| /* |
| Fast Fourier/Cosine/Sine Transform |
| dimension :one |
| data length :power of 2 |
| decimation :frequency |
| radix :split-radix |
| data :inplace |
| table :use |
| functions |
| cdft: Complex Discrete Fourier Transform |
| rdft: Real Discrete Fourier Transform |
| ddct: Discrete Cosine Transform |
| ddst: Discrete Sine Transform |
| dfct: Cosine Transform of RDFT (Real Symmetric DFT) |
| dfst: Sine Transform of RDFT (Real Anti-symmetric DFT) |
| function prototypes |
| void cdft(int, int, double *, int *, double *); |
| void rdft(int, int, double *, int *, double *); |
| void ddct(int, int, double *, int *, double *); |
| void ddst(int, int, double *, int *, double *); |
| void dfct(int, double *, double *, int *, double *); |
| void dfst(int, double *, double *, int *, double *); |
| macro definitions |
| USE_CDFT_PTHREADS : default=not defined |
| CDFT_THREADS_BEGIN_N : must be >= 512, default=8192 |
| CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536 |
| USE_CDFT_WINTHREADS : default=not defined |
| CDFT_THREADS_BEGIN_N : must be >= 512, default=32768 |
| CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288 |
| |
| |
| -------- Complex DFT (Discrete Fourier Transform) -------- |
| [definition] |
| <case1> |
| X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n |
| <case2> |
| X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n |
| (notes: sum_j=0^n-1 is a summation from j=0 to n-1) |
| [usage] |
| <case1> |
| ip[0] = 0; // first time only |
| cdft(2*n, 1, a, ip, w); |
| <case2> |
| ip[0] = 0; // first time only |
| cdft(2*n, -1, a, ip, w); |
| [parameters] |
| 2*n :data length (int) |
| n >= 1, n = power of 2 |
| a[0...2*n-1] :input/output data (double *) |
| input data |
| a[2*j] = Re(x[j]), |
| a[2*j+1] = Im(x[j]), 0<=j<n |
| output data |
| a[2*k] = Re(X[k]), |
| a[2*k+1] = Im(X[k]), 0<=k<n |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n/2-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| cdft(2*n, -1, a, ip, w); |
| is |
| cdft(2*n, 1, a, ip, w); |
| for (j = 0; j <= 2 * n - 1; j++) { |
| a[j] *= 1.0 / n; |
| } |
| . |
| |
| |
| -------- Real DFT / Inverse of Real DFT -------- |
| [definition] |
| <case1> RDFT |
| R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2 |
| I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2 |
| <case2> IRDFT (excluding scale) |
| a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + |
| sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + |
| sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n |
| [usage] |
| <case1> |
| ip[0] = 0; // first time only |
| rdft(n, 1, a, ip, w); |
| <case2> |
| ip[0] = 0; // first time only |
| rdft(n, -1, a, ip, w); |
| [parameters] |
| n :data length (int) |
| n >= 2, n = power of 2 |
| a[0...n-1] :input/output data (double *) |
| <case1> |
| output data |
| a[2*k] = R[k], 0<=k<n/2 |
| a[2*k+1] = I[k], 0<k<n/2 |
| a[1] = R[n/2] |
| <case2> |
| input data |
| a[2*j] = R[j], 0<=j<n/2 |
| a[2*j+1] = I[j], 0<j<n/2 |
| a[1] = R[n/2] |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n/2) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n/2-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| rdft(n, 1, a, ip, w); |
| is |
| rdft(n, -1, a, ip, w); |
| for (j = 0; j <= n - 1; j++) { |
| a[j] *= 2.0 / n; |
| } |
| . |
| |
| |
| -------- DCT (Discrete Cosine Transform) / Inverse of DCT -------- |
| [definition] |
| <case1> IDCT (excluding scale) |
| C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n |
| <case2> DCT |
| C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n |
| [usage] |
| <case1> |
| ip[0] = 0; // first time only |
| ddct(n, 1, a, ip, w); |
| <case2> |
| ip[0] = 0; // first time only |
| ddct(n, -1, a, ip, w); |
| [parameters] |
| n :data length (int) |
| n >= 2, n = power of 2 |
| a[0...n-1] :input/output data (double *) |
| output data |
| a[k] = C[k], 0<=k<n |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n/2) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n*5/4-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| ddct(n, -1, a, ip, w); |
| is |
| a[0] *= 0.5; |
| ddct(n, 1, a, ip, w); |
| for (j = 0; j <= n - 1; j++) { |
| a[j] *= 2.0 / n; |
| } |
| . |
| |
| |
