smallft.c

/********************************************************************
 *                                                                  *
 * THIS FILE IS PART OF THE OggVorbis SOFTWARE CODEC SOURCE CODE.   *
 * USE, DISTRIBUTION AND REPRODUCTION OF THIS LIBRARY SOURCE IS     *
 * GOVERNED BY A BSD-STYLE SOURCE LICENSE INCLUDED WITH THIS SOURCE *
 * IN 'COPYING'. PLEASE READ THESE TERMS BEFORE DISTRIBUTING.       *
 *                                                                  *
 * THE OggVorbis SOURCE CODE IS (C) COPYRIGHT 1994-2009             *
 * by the Xiph.Org Foundation https://xiph.org/                     *
 *                                                                  *
 ********************************************************************

 function: *unnormalized* fft transform

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

/* FFT implementation from OggSquish, minus cosine transforms,
 * minus all but radix 2/4 case.  In Vorbis we only need this
 * cut-down version.
 *
 * To do more than just power-of-two sized vectors, see the full
 * version I wrote for NetLib.
 *
 * Note that the packing is a little strange; rather than the FFT r/i
 * packing following R_0, I_n, R_1, I_1, R_2, I_2 ... R_n-1, I_n-1,
 * it follows R_0, R_1, I_1, R_2, I_2 ... R_n-1, I_n-1, I_n like the
 * FORTRAN version
 */

#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "smallft.h"
#include "os.h"
#include "misc.h"

static void drfti1(int n, float *wa, int *ifac){
  static int ntryh[4] = { 4,2,3,5 };
  static float tpi = 6.28318530717958648f;
  float 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=(float)ld*argh;
      fi=0.f;
      for (ii=2;ii<ido;ii+=2){
        fi+=1.f;
        arg=fi*argld;
        wa[i++]=cos(arg);
        wa[i++]=sin(arg);
      }
      is+=ido;
    }
    l1=l2;
  }
}

static void fdrffti(int n, float *wsave, int *ifac){

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

static void dradf2(int ido,int l1,float *cc,float *ch,float *wa1){
  int i,k;
  float 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;
  }
}

static void dradf4(int ido,int l1,float *cc,float *ch,float *wa1,
            float *wa2,float *wa3){
  static float hsqt2 = .70710678118654752f;
  int i,k,t0,t1,t2,t3,t4,t5,t6;
  float 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&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;
  }
}

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

  static float tpi=6.283185307179586f;
  int idij,ipph,i,j,k,l,ic,ik,is;
  int t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10;
  float dc2,ai1,ai2,ar1,ar2,ds2;
  int nbd;
  float dcp,arg,dsp,ar1h,ar2h;
  int idp2,ipp2;

  arg=tpi/(float)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.f;
  ai1=0.f;
  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;
      }
    }
  }
}

static void drftf1(int n,float *c,float *ch,float *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];
}

static void dradb2(int ido,int l1,float *cc,float *ch,float *wa1){
  int i,k,t0,t1,t2,t3,t4,t5,t6;
  float 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;
  }
}

static void dradb3(int ido,int l1,float *cc,float *ch,float *wa1,
                          float *wa2){
  static float taur = -.5f;
  static float taui = .8660254037844386f;
  int i,k,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10;
  float 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;
  }
}

static void dradb4(int ido,int l1,float *cc,float *ch,float *wa1,
                          float *wa2,float *wa3){
  static float sqrt2=1.414213562373095f;
  int i,k,t0,t1,t2,t3,t4,t5,t6,t7,t8;
  float 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;
  }
}

static void dradbg(int ido,int ip,int l1,int idl1,float *cc,float *c1,
            float *c2,float *ch,float *ch2,float *wa){
  static float tpi=6.283185307179586f;
  int idij,ipph,i,j,k,l,ik,is,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,
      t11,t12;
  float dc2,ai1,ai2,ar1,ar2,ds2;
  int nbd;
  float dcp,arg,dsp,ar1h,ar2h;
  int ipp2;

  t10=ip*ido;
  t0=l1*ido;
  arg=tpi/(float)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.f;
  ai1=0.f;
  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;
    }
  }
}

static void drftb1(int n, float *c, float *ch, float *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 drft_forward(drft_lookup *l,float *data){
  if(l->n==1)return;
  drftf1(l->n,data,l->trigcache,l->trigcache+l->n,l->splitcache);
}

void drft_backward(drft_lookup *l,float *data){
  if (l->n==1)return;
  drftb1(l->n,data,l->trigcache,l->trigcache+l->n,l->splitcache);
}

void drft_init(drft_lookup *l,int n){
  l->n=n;
  l->trigcache=_ogg_calloc(3*n,sizeof(*l->trigcache));
  l->splitcache=_ogg_calloc(32,sizeof(*l->splitcache));
  fdrffti(n, l->trigcache, l->splitcache);
}

void drft_clear(drft_lookup *l){
  if(l){
    if(l->trigcache)_ogg_free(l->trigcache);
    if(l->splitcache)_ogg_free(l->splitcache);
    memset(l,0,sizeof(*l));
  }
}