradfg(ido,ip,l1,idl1,ch,ch,ch,c,c,wa+iw-1);
    na=0;

  L110:
    l2=l1;
  }

  if(na==1)return;

  for(i=0;i<n;i++)c[i]=ch[i];
}

void __ogg_fdrfftf(int n,double *r,double *wsave,int *ifac){
  if(n==1)return;
  drftf1(n,r,wsave,wsave+n,ifac);
}

STIN void dcsqf1(int n,double *x,double *w,double *xh,int *ifac){
  int modn,i,k,kc;
  int np2,ns2;
  double xim1;

  ns2=(n+1)>>1;
  np2=n;

  kc=np2;
  for(k=1;k<ns2;k++){
    kc--;
    xh[k]=x[k]+x[kc];
    xh[kc]=x[k]-x[kc];
  }

  modn=n%2;
  if(modn==0)xh[ns2]=x[ns2]+x[ns2];

  for(k=1;k<ns2;k++){
    kc=np2-k;
    x[k]=w[k-1]*xh[kc]+w[kc-1]*xh[k];
    x[kc]=w[k-1]*xh[k]-w[kc-1]*xh[kc];
  }

  if(modn==0)x[ns2]=w[ns2-1]*xh[ns2];

  __ogg_fdrfftf(n,x,xh,ifac);

  for(i=2;i<n;i+=2){
    xim1=x[i-1]-x[i];
    x[i]=x[i-1]+x[i];
    x[i-1]=xim1;
  }
}

void __ogg_fdcosqf(int n,double *x,double *wsave,int *ifac){
    static double sqrt2=1.4142135623730950488016887242097;
    double tsqx;

  switch(n){
  case 0:case 1:
    return;
  case 2:
    tsqx=sqrt2*x[1];
    x[1]=x[0]-tsqx;
    x[0]+=tsqx;
    return;
  default:
    dcsqf1(n,x,wsave,wsave+n,ifac);
    return;
  }
}

STIN void dradb2(int ido,int l1,double *cc,double *ch,double *wa1){
  int i,k,t0,t1,t2,t3,t4,t5,t6;
  double ti2,tr2;

  t0=l1*ido;
  
  t1=0;
  t2=0;
  t3=(ido<<1)-1;
  for(k=0;k<l1;k++){
    ch[t1]=cc[t2]+cc[t3+t2];
    ch[t1+t0]=cc[t2]-cc[t3+t2];
    t2=(t1+=ido)<<1;
  }

  if(ido<2)return;
  if(ido==2)goto L105;

  t1=0;
  t2=0;
  for(k=0;k<l1;k++){
    t3=t1;
    t5=(t4=t2)+(ido<<1);
    t6=t0+t1;
    for(i=2;i<ido;i+=2){
      t3+=2;
      t4+=2;
      t5-=2;
      t6+=2;
      ch[t3-1]=cc[t4-1]+cc[t5-1];
      tr2=cc[t4-1]-cc[t5-1];
      ch[t3]=cc[t4]-cc[t5];
      ti2=cc[t4]+cc[t5];
      ch[t6-1]=wa1[i-2]*tr2-wa1[i-1]*ti2;
      ch[t6]=wa1[i-2]*ti2+wa1[i-1]*tr2;
    }
    t2=(t1+=ido)<<1;
  }

  if(ido%2==1)return;

L105:
  t1=ido-1;
  t2=ido-1;
  for(k=0;k<l1;k++){
    ch[t1]=cc[t2]+cc[t2];
    ch[t1+t0]=-(cc[t2+1]+cc[t2+1]);
    t1+=ido;
    t2+=ido<<1;
  }
}

STIN void dradb3(int ido,int l1,double *cc,double *ch,double *wa1,
                    double *wa2){
  static double taur = -.5;
  static double taui = .86602540378443864676372317075293618;
  int i,k,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10;
  double ci2,ci3,di2,di3,cr2,cr3,dr2,dr3,ti2,tr2;
  t0=l1*ido;

  t1=0;
  t2=t0<<1;
  t3=ido<<1;
  t4=ido+(ido<<1);
  t5=0;
  for(k=0;k<l1;k++){
    tr2=cc[t3-1]+cc[t3-1];
    cr2=cc[t5]+(taur*tr2);
    ch[t1]=cc[t5]+tr2;
    ci3=taui*(cc[t3]+cc[t3]);
    ch[t1+t0]=cr2-ci3;
    ch[t1+t2]=cr2+ci3;
    t1+=ido;
    t3+=t4;
    t5+=t4;
  }