| -------- DST (Discrete Sine Transform) / Inverse of DST -------- |
| [definition] |
| <case1> IDST (excluding scale) |
| S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n |
| <case2> DST |
| S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n |
| [usage] |
| <case1> |
| ip[0] = 0; // first time only |
| ddst(n, 1, a, ip, w); |
| <case2> |
| ip[0] = 0; // first time only |
| ddst(n, -1, a, ip, w); |
| [parameters] |
| n :data length (int) |
| n >= 2, n = power of 2 |
| a[0...n-1] :input/output data (double *) |
| <case1> |
| input data |
| a[j] = A[j], 0<j<n |
| a[0] = A[n] |
| output data |
| a[k] = S[k], 0<=k<n |
| <case2> |
| output data |
| a[k] = S[k], 0<k<n |
| a[0] = S[n] |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n/2) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n/2+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n*5/4-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| ddst(n, -1, a, ip, w); |
| is |
| a[0] *= 0.5; |
| ddst(n, 1, a, ip, w); |
| for (j = 0; j <= n - 1; j++) { |
| a[j] *= 2.0 / n; |
| } |
| . |
| |
| |
| -------- Cosine Transform of RDFT (Real Symmetric DFT) -------- |
| [definition] |
| C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n |
| [usage] |
| ip[0] = 0; // first time only |
| dfct(n, a, t, ip, w); |
| [parameters] |
| n :data length - 1 (int) |
| n >= 2, n = power of 2 |
| a[0...n] :input/output data (double *) |
| output data |
| a[k] = C[k], 0<=k<=n |
| t[0...n/2] :work area (double *) |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n/4) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n/4+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n*5/8-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| a[0] *= 0.5; |
| a[n] *= 0.5; |
| dfct(n, a, t, ip, w); |
| is |
| a[0] *= 0.5; |
| a[n] *= 0.5; |
| dfct(n, a, t, ip, w); |
| for (j = 0; j <= n; j++) { |
| a[j] *= 2.0 / n; |
| } |
| . |
| |
| |
| -------- Sine Transform of RDFT (Real Anti-symmetric DFT) -------- |
| [definition] |
| S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n |
| [usage] |
| ip[0] = 0; // first time only |
| dfst(n, a, t, ip, w); |
| [parameters] |
| n :data length + 1 (int) |
| n >= 2, n = power of 2 |
| a[0...n-1] :input/output data (double *) |
| output data |
| a[k] = S[k], 0<k<n |
| (a[0] is used for work area) |
| t[0...n/2-1] :work area (double *) |
| ip[0...*] :work area for bit reversal (int *) |
| length of ip >= 2+sqrt(n/4) |
| strictly, |
| length of ip >= |
| 2+(1<<(int)(log(n/4+0.5)/log(2))/2). |
| ip[0],ip[1] are pointers of the cos/sin table. |
| w[0...n*5/8-1] :cos/sin table (double *) |
| w[],ip[] are initialized if ip[0] == 0. |
| [remark] |
| Inverse of |
| dfst(n, a, t, ip, w); |
| is |
| dfst(n, a, t, ip, w); |
| for (j = 1; j <= n - 1; j++) { |
| a[j] *= 2.0 / n; |
| } |
| . |
| |
| |
| Appendix : |
| The cos/sin table is recalculated when the larger table required. |
| w[] and ip[] are compatible with all routines. |
| */ |
| |
| |
| void cdft(int n, int isgn, double *a, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void cftbsub(int n, double *a, int *ip, int nw, double *w); |
| int nw; |
| |
| nw = ip[0]; |
| if (n > (nw << 2)) { |
| nw = n >> 2; |
| makewt(nw, ip, w); |
| } |
| if (isgn >= 0) { |
| cftfsub(n, a, ip, nw, w); |
| } else { |
| cftbsub(n, a, ip, nw, w); |
| } |
| } |
| |
| |
| void rdft(int n, int isgn, double *a, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void makect(int nc, int *ip, double *c); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void cftbsub(int n, double *a, int *ip, int nw, double *w); |
| void rftfsub(int n, double *a, int nc, double *c); |
| void rftbsub(int n, double *a, int nc, double *c); |
| int nw, nc; |
| double xi; |
| |
| nw = ip[0]; |
| if (n > (nw << 2)) { |
| nw = n >> 2; |
| makewt(nw, ip, w); |
| } |
| nc = ip[1]; |
| if (n > (nc << 2)) { |
| nc = n >> 2; |
| makect(nc, ip, w + nw); |
| } |
| if (isgn >= 0) { |
| if (n > 4) { |
| cftfsub(n, a, ip, nw, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, ip, nw, w); |
| } |
| xi = a[0] - a[1]; |
| a[0] += a[1]; |
| a[1] = xi; |
| } else { |
| a[1] = 0.5 * (a[0] - a[1]); |
| a[0] -= a[1]; |
| if (n > 4) { |
| rftbsub(n, a, nc, w + nw); |
| cftbsub(n, a, ip, nw, w); |
