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lipsync/trunk/bocoree/fft.cs

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/*
* fft.cs
* Copyright (c) 2008-2009 kbinani
*
* Part of this is derived from
* General Purpose FFT (Fast Fourier/Cosine/Sine Transform) Package
* Copyright(C) 1996-2001 Takuya OOURA
* (http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html)
*
* This file is part of bocoree.
*
* bocoree is free software; you can redistribute it and/or
* modify it under the terms of the BSD License.
*
* bocoree is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
*/
using System;
namespace bocoree {
public static unsafe class fft_test {
const int NMAXSQRT = 64;
const int NMAX = 8192;
static double RND( ref int seed ) {
seed = (seed * 7141 + 54773) % 259200;
return seed * (1.0 / 259200.0);
}
public static int test() {
int n;
int[] ip_ = new int[NMAXSQRT + 2];
double[] a_ = new double[NMAX + 1];
double[] w_ = new double[NMAX * 5 / 4];
double[] t_ = new double[NMAX / 2 + 1];
double err;
fixed ( int* ip = &ip_[0] )
fixed ( double* a = &a_[0] )
fixed ( double* w = &w_[0] )
fixed ( double* t = &t_[0] ) {
Console.WriteLine( "data length n=? (must be 2^m)" );
string ret = Console.ReadLine();
n = int.Parse( ret );
ip[0] = 0;
int np = 100;
using ( System.IO.StreamWriter sw = new System.IO.StreamWriter( @"c:\rdft_data.txt" ) ) {
for ( int i = 0; i < n; i++ ) {
double x = (double)i / (double)n;
a_[i] = Math.Sin( x * np * Math.PI ) + Math.Sin( x * np * 2 * Math.PI ) + Math.Sin( x * np * 3 * Math.PI );
sw.WriteLine( a_[i] );
}
}
/* check of CDFT
putdata( 0, n - 1, a );
fft.cdft( n, 1, a, ip, w );
fft.cdft( n, -1, a, ip, w );
err = errorcheck( 0, n - 1, 2.0 / n, a );
Console.WriteLine( "cdft err= {0}", err );*/
/* check of RDFT */
//putdata( 0, n - 1, a );
fft.rdft( n, 1, a, ip, w );
using ( System.IO.StreamWriter sw_a = new System.IO.StreamWriter( @"c:\rdft_a.txt" ) ) {
for ( int i = 0; i < n; i++ ) {
sw_a.WriteLine( a[i] );
}
}
err = errorcheck( 0, n - 1, 2.0 / n, a );
Console.WriteLine( "rdft err= {0}", err );
/* check of DDCT
putdata( 0, n - 1, a );
fft.ddct( n, 1, a, ip, w );
fft.ddct( n, -1, a, ip, w );
a[0] *= 0.5;
err = errorcheck( 0, n - 1, 2.0 / n, a );
Console.WriteLine( "ddct err= {0}", err );*/
/* check of DDST
putdata( 0, n - 1, a );
fft.ddst( n, 1, a, ip, w );
fft.ddst( n, -1, a, ip, w );
a[0] *= 0.5;
err = errorcheck( 0, n - 1, 2.0 / n, a );
Console.WriteLine( "ddst err= {0} \n", err );*/
/* check of DFCT
putdata( 0, n, a );
a[0] *= 0.5;
a[n] *= 0.5;
fft.dfct( n, a, t, ip, w );
a[0] *= 0.5;
a[n] *= 0.5;
fft.dfct( n, a, t, ip, w );
err = errorcheck( 0, n, 2.0 / n, a );
Console.WriteLine( "dfct err= {0}", err );*/
/* check of DFST
putdata( 1, n - 1, a );
fft.dfst( n, a, t, ip, w );
fft.dfst( n, a, t, ip, w );
err = errorcheck( 1, n - 1, 2.0 / n, a );
Console.WriteLine( "dfst err= {0}", err );*/
}
return 0;
}
static void putdata( int nini, int nend, double* a ) {
int j, seed = 0;
for ( j = nini; j <= nend; j++ ) {
a[j] = RND( ref seed );
}
}
static double errorcheck( int nini, int nend, double scale, double* a ) {
int j, seed = 0;
double err = 0, e;
for ( j = nini; j <= nend; j++ ) {
e = RND( ref seed ) - a[j] * scale;
err = Math.Max( err, Math.Abs( e ) );
}
return err;
}
}
public static unsafe class fft {
/*
Fast Fourier/Cosine/Sine Transform
dimension :one
data length :power of 2
decimation :frequency
radix :split-radix
data :inplace
table :use
functions
cdft: Complex Discrete Fourier Transform
rdft: Real Discrete Fourier Transform
ddct: Discrete Cosine Transform
ddst: Discrete Sine Transform
dfct: Cosine Transform of RDFT (Real Symmetric DFT)
dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
void cdft(int, int, double *, int *, double *);
void rdft(int, int, double *, int *, double *);
void ddct(int, int, double *, int *, double *);
void ddst(int, int, double *, int *, double *);
void dfct(int, double *, double *, int *, double *);
void dfst(int, double *, double *, int *, double *);
macro definitions
USE_CDFT_PTHREADS : default=not defined
CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
USE_CDFT_WINTHREADS : default=not defined
CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
-------- Complex DFT (Discrete Fourier Transform) --------
[definition]
<case1>
X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
<case2>
X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
[usage]
<case1>
ip[0] = 0; // first time only
cdft(2*n, 1, a, ip, w);
<case2>
ip[0] = 0; // first time only
cdft(2*n, -1, a, ip, w);
[parameters]
2*n :data length (int)
n >= 1, n = power of 2
a[0...2*n-1] :input/output data (double *)
input data
a[2*j] = Re(x[j]),
a[2*j+1] = Im(x[j]), 0<=j<n
output data
a[2*k] = Re(X[k]),
a[2*k+1] = Im(X[k]), 0<=k<n
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n)
strictly,
length of ip >=
2+(1<<(int)(log(n+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n/2-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
cdft(2*n, -1, a, ip, w);
is
cdft(2*n, 1, a, ip, w);
for (j = 0; j <= 2 * n - 1; j++) {
a[j] *= 1.0 / n;
}
.
-------- Real DFT / Inverse of Real DFT --------
[definition]
<case1> RDFT
R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
<case2> IRDFT (excluding scale)
a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
[usage]
<case1>
ip[0] = 0; // first time only
rdft(n, 1, a, ip, w);
<case2>
ip[0] = 0; // first time only
rdft(n, -1, a, ip, w);
[parameters]
n :data length (int)
n >= 2, n = power of 2
a[0...n-1] :input/output data (double *)
<case1>
output data
a[2*k] = R[k], 0<=k<n/2
a[2*k+1] = I[k], 0<k<n/2
a[1] = R[n/2]
<case2>
input data
a[2*j] = R[j], 0<=j<n/2
a[2*j+1] = I[j], 0<j<n/2
a[1] = R[n/2]
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n/2)
strictly,
length of ip >=
2+(1<<(int)(log(n/2+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n/2-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
rdft(n, 1, a, ip, w);
is
rdft(n, -1, a, ip, w);
for (j = 0; j <= n - 1; j++) {
a[j] *= 2.0 / n;
}
.
-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
[definition]
<case1> IDCT (excluding scale)
C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
<case2> DCT
C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
[usage]
<case1>
ip[0] = 0; // first time only
ddct(n, 1, a, ip, w);
<case2>
ip[0] = 0; // first time only
ddct(n, -1, a, ip, w);
[parameters]
n :data length (int)
n >= 2, n = power of 2
a[0...n-1] :input/output data (double *)
output data
a[k] = C[k], 0<=k<n
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n/2)
strictly,
length of ip >=
2+(1<<(int)(log(n/2+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n*5/4-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
ddct(n, -1, a, ip, w);
is
a[0] *= 0.5;
ddct(n, 1, a, ip, w);
for (j = 0; j <= n - 1; j++) {
a[j] *= 2.0 / n;
}
.
-------- DST (Discrete Sine Transform) / Inverse of DST --------
[definition]
<case1> IDST (excluding scale)
S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
<case2> DST
S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
[usage]
<case1>
ip[0] = 0; // first time only
ddst(n, 1, a, ip, w);
<case2>
ip[0] = 0; // first time only
ddst(n, -1, a, ip, w);
[parameters]
n :data length (int)
n >= 2, n = power of 2
a[0...n-1] :input/output data (double *)
<case1>
input data
a[j] = A[j], 0<j<n
a[0] = A[n]
output data
a[k] = S[k], 0<=k<n
<case2>
output data
a[k] = S[k], 0<k<n
a[0] = S[n]
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n/2)
strictly,
length of ip >=
2+(1<<(int)(log(n/2+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n*5/4-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
ddst(n, -1, a, ip, w);
is
a[0] *= 0.5;
ddst(n, 1, a, ip, w);
for (j = 0; j <= n - 1; j++) {
a[j] *= 2.0 / n;
}
.
-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
[definition]
C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
[usage]
ip[0] = 0; // first time only
dfct(n, a, t, ip, w);
[parameters]
n :data length - 1 (int)
n >= 2, n = power of 2
a[0...n] :input/output data (double *)
output data
a[k] = C[k], 0<=k<=n
t[0...n/2] :work area (double *)
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n/4)
strictly,
length of ip >=
2+(1<<(int)(log(n/4+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n*5/8-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
a[0] *= 0.5;
a[n] *= 0.5;
dfct(n, a, t, ip, w);
is
a[0] *= 0.5;
a[n] *= 0.5;
dfct(n, a, t, ip, w);
for (j = 0; j <= n; j++) {
a[j] *= 2.0 / n;
}
.
