3315 lines
90 KiB
C++
3315 lines
90 KiB
C++
/*
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Fast Fourier/Cosine/Sine Transform
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dimension :one
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data length :power of 2
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decimation :frequency
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radix :split-radix
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data :inplace
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table :use
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functions
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cdft: Complex Discrete Fourier Transform
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rdft: Real Discrete Fourier Transform
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ddct: Discrete Cosine Transform
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ddst: Discrete Sine Transform
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dfct: Cosine Transform of RDFT (Real Symmetric DFT)
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dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
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function prototypes
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void cdft(int, int, double *, int *, double *);
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void rdft(int, int, double *, int *, double *);
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void ddct(int, int, double *, int *, double *);
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void ddst(int, int, double *, int *, double *);
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void dfct(int, double *, double *, int *, double *);
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void dfst(int, double *, double *, int *, double *);
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macro definitions
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USE_CDFT_PTHREADS : default=not defined
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CDFT_THREADS_BEGIN_N : must be >= 512, default=8192
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CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
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USE_CDFT_WINTHREADS : default=not defined
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CDFT_THREADS_BEGIN_N : must be >= 512, default=32768
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CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
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-------- Complex DFT (Discrete Fourier Transform) --------
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[definition]
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<case1>
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X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
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<case2>
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X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
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(notes: sum_j=0^n-1 is a summation from j=0 to n-1)
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[usage]
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<case1>
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ip[0] = 0; // first time only
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cdft(2*n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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cdft(2*n, -1, a, ip, w);
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[parameters]
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2*n :data length (int)
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n >= 1, n = power of 2
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a[0...2*n-1] :input/output data (double *)
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input data
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a[2*j] = Re(x[j]),
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a[2*j+1] = Im(x[j]), 0<=j<n
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output data
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a[2*k] = Re(X[k]),
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a[2*k+1] = Im(X[k]), 0<=k<n
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n/2-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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cdft(2*n, -1, a, ip, w);
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is
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cdft(2*n, 1, a, ip, w);
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for (j = 0; j <= 2 * n - 1; j++) {
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a[j] *= 1.0 / n;
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}
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.
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-------- Real DFT / Inverse of Real DFT --------
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[definition]
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<case1> RDFT
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R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
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I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
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<case2> IRDFT (excluding scale)
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a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
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sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
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sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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rdft(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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rdft(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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<case1>
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output data
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a[2*k] = R[k], 0<=k<n/2
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a[2*k+1] = I[k], 0<k<n/2
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a[1] = R[n/2]
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<case2>
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input data
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a[2*j] = R[j], 0<=j<n/2
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a[2*j+1] = I[j], 0<j<n/2
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a[1] = R[n/2]
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n/2-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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rdft(n, 1, a, ip, w);
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is
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rdft(n, -1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
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[definition]
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<case1> IDCT (excluding scale)
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C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
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<case2> DCT
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C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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ddct(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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ddct(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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output data
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a[k] = C[k], 0<=k<n
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/4-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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ddct(n, -1, a, ip, w);
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is
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a[0] *= 0.5;
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ddct(n, 1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- DST (Discrete Sine Transform) / Inverse of DST --------
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[definition]
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<case1> IDST (excluding scale)
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S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
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<case2> DST
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S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
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[usage]
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<case1>
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ip[0] = 0; // first time only
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ddst(n, 1, a, ip, w);
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<case2>
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ip[0] = 0; // first time only
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ddst(n, -1, a, ip, w);
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[parameters]
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n :data length (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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<case1>
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input data
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a[j] = A[j], 0<j<n
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a[0] = A[n]
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output data
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a[k] = S[k], 0<=k<n
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<case2>
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output data
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a[k] = S[k], 0<k<n
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a[0] = S[n]
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/2)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/2+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/4-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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ddst(n, -1, a, ip, w);
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is
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a[0] *= 0.5;
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ddst(n, 1, a, ip, w);
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for (j = 0; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
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[definition]
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C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
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[usage]
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ip[0] = 0; // first time only
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dfct(n, a, t, ip, w);
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[parameters]
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n :data length - 1 (int)
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n >= 2, n = power of 2
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a[0...n] :input/output data (double *)
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output data
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a[k] = C[k], 0<=k<=n
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t[0...n/2] :work area (double *)
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/4)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/4+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/8-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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a[0] *= 0.5;
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a[n] *= 0.5;
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dfct(n, a, t, ip, w);
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is
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a[0] *= 0.5;
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a[n] *= 0.5;
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dfct(n, a, t, ip, w);
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for (j = 0; j <= n; j++) {
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a[j] *= 2.0 / n;
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}
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.