  if(ido==1)return;

  t1=0;
  t3=ido<<1;
  for(k=0;k<l1;k++){
    t7=t1+(t1<<1);
    t6=(t5=t7+t3);
    t8=t1;
    t10=(t9=t1+t0)+t0;

    for(i=2;i<ido;i+=2){
      t5+=2;
      t6-=2;
      t7+=2;
      t8+=2;
      t9+=2;
      t10+=2;
      tr2=cc[t5-1]+cc[t6-1];
      cr2=cc[t7-1]+(taur*tr2);
      ch[t8-1]=cc[t7-1]+tr2;
      ti2=cc[t5]-cc[t6];
      ci2=cc[t7]+(taur*ti2);
      ch[t8]=cc[t7]+ti2;
      cr3=taui*(cc[t5-1]-cc[t6-1]);
      ci3=taui*(cc[t5]+cc[t6]);
      dr2=cr2-ci3;
      dr3=cr2+ci3;
      di2=ci2+cr3;
      di3=ci2-cr3;
      ch[t9-1]=wa1[i-2]*dr2-wa1[i-1]*di2;
      ch[t9]=wa1[i-2]*di2+wa1[i-1]*dr2;
      ch[t10-1]=wa2[i-2]*dr3-wa2[i-1]*di3;
      ch[t10]=wa2[i-2]*di3+wa2[i-1]*dr3;
    }
    t1+=ido;
  }
}

STIN void dradb4(int ido,int l1,double *cc,double *ch,double *wa1,
                    double *wa2,double *wa3){
  static double sqrt2=1.4142135623730950488016887242097;
  int i,k,t0,t1,t2,t3,t4,t5,t6,t7,t8;
  double ci2,ci3,ci4,cr2,cr3,cr4,ti1,ti2,ti3,ti4,tr1,tr2,tr3,tr4;
  t0=l1*ido;
  
  t1=0;
  t2=ido<<2;
  t3=0;
  t6=ido<<1;
  for(k=0;k<l1;k++){
    t4=t3+t6;
    t5=t1;
    tr3=cc[t4-1]+cc[t4-1];
    tr4=cc[t4]+cc[t4]; 
    tr1=cc[t3]-cc[(t4+=t6)-1];
    tr2=cc[t3]+cc[t4-1];
    ch[t5]=tr2+tr3;
    ch[t5+=t0]=tr1-tr4;
    ch[t5+=t0]=tr2-tr3;
    ch[t5+=t0]=tr1+tr4;
    t1+=ido;
    t3+=t2;
  }

  if(ido<2)return;
  if(ido==2)goto L105;

  t1=0;
  for(k=0;k<l1;k++){
    t5=(t4=(t3=(t2=t1<<2)+t6))+t6;
    t7=t1;
    for(i=2;i<ido;i+=2){
      t2+=2;
      t3+=2;
      t4-=2;
      t5-=2;
      t7+=2;
      ti1=cc[t2]+cc[t5];
      ti2=cc[t2]-cc[t5];
      ti3=cc[t3]-cc[t4];
      tr4=cc[t3]+cc[t4];
      tr1=cc[t2-1]-cc[t5-1];
      tr2=cc[t2-1]+cc[t5-1];
      ti4=cc[t3-1]-cc[t4-1];
      tr3=cc[t3-1]+cc[t4-1];
      ch[t7-1]=tr2+tr3;
      cr3=tr2-tr3;
      ch[t7]=ti2+ti3;
      ci3=ti2-ti3;
      cr2=tr1-tr4;
      cr4=tr1+tr4;
      ci2=ti1+ti4;
      ci4=ti1-ti4;

      ch[(t8=t7+t0)-1]=wa1[i-2]*cr2-wa1[i-1]*ci2;
      ch[t8]=wa1[i-2]*ci2+wa1[i-1]*cr2;
      ch[(t8+=t0)-1]=wa2[i-2]*cr3-wa2[i-1]*ci3;
      ch[t8]=wa2[i-2]*ci3+wa2[i-1]*cr3;
      ch[(t8+=t0)-1]=wa3[i-2]*cr4-wa3[i-1]*ci4;
      ch[t8]=wa3[i-2]*ci4+wa3[i-1]*cr4;
    }
    t1+=ido;
  }

  if(ido%2 == 1)return;