-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
[definition]
S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
[usage]
ip[0] = 0; // first time only
dfst(n, a, t, ip, w);
[parameters]
n :data length + 1 (int)
n >= 2, n = power of 2
a[0...n-1] :input/output data (double *)
output data
a[k] = S[k], 0<k<n
(a[0] is used for work area)
t[0...n/2-1] :work area (double *)
ip[0...*] :work area for bit reversal (int *)
length of ip >= 2+sqrt(n/4)
strictly,
length of ip >=
2+(1<<(int)(log(n/4+0.5)/log(2))/2).
ip[0],ip[1] are pointers of the cos/sin table.
w[0...n*5/8-1] :cos/sin table (double *)
w[],ip[] are initialized if ip[0] == 0.
[remark]
Inverse of
dfst(n, a, t, ip, w);
is
dfst(n, a, t, ip, w);
for (j = 1; j <= n - 1; j++) {
a[j] *= 2.0 / n;
}
.
Appendix :
The cos/sin table is recalculated when the larger table required.
w[] and ip[] are compatible with all routines.
*/
static double cos( double x ) {
return Math.Cos( x );
}
static double sin( double x ) {
return Math.Sin( x );
}
static double atan( double x ) {
return Math.Atan( x );
}
public static void cdft( int n, int isgn, double* a, int* ip, double* w ) {
//void makewt(int nw, int *ip, double *w);
//void cftfsub(int n, double *a, int *ip, int nw, double *w);
//void cftbsub(int n, double *a, int *ip, int nw, double *w);
int nw;
nw = ip[0];
if ( n > (nw << 2) ) {
nw = n >> 2;
makewt( nw, ip, w );
}
if ( isgn >= 0 ) {
cftfsub( n, a, ip, nw, w );
} else {
cftbsub( n, a, ip, nw, w );
}
}
public static void rdft( int n, int isgn, double* a, int* ip, double* w ) {
int nw, nc;
double xi;
nw = ip[0];
if ( n > (nw << 2) ) {
nw = n >> 2;
makewt( nw, ip, w );
}
nc = ip[1];
if ( n > (nc << 2) ) {
nc = n >> 2;
makect( nc, ip, w + nw );
}
if ( isgn >= 0 ) {
if ( n > 4 ) {
cftfsub( n, a, ip, nw, w );
rftfsub( n, a, nc, w + nw );
} else if ( n == 4 ) {
cftfsub( n, a, ip, nw, w );
}
xi = a[0] - a[1];
a[0] += a[1];
a[1] = xi;
} else {
a[1] = 0.5 * (a[0] - a[1]);
a[0] -= a[1];
if ( n > 4 ) {
rftbsub( n, a, nc, w + nw );
cftbsub( n, a, ip, nw, w );
} else if ( n == 4 ) {
cftbsub( n, a, ip, nw, w );
}
}
}
public static void ddct( int n, int isgn, double* a, int* ip, double* w ) {
//void makewt(int nw, int *ip, double *w);
//void makect(int nc, int *ip, double *c);
//void cftfsub(int n, double *a, int *ip, int nw, double *w);
//void cftbsub(int n, double *a, int *ip, int nw, double *w);
//void rftfsub(int n, double *a, int nc, double *c);
//void rftbsub(int n, double *a, int nc, double *c);
//void dctsub(int n, double *a, int nc, double *c);
int j, nw, nc;
double xr;
nw = ip[0];
if ( n > (nw << 2) ) {
nw = n >> 2;
makewt( nw, ip, w );
}
nc = ip[1];
if ( n > nc ) {
nc = n;
makect( nc, ip, w + nw );
}
if ( isgn < 0 ) {
xr = a[n - 1];
for ( j = n - 2; j >= 2; j -= 2 ) {
a[j + 1] = a[j] - a[j - 1];
a[j] += a[j - 1];
}
a[1] = a[0] - xr;
a[0] += xr;
if ( n > 4 ) {
rftbsub( n, a, nc, w + nw );
cftbsub( n, a, ip, nw, w );
} else if ( n == 4 ) {
cftbsub( n, a, ip, nw, w );
}
}
dctsub( n, a, nc, w + nw );
if ( isgn >= 0 ) {
if ( n > 4 ) {
cftfsub( n, a, ip, nw, w );
rftfsub( n, a, nc, w + nw );
} else if ( n == 4 ) {
cftfsub( n, a, ip, nw, w );
}
xr = a[0] - a[1];
a[0] += a[1];
for ( j = 2; j < n; j += 2 ) {
a[j - 1] = a[j] - a[j + 1];
a[j] += a[j + 1];
}
a[n - 1] = xr;
}
}
public static void ddst( int n, int isgn, double* a, int* ip, double* w ) {
//void makewt(int nw, int *ip, double *w);
//void makect(int nc, int *ip, double *c);
//void cftfsub(int n, double *a, int *ip, int nw, double *w);
//void cftbsub(int n, double *a, int *ip, int nw, double *w);
//void rftfsub(int n, double *a, int nc, double *c);
//void rftbsub(int n, double *a, int nc, double *c);
//void dstsub(int n, double *a, int nc, double *c);
int j, nw, nc;
double xr;
nw = ip[0];
if ( n > (nw << 2) ) {
nw = n >> 2;
makewt( nw, ip, w );
}
nc = ip[1];
if ( n > nc ) {
nc = n;
makect( nc, ip, w + nw );
}
if ( isgn < 0 ) {
xr = a[n - 1];
for ( j = n - 2; j >= 2; j -= 2 ) {
a[j + 1] = -a[j] - a[j - 1];
a[j] -= a[j - 1];
}
a[1] = a[0] + xr;
a[0] -= xr;
if ( n > 4 ) {
rftbsub( n, a, nc, w + nw );
cftbsub( n, a, ip, nw, w );
} else if ( n == 4 ) {
cftbsub( n, a, ip, nw, w );
}
}
dstsub( n, a, nc, w + nw );
if ( isgn >= 0 ) {
if ( n > 4 ) {
cftfsub( n, a, ip, nw, w );
rftfsub( n, a, nc, w + nw );
} else if ( n == 4 ) {
cftfsub( n, a, ip, nw, w );
}
xr = a[0] - a[1];
a[0] += a[1];
for ( j = 2; j < n; j += 2 ) {
a[j - 1] = -a[j] - a[j + 1];
a[j] -= a[j + 1];
}
a[n - 1] = -xr;
}
}
public static void dfct( int n, double* a, double* t, int* ip, double* w ) {
//void makewt(int nw, int *ip, double *w);
//void makect(int nc, int *ip, double *c);
//void cftfsub(int n, double *a, int *ip, int nw, double *w);
//void rftfsub(int n, double *a, int nc, double *c);
//void dctsub(int n, double *a, int nc, double *c);
int j, k, l, m, mh, nw, nc;
double xr, xi, yr, yi;
nw = ip[0];
if ( n > (nw << 3) ) {
nw = n >> 3;
makewt( nw, ip, w );
}
nc = ip[1];
if ( n > (nc << 1) ) {
nc = n >> 1;
makect( nc, ip, w + nw );
}
m = n >> 1;
yi = a[m];
xi = a[0] + a[n];
a[0] -= a[n];
t[0] = xi - yi;
t[m] = xi + yi;
if ( n > 2 ) {
mh = m >> 1;
for ( j = 1; j < mh; j++ ) {
k = m - j;
xr = a[j] - a[n - j];
xi = a[j] + a[n - j];
yr = a[k] - a[n - k];
yi = a[k] + a[n - k];
a[j] = xr;
a[k] = yr;
t[j] = xi - yi;
t[k] = xi + yi;
}
t[mh] = a[mh] + a[n - mh];
a[mh] -= a[n - mh];
dctsub( m, a, nc, w + nw );
if ( m > 4 ) {
cftfsub( m, a, ip, nw, w );
rftfsub( m, a, nc, w + nw );
} else if ( m == 4 ) {
cftfsub( m, a, ip, nw, w );
}
a[n - 1] = a[0] - a[1];
a[1] = a[0] + a[1];
for ( j = m - 2; j >= 2; j -= 2 ) {
a[2 * j + 1] = a[j] + a[j + 1];
a[2 * j - 1] = a[j] - a[j + 1];
}
l = 2;
m = mh;
while ( m >= 2 ) {
dctsub( m, t, nc, w + nw );
if ( m > 4 ) {
cftfsub( m, t, ip, nw, w );
rftfsub( m, t, nc, w + nw );
} else if ( m == 4 ) {
cftfsub( m, t, ip, nw, w );
}
a[n - l] = t[0] - t[1];
a[l] = t[0] + t[1];
k = 0;
for ( j = 2; j < m; j += 2 ) {
k += l << 2;
a[k - l] = t[j] - t[j + 1];
a[k + l] = t[j] + t[j + 1];
}
l <<= 1;
mh = m >> 1;
for ( j = 0; j < mh; j++ ) {
k = m - j;
t[j] = t[m + k] - t[m + j];
t[k] = t[m + k] + t[m + j];
}
t[mh] = t[m + mh];
m = mh;
}
a[l] = t[0];
a[n] = t[2] - t[1];
a[0] = t[2] + t[1];
} else {
a[1] = a[0];
a[2] = t[0];
a[0] = t[1];
}
}
public static void dfst( int n, double* a, double* t, int* ip, double* w ) {
//void makewt(int nw, int *ip, double *w);
//void makect(int nc, int *ip, double *c);
//void cftfsub(int n, double *a, int *ip, int nw, double *w);
//void rftfsub(int n, double *a, int nc, double *c);
//void dstsub(int n, double *a, int nc, double *c);
int j, k, l, m, mh, nw, nc;
double xr, xi, yr, yi;
nw = ip[0];
if ( n > (nw << 3) ) {
nw = n >> 3;
makewt( nw, ip, w );
}
nc = ip[1];
if ( n > (nc << 1) ) {
nc = n >> 1;
