/* 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 = 0.0;
			for ( ii=2; ii<ido; ii+=2 ) {
				fi += 1.0;
				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 = 0.0;
	for( k=0; k<n; k++ ) {
		fk += 1.0;
		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 = 0.70710678118654752440084436210485;
	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 = 1.0;
	ai1 = 0.0;
	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];
	}