blob: d005f77c58a54c5f5177fa5e95c771468f79ec11 [file] [log] [blame]
/*
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.
*/
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);
}
}
void rdft(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);
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);
}
}
}
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;
}
}
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;
}
}
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];
}
}
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>
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;
}
}
}
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;
}
}
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 -------- */
#ifdef USE_CDFT_PTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 8192
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 65536
#endif
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t pthread_t
#define cdft_thread_create(thp,func,argp) { \
if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
fprintf(stderr, "cdft thread error\n"); \
exit(1); \
} \
}
#define cdft_thread_wait(th) { \
if (pthread_join(th, NULL) != 0) { \
fprintf(stderr, "cdft thread error\n"); \
exit(1); \
} \
}
#endif /* USE_CDFT_PTHREADS */
#ifdef USE_CDFT_WINTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 32768
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 524288
#endif
#include <windows.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t HANDLE
#define cdft_thread_create(thp,func,argp) { \
DWORD thid; \
*(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
if (*(thp) == 0) { \
fprintf(stderr, "cdft thread error\n"); \
exit(1); \
} \
}
#define cdft_thread_wait(th) { \
WaitForSingleObject(th, INFINITE); \
CloseHandle(th); \
}
#endif /* USE_CDFT_WINTHREADS */
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);
#ifdef USE_CDFT_THREADS
void cftrec4_th(int n, double *a, int nw, double *w);
#endif /* USE_CDFT_THREADS */
if (n > 8) {
if (n > 32) {
cftf1st(n, a, &w[nw - (n >> 2)]);
#ifdef USE_CDFT_THREADS
if (n > CDFT_THREADS_BEGIN_N) {
cftrec4_th(n, a, nw, w);
} else
#endif /* USE_CDFT_THREADS */
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);
}
}
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);
#ifdef USE_CDFT_THREADS
void cftrec4_th(int n, double *a, int nw, double *w);
#endif /* USE_CDFT_THREADS */
if (n > 8) {
if (n > 32) {
cftb1st(n, a, &w[nw - (n >> 2)]);
#ifdef USE_CDFT_THREADS
if (n > CDFT_THREADS_BEGIN_N) {
cftrec4_th(n, a, nw, w);
} else
#endif /* USE_CDFT_THREADS */
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);
}
}
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;
}
}
}
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];
}
}
}
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;
}
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;
}
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;
}
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;
}
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;
}
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 +