makect( nc, ip, w + nw );
}
if ( n > 2 ) {
m = n >> 1;
mh = m >> 1;
for ( j = 1; j < mh; j++ ) {
k = m - j;
xr = a[j] + a[n - j];
xi = a[j] - a[n - j];
yr = a[k] + a[n - k];
yi = a[k] - a[n - k];
a[j] = xr;
a[k] = yr;
t[j] = xi + yi;
t[k] = xi - yi;
}
t[0] = a[mh] - a[n - mh];
a[mh] += a[n - mh];
a[0] = a[m];
dstsub( m, a, nc, w + nw );
if ( m > 4 ) {
cftfsub( m, a, ip, nw, w );
rftfsub( m, a, nc, w + nw );
} else if ( m == 4 ) {
cftfsub( m, a, ip, nw, w );
}
a[n - 1] = a[1] - a[0];
a[1] = a[0] + a[1];
for ( j = m - 2; j >= 2; j -= 2 ) {
a[2 * j + 1] = a[j] - a[j + 1];
a[2 * j - 1] = -a[j] - a[j + 1];
}
l = 2;
m = mh;
while ( m >= 2 ) {
dstsub( m, t, nc, w + nw );
if ( m > 4 ) {
cftfsub( m, t, ip, nw, w );
rftfsub( m, t, nc, w + nw );
} else if ( m == 4 ) {
cftfsub( m, t, ip, nw, w );
}
a[n - l] = t[1] - t[0];
a[l] = t[0] + t[1];
k = 0;
for ( j = 2; j < m; j += 2 ) {
k += l << 2;
a[k - l] = -t[j] - t[j + 1];
a[k + l] = t[j] - t[j + 1];
}
l <<= 1;
mh = m >> 1;
for ( j = 1; j < mh; j++ ) {
k = m - j;
t[j] = t[m + k] + t[m + j];
t[k] = t[m + k] - t[m + j];
}
t[0] = t[m + mh];
m = mh;
}
a[l] = t[0];
}
a[0] = 0;
}
/* -------- initializing routines -------- */
//#include <math.h>
static void makewt( int nw, int* ip, double* w ) {
//void makeipt(int nw, int *ip);
int j, nwh, nw0, nw1;
double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
ip[0] = nw;
ip[1] = 1;
if ( nw > 2 ) {
nwh = nw >> 1;
delta = atan( 1.0 ) / nwh;
wn4r = cos( delta * nwh );
w[0] = 1;
w[1] = wn4r;
if ( nwh == 4 ) {
w[2] = cos( delta * 2 );
w[3] = sin( delta * 2 );
} else if ( nwh > 4 ) {
makeipt( nw, ip );
w[2] = 0.5 / cos( delta * 2 );
w[3] = 0.5 / cos( delta * 6 );
for ( j = 4; j < nwh; j += 4 ) {
w[j] = cos( delta * j );
w[j + 1] = sin( delta * j );
w[j + 2] = cos( 3 * delta * j );
w[j + 3] = -sin( 3 * delta * j );
}
}
nw0 = 0;
while ( nwh > 2 ) {
nw1 = nw0 + nwh;
nwh >>= 1;
w[nw1] = 1;
w[nw1 + 1] = wn4r;
if ( nwh == 4 ) {
wk1r = w[nw0 + 4];
wk1i = w[nw0 + 5];
w[nw1 + 2] = wk1r;
w[nw1 + 3] = wk1i;
} else if ( nwh > 4 ) {
wk1r = w[nw0 + 4];
wk3r = w[nw0 + 6];
w[nw1 + 2] = 0.5 / wk1r;
w[nw1 + 3] = 0.5 / wk3r;
for ( j = 4; j < nwh; j += 4 ) {
wk1r = w[nw0 + 2 * j];
wk1i = w[nw0 + 2 * j + 1];
wk3r = w[nw0 + 2 * j + 2];
wk3i = w[nw0 + 2 * j + 3];
w[nw1 + j] = wk1r;
w[nw1 + j + 1] = wk1i;
w[nw1 + j + 2] = wk3r;
w[nw1 + j + 3] = wk3i;
}
}
nw0 = nw1;
}
}
}
static void makeipt( int nw, int* ip ) {
int j, l, m, m2, p, q;
ip[2] = 0;
ip[3] = 16;
m = 2;
for ( l = nw; l > 32; l >>= 2 ) {
m2 = m << 1;
q = m2 << 3;
for ( j = m; j < m2; j++ ) {
p = ip[j] << 2;
ip[m + j] = p;
ip[m2 + j] = p + q;
}
m = m2;
}
}
static void makect( int nc, int* ip, double* c ) {
int j, nch;
double delta;
ip[1] = nc;
if ( nc > 1 ) {
nch = nc >> 1;
delta = atan( 1.0 ) / nch;
c[0] = cos( delta * nch );
c[nch] = 0.5 * c[0];
for ( j = 1; j < nch; j++ ) {
c[j] = 0.5 * cos( delta * j );
c[nc - j] = 0.5 * sin( delta * j );
}
}
}
/* -------- child routines -------- */
static void cftfsub( int n, double* a, int* ip, int nw, double* w ) {
//void bitrv2(int n, int *ip, double *a);
//void bitrv216(double *a);
//void bitrv208(double *a);
//void cftf1st(int n, double *a, double *w);
//void cftrec4(int n, double *a, int nw, double *w);
//void cftleaf(int n, int isplt, double *a, int nw, double *w);
//void cftfx41(int n, double *a, int nw, double *w);
//void cftf161(double *a, double *w);
//void cftf081(double *a, double *w);
//void cftf040(double *a);
//void cftx020(double *a);
if ( n > 8 ) {
if ( n > 32 ) {
cftf1st( n, a, &w[nw - (n >> 2)] );
if ( n > 512 ) {
cftrec4( n, a, nw, w );
} else if ( n > 128 ) {
cftleaf( n, 1, a, nw, w );
} else {
cftfx41( n, a, nw, w );
}
bitrv2( n, ip, a );
} else if ( n == 32 ) {
cftf161( a, &w[nw - 8] );
bitrv216( a );
} else {
cftf081( a, w );
bitrv208( a );
}
} else if ( n == 8 ) {
cftf040( a );
} else if ( n == 4 ) {
cftx020( a );
}
}
static void cftbsub( int n, double* a, int* ip, int nw, double* w ) {
//void bitrv2conj(int n, int *ip, double *a);
//void bitrv216neg(double *a);
//void bitrv208neg(double *a);
//void cftb1st(int n, double *a, double *w);
//void cftrec4(int n, double *a, int nw, double *w);
//void cftleaf(int n, int isplt, double *a, int nw, double *w);
//void cftfx41(int n, double *a, int nw, double *w);
//void cftf161(double *a, double *w);
//void cftf081(double *a, double *w);
//void cftb040(double *a);
//void cftx020(double *a);
if ( n > 8 ) {
if ( n > 32 ) {
cftb1st( n, a, &w[nw - (n >> 2)] );
if ( n > 512 ) {
cftrec4( n, a, nw, w );
} else if ( n > 128 ) {
cftleaf( n, 1, a, nw, w );
} else {
cftfx41( n, a, nw, w );
}
bitrv2conj( n, ip, a );
} else if ( n == 32 ) {
cftf161( a, &w[nw - 8] );
bitrv216neg( a );
} else {
cftf081( a, w );
bitrv208neg( a );
}
} else if ( n == 8 ) {
cftb040( a );
} else if ( n == 4 ) {
cftx020( a );
}
}
static void bitrv2( int n, int* ip, double* a ) {
int j, j1, k, k1, l, m, nh, nm;
double xr, xi, yr, yi;
m = 1;
for ( l = n >> 2; l > 8; l >>= 2 ) {
m <<= 1;
}
nh = n >> 1;
nm = 4 * m;
if ( l == 8 ) {
for ( k = 0; k < m; k++ ) {
for ( j = 0; j < k; j++ ) {
j1 = 4 * j + 2 * ip[m + k];
k1 = 4 * k + 2 * ip[m + j];
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh;
k1 += 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 += nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += 2;
k1 += nh;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh;
k1 -= 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 += nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
k1 = 4 * k + 2 * ip[m + k];
j1 = k1 + 2;
k1 += nh;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= 2;
k1 -= nh;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh + 2;
k1 += nh + 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh - nm;
k1 += 2 * nm - 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
} else {
for ( k = 0; k < m; k++ ) {
for ( j = 0; j < k; j++ ) {
j1 = 4 * j + ip[m + k];
k1 = 4 * k + ip[m + j];
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh;
k1 += 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += 2;
k1 += nh;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh;
k1 -= 2;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
k1 = 4 * k + ip[m + k];
j1 = k1 + 2;
k1 += nh;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += nm;
xr = a[j1];
xi = a[j1 + 1];
yr = a[k1];
yi = a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
}
}
static void bitrv2conj( int n, int* ip, double* a ) {
int j, j1, k, k1, l, m, nh, nm;
double xr, xi, yr, yi;
m = 1;
for ( l = n >> 2; l > 8; l >>= 2 ) {
m <<= 1;
}
nh = n >> 1;
nm = 4 * m;
if ( l == 8 ) {
for ( k = 0; k < m; k++ ) {
for ( j = 0; j < k; j++ ) {
j1 = 4 * j + 2 * ip[m + k];
k1 = 4 * k + 2 * ip[m + j];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh;