| } else if (n == 4) { |
| cftbsub(n, a, ip, nw, w); |
| } |
| } |
| } |
| |
| |
| void ddct(int n, int isgn, double *a, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void makect(int nc, int *ip, double *c); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void cftbsub(int n, double *a, int *ip, int nw, double *w); |
| void rftfsub(int n, double *a, int nc, double *c); |
| void rftbsub(int n, double *a, int nc, double *c); |
| void dctsub(int n, double *a, int nc, double *c); |
| int j, nw, nc; |
| double xr; |
| |
| nw = ip[0]; |
| if (n > (nw << 2)) { |
| nw = n >> 2; |
| makewt(nw, ip, w); |
| } |
| nc = ip[1]; |
| if (n > nc) { |
| nc = n; |
| makect(nc, ip, w + nw); |
| } |
| if (isgn < 0) { |
| xr = a[n - 1]; |
| for (j = n - 2; j >= 2; j -= 2) { |
| a[j + 1] = a[j] - a[j - 1]; |
| a[j] += a[j - 1]; |
| } |
| a[1] = a[0] - xr; |
| a[0] += xr; |
| if (n > 4) { |
| rftbsub(n, a, nc, w + nw); |
| cftbsub(n, a, ip, nw, w); |
| } else if (n == 4) { |
| cftbsub(n, a, ip, nw, w); |
| } |
| } |
| dctsub(n, a, nc, w + nw); |
| if (isgn >= 0) { |
| if (n > 4) { |
| cftfsub(n, a, ip, nw, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, ip, nw, w); |
| } |
| xr = a[0] - a[1]; |
| a[0] += a[1]; |
| for (j = 2; j < n; j += 2) { |
| a[j - 1] = a[j] - a[j + 1]; |
| a[j] += a[j + 1]; |
| } |
| a[n - 1] = xr; |
| } |
| } |
| |
| |
| void ddst(int n, int isgn, double *a, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void makect(int nc, int *ip, double *c); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void cftbsub(int n, double *a, int *ip, int nw, double *w); |
| void rftfsub(int n, double *a, int nc, double *c); |
| void rftbsub(int n, double *a, int nc, double *c); |
| void dstsub(int n, double *a, int nc, double *c); |
| int j, nw, nc; |
| double xr; |
| |
| nw = ip[0]; |
| if (n > (nw << 2)) { |
| nw = n >> 2; |
| makewt(nw, ip, w); |
| } |
| nc = ip[1]; |
| if (n > nc) { |
| nc = n; |
| makect(nc, ip, w + nw); |
| } |
| if (isgn < 0) { |
| xr = a[n - 1]; |
| for (j = n - 2; j >= 2; j -= 2) { |
| a[j + 1] = -a[j] - a[j - 1]; |
| a[j] -= a[j - 1]; |
| } |
| a[1] = a[0] + xr; |
| a[0] -= xr; |
| if (n > 4) { |
| rftbsub(n, a, nc, w + nw); |
| cftbsub(n, a, ip, nw, w); |
| } else if (n == 4) { |
| cftbsub(n, a, ip, nw, w); |
| } |
| } |
| dstsub(n, a, nc, w + nw); |
| if (isgn >= 0) { |
| if (n > 4) { |
| cftfsub(n, a, ip, nw, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, ip, nw, w); |
| } |
| xr = a[0] - a[1]; |
| a[0] += a[1]; |
| for (j = 2; j < n; j += 2) { |
| a[j - 1] = -a[j] - a[j + 1]; |
| a[j] -= a[j + 1]; |
| } |
| a[n - 1] = -xr; |
| } |
| } |
| |
| |
| void dfct(int n, double *a, double *t, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void makect(int nc, int *ip, double *c); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void rftfsub(int n, double *a, int nc, double *c); |
| void dctsub(int n, double *a, int nc, double *c); |
| int j, k, l, m, mh, nw, nc; |
| double xr, xi, yr, yi; |
| |
| nw = ip[0]; |
| if (n > (nw << 3)) { |
| nw = n >> 3; |
| makewt(nw, ip, w); |
| } |
| nc = ip[1]; |
| if (n > (nc << 1)) { |
| nc = n >> 1; |
| makect(nc, ip, w + nw); |
| } |
| m = n >> 1; |
| yi = a[m]; |
| xi = a[0] + a[n]; |
| a[0] -= a[n]; |
| t[0] = xi - yi; |
| t[m] = xi + yi; |
| if (n > 2) { |
| mh = m >> 1; |
| for (j = 1; j < mh; j++) { |
| k = m - j; |
| xr = a[j] - a[n - j]; |
| xi = a[j] + a[n - j]; |
| yr = a[k] - a[n - k]; |
| yi = a[k] + a[n - k]; |
| a[j] = xr; |
| a[k] = yr; |
| t[j] = xi - yi; |
| t[k] = xi + yi; |
| } |
| t[mh] = a[mh] + a[n - mh]; |
| a[mh] -= a[n - mh]; |
| dctsub(m, a, nc, w + nw); |
| if (m > 4) { |
| cftfsub(m, a, ip, nw, w); |
| rftfsub(m, a, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, a, ip, nw, w); |
| } |
| a[n - 1] = a[0] - a[1]; |
| a[1] = a[0] + a[1]; |
| for (j = m - 2; j >= 2; j -= 2) { |
| a[2 * j + 1] = a[j] + a[j + 1]; |
| a[2 * j - 1] = a[j] - a[j + 1]; |
| } |
| l = 2; |
| m = mh; |
| while (m >= 2) { |
| dctsub(m, t, nc, w + nw); |
| if (m > 4) { |
| cftfsub(m, t, ip, nw, w); |
| rftfsub(m, t, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, t, ip, nw, w); |
| } |
| a[n - l] = t[0] - t[1]; |
| a[l] = t[0] + t[1]; |
| k = 0; |
