1366 lines
33 KiB
C++
1366 lines
33 KiB
C++
//$ nobt
|
|
//$ nocpp
|
|
|
|
/**
|
|
* @file fft4g.h
|
|
*
|
|
* @brief Wrapper class for Takuya OOURA's FFT functions.
|
|
*
|
|
* Functions from the FFT package by: Copyright(C) 1996-2001 Takuya OOURA
|
|
* http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html
|
|
*
|
|
* Modified and used with permission granted by the license.
|
|
*
|
|
* Here, the original "fft4g.c" file was wrapped into the "ooura_fft" class.
|
|
*/
|
|
|
|
#ifndef R8B_FFT4G_INCLUDED
|
|
#define R8B_FFT4G_INCLUDED
|
|
|
|
/*
|
|
Fast Fourier/Cosine/Sine Transform
|
|
dimension :one
|
|
data length :power of 2
|
|
decimation :frequency
|
|
radix :4, 2
|
|
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, FPType *, int *, FPType *);
|
|
void rdft(int, int, FPType *, int *, FPType *);
|
|
void ddct(int, int, FPType *, int *, FPType *);
|
|
void ddst(int, int, FPType *, int *, FPType *);
|
|
void dfct(int, FPType *, FPType *, int *, FPType *);
|
|
void dfst(int, FPType *, FPType *, int *, FPType *);
|
|
|
|
|
|
-------- 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 (FPType *)
|
|
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 (FPType *)
|
|
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 (FPType *)
|
|
<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 (FPType *)
|
|
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 (FPType *)
|
|
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 (FPType *)
|
|
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 (FPType *)
|
|
<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 (FPType *)
|
|
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 (FPType *)
|
|
output data
|
|
a[k] = C[k], 0<=k<=n
|
|
t[0...n/2] :work area (FPType *)
|
|
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 (FPType *)
|
|
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 (FPType *)
|
|
output data
|
|
a[k] = S[k], 0<k<n
|
|
(a[0] is used for work area)
|
|
t[0...n/2-1] :work area (FPType *)
|
|
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 (FPType *)
|
|
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.
|
|
*/
|
|
|
|
namespace r8b
|
|
{
|
|
|
|
/**
|
|
* @brief A wrapper class around Takuya OOURA's FFT functions.
|
|
*
|
|
* A wrapper class around fft4g.c file's FFT functions by Takuya OOURA.
|
|
* Provides static private functions for use by the CDSPRealFFT class.
|
|
*/
|
|
|
|
class ooura_fft
|
|
{
|
|
friend class CDSPRealFFT;
|
|
|
|
typedef double FPType;
|
|
|
|
static void cdft(int n, int isgn, FPType* a, int* ip, FPType* w)
|
|
{
|
|
if (n > (ip[0] << 2)) { makewt(n >> 2, ip, w); }
|
|
if (n > 4)
|
|
{
|
|
if (isgn >= 0)
|
|
{
|
|
bitrv2(n, ip + 2, a);
|
|
cftfsub(n, a, w);
|
|
}
|
|
else
|
|
{
|
|
bitrv2conj(n, ip + 2, a);