k1 += 2;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 += nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += 2;
k1 += nh;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh;
k1 -= 2;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 += nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
k1 = 4 * k + 2 * ip[m + k];
j1 = k1 + 2;
k1 += nh;
a[j1 - 1] = -a[j1 - 1];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
a[k1 + 3] = -a[k1 + 3];
j1 += nm;
k1 += 2 * nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 -= nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= 2;
k1 -= nh;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh + 2;
k1 += nh + 2;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh - nm;
k1 += 2 * nm - 2;
a[j1 - 1] = -a[j1 - 1];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
a[k1 + 3] = -a[k1 + 3];
}
} else {
for ( k = 0; k < m; k++ ) {
for ( j = 0; j < k; j++ ) {
j1 = 4 * j + ip[m + k];
k1 = 4 * k + ip[m + j];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nh;
k1 += 2;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += 2;
k1 += nh;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 += nm;
k1 += nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nh;
k1 -= 2;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
j1 -= nm;
k1 -= nm;
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
}
k1 = 4 * k + ip[m + k];
j1 = k1 + 2;
k1 += nh;
a[j1 - 1] = -a[j1 - 1];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
a[k1 + 3] = -a[k1 + 3];
j1 += nm;
k1 += nm;
a[j1 - 1] = -a[j1 - 1];
xr = a[j1];
xi = -a[j1 + 1];
yr = a[k1];
yi = -a[k1 + 1];
a[j1] = yr;
a[j1 + 1] = yi;
a[k1] = xr;
a[k1 + 1] = xi;
a[k1 + 3] = -a[k1 + 3];
}
}
}
static void bitrv216( double* a ) {
double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i,
x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
x1r = a[2];
x1i = a[3];
x2r = a[4];
x2i = a[5];
x3r = a[6];
x3i = a[7];
x4r = a[8];
x4i = a[9];
x5r = a[10];
x5i = a[11];
x7r = a[14];
x7i = a[15];
x8r = a[16];
x8i = a[17];
x10r = a[20];
x10i = a[21];
x11r = a[22];
x11i = a[23];
x12r = a[24];
x12i = a[25];
x13r = a[26];
x13i = a[27];
x14r = a[28];
x14i = a[29];
a[2] = x8r;
a[3] = x8i;
a[4] = x4r;
a[5] = x4i;
a[6] = x12r;
a[7] = x12i;
a[8] = x2r;
a[9] = x2i;
a[10] = x10r;
a[11] = x10i;
a[14] = x14r;
a[15] = x14i;
a[16] = x1r;
a[17] = x1i;
a[20] = x5r;
a[21] = x5i;
a[22] = x13r;
a[23] = x13i;
a[24] = x3r;
a[25] = x3i;
a[26] = x11r;
a[27] = x11i;
a[28] = x7r;
a[29] = x7i;
}
static void bitrv216neg( double* a ) {
double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i,
x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i,
x13r, x13i, x14r, x14i, x15r, x15i;
x1r = a[2];
x1i = a[3];
x2r = a[4];
x2i = a[5];
x3r = a[6];
x3i = a[7];
x4r = a[8];
x4i = a[9];
x5r = a[10];
x5i = a[11];
x6r = a[12];
x6i = a[13];
x7r = a[14];
x7i = a[15];
x8r = a[16];
x8i = a[17];
x9r = a[18];
x9i = a[19];
x10r = a[20];
x10i = a[21];
x11r = a[22];
x11i = a[23];
x12r = a[24];
x12i = a[25];
x13r = a[26];
x13i = a[27];
x14r = a[28];
x14i = a[29];
x15r = a[30];
x15i = a[31];
a[2] = x15r;
a[3] = x15i;
a[4] = x7r;
a[5] = x7i;
a[6] = x11r;
a[7] = x11i;
a[8] = x3r;
a[9] = x3i;
a[10] = x13r;
a[11] = x13i;
a[12] = x5r;
a[13] = x5i;
a[14] = x9r;
a[15] = x9i;
a[16] = x1r;
a[17] = x1i;
a[18] = x14r;
a[19] = x14i;
a[20] = x6r;
a[21] = x6i;
a[22] = x10r;
a[23] = x10i;
a[24] = x2r;
a[25] = x2i;
a[26] = x12r;
a[27] = x12i;
a[28] = x4r;
a[29] = x4i;
a[30] = x8r;
a[31] = x8i;
}
static void bitrv208( double* a ) {
double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;
x1r = a[2];
x1i = a[3];
x3r = a[6];
x3i = a[7];
x4r = a[8];
x4i = a[9];
x6r = a[12];
x6i = a[13];
a[2] = x4r;
a[3] = x4i;
a[6] = x6r;
a[7] = x6i;
a[8] = x1r;
a[9] = x1i;
a[12] = x3r;
a[13] = x3i;
}
static void bitrv208neg( double* a ) {
double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
x5r, x5i, x6r, x6i, x7r, x7i;
x1r = a[2];
x1i = a[3];
x2r = a[4];
x2i = a[5];
x3r = a[6];
x3i = a[7];
x4r = a[8];
x4i = a[9];
x5r = a[10];
x5i = a[11];
x6r = a[12];
x6i = a[13];
x7r = a[14];
x7i = a[15];
a[2] = x7r;
a[3] = x7i;
a[4] = x3r;
a[5] = x3i;
a[6] = x5r;
a[7] = x5i;
a[8] = x1r;
a[9] = x1i;
a[10] = x6r;
a[11] = x6i;
a[12] = x2r;
a[13] = x2i;
a[14] = x4r;
a[15] = x4i;
}
static void cftf1st( int n, double* a, double* w ) {
int j, j0, j1, j2, j3, k, m, mh;
double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
wd1r, wd1i, wd3r, wd3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
mh = n >> 3;
m = 2 * mh;
j1 = m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[0] + a[j2];
x0i = a[1] + a[j2 + 1];
x1r = a[0] - a[j2];
x1i = a[1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
a[j2] = x1r - x3i;
a[j2 + 1] = x1i + x3r;
a[j3] = x1r + x3i;
a[j3 + 1] = x1i - x3r;
wn4r = w[1];
csc1 = w[2];
csc3 = w[3];
wd1r = 1;
wd1i = 0;
wd3r = 1;
wd3i = 0;
k = 0;
for ( j = 2; j < mh - 2; j += 4 ) {
k += 4;
wk1r = csc1 * (wd1r + w[k]);
wk1i = csc1 * (wd1i + w[k + 1]);
wk3r = csc3 * (wd3r + w[k + 2]);
wk3i = csc3 * (wd3i + w[k + 3]);
wd1r = w[k];
wd1i = w[k + 1];
wd3r = w[k + 2];
wd3i = w[k + 3];
j1 = j + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j] + a[j2];
x0i = a[j + 1] + a[j2 + 1];
x1r = a[j] - a[j2];
x1i = a[j + 1] - a[j2 + 1];
y0r = a[j + 2] + a[j2 + 2];
y0i = a[j + 3] + a[j2 + 3];
y1r = a[j + 2] - a[j2 + 2];
y1i = a[j + 3] - a[j2 + 3];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
y2r = a[j1 + 2] + a[j3 + 2];
y2i = a[j1 + 3] + a[j3 + 3];
y3r = a[j1 + 2] - a[j3 + 2];
y3i = a[j1 + 3] - a[j3 + 3];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
a[j + 2] = y0r + y2r;
a[j + 3] = y0i + y2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
a[j1 + 2] = y0r - y2r;
a[j1 + 3] = y0i - y2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wk1r * x0r - wk1i * x0i;
a[j2 + 1] = wk1r * x0i + wk1i * x0r;
x0r = y1r - y3i;
x0i = y1i + y3r;
a[j2 + 2] = wd1r * x0r - wd1i * x0i;
a[j2 + 3] = wd1r * x0i + wd1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3r * x0r + wk3i * x0i;
a[j3 + 1] = wk3r * x0i - wk3i * x0r;
x0r = y1r + y3i;
x0i = y1i - y3r;
a[j3 + 2] = wd3r * x0r + wd3i * x0i;
a[j3 + 3] = wd3r * x0i - wd3i * x0r;
j0 = m - j;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] + a[j2];
x0i = a[j0 + 1] + a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = a[j0 + 1] - a[j2 + 1];
y0r = a[j0 - 2] + a[j2 - 2];
y0i = a[j0 - 1] + a[j2 - 1];
y1r = a[j0 - 2] - a[j2 - 2];
y1i = a[j0 - 1] - a[j2 - 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
y2r = a[j1 - 2] + a[j3 - 2];
y2i = a[j1 - 1] + a[j3 - 1];
y3r = a[j1 - 2] - a[j3 - 2];
y3i = a[j1 - 1] - a[j3 - 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i + x2i;
a[j0 - 2] = y0r + y2r;
