fftsource.c

These Fourier routines were originally based on the Fourier routines of the same names from the

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



> From [e-mail] Tue Jun  3 14:50:15 1997
> Subject: Re: fft.c 
> Date: Tue, 03 Jun 1997 14:50:11 EDT
> From: Monty <[e-mail]>
> 
> The include files are not really necessary; they define a few macros
> depending on the compiler in use (eg, STIN becomes one of "static" or
> "static inline") and the prototypes for the functions in fft.c.  You
> should be able to compile and use the code without the headers with
> minimal modification.  The C code behaves nearly identically to the
> fortran code; inspection of the code should clarify the differences
> (eg, the 'ifac' argument).  Let me know if you need any other help
> with the code.
> 
> Monty




  file: fft.c
  function: Fast discrete Fourier and cosine transforms and inverses
  author: Monty <[e-mail]>
  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>
#include "ogg.h"
#include "fft.h"

static void drfti1(int n, float *wa, int *ifac){
  static int ntryh[4] = { 4,2,3,5 };
  static float tpi = 6.28318530717958647692528676655900577;
  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.;
      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, float *wsave, int *ifac){

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

void __ogg_fdcosqi(int n, float *wsave, int *ifac){
  static float pih = 1.57079632679489661923132169163975;
  static int k;
  static float 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,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;
  }
}

STIN void dradf4(int ido,int l1,float *cc,float *ch,float *wa1,
	    float *wa2,float *wa3){
  static float hsqt2 = .70710678118654752440084436210485;
  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%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,float *cc,float *c1,
			  float *c2,float *ch,float *ch2,float *wa){

  static float 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;
  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.;
  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,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];
}

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

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