|
|
cftbsub(n, a, w);
|
|
}
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, w); }
|
|
}
|
|
|
|
static void rdft(int n, int isgn, FPType* a, int* ip, FPType* w)
|
|
{
|
|
int nw = ip[0];
|
|
if (n > (nw << 2))
|
|
{
|
|
nw = n >> 2;
|
|
makewt(nw, ip, w);
|
|
}
|
|
int nc = ip[1];
|
|
if (n > (nc << 2))
|
|
{
|
|
nc = n >> 2;
|
|
makect(nc, ip, w + nw);
|
|
}
|
|
if (isgn >= 0)
|
|
{
|
|
if (n > 4)
|
|
{
|
|
bitrv2(n, ip + 2, a);
|
|
cftfsub(n, a, w);
|
|
rftfsub(n, a, nc, w + nw);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, w); }
|
|
double 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);
|
|
bitrv2(n, ip + 2, a);
|
|
cftbsub(n, a, w);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, w); }
|
|
}
|
|
}
|
|
|
|
static void ddct(int n, int isgn, FPType* a, int* ip, FPType* w)
|
|
{
|
|
int j;
|
|
double xr;
|
|
|
|
int nw = ip[0];
|
|
if (n > (nw << 2))
|
|
{
|
|
nw = n >> 2;
|
|
makewt(nw, ip, w);
|
|
}
|
|
int 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);
|
|
bitrv2(n, ip + 2, a);
|
|
cftbsub(n, a, w);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, w); }
|
|
}
|
|
dctsub(n, a, nc, w + nw);
|
|
if (isgn >= 0)
|
|
{
|
|
if (n > 4)
|
|
{
|
|
bitrv2(n, ip + 2, a);
|
|
cftfsub(n, a, w);
|
|
rftfsub(n, a, nc, w + nw);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, 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;
|
|
}
|
|
}
|
|
|
|
static void ddst(int n, int isgn, FPType* a, int* ip, FPType* w)
|
|
{
|
|
int j;
|
|
double xr;
|
|
|
|
int nw = ip[0];
|
|
if (n > (nw << 2))
|
|
{
|
|
nw = n >> 2;
|
|
makewt(nw, ip, w);
|
|
}
|
|
int 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);
|
|
bitrv2(n, ip + 2, a);
|
|
cftbsub(n, a, w);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, w); }
|
|
}
|
|
dstsub(n, a, nc, w + nw);
|
|
if (isgn >= 0)
|
|
{
|
|
if (n > 4)
|
|
{
|
|
bitrv2(n, ip + 2, a);
|
|
cftfsub(n, a, w);
|
|
rftfsub(n, a, nc, w + nw);
|
|
}
|
|
else if (n == 4) { cftfsub(n, a, 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;
|
|
}
|
|
}
|
|
|
|
static void dfct(int n, FPType* a, FPType* t, int* ip, FPType* w)
|
|
{
|
|
int j, k;
|
|
|
|
int nw = ip[0];
|
|
if (n > (nw << 3))
|
|
{
|
|
nw = n >> 3;
|
|
makewt(nw, ip, w);
|
|
}
|
|
int nc = ip[1];
|
|
if (n > (nc << 1))
|
|
{
|
|
nc = n >> 1;
|
|
makect(nc, ip, w + nw);
|
|
}
|
|
int m = n >> 1;
|
|
double yi = a[m];
|
|
double xi = a[0] + a[n];
|
|
a[0] -= a[n];
|
|
t[0] = xi - yi;
|
|
t[m] = xi + yi;
|
|
if (n > 2)
|
|
{
|
|
int mh = m >> 1;
|
|
for (j = 1; j < mh; ++j)
|
|
{
|
|
k = m - j;
|
|
double xr = a[j] - a[n - j];
|
|
xi = a[j] + a[n - j];
|
|
double 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)
|
|
{
|
|
bitrv2(m, ip + 2, a);
|
|
cftfsub(m, a, w);
|
|
rftfsub(m, a, nc, w + nw);
