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

  function: Fast discrete Fourier and cosine transforms and inverses
  author: Monty <xiphmont@mit.edu>
  modifications by: Monty
  last modification date: Jul 1 1996
  
  djmw 20030630 Adapted for praat (replaced 'int' declarations with 'long').
  djmw 20040511 Made all local variables type double to increase numerical precision.

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

/* 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. */

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

static void NUMrffti (long n, FFT_DATA_TYPE * wsave, long *ifac)
{

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

/* void NUMcosqi(long n, FFT_DATA_TYPE *wsave, long *ifac){ static
   double pih = 1.57079632679489661923132169163975; static long k;
   static double fk, dt;

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

   NUMrffti(n, wsave+n,ifac); } */

static void dradf2 (long ido, long l1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa1)
{
	long i, k;
	double ti2, tr2;
	long 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 (long ido, long l1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa1,
	FFT_DATA_TYPE * wa2, FFT_DATA_TYPE * wa3)
{
	static double hsqt2 = .70710678118654752440084436210485;
	long 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;
	}
}

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

	static double tpi = 6.28318530717958647692528676655900577;
	long idij, ipph, i, j, k, l, ic, ik, is;
	long t0, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10;
	double dc2, ai1, ai2, ar1, ar2, ds2;
	long nbd;
	double dcp, arg, dsp, ar1h, ar2h;
	long 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;
			}
		}
	}
}

static void drftf1 (long n, FFT_DATA_TYPE * c, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa, long *ifac)
{
	long i, k1, l1, l2;
	long na, kh, nf;
	long 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 (long ido, long l1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa1)
{
	long 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;
	}
}

static void dradb3 (long ido, long l1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa1,
	FFT_DATA_TYPE * wa2)
{
	static double taur = -.5;
	static double taui = .86602540378443864676372317075293618;
	long 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;
	}
}

static void dradb4 (long ido, long l1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa1,
	FFT_DATA_TYPE * wa2, FFT_DATA_TYPE * wa3)
{
	static double sqrt2 = 1.4142135623730950488016887242097;
	long 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;
	}
}

static void dradbg (long ido, long ip, long l1, long idl1, FFT_DATA_TYPE * cc, FFT_DATA_TYPE * c1,
	FFT_DATA_TYPE * c2, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * ch2, FFT_DATA_TYPE * wa)
{
	static double tpi = 6.28318530717958647692528676655900577;
	long 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;
	long nbd;
	double dcp, arg, dsp, ar1h, ar2h;
	long 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;
		}
	}
}

static void drftb1 (long n, FFT_DATA_TYPE * c, FFT_DATA_TYPE * ch, FFT_DATA_TYPE * wa, long *ifac)
{
	long i, k1, l1, l2;
	long na;
	long 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];
}

/* End of file NUMfft_core.h */