 L105:

  t1=ido;
  t2=ido<<2;
  t3=ido-1;
  t4=ido+(ido<<1);
  for(k=0;k<l1;k++){
    t5=t3;
    ti1=cc[t1]+cc[t4];
    ti2=cc[t4]-cc[t1];
    tr1=cc[t1-1]-cc[t4-1];
    tr2=cc[t1-1]+cc[t4-1];
    ch[t5]=tr2+tr2;
    ch[t5+=t0]=sqrt2*(tr1-ti1);
    ch[t5+=t0]=ti2+ti2;
    ch[t5+=t0]=-sqrt2*(tr1+ti1);

    t3+=ido;
    t1+=t2;
    t4+=t2;
  }
}

STIN void dradbg(int ido,int ip,int l1,int idl1,double *cc,double *c1,
          double *c2,double *ch,double *ch2,double *wa){
  static double tpi=6.28318530717958647692528676655900577;
  int idij,ipph,i,j,k,l,ik,is,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,
      t11,t12;
  double dc2,ai1,ai2,ar1,ar2,ds2;
  int nbd;
  double dcp,arg,dsp,ar1h,ar2h;
  int ipp2;

  t10=ip*ido;
  t0=l1*ido;
  arg=tpi/(double)ip;
  dcp=cos(arg);
  dsp=sin(arg);
  nbd=(ido-1)>>1;
  ipp2=ip;
  ipph=(ip+1)>>1;
  if(ido<l1)goto L103;
  
  t1=0;
  t2=0;
  for(k=0;k<l1;k++){
    t3=t1;
    t4=t2;
    for(i=0;i<ido;i++){
      ch[t3]=cc[t4];
      t3++;
      t4++;
    }
    t1+=ido;
    t2+=t10;
  }
  goto L106;

 L103:
  t1=0;
  for(i=0;i<ido;i++){
    t2=t1;
    t3=t1;
    for(k=0;k<l1;k++){
      ch[t2]=cc[t3];
      t2+=ido;
      t3+=t10;
    }
    t1++;
  }

 L106:
  t1=0;
  t2=ipp2*t0;
  t7=(t5=ido<<1);
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;
    t6=t5;
    for(k=0;k<l1;k++){
      ch[t3]=cc[t6-1]+cc[t6-1];
      ch[t4]=cc[t6]+cc[t6];
      t3+=ido;
      t4+=ido;
      t6+=t10;
    }
    t5+=t7;
  }

  if (ido == 1)goto L116;
  if(nbd<l1)goto L112;

  t1=0;
  t2=ipp2*t0;
  t7=0;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;

    t7+=(ido<<1);
    t8=t7;
    for(k=0;k<l1;k++){
      t5=t3;
      t6=t4;
      t9=t8;
      t11=t8;
      for(i=2;i<ido;i+=2){
      t5+=2;
      t6+=2;
      t9+=2;
      t11-=2;
      ch[t5-1]=cc[t9-1]+cc[t11-1];
      ch[t6-1]=cc[t9-1]-cc[t11-1];
      ch[t5]=cc[t9]-cc[t11];
      ch[t6]=cc[t9]+cc[t11];
      }
      t3+=ido;
      t4+=ido;
      t8+=t10;
    }
  }
  goto L116;

 L112:
  t1=0;
  t2=ipp2*t0;
  t7=0;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;
    t7+=(ido<<1);
    t8=t7;
    t9=t7;
    for(i=2;i<ido;i+=2){
      t3+=2;
      t4+=2;
      t8+=2;
      t9-=2;
      t5=t3;
      t6=t4;
      t11=t8;
      t12=t9;
      for(k=0;k<l1;k++){
      ch[t5-1]=cc[t11-1]+cc[t12-1];
      ch[t6-1]=cc[t11-1]-cc[t12-1];
      ch[t5]=cc[t11]-cc[t12];
      ch[t6]=cc[t11]+cc[t12];
      t5+=ido;
      t6+=ido;
      t11+=t10;
      t12+=t10;
      }
    }
  }