|
|
}
|
|
else if (m == 4) { cftfsub(m, a, 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];
|
|
}
|
|
int l = 2;
|
|
m = mh;
|
|
while (m >= 2)
|
|
{
|
|
dctsub(m, t, nc, w + nw);
|
|
if (m > 4)
|
|
{
|
|
bitrv2(m, ip + 2, t);
|
|
cftfsub(m, t, w);
|
|
rftfsub(m, t, nc, w + nw);
|
|
}
|
|
else if (m == 4) { cftfsub(m, t, 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];
|
|
}
|
|
}
|
|
|
|
static void dfst(int n, FPType* a, FPType* t, int* ip, FPType* w)
|
|
{
|
|
int j, k;
|
|
|
|
int nw = ip[0];
|
|
if (n > (nw << 3))
|
|
{
|
|
nw = n >> 3;
|
|
makewt(nw, ip, w);
|
|
}
|
|
int nc = ip[1];
|
|
if (n > (nc << 1))
|
|
{
|
|
nc = n >> 1;
|
|
makect(nc, ip, w + nw);
|
|
}
|
|
if (n > 2)
|
|
{
|
|
int m = n >> 1;
|
|
int mh = m >> 1;
|
|
for (j = 1; j < mh; ++j)
|
|
{
|
|
k = m - j;
|
|
double xr = a[j] + a[n - j];
|
|
double xi = a[j] - a[n - j];
|
|
double yr = a[k] + a[n - k];
|
|
double 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)
|
|
{
|
|
bitrv2(m, ip + 2, a);
|
|
cftfsub(m, a, w);
|
|
rftfsub(m, a, nc, w + nw);
|
|
}
|
|
else if (m == 4) { cftfsub(m, a, 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];
|
|
}
|
|
int l = 2;
|
|
m = mh;
|
|
while (m >= 2)
|
|
{
|
|
dstsub(m, t, nc, w + nw);
|
|
if (m > 4)
|
|
{
|
|
bitrv2(m, ip + 2, t);
|
|
cftfsub(m, t, w);
|
|
rftfsub(m, t, nc, w + nw);
|
|
}
|
|
else if (m == 4) { cftfsub(m, t, 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 -------- */
|
|
|
|
static void makewt(int nw, int* ip, FPType* w)
|
|
{
|
|
ip[0] = nw;
|
|
ip[1] = 1;
|
|
if (nw > 2)
|
|
{
|
|
int nwh = nw >> 1;
|
|
double delta = atan(1.0) / nwh;
|
|
w[0] = 1;
|
|
w[1] = 0;
|
|
w[nwh] = cos(delta * nwh);
|
|
w[nwh + 1] = w[nwh];
|
|
if (nwh > 2)
|
|
{
|
|
for (int j = 2; j < nwh; j += 2)
|
|
{
|
|
double x = cos(delta * j);
|
|
double y = sin(delta * j);
|
|
w[j] = x;
|
|
w[j + 1] = y;
|
|
w[nw - j] = y;
|
|
w[nw - j + 1] = x;
|
|
}
|
|
bitrv2(nw, ip + 2, w);
|
|
}
|
|
}
|
|
}
|
|
|
|
static void makect(int nc, int* ip, FPType* c)
|
|
{
|
|
ip[1] = nc;
|
|
if (nc > 1)
|
|
{
|
|
int nch = nc >> 1;
|
|
double delta = atan(1.0) / nch;
|
|
c[0] = cos(delta * nch);
|
|
c[nch] = 0.5 * c[0];
|
|
for (int j = 1; j < nch; ++j)
|
|
{
|
|
c[j] = 0.5 * cos(delta * j);
|
|
c[nc - j] = 0.5 * sin(delta * j);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* -------- child routines -------- */
|
|
|
|
static void bitrv2(int n, int* ip, FPType* a)
|
|
{
|
|
int j, j1, k, k1;
|
|
double xr, xi, yr, yi;
|
|
|
|
ip[0] = 0;
|
|
int l = n;
|
|
int m = 1;
|
|
while ((m << 3) < l)
|
|
{
|
|
l >>= 1;
|
|
for (j = 0; j < m; ++j) { ip[m + j] = ip[j] + l; }
|
|
m <<= 1;
|
|
}
|
|
int m2 = 2 * m;
|
|
if ((m << 3) == l)
|
|
{
|
|
for (k = 0; k < m; ++k)
|
|
{
|
|
for (j = 0; j < k; ++j)
|
|
{