a[j0 - 1] = y0i + y2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
a[j1 - 2] = y0r - y2r;
a[j1 - 1] = y0i - y2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wk1i * x0r - wk1r * x0i;
a[j2 + 1] = wk1i * x0i + wk1r * x0r;
x0r = y1r - y3i;
x0i = y1i + y3r;
a[j2 - 2] = wd1i * x0r - wd1r * x0i;
a[j2 - 1] = wd1i * x0i + wd1r * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3i * x0r + wk3r * x0i;
a[j3 + 1] = wk3i * x0i - wk3r * x0r;
x0r = y1r + y3i;
x0i = y1i - y3r;
a[j3 - 2] = wd3i * x0r + wd3r * x0i;
a[j3 - 1] = wd3i * x0i - wd3r * x0r;
}
wk1r = csc1 * (wd1r + wn4r);
wk1i = csc1 * (wd1i + wn4r);
wk3r = csc3 * (wd3r - wn4r);
wk3i = csc3 * (wd3i - wn4r);
j0 = mh;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0 - 2] + a[j2 - 2];
x0i = a[j0 - 1] + a[j2 - 1];
x1r = a[j0 - 2] - a[j2 - 2];
x1i = a[j0 - 1] - a[j2 - 1];
x2r = a[j1 - 2] + a[j3 - 2];
x2i = a[j1 - 1] + a[j3 - 1];
x3r = a[j1 - 2] - a[j3 - 2];
x3i = a[j1 - 1] - a[j3 - 1];
a[j0 - 2] = x0r + x2r;
a[j0 - 1] = x0i + x2i;
a[j1 - 2] = x0r - x2r;
a[j1 - 1] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2 - 2] = wk1r * x0r - wk1i * x0i;
a[j2 - 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3 - 2] = wk3r * x0r + wk3i * x0i;
a[j3 - 1] = wk3r * x0i - wk3i * x0r;
x0r = a[j0] + a[j2];
x0i = a[j0 + 1] + a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = a[j0 + 1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wn4r * (x0r - x0i);
a[j2 + 1] = wn4r * (x0i + x0r);
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = -wn4r * (x0r + x0i);
a[j3 + 1] = -wn4r * (x0i - x0r);
x0r = a[j0 + 2] + a[j2 + 2];
x0i = a[j0 + 3] + a[j2 + 3];
x1r = a[j0 + 2] - a[j2 + 2];
x1i = a[j0 + 3] - a[j2 + 3];
x2r = a[j1 + 2] + a[j3 + 2];
x2i = a[j1 + 3] + a[j3 + 3];
x3r = a[j1 + 2] - a[j3 + 2];
x3i = a[j1 + 3] - a[j3 + 3];
a[j0 + 2] = x0r + x2r;
a[j0 + 3] = x0i + x2i;
a[j1 + 2] = x0r - x2r;
a[j1 + 3] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2 + 2] = wk1i * x0r - wk1r * x0i;
a[j2 + 3] = wk1i * x0i + wk1r * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3 + 2] = wk3i * x0r + wk3r * x0i;
a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}
static void cftb1st( int n, double* a, double* w ) {
int j, j0, j1, j2, j3, k, m, mh;
double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
wd1r, wd1i, wd3r, wd3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
mh = n >> 3;
m = 2 * mh;
j1 = m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[0] + a[j2];
x0i = -a[1] - a[j2 + 1];
x1r = a[0] - a[j2];
x1i = -a[1] + a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[0] = x0r + x2r;
a[1] = x0i - x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i + x2i;
a[j2] = x1r + x3i;
a[j2 + 1] = x1i + x3r;
a[j3] = x1r - x3i;
a[j3 + 1] = x1i - x3r;
wn4r = w[1];
csc1 = w[2];
csc3 = w[3];
wd1r = 1;
wd1i = 0;
wd3r = 1;
wd3i = 0;
k = 0;
for ( j = 2; j < mh - 2; j += 4 ) {
k += 4;
wk1r = csc1 * (wd1r + w[k]);
wk1i = csc1 * (wd1i + w[k + 1]);
wk3r = csc3 * (wd3r + w[k + 2]);
wk3i = csc3 * (wd3i + w[k + 3]);
wd1r = w[k];
wd1i = w[k + 1];
wd3r = w[k + 2];
wd3i = w[k + 3];
j1 = j + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j] + a[j2];
x0i = -a[j + 1] - a[j2 + 1];
x1r = a[j] - a[j2];
x1i = -a[j + 1] + a[j2 + 1];
y0r = a[j + 2] + a[j2 + 2];
y0i = -a[j + 3] - a[j2 + 3];
y1r = a[j + 2] - a[j2 + 2];
y1i = -a[j + 3] + a[j2 + 3];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
y2r = a[j1 + 2] + a[j3 + 2];
y2i = a[j1 + 3] + a[j3 + 3];
y3r = a[j1 + 2] - a[j3 + 2];
y3i = a[j1 + 3] - a[j3 + 3];
a[j] = x0r + x2r;
a[j + 1] = x0i - x2i;
a[j + 2] = y0r + y2r;
a[j + 3] = y0i - y2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i + x2i;
a[j1 + 2] = y0r - y2r;
a[j1 + 3] = y0i + y2i;
x0r = x1r + x3i;
x0i = x1i + x3r;
a[j2] = wk1r * x0r - wk1i * x0i;
a[j2 + 1] = wk1r * x0i + wk1i * x0r;
x0r = y1r + y3i;
x0i = y1i + y3r;
a[j2 + 2] = wd1r * x0r - wd1i * x0i;
a[j2 + 3] = wd1r * x0i + wd1i * x0r;
x0r = x1r - x3i;
x0i = x1i - x3r;
a[j3] = wk3r * x0r + wk3i * x0i;
a[j3 + 1] = wk3r * x0i - wk3i * x0r;
x0r = y1r - y3i;
x0i = y1i - y3r;
a[j3 + 2] = wd3r * x0r + wd3i * x0i;
a[j3 + 3] = wd3r * x0i - wd3i * x0r;
j0 = m - j;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] + a[j2];
x0i = -a[j0 + 1] - a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = -a[j0 + 1] + a[j2 + 1];
y0r = a[j0 - 2] + a[j2 - 2];
y0i = -a[j0 - 1] - a[j2 - 1];
y1r = a[j0 - 2] - a[j2 - 2];
y1i = -a[j0 - 1] + a[j2 - 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
y2r = a[j1 - 2] + a[j3 - 2];
y2i = a[j1 - 1] + a[j3 - 1];
y3r = a[j1 - 2] - a[j3 - 2];
y3i = a[j1 - 1] - a[j3 - 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i - x2i;
a[j0 - 2] = y0r + y2r;
a[j0 - 1] = y0i - y2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i + x2i;
a[j1 - 2] = y0r - y2r;
a[j1 - 1] = y0i + y2i;
x0r = x1r + x3i;
x0i = x1i + x3r;
a[j2] = wk1i * x0r - wk1r * x0i;
a[j2 + 1] = wk1i * x0i + wk1r * x0r;
x0r = y1r + y3i;
x0i = y1i + y3r;
a[j2 - 2] = wd1i * x0r - wd1r * x0i;
a[j2 - 1] = wd1i * x0i + wd1r * x0r;
x0r = x1r - x3i;
x0i = x1i - x3r;
a[j3] = wk3i * x0r + wk3r * x0i;
a[j3 + 1] = wk3i * x0i - wk3r * x0r;
x0r = y1r - y3i;
x0i = y1i - y3r;
a[j3 - 2] = wd3i * x0r + wd3r * x0i;
a[j3 - 1] = wd3i * x0i - wd3r * x0r;
}
wk1r = csc1 * (wd1r + wn4r);
wk1i = csc1 * (wd1i + wn4r);
wk3r = csc3 * (wd3r - wn4r);
wk3i = csc3 * (wd3i - wn4r);
j0 = mh;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0 - 2] + a[j2 - 2];
x0i = -a[j0 - 1] - a[j2 - 1];
x1r = a[j0 - 2] - a[j2 - 2];
x1i = -a[j0 - 1] + a[j2 - 1];
x2r = a[j1 - 2] + a[j3 - 2];
x2i = a[j1 - 1] + a[j3 - 1];
x3r = a[j1 - 2] - a[j3 - 2];
x3i = a[j1 - 1] - a[j3 - 1];
a[j0 - 2] = x0r + x2r;
a[j0 - 1] = x0i - x2i;
a[j1 - 2] = x0r - x2r;
a[j1 - 1] = x0i + x2i;
x0r = x1r + x3i;
x0i = x1i + x3r;
a[j2 - 2] = wk1r * x0r - wk1i * x0i;
a[j2 - 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r - x3i;
x0i = x1i - x3r;
a[j3 - 2] = wk3r * x0r + wk3i * x0i;
a[j3 - 1] = wk3r * x0i - wk3i * x0r;
x0r = a[j0] + a[j2];
x0i = -a[j0 + 1] - a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = -a[j0 + 1] + a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i - x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i + x2i;
x0r = x1r + x3i;
x0i = x1i + x3r;
a[j2] = wn4r * (x0r - x0i);
a[j2 + 1] = wn4r * (x0i + x0r);
x0r = x1r - x3i;
x0i = x1i - x3r;
a[j3] = -wn4r * (x0r + x0i);
a[j3 + 1] = -wn4r * (x0i - x0r);
x0r = a[j0 + 2] + a[j2 + 2];
x0i = -a[j0 + 3] - a[j2 + 3];
x1r = a[j0 + 2] - a[j2 + 2];
x1i = -a[j0 + 3] + a[j2 + 3];
x2r = a[j1 + 2] + a[j3 + 2];
x2i = a[j1 + 3] + a[j3 + 3];
x3r = a[j1 + 2] - a[j3 + 2];
x3i = a[j1 + 3] - a[j3 + 3];
a[j0 + 2] = x0r + x2r;
a[j0 + 3] = x0i - x2i;
a[j1 + 2] = x0r - x2r;
a[j1 + 3] = x0i + x2i;
x0r = x1r + x3i;
x0i = x1i + x3r;
a[j2 + 2] = wk1i * x0r - wk1r * x0i;