L116:
  ar1=1.;
  ai1=0.;
  t1=0;
  t9=(t2=ipp2*idl1);
  t3=(ip-1)*idl1;
  for(l=1;l<ipph;l++){
    t1+=idl1;
    t2-=idl1;

    ar1h=dcp*ar1-dsp*ai1;
    ai1=dcp*ai1+dsp*ar1;
    ar1=ar1h;
    t4=t1;
    t5=t2;
    t6=0;
    t7=idl1;
    t8=t3;
    for(ik=0;ik<idl1;ik++){
      c2[t4++]=ch2[t6++]+ar1*ch2[t7++];
      c2[t5++]=ai1*ch2[t8++];
    }
    dc2=ar1;
    ds2=ai1;
    ar2=ar1;
    ai2=ai1;

    t6=idl1;
    t7=t9-idl1;
    for(j=2;j<ipph;j++){
      t6+=idl1;
      t7-=idl1;
      ar2h=dc2*ar2-ds2*ai2;
      ai2=dc2*ai2+ds2*ar2;
      ar2=ar2h;
      t4=t1;
      t5=t2;
      t11=t6;
      t12=t7;
      for(ik=0;ik<idl1;ik++){
      c2[t4++]+=ar2*ch2[t11++];
      c2[t5++]+=ai2*ch2[t12++];
      }
    }
  }

  t1=0;
  for(j=1;j<ipph;j++){
    t1+=idl1;
    t2=t1;
    for(ik=0;ik<idl1;ik++)ch2[ik]+=ch2[t2++];
  }

  t1=0;
  t2=ipp2*t0;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;
    for(k=0;k<l1;k++){
      ch[t3]=c1[t3]-c1[t4];
      ch[t4]=c1[t3]+c1[t4];
      t3+=ido;
      t4+=ido;
    }
  }

  if(ido==1)goto L132;
  if(nbd<l1)goto L128;

  t1=0;
  t2=ipp2*t0;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;
    for(k=0;k<l1;k++){
      t5=t3;
      t6=t4;
      for(i=2;i<ido;i+=2){
      t5+=2;
      t6+=2;
      ch[t5-1]=c1[t5-1]-c1[t6];
      ch[t6-1]=c1[t5-1]+c1[t6];
      ch[t5]=c1[t5]+c1[t6-1];
      ch[t6]=c1[t5]-c1[t6-1];
      }
      t3+=ido;
      t4+=ido;
    }
  }
  goto L132;

 L128:
  t1=0;
  t2=ipp2*t0;
  for(j=1;j<ipph;j++){
    t1+=t0;
    t2-=t0;
    t3=t1;
    t4=t2;
    for(i=2;i<ido;i+=2){
      t3+=2;
      t4+=2;
      t5=t3;
      t6=t4;
      for(k=0;k<l1;k++){
      ch[t5-1]=c1[t5-1]-c1[t6];
      ch[t6-1]=c1[t5-1]+c1[t6];
      ch[t5]=c1[t5]+c1[t6-1];
      ch[t6]=c1[t5]-c1[t6-1];
      t5+=ido;
      t6+=ido;
      }
    }
  }

L132:
  if(ido==1)return;

  for(ik=0;ik<idl1;ik++)c2[ik]=ch2[ik];

  t1=0;
  for(j=1;j<ip;j++){
    t2=(t1+=t0);
    for(k=0;k<l1;k++){
      c1[t2]=ch[t2];
      t2+=ido;
    }
  }

  if(nbd>l1)goto L139;

  is= -ido-1;
  t1=0;
  for(j=1;j<ip;j++){
    is+=ido;
    t1+=t0;
    idij=is;
    t2=t1;
    for(i=2;i<ido;i+=2){
      t2+=2;
      idij+=2;
      t3=t2;
      for(k=0;k<l1;k++){
      c1[t3-1]=wa[idij-1]*ch[t3-1]-wa[idij]*ch[t3];
      c1[t3]=wa[idij-1]*ch[t3]+wa[idij]*ch[t3-1];
      t3+=ido;
      }
    }
  }
  return;

 L139:
  is= -ido-1;
  t1=0;
  for(j=1;j<ip;j++){
    is+=ido;
    t1+=t0;
    t2=t1;
    for(k=0;k<l1;k++){
      idij=is;
      t3=t2;
      for(i=2;i<ido;i+=2){
      idij+=2;
      t3+=2;
      c1[t3-1]=wa[idij-1]*ch[t3-1]-wa[idij]*ch[t3];
      c1[t3]=wa[idij-1]*ch[t3]+wa[idij]*ch[t3-1];
      }
      t2+=ido;
    }
  }
}