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[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 += m2;
|
|
k1 += 2 * m2;
|
|
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 += m2;
|
|
k1 -= m2;
|
|
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 += m2;
|
|
k1 += 2 * m2;
|
|
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 * k + m2 + ip[k];
|
|
k1 = j1 + m2;
|
|
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 = 1; k < m; ++k)
|
|
{
|
|
for (j = 0; j < k; ++j)
|
|
{
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[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 += m2;
|
|
k1 += m2;
|
|
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, FPType* a)
|
|
{
|
|
int j, j1, k, k1;
|
|
double xr, xi, yr, yi;
|
|
|
|
ip[0] = 0;
|
|
int l = n;
|
|
int m = 1;
|
|
while ((m << 3) < l)
|
|
{
|
|
l >>= 1;
|
|
for (j = 0; j < m; ++j) { ip[m + j] = ip[j] + l; }
|
|
m <<= 1;
|
|
}
|
|
int m2 = 2 * m;
|
|
if ((m << 3) == l)
|
|
{
|
|
for (k = 0; k < m; ++k)
|
|
{
|
|
for (j = 0; j < k; ++j)
|
|
{
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[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 += m2;
|
|
k1 += 2 * m2;
|
|
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 += m2;
|
|
k1 -= m2;
|
|
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 += m2;
|
|
k1 += 2 * m2;
|
|
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 = 2 * k + ip[k];
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
j1 = k1 + m2;
|
|
k1 = j1 + m2;
|
|
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 += m2;
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
}
|
|
}
|
|
else
|
|
{
|
|
a[1] = -a[1];
|
|
a[m2 + 1] = -a[m2 + 1];
|
|
for (k = 1; k < m; ++k)
|
|
{
|
|
for (j = 0; j < k; ++j)
|
|
{
|
|
j1 = 2 * j + ip[k];
|
|
k1 = 2 * k + ip[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 += m2;
|
|
k1 += m2;
|
|
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 = 2 * k + ip[k];
|
|
a[k1 + 1] = -a[k1 + 1];
|
|
a[k1 + m2 + 1] = -a[k1 + m2 + 1];
|
|
}
|
|
}
|
|
}
|
|
|
|
static void cftfsub(int n, FPType* a, const FPType* w)
|
|
{
|
|
int j, j1;
|
|
double x0r, x0i;
|
|
|
|
int l = 2;
|
|
if (n > 8)
|
|
{
|
|
cft1st(n, a, w);
|
|
l = 8;
|
|
while ((l << 2) < n)
|
|
{
|
|
cftmdl(n, l, a, w);
|
|
l <<= 2;
|
|
}
|
|
}
|
|
if ((l << 2) == n)
|
|
{
|
|
for (j = 0; j < l; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
int j2 = j1 + l;
|
|
int j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
double x1r = a[j] - a[j1];
|
|
double x1i = a[j + 1] - a[j1 + 1];
|
|
double x2r = a[j2] + a[j3];
|
|
double x2i = a[j2 + 1] + a[j3 + 1];
|
|
double x3r = a[j2] - a[j3];
|
|
double x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j2] = x0r - x2r;
|
|
a[j2 + 1] = x0i - x2i;
|
|
a[j1] = x1r - x3i;
|
|