| for (j = 2; j < m; j += 2) { |
| k += l << 2; |
| a[k - l] = t[j] - t[j + 1]; |
| a[k + l] = t[j] + t[j + 1]; |
| } |
| l <<= 1; |
| mh = m >> 1; |
| for (j = 0; j < mh; j++) { |
| k = m - j; |
| t[j] = t[m + k] - t[m + j]; |
| t[k] = t[m + k] + t[m + j]; |
| } |
| t[mh] = t[m + mh]; |
| m = mh; |
| } |
| a[l] = t[0]; |
| a[n] = t[2] - t[1]; |
| a[0] = t[2] + t[1]; |
| } else { |
| a[1] = a[0]; |
| a[2] = t[0]; |
| a[0] = t[1]; |
| } |
| } |
| |
| |
| void dfst(int n, double *a, double *t, int *ip, double *w) |
| { |
| void makewt(int nw, int *ip, double *w); |
| void makect(int nc, int *ip, double *c); |
| void cftfsub(int n, double *a, int *ip, int nw, double *w); |
| void rftfsub(int n, double *a, int nc, double *c); |
| void dstsub(int n, double *a, int nc, double *c); |
| int j, k, l, m, mh, nw, nc; |
| double xr, xi, yr, yi; |
| |
| nw = ip[0]; |
| if (n > (nw << 3)) { |
| nw = n >> 3; |
| makewt(nw, ip, w); |
| } |
| nc = ip[1]; |
| if (n > (nc << 1)) { |
| nc = n >> 1; |
| makect(nc, ip, w + nw); |
| } |
| if (n > 2) { |
| m = n >> 1; |
| mh = m >> 1; |
| for (j = 1; j < mh; j++) { |
| k = m - j; |
| xr = a[j] + a[n - j]; |
| xi = a[j] - a[n - j]; |
| yr = a[k] + a[n - k]; |
| yi = a[k] - a[n - k]; |
| a[j] = xr; |
| a[k] = yr; |
| t[j] = xi + yi; |
| t[k] = xi - yi; |
| } |
| t[0] = a[mh] - a[n - mh]; |
| a[mh] += a[n - mh]; |
| a[0] = a[m]; |
| dstsub(m, a, nc, w + nw); |
| if (m > 4) { |
| cftfsub(m, a, ip, nw, w); |
| rftfsub(m, a, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, a, ip, nw, w); |
| } |
| a[n - 1] = a[1] - a[0]; |
| a[1] = a[0] + a[1]; |
| for (j = m - 2; j >= 2; j -= 2) { |
| a[2 * j + 1] = a[j] - a[j + 1]; |
| a[2 * j - 1] = -a[j] - a[j + 1]; |
| } |
| l = 2; |
| m = mh; |
| while (m >= 2) { |
| dstsub(m, t, nc, w + nw); |
| if (m > 4) { |
| cftfsub(m, t, ip, nw, w); |
| rftfsub(m, t, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, t, ip, nw, w); |
| } |
| a[n - l] = t[1] - t[0]; |
| a[l] = t[0] + t[1]; |
| k = 0; |
| for (j = 2; j < m; j += 2) { |
| k += l << 2; |
| a[k - l] = -t[j] - t[j + 1]; |
| a[k + l] = t[j] - t[j + 1]; |
| } |
| l <<= 1; |
| mh = m >> 1; |
| for (j = 1; j < mh; j++) { |
| k = m - j; |
| t[j] = t[m + k] + t[m + j]; |
| t[k] = t[m + k] - t[m + j]; |
| } |
| t[0] = t[m + mh]; |
| m = mh; |
| } |
| a[l] = t[0]; |
| } |
| a[0] = 0; |
| } |
| |
| |
| /* -------- initializing routines -------- */ |
| |
| |
| #include <math.h> |
| |
| void makewt(int nw, int *ip, double *w) |
| { |
| void makeipt(int nw, int *ip); |
| int j, nwh, nw0, nw1; |
| double delta, wn4r, wk1r, wk1i, wk3r, wk3i; |
| |
| ip[0] = nw; |
| ip[1] = 1; |
| if (nw > 2) { |
| nwh = nw >> 1; |
| delta = atan(1.0) / nwh; |
| wn4r = cos(delta * nwh); |
| w[0] = 1; |
| w[1] = wn4r; |
| if (nwh == 4) { |
| w[2] = cos(delta * 2); |
| w[3] = sin(delta * 2); |
| } else if (nwh > 4) { |
| makeipt(nw, ip); |
| w[2] = 0.5 / cos(delta * 2); |
| w[3] = 0.5 / cos(delta * 6); |
| for (j = 4; j < nwh; j += 4) { |
| w[j] = cos(delta * j); |
| w[j + 1] = sin(delta * j); |
| w[j + 2] = cos(3 * delta * j); |
| w[j + 3] = -sin(3 * delta * j); |
| } |
| } |
| nw0 = 0; |
| while (nwh > 2) { |
| nw1 = nw0 + nwh; |
| nwh >>= 1; |
| w[nw1] = 1; |
| w[nw1 + 1] = wn4r; |
| if (nwh == 4) { |
| wk1r = w[nw0 + 4]; |
| wk1i = w[nw0 + 5]; |
| w[nw1 + 2] = wk1r; |
| w[nw1 + 3] = wk1i; |
| } else if (nwh > 4) { |
| wk1r = w[nw0 + 4]; |
| wk3r = w[nw0 + 6]; |
| w[nw1 + 2] = 0.5 / wk1r; |
| w[nw1 + 3] = 0.5 / wk3r; |
| for (j = 4; j < nwh; j += 4) { |
| wk1r = w[nw0 + 2 * j]; |
| wk1i = w[nw0 + 2 * j + 1]; |
| wk3r = w[nw0 + 2 * j + 2]; |
| wk3i = w[nw0 + 2 * j + 3]; |
| w[nw1 + j] = wk1r; |
| w[nw1 + j + 1] = wk1i; |
| w[nw1 + j + 2] = wk3r; |
| w[nw1 + j + 3] = wk3i; |
| } |
| } |
| nw0 = nw1; |
| } |
| } |
| } |
| |
| |
| void makeipt(int nw, int *ip) |
| { |
| int j, l, m, m2, p, q; |
| |
| ip[2] = 0; |
| ip[3] = 16; |
| m = 2; |
| for (l = nw; l > 32; l >>= 2) { |
| m2 = m << 1; |
| q = m2 << 3; |
| for (j = m; j < m2; j++) { |
| p = ip[j] << 2; |
| ip[m + j] = p; |
| ip[m2 + j] = p + q; |
| } |
| m = m2; |
| } |
| } |
| |
| |
| void makect(int nc, int *ip, double *c) |
| { |
| int j, nch; |
| double delta; |
| |
| ip[1] = nc; |
| if (nc > 1) { |