a[j2 + 3] = wk1i * x0i + wk1r * x0r;
x0r = x1r - x3i;
x0i = x1i - x3r;
a[j3 + 2] = wk3i * x0r + wk3r * x0i;
a[j3 + 3] = wk3i * x0i - wk3r * x0r;
}
static void cftrec4( int n, double* a, int nw, double* w ) {
//int cfttree(int n, int j, int k, double *a, int nw, double *w);
//void cftleaf(int n, int isplt, double *a, int nw, double *w);
//void cftmdl1(int n, double *a, double *w);
int isplt, j, k, m;
m = n;
while ( m > 512 ) {
m >>= 2;
cftmdl1( m, &a[n - m], &w[nw - (m >> 1)] );
}
cftleaf( m, 1, &a[n - m], nw, w );
k = 0;
for ( j = n - m; j > 0; j -= m ) {
k++;
isplt = cfttree( m, j, k, a, nw, w );
cftleaf( m, isplt, &a[j - m], nw, w );
}
}
static int cfttree( int n, int j, int k, double* a, int nw, double* w ) {
//void cftmdl1(int n, double *a, double *w);
//void cftmdl2(int n, double *a, double *w);
int i, isplt, m;
if ( (k & 3) != 0 ) {
isplt = k & 1;
if ( isplt != 0 ) {
cftmdl1( n, &a[j - n], &w[nw - (n >> 1)] );
} else {
cftmdl2( n, &a[j - n], &w[nw - n] );
}
} else {
m = n;
for ( i = k; (i & 3) == 0; i >>= 2 ) {
m <<= 2;
}
isplt = i & 1;
if ( isplt != 0 ) {
while ( m > 128 ) {
cftmdl1( m, &a[j - m], &w[nw - (m >> 1)] );
m >>= 2;
}
} else {
while ( m > 128 ) {
cftmdl2( m, &a[j - m], &w[nw - m] );
m >>= 2;
}
}
}
return isplt;
}
static void cftleaf( int n, int isplt, double* a, int nw, double* w ) {
//void cftmdl1(int n, double *a, double *w);
//void cftmdl2(int n, double *a, double *w);
//void cftf161(double *a, double *w);
//void cftf162(double *a, double *w);
//void cftf081(double *a, double *w);
//void cftf082(double *a, double *w);
if ( n == 512 ) {
cftmdl1( 128, a, &w[nw - 64] );
cftf161( a, &w[nw - 8] );
cftf162( &a[32], &w[nw - 32] );
cftf161( &a[64], &w[nw - 8] );
cftf161( &a[96], &w[nw - 8] );
cftmdl2( 128, &a[128], &w[nw - 128] );
cftf161( &a[128], &w[nw - 8] );
cftf162( &a[160], &w[nw - 32] );
cftf161( &a[192], &w[nw - 8] );
cftf162( &a[224], &w[nw - 32] );
cftmdl1( 128, &a[256], &w[nw - 64] );
cftf161( &a[256], &w[nw - 8] );
cftf162( &a[288], &w[nw - 32] );
cftf161( &a[320], &w[nw - 8] );
cftf161( &a[352], &w[nw - 8] );
if ( isplt != 0 ) {
cftmdl1( 128, &a[384], &w[nw - 64] );
cftf161( &a[480], &w[nw - 8] );
} else {
cftmdl2( 128, &a[384], &w[nw - 128] );
cftf162( &a[480], &w[nw - 32] );
}
cftf161( &a[384], &w[nw - 8] );
cftf162( &a[416], &w[nw - 32] );
cftf161( &a[448], &w[nw - 8] );
} else {
cftmdl1( 64, a, &w[nw - 32] );
cftf081( a, &w[nw - 8] );
cftf082( &a[16], &w[nw - 8] );
cftf081( &a[32], &w[nw - 8] );
cftf081( &a[48], &w[nw - 8] );
cftmdl2( 64, &a[64], &w[nw - 64] );
cftf081( &a[64], &w[nw - 8] );
cftf082( &a[80], &w[nw - 8] );
cftf081( &a[96], &w[nw - 8] );
cftf082( &a[112], &w[nw - 8] );
cftmdl1( 64, &a[128], &w[nw - 32] );
cftf081( &a[128], &w[nw - 8] );
cftf082( &a[144], &w[nw - 8] );
cftf081( &a[160], &w[nw - 8] );
cftf081( &a[176], &w[nw - 8] );
if ( isplt != 0 ) {
cftmdl1( 64, &a[192], &w[nw - 32] );
cftf081( &a[240], &w[nw - 8] );
} else {
cftmdl2( 64, &a[192], &w[nw - 64] );
cftf082( &a[240], &w[nw - 8] );
}
cftf081( &a[192], &w[nw - 8] );
cftf082( &a[208], &w[nw - 8] );
cftf081( &a[224], &w[nw - 8] );
}
}
static void cftmdl1( int n, double* a, double* w ) {
int j, j0, j1, j2, j3, k, m, mh;
double wn4r, wk1r, wk1i, wk3r, wk3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
mh = n >> 3;
m = 2 * mh;
j1 = m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[0] + a[j2];
x0i = a[1] + a[j2 + 1];
x1r = a[0] - a[j2];
x1i = a[1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
a[j2] = x1r - x3i;
a[j2 + 1] = x1i + x3r;
a[j3] = x1r + x3i;
a[j3 + 1] = x1i - x3r;
wn4r = w[1];
k = 0;
for ( j = 2; j < mh; j += 2 ) {
k += 4;
wk1r = w[k];
wk1i = w[k + 1];
wk3r = w[k + 2];
wk3i = w[k + 3];
j1 = j + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j] + a[j2];
x0i = a[j + 1] + a[j2 + 1];
x1r = a[j] - a[j2];
x1i = a[j + 1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[j] = x0r + x2r;
a[j + 1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wk1r * x0r - wk1i * x0i;
a[j2 + 1] = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3r * x0r + wk3i * x0i;
a[j3 + 1] = wk3r * x0i - wk3i * x0r;
j0 = m - j;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] + a[j2];
x0i = a[j0 + 1] + a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = a[j0 + 1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wk1i * x0r - wk1r * x0i;
a[j2 + 1] = wk1i * x0i + wk1r * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = wk3i * x0r + wk3r * x0i;
a[j3 + 1] = wk3i * x0i - wk3r * x0r;
}
j0 = mh;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] + a[j2];
x0i = a[j0 + 1] + a[j2 + 1];
x1r = a[j0] - a[j2];
x1i = a[j0 + 1] - a[j2 + 1];
x2r = a[j1] + a[j3];
x2i = a[j1 + 1] + a[j3 + 1];
x3r = a[j1] - a[j3];
x3i = a[j1 + 1] - a[j3 + 1];
a[j0] = x0r + x2r;
a[j0 + 1] = x0i + x2i;
a[j1] = x0r - x2r;
a[j1 + 1] = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
a[j2] = wn4r * (x0r - x0i);
a[j2 + 1] = wn4r * (x0i + x0r);
x0r = x1r + x3i;
x0i = x1i - x3r;
a[j3] = -wn4r * (x0r + x0i);
a[j3 + 1] = -wn4r * (x0i - x0r);
}
static void cftmdl2( int n, double* a, double* w ) {
int j, j0, j1, j2, j3, k, kr, m, mh;
double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
mh = n >> 3;
m = 2 * mh;
wn4r = w[1];
j1 = m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[0] - a[j2 + 1];
x0i = a[1] + a[j2];
x1r = a[0] + a[j2 + 1];
x1i = a[1] - a[j2];
x2r = a[j1] - a[j3 + 1];
x2i = a[j1 + 1] + a[j3];
x3r = a[j1] + a[j3 + 1];
x3i = a[j1 + 1] - a[j3];
y0r = wn4r * (x2r - x2i);
y0i = wn4r * (x2i + x2r);
a[0] = x0r + y0r;
a[1] = x0i + y0i;
a[j1] = x0r - y0r;
a[j1 + 1] = x0i - y0i;
y0r = wn4r * (x3r - x3i);
y0i = wn4r * (x3i + x3r);
a[j2] = x1r - y0i;
a[j2 + 1] = x1i + y0r;
a[j3] = x1r + y0i;
a[j3 + 1] = x1i - y0r;
k = 0;
kr = 2 * m;
for ( j = 2; j < mh; j += 2 ) {
k += 4;
wk1r = w[k];
wk1i = w[k + 1];
wk3r = w[k + 2];
wk3i = w[k + 3];
kr -= 4;
wd1i = w[kr];
wd1r = w[kr + 1];
wd3i = w[kr + 2];
wd3r = w[kr + 3];
j1 = j + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j] - a[j2 + 1];
x0i = a[j + 1] + a[j2];
x1r = a[j] + a[j2 + 1];
x1i = a[j + 1] - a[j2];
x2r = a[j1] - a[j3 + 1];
x2i = a[j1 + 1] + a[j3];
x3r = a[j1] + a[j3 + 1];
x3i = a[j1 + 1] - a[j3];
y0r = wk1r * x0r - wk1i * x0i;
y0i = wk1r * x0i + wk1i * x0r;
y2r = wd1r * x2r - wd1i * x2i;
y2i = wd1r * x2i + wd1i * x2r;
a[j] = y0r + y2r;
a[j + 1] = y0i + y2i;
a[j1] = y0r - y2r;
a[j1 + 1] = y0i - y2i;
y0r = wk3r * x1r + wk3i * x1i;
y0i = wk3r * x1i - wk3i * x1r;
y2r = wd3r * x3r + wd3i * x3i;
y2i = wd3r * x3i - wd3i * x3r;
a[j2] = y0r + y2r;
a[j2 + 1] = y0i + y2i;
a[j3] = y0r - y2r;
a[j3 + 1] = y0i - y2i;
j0 = m - j;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] - a[j2 + 1];
x0i = a[j0 + 1] + a[j2];
x1r = a[j0] + a[j2 + 1];