a[j1 + 1] = x1i + x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i - x3r;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (j = 0; j < l; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
x0r = a[j] - a[j1];
|
|
x0i = a[j + 1] - a[j1 + 1];
|
|
a[j] += a[j1];
|
|
a[j + 1] += a[j1 + 1];
|
|
a[j1] = x0r;
|
|
a[j1 + 1] = x0i;
|
|
}
|
|
}
|
|
}
|
|
|
|
static void cftbsub(int n, FPType* a, const FPType* w)
|
|
{
|
|
int j, j1;
|
|
double x0r, x0i;
|
|
|
|
int l = 2;
|
|
if (n > 8)
|
|
{
|
|
cft1st(n, a, w);
|
|
l = 8;
|
|
while ((l << 2) < n)
|
|
{
|
|
cftmdl(n, l, a, w);
|
|
l <<= 2;
|
|
}
|
|
}
|
|
if ((l << 2) == n)
|
|
{
|
|
for (j = 0; j < l; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
int j2 = j1 + l;
|
|
int j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = -a[j + 1] - a[j1 + 1];
|
|
double x1r = a[j] - a[j1];
|
|
double x1i = -a[j + 1] + a[j1 + 1];
|
|
double x2r = a[j2] + a[j3];
|
|
double x2i = a[j2 + 1] + a[j3 + 1];
|
|
double x3r = a[j2] - a[j3];
|
|
double x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i - x2i;
|
|
a[j2] = x0r - x2r;
|
|
a[j2 + 1] = x0i + x2i;
|
|
a[j1] = x1r - x3i;
|
|
a[j1 + 1] = x1i - x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i + x3r;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (j = 0; j < l; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
x0r = a[j] - a[j1];
|
|
x0i = -a[j + 1] + a[j1 + 1];
|
|
a[j] += a[j1];
|
|
a[j + 1] = -a[j + 1] - a[j1 + 1];
|
|
a[j1] = x0r;
|
|
a[j1 + 1] = x0i;
|
|
}
|
|
}
|
|
}
|
|
|
|
static void cft1st(int n, FPType* a, const FPType* w)
|
|
{
|
|
double x0r = a[0] + a[2];
|
|
double x0i = a[1] + a[3];
|
|
double x1r = a[0] - a[2];
|
|
double x1i = a[1] - a[3];
|
|
double x2r = a[4] + a[6];
|
|
double x2i = a[5] + a[7];
|
|
double x3r = a[4] - a[6];
|
|
double x3i = a[5] - a[7];
|
|
a[0] = x0r + x2r;
|
|
a[1] = x0i + x2i;
|
|
a[4] = x0r - x2r;
|
|
a[5] = x0i - x2i;
|
|
a[2] = x1r - x3i;
|
|
a[3] = x1i + x3r;
|
|
a[6] = x1r + x3i;
|
|
a[7] = x1i - x3r;
|
|
double wk1r = w[2];
|
|
x0r = a[8] + a[10];
|
|
x0i = a[9] + a[11];
|
|
x1r = a[8] - a[10];
|
|
x1i = a[9] - a[11];
|
|
x2r = a[12] + a[14];
|
|
x2i = a[13] + a[15];
|
|
x3r = a[12] - a[14];
|
|
x3i = a[13] - a[15];
|
|
a[8] = x0r + x2r;
|
|
a[9] = x0i + x2i;
|
|
a[12] = x2i - x0i;
|
|
a[13] = x0r - x2r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[10] = wk1r * (x0r - x0i);
|
|
a[11] = wk1r * (x0r + x0i);
|
|
x0r = x3i + x1r;
|
|
x0i = x3r - x1i;
|
|
a[14] = wk1r * (x0i - x0r);
|
|
a[15] = wk1r * (x0i + x0r);
|
|
int k1 = 0;
|
|
for (int j = 16; j < n; j += 16)
|
|
{
|
|
k1 += 2;
|
|
int k2 = 2 * k1;
|
|
double wk2r = w[k1];
|
|
double wk2i = w[k1 + 1];
|
|
wk1r = w[k2];
|
|
double wk1i = w[k2 + 1];
|
|
double wk3r = wk1r - 2 * wk2i * wk1i;
|
|