| nch = nc >> 1; |
| delta = atan(1.0) / nch; |
| c[0] = cos(delta * nch); |
| c[nch] = 0.5 * c[0]; |
| for (j = 1; j < nch; j++) { |
| c[j] = 0.5 * cos(delta * j); |
| c[nc - j] = 0.5 * sin(delta * j); |
| } |
| } |
| } |
| |
| |
| /* -------- child routines -------- */ |
| |
| |
| #ifdef USE_CDFT_PTHREADS |
| #define USE_CDFT_THREADS |
| #ifndef CDFT_THREADS_BEGIN_N |
| #define CDFT_THREADS_BEGIN_N 8192 |
| #endif |
| #ifndef CDFT_4THREADS_BEGIN_N |
| #define CDFT_4THREADS_BEGIN_N 65536 |
| #endif |
| #include <pthread.h> |
| #include <stdio.h> |
| #include <stdlib.h> |
| #define cdft_thread_t pthread_t |
| #define cdft_thread_create(thp,func,argp) { \ |
| if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \ |
| fprintf(stderr, "cdft thread error\n"); \ |
| exit(1); \ |
| } \ |
| } |
| #define cdft_thread_wait(th) { \ |
| if (pthread_join(th, NULL) != 0) { \ |
| fprintf(stderr, "cdft thread error\n"); \ |
| exit(1); \ |
| } \ |
| } |
| #endif /* USE_CDFT_PTHREADS */ |
| |
| |
| #ifdef USE_CDFT_WINTHREADS |
| #define USE_CDFT_THREADS |
| #ifndef CDFT_THREADS_BEGIN_N |
| #define CDFT_THREADS_BEGIN_N 32768 |
| #endif |
| #ifndef CDFT_4THREADS_BEGIN_N |
| #define CDFT_4THREADS_BEGIN_N 524288 |
| #endif |
| #include <windows.h> |
| #include <stdio.h> |
| #include <stdlib.h> |
| #define cdft_thread_t HANDLE |
| #define cdft_thread_create(thp,func,argp) { \ |
| DWORD thid; \ |
| *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \ |
| if (*(thp) == 0) { \ |
| fprintf(stderr, "cdft thread error\n"); \ |
| exit(1); \ |
| } \ |
| } |
| #define cdft_thread_wait(th) { \ |
| WaitForSingleObject(th, INFINITE); \ |
| CloseHandle(th); \ |
| } |
| #endif /* USE_CDFT_WINTHREADS */ |
| |
| |
| void cftfsub(int n, double *a, int *ip, int nw, double *w) |
| { |
| void bitrv2(int n, int *ip, double *a); |
| void bitrv216(double *a); |
| void bitrv208(double *a); |
| void cftf1st(int n, double *a, double *w); |
| void cftrec4(int n, double *a, int nw, double *w); |
| void cftleaf(int n, int isplt, double *a, int nw, double *w); |
| void cftfx41(int n, double *a, int nw, double *w); |
| void cftf161(double *a, double *w); |
| void cftf081(double *a, double *w); |
| void cftf040(double *a); |
| void cftx020(double *a); |
| #ifdef USE_CDFT_THREADS |
| void cftrec4_th(int n, double *a, int nw, double *w); |
| #endif /* USE_CDFT_THREADS */ |
| |
| if (n > 8) { |
| if (n > 32) { |
| cftf1st(n, a, &w[nw - (n >> 2)]); |
| #ifdef USE_CDFT_THREADS |
| if (n > CDFT_THREADS_BEGIN_N) { |
| cftrec4_th(n, a, nw, w); |
| } else |
| #endif /* USE_CDFT_THREADS */ |
| if (n > 512) { |
| cftrec4(n, a, nw, w); |
| } else if (n > 128) { |
| cftleaf(n, 1, a, nw, w); |
| } else { |
| cftfx41(n, a, nw, w); |
| } |
| bitrv2(n, ip, a); |
| } else if (n == 32) { |
| cftf161(a, &w[nw - 8]); |
| bitrv216(a); |
| } else { |
| cftf081(a, w); |
| bitrv208(a); |
| } |
| } else if (n == 8) { |
| cftf040(a); |
| } else if (n == 4) { |
| cftx020(a); |
| } |
| } |
| |
| |
| void cftbsub(int n, double *a, int *ip, int nw, double *w) |
| { |
| void bitrv2conj(int n, int *ip, double *a); |
| void bitrv216neg(double *a); |
| void bitrv208neg(double *a); |
| void cftb1st(int n, double *a, double *w); |
| void cftrec4(int n, double *a, int nw, double *w); |
| void cftleaf(int n, int isplt, double *a, int nw, double *w); |
| void cftfx41(int n, double *a, int nw, double *w); |
| void cftf161(double *a, double *w); |
| void cftf081(double *a, double *w); |
| void cftb040(double *a); |
| void cftx020(double *a); |
| #ifdef USE_CDFT_THREADS |
| void cftrec4_th(int n, double *a, int nw, double *w); |
| #endif /* USE_CDFT_THREADS */ |
| |
| if (n > 8) { |
| if (n > 32) { |
| cftb1st(n, a, &w[nw - (n >> 2)]); |
| #ifdef USE_CDFT_THREADS |
| if (n > CDFT_THREADS_BEGIN_N) { |
| cftrec4_th(n, a, nw, w); |
| } else |
| #endif /* USE_CDFT_THREADS */ |
| if (n > 512) { |
| cftrec4(n, a, nw, w); |
| } else if (n > 128) { |
| cftleaf(n, 1, a, nw, w); |
| } else { |
| cftfx41(n, a, nw, w); |
| } |
| bitrv2conj(n, ip, a); |
| } else if (n == 32) { |
| cftf161(a, &w[nw - 8]); |
| bitrv216neg(a); |
| } else { |
| cftf081(a, w); |
| bitrv208neg(a); |
| } |
| } else if (n == 8) { |
| cftb040(a); |
| } else if (n == 4) { |