x1i = a[j0 + 1] - a[j2];
x2r = a[j1] - a[j3 + 1];
x2i = a[j1 + 1] + a[j3];
x3r = a[j1] + a[j3 + 1];
x3i = a[j1 + 1] - a[j3];
y0r = wd1i * x0r - wd1r * x0i;
y0i = wd1i * x0i + wd1r * x0r;
y2r = wk1i * x2r - wk1r * x2i;
y2i = wk1i * x2i + wk1r * x2r;
a[j0] = y0r + y2r;
a[j0 + 1] = y0i + y2i;
a[j1] = y0r - y2r;
a[j1 + 1] = y0i - y2i;
y0r = wd3i * x1r + wd3r * x1i;
y0i = wd3i * x1i - wd3r * x1r;
y2r = wk3i * x3r + wk3r * x3i;
y2i = wk3i * x3i - wk3r * x3r;
a[j2] = y0r + y2r;
a[j2 + 1] = y0i + y2i;
a[j3] = y0r - y2r;
a[j3 + 1] = y0i - y2i;
}
wk1r = w[m];
wk1i = w[m + 1];
j0 = mh;
j1 = j0 + m;
j2 = j1 + m;
j3 = j2 + m;
x0r = a[j0] - a[j2 + 1];
x0i = a[j0 + 1] + a[j2];
x1r = a[j0] + a[j2 + 1];
x1i = a[j0 + 1] - a[j2];
x2r = a[j1] - a[j3 + 1];
x2i = a[j1 + 1] + a[j3];
x3r = a[j1] + a[j3 + 1];
x3i = a[j1 + 1] - a[j3];
y0r = wk1r * x0r - wk1i * x0i;
y0i = wk1r * x0i + wk1i * x0r;
y2r = wk1i * x2r - wk1r * x2i;
y2i = wk1i * x2i + wk1r * x2r;
a[j0] = y0r + y2r;
a[j0 + 1] = y0i + y2i;
a[j1] = y0r - y2r;
a[j1 + 1] = y0i - y2i;
y0r = wk1i * x1r - wk1r * x1i;
y0i = wk1i * x1i + wk1r * x1r;
y2r = wk1r * x3r - wk1i * x3i;
y2i = wk1r * x3i + wk1i * x3r;
a[j2] = y0r - y2r;
a[j2 + 1] = y0i - y2i;
a[j3] = y0r + y2r;
a[j3 + 1] = y0i + y2i;
}
static void cftfx41( int n, double* a, int nw, double* w ) {
//void cftf161(double *a, double *w);
//void cftf162(double *a, double *w);
//void cftf081(double *a, double *w);
//void cftf082(double *a, double *w);
if ( n == 128 ) {
cftf161( a, &w[nw - 8] );
cftf162( &a[32], &w[nw - 32] );
cftf161( &a[64], &w[nw - 8] );
cftf161( &a[96], &w[nw - 8] );
} else {
cftf081( a, &w[nw - 8] );
cftf082( &a[16], &w[nw - 8] );
cftf081( &a[32], &w[nw - 8] );
cftf081( &a[48], &w[nw - 8] );
}
}
static void cftf161( double* a, double* w ) {
double wn4r, wk1r, wk1i,
x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
wn4r = w[1];
wk1r = w[2];
wk1i = w[3];
x0r = a[0] + a[16];
x0i = a[1] + a[17];
x1r = a[0] - a[16];
x1i = a[1] - a[17];
x2r = a[8] + a[24];
x2i = a[9] + a[25];
x3r = a[8] - a[24];
x3i = a[9] - a[25];
y0r = x0r + x2r;
y0i = x0i + x2i;
y4r = x0r - x2r;
y4i = x0i - x2i;
y8r = x1r - x3i;
y8i = x1i + x3r;
y12r = x1r + x3i;
y12i = x1i - x3r;
x0r = a[2] + a[18];
x0i = a[3] + a[19];
x1r = a[2] - a[18];
x1i = a[3] - a[19];
x2r = a[10] + a[26];
x2i = a[11] + a[27];
x3r = a[10] - a[26];
x3i = a[11] - a[27];
y1r = x0r + x2r;
y1i = x0i + x2i;
y5r = x0r - x2r;
y5i = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
y9r = wk1r * x0r - wk1i * x0i;
y9i = wk1r * x0i + wk1i * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
y13r = wk1i * x0r - wk1r * x0i;
y13i = wk1i * x0i + wk1r * x0r;
x0r = a[4] + a[20];
x0i = a[5] + a[21];
x1r = a[4] - a[20];
x1i = a[5] - a[21];
x2r = a[12] + a[28];
x2i = a[13] + a[29];
x3r = a[12] - a[28];
x3i = a[13] - a[29];
y2r = x0r + x2r;
y2i = x0i + x2i;
y6r = x0r - x2r;
y6i = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
y10r = wn4r * (x0r - x0i);
y10i = wn4r * (x0i + x0r);
x0r = x1r + x3i;
x0i = x1i - x3r;
y14r = wn4r * (x0r + x0i);
y14i = wn4r * (x0i - x0r);
x0r = a[6] + a[22];
x0i = a[7] + a[23];
x1r = a[6] - a[22];
x1i = a[7] - a[23];
x2r = a[14] + a[30];
x2i = a[15] + a[31];
x3r = a[14] - a[30];
x3i = a[15] - a[31];
y3r = x0r + x2r;
y3i = x0i + x2i;
y7r = x0r - x2r;
y7i = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
y11r = wk1i * x0r - wk1r * x0i;
y11i = wk1i * x0i + wk1r * x0r;
x0r = x1r + x3i;
x0i = x1i - x3r;
y15r = wk1r * x0r - wk1i * x0i;
y15i = wk1r * x0i + wk1i * x0r;
x0r = y12r - y14r;
x0i = y12i - y14i;
x1r = y12r + y14r;
x1i = y12i + y14i;
x2r = y13r - y15r;
x2i = y13i - y15i;
x3r = y13r + y15r;
x3i = y13i + y15i;
a[24] = x0r + x2r;
a[25] = x0i + x2i;
a[26] = x0r - x2r;
a[27] = x0i - x2i;
a[28] = x1r - x3i;
a[29] = x1i + x3r;
a[30] = x1r + x3i;
a[31] = x1i - x3r;
x0r = y8r + y10r;
x0i = y8i + y10i;
x1r = y8r - y10r;
x1i = y8i - y10i;
x2r = y9r + y11r;
x2i = y9i + y11i;
x3r = y9r - y11r;
x3i = y9i - y11i;
a[16] = x0r + x2r;
a[17] = x0i + x2i;
a[18] = x0r - x2r;
a[19] = x0i - x2i;
a[20] = x1r - x3i;
a[21] = x1i + x3r;
a[22] = x1r + x3i;
a[23] = x1i - x3r;
x0r = y5r - y7i;
x0i = y5i + y7r;
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
x0r = y5r + y7i;
x0i = y5i - y7r;
x3r = wn4r * (x0r - x0i);
x3i = wn4r * (x0i + x0r);
x0r = y4r - y6i;
x0i = y4i + y6r;
x1r = y4r + y6i;
x1i = y4i - y6r;
a[8] = x0r + x2r;
a[9] = x0i + x2i;
a[10] = x0r - x2r;
a[11] = x0i - x2i;
a[12] = x1r - x3i;
a[13] = x1i + x3r;
a[14] = x1r + x3i;
a[15] = x1i - x3r;
x0r = y0r + y2r;
x0i = y0i + y2i;
x1r = y0r - y2r;
x1i = y0i - y2i;
x2r = y1r + y3r;
x2i = y1i + y3i;
x3r = y1r - y3r;
x3i = y1i - y3i;
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[2] = x0r - x2r;
a[3] = x0i - x2i;
a[4] = x1r - x3i;
a[5] = x1i + x3r;
a[6] = x1r + x3i;
a[7] = x1i - x3r;
}
static void cftf162( double* a, double* w ) {
double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
x0r, x0i, x1r, x1i, x2r, x2i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
wn4r = w[1];
wk1r = w[4];
wk1i = w[5];
wk3r = w[6];
wk3i = -w[7];
wk2r = w[8];
wk2i = w[9];
x1r = a[0] - a[17];
x1i = a[1] + a[16];
x0r = a[8] - a[25];
x0i = a[9] + a[24];
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
y0r = x1r + x2r;
y0i = x1i + x2i;
y4r = x1r - x2r;
y4i = x1i - x2i;
x1r = a[0] + a[17];
x1i = a[1] - a[16];
x0r = a[8] + a[25];
x0i = a[9] - a[24];
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
y8r = x1r - x2i;
y8i = x1i + x2r;
y12r = x1r + x2i;
y12i = x1i - x2r;
x0r = a[2] - a[19];
x0i = a[3] + a[18];
x1r = wk1r * x0r - wk1i * x0i;
x1i = wk1r * x0i + wk1i * x0r;
x0r = a[10] - a[27];
x0i = a[11] + a[26];
x2r = wk3i * x0r - wk3r * x0i;
x2i = wk3i * x0i + wk3r * x0r;
y1r = x1r + x2r;
y1i = x1i + x2i;
y5r = x1r - x2r;
y5i = x1i - x2i;
x0r = a[2] + a[19];
x0i = a[3] - a[18];
x1r = wk3r * x0r - wk3i * x0i;
x1i = wk3r * x0i + wk3i * x0r;
x0r = a[10] + a[27];
x0i = a[11] - a[26];
x2r = wk1r * x0r + wk1i * x0i;
x2i = wk1r * x0i - wk1i * x0r;
y9r = x1r - x2r;
y9i = x1i - x2i;
y13r = x1r + x2r;
y13i = x1i + x2i;
x0r = a[4] - a[21];
x0i = a[5] + a[20];
x1r = wk2r * x0r - wk2i * x0i;
x1i = wk2r * x0i + wk2i * x0r;
x0r = a[12] - a[29];
x0i = a[13] + a[28];
x2r = wk2i * x0r - wk2r * x0i;
x2i = wk2i * x0i + wk2r * x0r;
y2r = x1r + x2r;
y2i = x1i + x2i;
y6r = x1r - x2r;
y6i = x1i - x2i;
x0r = a[4] + a[21];
x0i = a[5] - a[20];
x1r = wk2i * x0r - wk2r * x0i;
x1i = wk2i * x0i + wk2r * x0r;
x0r = a[12] + a[29];
x0i = a[13] - a[28];
x2r = wk2r * x0r - wk2i * x0i;
x2i = wk2r * x0i + wk2i * x0r;
y10r = x1r - x2r;
y10i = x1i - x2i;
y14r = x1r + x2r;
y14i = x1i + x2i;
x0r = a[6] - a[23];
x0i = a[7] + a[22];
x1r = wk3r * x0r - wk3i * x0i;
x1i = wk3r * x0i + wk3i * x0r;
x0r = a[14] - a[31];
x0i = a[15] + a[30];