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-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
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[definition]
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S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
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[usage]
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ip[0] = 0; // first time only
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dfst(n, a, t, ip, w);
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[parameters]
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n :data length + 1 (int)
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n >= 2, n = power of 2
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a[0...n-1] :input/output data (double *)
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output data
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a[k] = S[k], 0<k<n
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(a[0] is used for work area)
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t[0...n/2-1] :work area (double *)
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ip[0...*] :work area for bit reversal (int *)
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length of ip >= 2+sqrt(n/4)
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strictly,
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length of ip >=
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2+(1<<(int)(log(n/4+0.5)/log(2))/2).
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ip[0],ip[1] are pointers of the cos/sin table.
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w[0...n*5/8-1] :cos/sin table (double *)
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w[],ip[] are initialized if ip[0] == 0.
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[remark]
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Inverse of
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dfst(n, a, t, ip, w);
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is
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dfst(n, a, t, ip, w);
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for (j = 1; j <= n - 1; j++) {
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a[j] *= 2.0 / n;
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}
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.
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Appendix :
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The cos/sin table is recalculated when the larger table required.
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w[] and ip[] are compatible with all routines.
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*/
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void cdft(int n, int isgn, double *a, int *ip, double *w)
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{
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void makewt(int nw, int *ip, double *w);
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void cftfsub(int n, double *a, int *ip, int nw, double *w);
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void cftbsub(int n, double *a, int *ip, int nw, double *w);
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int nw;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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if (isgn >= 0) {
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cftfsub(n, a, ip, nw, w);
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} else {
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cftbsub(n, a, ip, nw, w);
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}
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}
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void rdft(int n, int isgn, double *a, int *ip, double *w)
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{
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void makewt(int nw, int *ip, double *w);
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void makect(int nc, int *ip, double *c);
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void cftfsub(int n, double *a, int *ip, int nw, double *w);
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void cftbsub(int n, double *a, int *ip, int nw, double *w);
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void rftfsub(int n, double *a, int nc, double *c);
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void rftbsub(int n, double *a, int nc, double *c);
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int nw, nc;
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double xi;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > (nc << 2)) {
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nc = n >> 2;
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makect(nc, ip, w + nw);
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}
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a, ip, nw, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, ip, nw, w);
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}
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xi = a[0] - a[1];
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a[0] += a[1];
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a[1] = xi;
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} else {
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a[1] = 0.5 * (a[0] - a[1]);
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a[0] -= a[1];
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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cftbsub(n, a, ip, nw, w);
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} else if (n == 4) {
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cftbsub(n, a, ip, nw, w);
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}
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}
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}
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void ddct(int n, int isgn, double *a, int *ip, double *w)
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{
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void makewt(int nw, int *ip, double *w);
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void makect(int nc, int *ip, double *c);
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void cftfsub(int n, double *a, int *ip, int nw, double *w);
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void cftbsub(int n, double *a, int *ip, int nw, double *w);
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void rftfsub(int n, double *a, int nc, double *c);
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void rftbsub(int n, double *a, int nc, double *c);
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void dctsub(int n, double *a, int nc, double *c);
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int j, nw, nc;
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double xr;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > nc) {
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nc = n;
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makect(nc, ip, w + nw);
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}
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = a[j] - a[j - 1];
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a[j] += a[j - 1];
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}
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a[1] = a[0] - xr;
