/******************************************************************
 * CopyPolicy: GNU Lesser General Public License 2.1 applies
 * Copyright (C) 1998-2008 Monty xiphmont@mit.edu
 *
 * FFT implementation from OggSquish, minus cosine transforms,
 * minus all but radix 2/4 case
 *
 * See OggSquish or NetLib for the version that can do other than just
 * power-of-two sized vectors.
 *
 ******************************************************************/

#include <stdlib.h>
#include <math.h>
#include "smallft.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;
  }
}

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 = .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&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 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:
    return; /* We're restricted to powers of two.  just fail */

  L110:
    l2=l1;
  }

  if(na==1)return;

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

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

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 dradb4(int ido,int l1,float *cc,float *ch,float *wa1,
			  float *wa2,float *wa3){
  static float sqrt2=1.4142135623730950488016887242097;
  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 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:
    return; /* silently fail.  we only do powers of two in this version */

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

  if(na==0)return;

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

static void fdrfftb(int n, float *r, float *wsave, int *ifac){
  if (n == 1)return;
  drftb1(n, r, wsave, wsave+n, ifac);
}

void fft_forward(int n, float *buf,float *trigcache,int *splitcache){
  int flag=0;

  if(!trigcache || !splitcache){
    trigcache=calloc(3*n,sizeof(float));
    splitcache=calloc(32,sizeof(int));
    fdrffti(n, trigcache, splitcache);
    flag=1;
  }

  fdrfftf(n, buf, trigcache, splitcache);

  if(flag){
    free(trigcache);
    free(splitcache);
  }
}

void fft_backward(int n, float *buf, float *trigcache,int *splitcache){
  int i;
  int flag=0;

  if(!trigcache || !splitcache){
    trigcache=calloc(3*n,sizeof(float));
    splitcache=calloc(32,sizeof(int));
    fdrffti(n, trigcache, splitcache);
    flag=1;
  }

  fdrfftb(n, buf, trigcache, splitcache);

  for(i=0;i<n;i++)buf[i]/=n;

  if(flag){
    free(trigcache);
    free(splitcache);
  }
}

void fft_i(int n, float **trigcache, int **splitcache){
  *trigcache=calloc(3*n,sizeof(float));
  *splitcache=calloc(32,sizeof(int));
  fdrffti(n, *trigcache, *splitcache);
}