double wk3i = 2 * wk2i * wk1r - wk1i;
|
|
x0r = a[j] + a[j + 2];
|
|
x0i = a[j + 1] + a[j + 3];
|
|
x1r = a[j] - a[j + 2];
|
|
x1i = a[j + 1] - a[j + 3];
|
|
x2r = a[j + 4] + a[j + 6];
|
|
x2i = a[j + 5] + a[j + 7];
|
|
x3r = a[j + 4] - a[j + 6];
|
|
x3i = a[j + 5] - a[j + 7];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j + 4] = wk2r * x0r - wk2i * x0i;
|
|
a[j + 5] = wk2r * x0i + wk2i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j + 2] = wk1r * x0r - wk1i * x0i;
|
|
a[j + 3] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j + 6] = wk3r * x0r - wk3i * x0i;
|
|
a[j + 7] = wk3r * x0i + wk3i * x0r;
|
|
wk1r = w[k2 + 2];
|
|
wk1i = w[k2 + 3];
|
|
wk3r = wk1r - 2 * wk2r * wk1i;
|
|
wk3i = 2 * wk2r * wk1r - wk1i;
|
|
x0r = a[j + 8] + a[j + 10];
|
|
x0i = a[j + 9] + a[j + 11];
|
|
x1r = a[j + 8] - a[j + 10];
|
|
x1i = a[j + 9] - a[j + 11];
|
|
x2r = a[j + 12] + a[j + 14];
|
|
x2i = a[j + 13] + a[j + 15];
|
|
x3r = a[j + 12] - a[j + 14];
|
|
x3i = a[j + 13] - a[j + 15];
|
|
a[j + 8] = x0r + x2r;
|
|
a[j + 9] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j + 12] = -wk2i * x0r - wk2r * x0i;
|
|
a[j + 13] = -wk2i * x0i + wk2r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j + 10] = wk1r * x0r - wk1i * x0i;
|
|
a[j + 11] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j + 14] = wk3r * x0r - wk3i * x0i;
|
|
a[j + 15] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
}
|
|
|
|
static void cftmdl(int n, int l, FPType* a, const FPType* w)
|
|
{
|
|
int j, j1, j2, j3, k, k1, k2, m, m2;
|
|
double wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
|
|
double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
|
|
|
|
m = l << 2;
|
|
for (j = 0; j < l; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j2] = x0r - x2r;
|
|
a[j2 + 1] = x0i - x2i;
|
|
a[j1] = x1r - x3i;
|
|
a[j1 + 1] = x1i + x3r;
|
|
a[j3] = x1r + x3i;
|
|
a[j3 + 1] = x1i - x3r;
|
|
}
|
|
wk1r = w[2];
|
|
for (j = m; j < l + m; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
a[j2] = x2i - x0i;
|
|
a[j2 + 1] = x0r - x2r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * (x0r - x0i);
|
|
a[j1 + 1] = wk1r * (x0r + x0i);
|
|
x0r = x3i + x1r;
|
|
x0i = x3r - x1i;
|
|
a[j3] = wk1r * (x0i - x0r);
|
|
a[j3 + 1] = wk1r * (x0i + x0r);
|
|
}
|
|
k1 = 0;
|
|
m2 = 2 * m;
|
|
for (k = m2; k < n; k += m2)
|
|
{
|
|
k1 += 2;
|
|
k2 = 2 * k1;
|
|
wk2r = w[k1];
|
|
wk2i = w[k1 + 1];
|
|
wk1r = w[k2];
|
|
wk1i = w[k2 + 1];
|
|
wk3r = wk1r - 2 * wk2i * wk1i;
|
|
wk3i = 2 * wk2i * wk1r - wk1i;
|
|
for (j = k; j < l + k; j += 2)
|
|
{
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j2] = wk2r * x0r - wk2i * x0i;
|
|
a[j2 + 1] = wk2r * x0i + wk2i * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * x0r - wk1i * x0i;
|
|