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a[0] += xr;
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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cftbsub(n, a, ip, nw, w);
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} else if (n == 4) {
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cftbsub(n, a, ip, nw, w);
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}
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}
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dctsub(n, a, nc, w + nw);
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a, ip, nw, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, ip, nw, w);
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}
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xr = a[0] - a[1];
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a[0] += a[1];
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for (j = 2; j < n; j += 2) {
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a[j - 1] = a[j] - a[j + 1];
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a[j] += a[j + 1];
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}
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a[n - 1] = xr;
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}
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}
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void ddst(int n, int isgn, double *a, int *ip, double *w)
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{
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void makewt(int nw, int *ip, double *w);
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void makect(int nc, int *ip, double *c);
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void cftfsub(int n, double *a, int *ip, int nw, double *w);
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void cftbsub(int n, double *a, int *ip, int nw, double *w);
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void rftfsub(int n, double *a, int nc, double *c);
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void rftbsub(int n, double *a, int nc, double *c);
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void dstsub(int n, double *a, int nc, double *c);
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int j, nw, nc;
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double xr;
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nw = ip[0];
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if (n > (nw << 2)) {
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nw = n >> 2;
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makewt(nw, ip, w);
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}
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nc = ip[1];
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if (n > nc) {
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nc = n;
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makect(nc, ip, w + nw);
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}
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if (isgn < 0) {
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xr = a[n - 1];
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for (j = n - 2; j >= 2; j -= 2) {
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a[j + 1] = -a[j] - a[j - 1];
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a[j] -= a[j - 1];
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}
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a[1] = a[0] + xr;
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a[0] -= xr;
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if (n > 4) {
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rftbsub(n, a, nc, w + nw);
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cftbsub(n, a, ip, nw, w);
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} else if (n == 4) {
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cftbsub(n, a, ip, nw, w);
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}
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}
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dstsub(n, a, nc, w + nw);
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if (isgn >= 0) {
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if (n > 4) {
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cftfsub(n, a, ip, nw, w);
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rftfsub(n, a, nc, w + nw);
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} else if (n == 4) {
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cftfsub(n, a, ip, nw, w);
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}
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xr = a[0] - a[1];
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a[0] += a[1];
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for (j = 2; j < n; j += 2) {
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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 + 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;
|
|
}
|
|
|
|
|
|
#ifdef USE_CDFT_THREADS
|
|
struct cdft_arg_st {
|
|
int n0;
|
|
int n;
|
|
double *a;
|
|
int nw;
|
|
double *w;
|
|
};
|
|
typedef struct cdft_arg_st cdft_arg_t;
|
|
|
|
|
|
void cftrec4_th(int n, double *a, int nw, double *w)
|
|
{
|
|
void *cftrec1_th(void *p);
|
|
void *cftrec2_th(void *p);
|
|
int i, idiv4, m, nthread;
|
|
cdft_thread_t th[4];
|
|
cdft_arg_t ag[4];
|
|
|
|
nthread = 2;
|
|
idiv4 = 0;
|
|
m = n >> 1;
|
|
if (n > CDFT_4THREADS_BEGIN_N) {
|
|
nthread = 4;
|
|
idiv4 = 1;
|
|
m >>= 1;
|
|
}
|
|
for (i = 0; i < nthread; i++) {
|
|
ag[i].n0 = n;
|
|
ag[i].n = m;
|
|
ag[i].a = &a[i * m];
|
|
ag[i].nw = nw;
|
|
ag[i].w = w;
|
|
if (i != idiv4) {
|
|
cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
|
|
} else {
|
|
cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
|
|
}
|
|
}
|
|
for (i = 0; i < nthread; i++) {
|
|
cdft_thread_wait(th[i]);
|
|
}
|
|
}
|
|
|
|
|
|
void *cftrec1_th(void *p)
|
|
{
|
|
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, n, n0, nw;
|
|
double *a, *w;
|
|
|
|
n0 = ((cdft_arg_t *) p)->n0;
|
|
n = ((cdft_arg_t *) p)->n;
|
|
a = ((cdft_arg_t *) p)->a;
|
|
nw = ((cdft_arg_t *) p)->nw;
|
|
w = ((cdft_arg_t *) p)->w;
|
|
m = n0;
|
|
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);
|
|
}
|
|
return (void *) 0;
|
|
}
|
|
|
|
|
|
void *cftrec2_th(void *p)
|
|
{
|
|
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 cftmdl2(int n, double *a, double *w);
|
|
int isplt, j, k, m, n, n0, nw;
|
|
double *a, *w;
|
|
|
|
n0 = ((cdft_arg_t *) p)->n0;
|
|
n = ((cdft_arg_t *) p)->n;
|
|
a = ((cdft_arg_t *) p)->a;
|
|
nw = ((cdft_arg_t *) p)->nw;
|
|
w = ((cdft_arg_t *) p)->w;
|
|
k = 1;
|
|
m = n0;
|
|
while (m > 512) {
|
|
m >>= 2;
|
|
k <<= 2;
|
|
cftmdl2(m, &a[n - m], &w[nw - m]);
|
|
}
|
|
cftleaf(m, 0, &a[n - m], nw, w);
|
|
k >>= 1;
|
|
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);
|
|
}
|
|
return (void *) 0;
|
|
}
|
|
#endif /* USE_CDFT_THREADS */
|
|
|
|
|
|
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);
|
|
}
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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]);
|
|
}
|
|
}
|
|
|
|
|
|
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);
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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]);
|
|
}
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
|
|
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];
|
|
}
|
|
|
|
|
|
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];
|
|
}
|
|
|