| cftx020(a); |
| } |
| } |
| |
| |
| void bitrv2(int n, int *ip, double *a) |
| { |
| int j, j1, k, k1, l, m, nh, nm; |
| double xr, xi, yr, yi; |
| |
| m = 1; |
| for (l = n >> 2; l > 8; l >>= 2) { |
| m <<= 1; |
| } |
| nh = n >> 1; |
| nm = 4 * m; |
| if (l == 8) { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 4 * j + 2 * ip[m + k]; |
| k1 = 4 * k + 2 * ip[m + j]; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh; |
| k1 += 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh; |
| k1 -= 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 4 * k + 2 * ip[m + k]; |
| j1 = k1 + 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= 2; |
| k1 -= nh; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh + 2; |
| k1 += nh + 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh - nm; |
| k1 += 2 * nm - 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| } else { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 4 * j + ip[m + k]; |
| k1 = 4 * k + ip[m + j]; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh; |
| k1 += 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh; |
| k1 -= 2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 4 * k + ip[m + k]; |
| j1 = k1 + 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| } |
| } |
| |
| |
| void bitrv2conj(int n, int *ip, double *a) |
| { |
| int j, j1, k, k1, l, m, nh, nm; |
| double xr, xi, yr, yi; |
| |
| m = 1; |
| for (l = n >> 2; l > 8; l >>= 2) { |
| m <<= 1; |
| } |
| nh = n >> 1; |
| nm = 4 * m; |
| if (l == 8) { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 4 * j + 2 * ip[m + k]; |
| k1 = 4 * k + 2 * ip[m + j]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh; |
| k1 += 2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh; |
| k1 -= 2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 4 * k + 2 * ip[m + k]; |
| j1 = k1 + 2; |
| k1 += nh; |
| a[j1 - 1] = -a[j1 - 1]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| a[k1 + 3] = -a[k1 + 3]; |
| j1 += nm; |
| k1 += 2 * nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= 2; |
| k1 -= nh; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh + 2; |
| k1 += nh + 2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh - nm; |
| k1 += 2 * nm - 2; |
| a[j1 - 1] = -a[j1 - 1]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| a[k1 + 3] = -a[k1 + 3]; |
| } |
| } else { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 4 * j + ip[m + k]; |
| k1 = 4 * k + ip[m + j]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nh; |
| k1 += 2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += 2; |
| k1 += nh; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += nm; |
| k1 += nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nh; |
| k1 -= 2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 -= nm; |
| k1 -= nm; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 4 * k + ip[m + k]; |
| j1 = k1 + 2; |
| k1 += nh; |
| a[j1 - 1] = -a[j1 - 1]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| a[k1 + 3] = -a[k1 + 3]; |
| j1 += nm; |
| k1 += nm; |
| a[j1 - 1] = -a[j1 - 1]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| a[k1 + 3] = -a[k1 + 3]; |
| } |
| } |
| } |
| |
| |
| void bitrv216(double *a) |
| { |
| double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, |
| x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, |
| x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i; |
| |
| x1r = a[2]; |
| x1i = a[3]; |
| x2r = a[4]; |
| x2i = a[5]; |
| x3r = a[6]; |
| x3i = a[7]; |
| x4r = a[8]; |
| x4i = a[9]; |
| x5r = a[10]; |
| x5i = a[11]; |
| x7r = a[14]; |
| x7i = a[15]; |
| x8r = a[16]; |
| x8i = a[17]; |
| x10r = a[20]; |
| x10i = a[21]; |
| x11r = a[22]; |
| x11i = a[23]; |
| x12r = a[24]; |
| x12i = a[25]; |
| x13r = a[26]; |
| x13i = a[27]; |
| x14r = a[28]; |
| x14i = a[29]; |
| a[2] = x8r; |
| a[3] = x8i; |
| a[4] = x4r; |
| a[5] = x4i; |
| a[6] = x12r; |
| a[7] = x12i; |
| a[8] = x2r; |
| a[9] = x2i; |
| a[10] = x10r; |
| a[11] = x10i; |
| a[14] = x14r; |
| a[15] = x14i; |
| a[16] = x1r; |
| a[17] = x1i; |
| a[20] = x5r; |
| a[21] = x5i; |
| a[22] = x13r; |
| a[23] = x13i; |
| a[24] = x3r; |
| a[25] = x3i; |
| a[26] = x11r; |
| a[27] = x11i; |
| a[28] = x7r; |
| a[29] = x7i; |