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r - wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
wk1r = w[k2 + 2];
|
|
wk1i = w[k2 + 3];
|
|
wk3r = wk1r - 2 * wk2r * wk1i;
|
|
wk3i = 2 * wk2r * wk1r - wk1i;
|
|
for (j = k + m; j < l + (k + m); j += 2)
|
|
{
|
|
j1 = j + l;
|
|
j2 = j1 + l;
|
|
j3 = j2 + l;
|
|
x0r = a[j] + a[j1];
|
|
x0i = a[j + 1] + a[j1 + 1];
|
|
x1r = a[j] - a[j1];
|
|
x1i = a[j + 1] - a[j1 + 1];
|
|
x2r = a[j2] + a[j3];
|
|
x2i = a[j2 + 1] + a[j3 + 1];
|
|
x3r = a[j2] - a[j3];
|
|
x3i = a[j2 + 1] - a[j3 + 1];
|
|
a[j] = x0r + x2r;
|
|
a[j + 1] = x0i + x2i;
|
|
x0r -= x2r;
|
|
x0i -= x2i;
|
|
a[j2] = -wk2i * x0r - wk2r * x0i;
|
|
a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
|
|
x0r = x1r - x3i;
|
|
x0i = x1i + x3r;
|
|
a[j1] = wk1r * x0r - wk1i * x0i;
|
|
a[j1 + 1] = wk1r * x0i + wk1i * x0r;
|
|
x0r = x1r + x3i;
|
|
x0i = x1i - x3r;
|
|
a[j3] = wk3r * x0r - wk3i * x0i;
|
|
a[j3 + 1] = wk3r * x0i + wk3i * x0r;
|
|
}
|
|
}
|
|
}
|
|
|
|
static void rftfsub(int n, FPType* a, int nc, const FPType* c)
|
|
{
|
|
int m = n >> 1;
|
|
int ks = 2 * nc / m;
|
|
int kk = 0;
|
|
for (int j = 2; j < m; j += 2)
|
|
{
|
|
int k = n - j;
|
|
kk += ks;
|
|
double wkr = 0.5 - c[nc - kk];
|
|
double wki = c[kk];
|
|
double xr = a[j] - a[k];
|
|
double xi = a[j + 1] + a[k + 1];
|
|
double yr = wkr * xr - wki * xi;
|
|
double yi = wkr * xi + wki * xr;
|
|
a[j] -= yr;
|
|
a[j + 1] -= yi;
|
|
a[k] += yr;
|
|
a[k + 1] -= yi;
|
|
}
|
|
}
|
|
|
|
static void rftbsub(int n, FPType* a, int nc, const FPType* c)
|
|
{
|
|
a[1] = -a[1];
|
|
int m = n >> 1;
|
|
int ks = 2 * nc / m;
|
|
int kk = 0;
|
|
for (int j = 2; j < m; j += 2)
|
|
{
|
|
int k = n - j;
|
|
kk += ks;
|
|
double wkr = 0.5 - c[nc - kk];
|
|
double wki = c[kk];
|
|
double xr = a[j] - a[k];
|
|
double xi = a[j + 1] + a[k + 1];
|
|
double yr = wkr * xr + wki * xi;
|
|
double yi = wkr * xi - wki * xr;
|
|
a[j] -= yr;
|
|
a[j + 1] = yi - a[j + 1];
|
|
a[k] += yr;
|
|
a[k + 1] = yi - a[k + 1];
|
|
}
|
|
a[m + 1] = -a[m + 1];
|
|
}
|
|
|
|
static void dctsub(int n, FPType* a, int nc, const FPType* c)
|
|
{
|
|
int m = n >> 1;
|
|
int ks = nc / n;
|
|
int kk = 0;
|
|
for (int j = 1; j < m; ++j)
|
|
{
|
|
int k = n - j;
|
|
kk += ks;
|
|
double wkr = c[kk] - c[nc - kk];
|
|
double wki = c[kk] + c[nc - kk];
|
|
double 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, FPType* a, int nc, const FPType* c)
|
|
{
|
|
int m = n >> 1;
|
|
int ks = nc / n;
|
|
int kk = 0;
|
|
for (int j = 1; j < m; ++j)
|
|
{
|
|
int k = n - j;
|
|
kk += ks;
|
|
double wkr = c[kk] - c[nc - kk];
|
|
double wki = c[kk] + c[nc - kk];
|
|
double xr = wki * a[k] - wkr * a[j];
|
|
a[k] = wkr * a[k] + wki * a[j];
|
|
a[j] = xr;
|
|
}
|
|
a[m] *= c[0];
|
|
}
|
|
};
|
|
} // namespace r8b
|
|
|
|
#endif // R8B_FFT4G_INCLUDED
|