x2r = wk1i * x0r - wk1r * x0i;
x2i = wk1i * x0i + wk1r * x0r;
y3r = x1r + x2r;
y3i = x1i + x2i;
y7r = x1r - x2r;
y7i = x1i - x2i;
x0r = a[6] + a[23];
x0i = a[7] - a[22];
x1r = wk1i * x0r + wk1r * x0i;
x1i = wk1i * x0i - wk1r * x0r;
x0r = a[14] + a[31];
x0i = a[15] - a[30];
x2r = wk3i * x0r - wk3r * x0i;
x2i = wk3i * x0i + wk3r * x0r;
y11r = x1r + x2r;
y11i = x1i + x2i;
y15r = x1r - x2r;
y15i = x1i - x2i;
x1r = y0r + y2r;
x1i = y0i + y2i;
x2r = y1r + y3r;
x2i = y1i + y3i;
a[0] = x1r + x2r;
a[1] = x1i + x2i;
a[2] = x1r - x2r;
a[3] = x1i - x2i;
x1r = y0r - y2r;
x1i = y0i - y2i;
x2r = y1r - y3r;
x2i = y1i - y3i;
a[4] = x1r - x2i;
a[5] = x1i + x2r;
a[6] = x1r + x2i;
a[7] = x1i - x2r;
x1r = y4r - y6i;
x1i = y4i + y6r;
x0r = y5r - y7i;
x0i = y5i + y7r;
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
a[8] = x1r + x2r;
a[9] = x1i + x2i;
a[10] = x1r - x2r;
a[11] = x1i - x2i;
x1r = y4r + y6i;
x1i = y4i - y6r;
x0r = y5r + y7i;
x0i = y5i - y7r;
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
a[12] = x1r - x2i;
a[13] = x1i + x2r;
a[14] = x1r + x2i;
a[15] = x1i - x2r;
x1r = y8r + y10r;
x1i = y8i + y10i;
x2r = y9r - y11r;
x2i = y9i - y11i;
a[16] = x1r + x2r;
a[17] = x1i + x2i;
a[18] = x1r - x2r;
a[19] = x1i - x2i;
x1r = y8r - y10r;
x1i = y8i - y10i;
x2r = y9r + y11r;
x2i = y9i + y11i;
a[20] = x1r - x2i;
a[21] = x1i + x2r;
a[22] = x1r + x2i;
a[23] = x1i - x2r;
x1r = y12r - y14i;
x1i = y12i + y14r;
x0r = y13r + y15i;
x0i = y13i - y15r;
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
a[24] = x1r + x2r;
a[25] = x1i + x2i;
a[26] = x1r - x2r;
a[27] = x1i - x2i;
x1r = y12r + y14i;
x1i = y12i - y14r;
x0r = y13r - y15i;
x0i = y13i + y15r;
x2r = wn4r * (x0r - x0i);
x2i = wn4r * (x0i + x0r);
a[28] = x1r - x2i;
a[29] = x1i + x2r;
a[30] = x1r + x2i;
a[31] = x1i - x2r;
}
static void cftf081( double* a, double* w ) {
double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
wn4r = w[1];
x0r = a[0] + a[8];
x0i = a[1] + a[9];
x1r = a[0] - a[8];
x1i = a[1] - a[9];
x2r = a[4] + a[12];
x2i = a[5] + a[13];
x3r = a[4] - a[12];
x3i = a[5] - a[13];
y0r = x0r + x2r;
y0i = x0i + x2i;
y2r = x0r - x2r;
y2i = x0i - x2i;
y1r = x1r - x3i;
y1i = x1i + x3r;
y3r = x1r + x3i;
y3i = x1i - x3r;
x0r = a[2] + a[10];
x0i = a[3] + a[11];
x1r = a[2] - a[10];
x1i = a[3] - a[11];
x2r = a[6] + a[14];
x2i = a[7] + a[15];
x3r = a[6] - a[14];
x3i = a[7] - a[15];
y4r = x0r + x2r;
y4i = x0i + x2i;
y6r = x0r - x2r;
y6i = x0i - x2i;
x0r = x1r - x3i;
x0i = x1i + x3r;
x2r = x1r + x3i;
x2i = x1i - x3r;
y5r = wn4r * (x0r - x0i);
y5i = wn4r * (x0r + x0i);
y7r = wn4r * (x2r - x2i);
y7i = wn4r * (x2r + x2i);
a[8] = y1r + y5r;
a[9] = y1i + y5i;
a[10] = y1r - y5r;
a[11] = y1i - y5i;
a[12] = y3r - y7i;
a[13] = y3i + y7r;
a[14] = y3r + y7i;
a[15] = y3i - y7r;
a[0] = y0r + y4r;
a[1] = y0i + y4i;
a[2] = y0r - y4r;
a[3] = y0i - y4i;
a[4] = y2r - y6i;
a[5] = y2i + y6r;
a[6] = y2r + y6i;
a[7] = y2i - y6r;
}
static void cftf082( double* a, double* w ) {
double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
wn4r = w[1];
wk1r = w[2];
wk1i = w[3];
y0r = a[0] - a[9];
y0i = a[1] + a[8];
y1r = a[0] + a[9];
y1i = a[1] - a[8];
x0r = a[4] - a[13];
x0i = a[5] + a[12];
y2r = wn4r * (x0r - x0i);
y2i = wn4r * (x0i + x0r);
x0r = a[4] + a[13];
x0i = a[5] - a[12];
y3r = wn4r * (x0r - x0i);
y3i = wn4r * (x0i + x0r);
x0r = a[2] - a[11];
x0i = a[3] + a[10];
y4r = wk1r * x0r - wk1i * x0i;
y4i = wk1r * x0i + wk1i * x0r;
x0r = a[2] + a[11];
x0i = a[3] - a[10];
y5r = wk1i * x0r - wk1r * x0i;
y5i = wk1i * x0i + wk1r * x0r;
x0r = a[6] - a[15];
x0i = a[7] + a[14];
y6r = wk1i * x0r - wk1r * x0i;
y6i = wk1i * x0i + wk1r * x0r;
x0r = a[6] + a[15];
x0i = a[7] - a[14];
y7r = wk1r * x0r - wk1i * x0i;
y7i = wk1r * x0i + wk1i * x0r;
x0r = y0r + y2r;
x0i = y0i + y2i;
x1r = y4r + y6r;
x1i = y4i + y6i;
a[0] = x0r + x1r;
a[1] = x0i + x1i;
a[2] = x0r - x1r;
a[3] = x0i - x1i;
x0r = y0r - y2r;
x0i = y0i - y2i;
x1r = y4r - y6r;
x1i = y4i - y6i;
a[4] = x0r - x1i;
a[5] = x0i + x1r;
a[6] = x0r + x1i;
a[7] = x0i - x1r;
x0r = y1r - y3i;
x0i = y1i + y3r;
x1r = y5r - y7r;
x1i = y5i - y7i;
a[8] = x0r + x1r;
a[9] = x0i + x1i;
a[10] = x0r - x1r;
a[11] = x0i - x1i;
x0r = y1r + y3i;
x0i = y1i - y3r;
x1r = y5r + y7r;
x1i = y5i + y7i;
a[12] = x0r - x1i;
a[13] = x0i + x1r;
a[14] = x0r + x1i;
a[15] = x0i - x1r;
}
static void cftf040( double* a ) {
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
x0r = a[0] + a[4];
x0i = a[1] + a[5];
x1r = a[0] - a[4];
x1i = a[1] - a[5];
x2r = a[2] + a[6];
x2i = a[3] + a[7];
x3r = a[2] - a[6];
x3i = a[3] - a[7];
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[2] = x1r - x3i;
a[3] = x1i + x3r;
a[4] = x0r - x2r;
a[5] = x0i - x2i;
a[6] = x1r + x3i;
a[7] = x1i - x3r;
}
static void cftb040( double* a ) {
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
x0r = a[0] + a[4];
x0i = a[1] + a[5];
x1r = a[0] - a[4];
x1i = a[1] - a[5];
x2r = a[2] + a[6];
x2i = a[3] + a[7];
x3r = a[2] - a[6];
x3i = a[3] - a[7];
a[0] = x0r + x2r;
a[1] = x0i + x2i;
a[2] = x1r + x3i;
a[3] = x1i - x3r;
a[4] = x0r - x2r;
a[5] = x0i - x2i;
a[6] = x1r - x3i;
a[7] = x1i + x3r;
}
static void cftx020( double* a ) {
double x0r, x0i;
x0r = a[0] - a[2];
x0i = a[1] - a[3];
a[0] += a[2];
a[1] += a[3];
a[2] = x0r;
a[3] = x0i;
}
static void rftfsub( int n, double* a, int nc, double* c ) {
int j, k, kk, ks, m;
double wkr, wki, xr, xi, yr, yi;
m = n >> 1;
ks = 2 * nc / m;
kk = 0;
for ( j = 2; j < m; j += 2 ) {
k = n - j;
kk += ks;
wkr = 0.5 - c[nc - kk];
wki = c[kk];
xr = a[j] - a[k];
xi = a[j + 1] + a[k + 1];
yr = wkr * xr - wki * xi;
yi = wkr * xi + wki * xr;
a[j] -= yr;
a[j + 1] -= yi;
a[k] += yr;
a[k + 1] -= yi;
}
}
static void rftbsub( int n, double* a, int nc, double* c ) {
int j, k, kk, ks, m;
double wkr, wki, xr, xi, yr, yi;
m = n >> 1;
ks = 2 * nc / m;
kk = 0;
for ( j = 2; j < m; j += 2 ) {
k = n - j;
kk += ks;
wkr = 0.5 - c[nc - kk];
wki = c[kk];
xr = a[j] - a[k];
xi = a[j + 1] + a[k + 1];
yr = wkr * xr + wki * xi;
yi = wkr * xi - wki * xr;
a[j] -= yr;
a[j + 1] -= yi;
a[k] += yr;
a[k + 1] -= yi;
}
}
static void dctsub( int n, double* a, int nc, double* c ) {
int j, k, kk, ks, m;
double wkr, wki, xr;
m = n >> 1;
ks = nc / n;
kk = 0;
for ( j = 1; j < m; j++ ) {
k = n - j;
kk += ks;
wkr = c[kk] - c[nc - kk];
wki = c[kk] + c[nc - kk];
xr = wki * a[j] - wkr * a[k];
a[j] = wkr * a[j] + wki * a[k];
a[k] = xr;
}
a[m] *= c[0];
}
static void dstsub( int n, double* a, int nc, double* c ) {
int j, k, kk, ks, m;
double wkr, wki, xr;
m = n >> 1;
ks = nc / n;
kk = 0;
for ( j = 1; j < m; j++ ) {
k = n - j;
kk += ks;
wkr = c[kk] - c[nc - kk];
wki = c[kk] + c[nc - kk];
xr = wki * a[k] - wkr * a[j];
a[k] = wkr * a[k] + wki * a[j];
a[j] = xr;
}
a[m] *= c[0];
}
}
}
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