| } |
| |
| |
| void bitrv216neg(double *a) |
| { |
| double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, |
| x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, |
| x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, |
| x13r, x13i, x14r, x14i, x15r, x15i; |
| |
| x1r = a[2]; |
| x1i = a[3]; |
| x2r = a[4]; |
| x2i = a[5]; |
| x3r = a[6]; |
| x3i = a[7]; |
| x4r = a[8]; |
| x4i = a[9]; |
| x5r = a[10]; |
| x5i = a[11]; |
| x6r = a[12]; |
| x6i = a[13]; |
| x7r = a[14]; |
| x7i = a[15]; |
| x8r = a[16]; |
| x8i = a[17]; |
| x9r = a[18]; |
| x9i = a[19]; |
| x10r = a[20]; |
| x10i = a[21]; |
| x11r = a[22]; |
| x11i = a[23]; |
| x12r = a[24]; |
| x12i = a[25]; |
| x13r = a[26]; |
| x13i = a[27]; |
| x14r = a[28]; |
| x14i = a[29]; |
| x15r = a[30]; |
| x15i = a[31]; |
| a[2] = x15r; |
| a[3] = x15i; |
| a[4] = x7r; |
| a[5] = x7i; |
| a[6] = x11r; |
| a[7] = x11i; |
| a[8] = x3r; |
| a[9] = x3i; |
| a[10] = x13r; |
| a[11] = x13i; |
| a[12] = x5r; |
| a[13] = x5i; |
| a[14] = x9r; |
| a[15] = x9i; |
| a[16] = x1r; |
| a[17] = x1i; |
| a[18] = x14r; |
| a[19] = x14i; |
| a[20] = x6r; |
| a[21] = x6i; |
| a[22] = x10r; |
| a[23] = x10i; |
| a[24] = x2r; |
| a[25] = x2i; |
| a[26] = x12r; |
| a[27] = x12i; |
| a[28] = x4r; |
| a[29] = x4i; |
| a[30] = x8r; |
| a[31] = x8i; |
| } |
| |
| |
| void bitrv208(double *a) |
| { |
| double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i; |
| |
| x1r = a[2]; |
| x1i = a[3]; |
| x3r = a[6]; |
| x3i = a[7]; |
| x4r = a[8]; |
| x4i = a[9]; |
| x6r = a[12]; |
| x6i = a[13]; |
| a[2] = x4r; |
| a[3] = x4i; |
| a[6] = x6r; |
| a[7] = x6i; |
| a[8] = x1r; |
| a[9] = x1i; |
| a[12] = x3r; |
| a[13] = x3i; |
| } |
| |
| |
| void bitrv208neg(double *a) |
| { |
| double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, |
| x5r, x5i, x6r, x6i, x7r, x7i; |
| |
| x1r = a[2]; |
| x1i = a[3]; |
| x2r = a[4]; |
| x2i = a[5]; |
| x3r = a[6]; |
| x3i = a[7]; |
| x4r = a[8]; |
| x4i = a[9]; |
| x5r = a[10]; |
| x5i = a[11]; |
| x6r = a[12]; |
| x6i = a[13]; |
| x7r = a[14]; |
| x7i = a[15]; |
| a[2] = x7r; |
| a[3] = x7i; |
| a[4] = x3r; |
| a[5] = x3i; |
| a[6] = x5r; |
| a[7] = x5i; |
| a[8] = x1r; |
| a[9] = x1i; |
| a[10] = x6r; |
| a[11] = x6i; |
| a[12] = x2r; |
| a[13] = x2i; |
| a[14] = x4r; |
| a[15] = x4i; |
| } |
| |
| |
| void cftf1st(int n, double *a, double *w) |
| { |
| int j, j0, j1, j2, j3, k, m, mh; |
| double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, |
| wd1r, wd1i, wd3r, wd3i; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, |
| y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; |
| |
| mh = n >> 3; |
| m = 2 * mh; |
| j1 = m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[0] + a[j2]; |
| x0i = a[1] + a[j2 + 1]; |
| x1r = a[0] - a[j2]; |
| x1i = a[1] - a[j2 + 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| a[0] = x0r + x2r; |
| a[1] = x0i + x2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i - x2i; |
| a[j2] = x1r - x3i; |
| a[j2 + 1] = x1i + x3r; |
| a[j3] = x1r + x3i; |
| a[j3 + 1] = x1i - x3r; |
| wn4r = w[1]; |
| csc1 = w[2]; |
| csc3 = w[3]; |
| wd1r = 1; |
| wd1i = 0; |
| wd3r = 1; |
| wd3i = 0; |
| k = 0; |
| for (j = 2; j < mh - 2; j += 4) { |
| k += 4; |
| wk1r = csc1 * (wd1r + w[k]); |
| wk1i = csc1 * (wd1i + w[k + 1]); |
| wk3r = csc3 * (wd3r + w[k + 2]); |
| wk3i = csc3 * (wd3i + w[k + 3]); |
| wd1r = w[k]; |
| wd1i = w[k + 1]; |
| wd3r = w[k + 2]; |
| wd3i = w[k + 3]; |
| j1 = j + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j] + a[j2]; |
| x0i = a[j + 1] + a[j2 + 1]; |
| x1r = a[j] - a[j2]; |
| x1i = a[j + 1] - a[j2 + 1]; |
| y0r = a[j + 2] + a[j2 + 2]; |
| y0i = a[j + 3] + a[j2 + 3]; |
| y1r = a[j + 2] - a[j2 + 2]; |
| y1i = a[j + 3] - a[j2 + 3]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| y2r = a[j1 + 2] + a[j3 + 2]; |
| y2i = a[j1 + 3] + a[j3 + 3]; |
| y3r = a[j1 + 2] - a[j3 + 2]; |
| y3i = a[j1 + 3] - a[j3 + 3]; |
| a[j] = x0r + x2r; |
| a[j + 1] = x0i + x2i; |
| a[j + 2] = y0r + y2r; |
| a[j + 3] = y0i + y2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i - x2i; |
| a[j1 + 2] = y0r - y2r; |
| a[j1 + 3] = y0i - y2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| a[j2] = wk1r * x0r - wk1i * x0i; |