STIN void drftb1(int n, double *c, double *ch, double *wa, int *ifac){
  int i,k1,l1,l2;
  int na;
  int nf,ip,iw,ix2,ix3,ido,idl1;

  nf=ifac[1];
  na=0;
  l1=1;
  iw=1;

  for(k1=0;k1<nf;k1++){
    ip=ifac[k1 + 2];
    l2=ip*l1;
    ido=n/l2;
    idl1=ido*l1;
    if(ip!=4)goto L103;
    ix2=iw+ido;
    ix3=ix2+ido;

    if(na!=0)
      dradb4(ido,l1,ch,c,wa+iw-1,wa+ix2-1,wa+ix3-1);
    else
      dradb4(ido,l1,c,ch,wa+iw-1,wa+ix2-1,wa+ix3-1);
    na=1-na;
    goto L115;

  L103:
    if(ip!=2)goto L106;

    if(na!=0)
      dradb2(ido,l1,ch,c,wa+iw-1);
    else
      dradb2(ido,l1,c,ch,wa+iw-1);
    na=1-na;
    goto L115;

  L106:
    if(ip!=3)goto L109;

    ix2=iw+ido;
    if(na!=0)
      dradb3(ido,l1,ch,c,wa+iw-1,wa+ix2-1);
    else
      dradb3(ido,l1,c,ch,wa+iw-1,wa+ix2-1);
    na=1-na;
    goto L115;

  L109:
/*    The radix five case can be translated later..... */
/*    if(ip!=5)goto L112;

    ix2=iw+ido;
    ix3=ix2+ido;
    ix4=ix3+ido;
    if(na!=0)
      dradb5(ido,l1,ch,c,wa+iw-1,wa+ix2-1,wa+ix3-1,wa+ix4-1);
    else
      dradb5(ido,l1,c,ch,wa+iw-1,wa+ix2-1,wa+ix3-1,wa+ix4-1);
    na=1-na;
    goto L115;

  L112:*/
    if(na!=0)
      dradbg(ido,ip,l1,idl1,ch,ch,ch,c,c,wa+iw-1);
    else
      dradbg(ido,ip,l1,idl1,c,c,c,ch,ch,wa+iw-1);
    if(ido==1)na=1-na;

  L115:
    l1=l2;
    iw+=(ip-1)*ido;
  }

  if(na==0)return;

  for(i=0;i<n;i++)c[i]=ch[i];
}

void __ogg_fdrfftb(int n, double *r, double *wsave, int *ifac){
  if (n == 1)return;
  drftb1(n, r, wsave, wsave+n, ifac);
}

STIN void dcsqb1(int n,double *x,double *w,double *xh,int *ifac){
  int modn,i,k,kc;
  int np2,ns2;
  double xim1;

  ns2=(n+1)>>1;
  np2=n;

  for(i=2;i<n;i+=2){
    xim1=x[i-1]+x[i];
    x[i]-=x[i-1];
    x[i-1]=xim1;
  }

  x[0]+=x[0];
  modn=n%2;
  if(modn==0)x[n-1]+=x[n-1];

  __ogg_fdrfftb(n,x,xh,ifac);

  kc=np2;
  for(k=1;k<ns2;k++){
    kc--;
    xh[k]=w[k-1]*x[kc]+w[kc-1]*x[k];
    xh[kc]=w[k-1]*x[k]-w[kc-1]*x[kc];
  }

  if(modn==0)x[ns2]=w[ns2-1]*(x[ns2]+x[ns2]);

  kc=np2;
  for(k=1;k<ns2;k++){
    kc--;
    x[k]=xh[k]+xh[kc];
    x[kc]=xh[k]-xh[kc];
  }
  x[0]+=x[0];
}

void __ogg_fdcosqb(int n,double *x,double *wsave,int *ifac){
  static double tsqrt2 = 2.8284271247461900976033774484194;
  double x1;

  if(n<2){
    x[0]*=4;
    return;
  }
  if(n==2){
    x1=(x[0]+x[1])*4;
    x[1]=tsqrt2*(x[0]-x[1]);
    x[0]=x1;
    return;
  }
  
  dcsqb1(n,x,wsave,wsave+n,ifac);
}

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