| a[j2 + 1] = wk1r * x0i + wk1i * x0r; |
| x0r = y1r - y3i; |
| x0i = y1i + y3r; |
| a[j2 + 2] = wd1r * x0r - wd1i * x0i; |
| a[j2 + 3] = wd1r * x0i + wd1i * x0r; |
| x0r = x1r + x3i; |
| x0i = x1i - x3r; |
| a[j3] = wk3r * x0r + wk3i * x0i; |
| a[j3 + 1] = wk3r * x0i - wk3i * x0r; |
| x0r = y1r + y3i; |
| x0i = y1i - y3r; |
| a[j3 + 2] = wd3r * x0r + wd3i * x0i; |
| a[j3 + 3] = wd3r * x0i - wd3i * x0r; |
| j0 = m - j; |
| j1 = j0 + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j0] + a[j2]; |
| x0i = a[j0 + 1] + a[j2 + 1]; |
| x1r = a[j0] - a[j2]; |
| x1i = a[j0 + 1] - a[j2 + 1]; |
| y0r = a[j0 - 2] + a[j2 - 2]; |
| y0i = a[j0 - 1] + a[j2 - 1]; |
| y1r = a[j0 - 2] - a[j2 - 2]; |
| y1i = a[j0 - 1] - a[j2 - 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| y2r = a[j1 - 2] + a[j3 - 2]; |
| y2i = a[j1 - 1] + a[j3 - 1]; |
| y3r = a[j1 - 2] - a[j3 - 2]; |
| y3i = a[j1 - 1] - a[j3 - 1]; |
| a[j0] = x0r + x2r; |
| a[j0 + 1] = x0i + x2i; |
| a[j0 - 2] = y0r + y2r; |
| a[j0 - 1] = y0i + y2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i - x2i; |
| a[j1 - 2] = y0r - y2r; |
| a[j1 - 1] = y0i - y2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| a[j2] = wk1i * x0r - wk1r * x0i; |
| a[j2 + 1] = wk1i * x0i + wk1r * x0r; |
| x0r = y1r - y3i; |
| x0i = y1i + y3r; |
| a[j2 - 2] = wd1i * x0r - wd1r * x0i; |
| a[j2 - 1] = wd1i * x0i + wd1r * x0r; |
| x0r = x1r + x3i; |
| x0i = x1i - x3r; |
| a[j3] = wk3i * x0r + wk3r * x0i; |
| a[j3 + 1] = wk3i * x0i - wk3r * x0r; |
| x0r = y1r + y3i; |
| x0i = y1i - y3r; |
| a[j3 - 2] = wd3i * x0r + wd3r * x0i; |
| a[j3 - 1] = wd3i * x0i - wd3r * x0r; |
| } |
| wk1r = csc1 * (wd1r + wn4r); |
| wk1i = csc1 * (wd1i + wn4r); |
| wk3r = csc3 * (wd3r - wn4r); |
| wk3i = csc3 * (wd3i - wn4r); |
| j0 = mh; |
| j1 = j0 + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j0 - 2] + a[j2 - 2]; |
| x0i = a[j0 - 1] + a[j2 - 1]; |
| x1r = a[j0 - 2] - a[j2 - 2]; |
| x1i = a[j0 - 1] - a[j2 - 1]; |
| x2r = a[j1 - 2] + a[j3 - 2]; |
| x2i = a[j1 - 1] + a[j3 - 1]; |
| x3r = a[j1 - 2] - a[j3 - 2]; |
| x3i = a[j1 - 1] - a[j3 - 1]; |
| a[j0 - 2] = x0r + x2r; |
| a[j0 - 1] = x0i + x2i; |
| a[j1 - 2] = x0r - x2r; |
| a[j1 - 1] = x0i - x2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| a[j2 - 2] = wk1r * x0r - wk1i * x0i; |
| a[j2 - 1] = wk1r * x0i + wk1i * x0r; |
| x0r = x1r + x3i; |
| x0i = x1i - x3r; |
| a[j3 - 2] = wk3r * x0r + wk3i * x0i; |
| a[j3 - 1] = wk3r * x0i - wk3i * x0r; |
| x0r = a[j0] + a[j2]; |
| x0i = a[j0 + 1] + a[j2 + 1]; |
| x1r = a[j0] - a[j2]; |
| x1i = a[j0 + 1] - a[j2 + 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| a[j0] = x0r + x2r; |
| a[j0 + 1] = x0i + x2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i - x2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| a[j2] = wn4r * (x0r - x0i); |
| a[j2 + 1] = wn4r * (x0i + x0r); |
| x0r = x1r + x3i; |
| x0i = x1i - x3r; |
| a[j3] = -wn4r * (x0r + x0i); |
| a[j3 + 1] = -wn4r * (x0i - x0r); |
| x0r = a[j0 + 2] + a[j2 + 2]; |
| x0i = a[j0 + 3] + a[j2 + 3]; |
| x1r = a[j0 + 2] - a[j2 + 2]; |
| x1i = a[j0 + 3] - a[j2 + 3]; |
| x2r = a[j1 + 2] + a[j3 + 2]; |
| x2i = a[j1 + 3] + a[j3 + 3]; |
| x3r = a[j1 + 2] - a[j3 + 2]; |
| x3i = a[j1 + 3] - a[j3 + 3]; |
| a[j0 + 2] = x0r + x2r; |
| a[j0 + 3] = x0i + x2i; |
| a[j1 + 2] = x0r - x2r; |
| a[j1 + 3] = x0i - x2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| a[j2 + 2] = wk1i * x0r - wk1r * x0i; |
| a[j2 + 3] = wk1i * x0i + wk1r * x0r; |
| x0r = x1r + x3i; |
| x0i = x1i - x3r; |
| a[j3 + 2] = wk3i * x0r + wk3r * x0i; |
| a[j3 + 3] = wk3i * x0i - wk3r * x0r; |
| } |
| |
| |
| void cftb1st(int n, double *a, double *w) |
| { |
| int j, j0, j1, j2, j3, k, m, mh; |
| double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i, |
| wd1r, wd1i, wd3r, wd3i; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, |
| y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i; |
| |
| mh = n >> 3; |
| m = 2 * mh; |
| j1 = m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[0] + a[j2]; |
| x0i = -a[1] - a[j2 + 1]; |
| x1r = a[0] - a[j2]; |
| x1i = -a[1] + a[j2 + 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| a[0] = x0r + x2r; |
| a[1] = x0i - x2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i + x2i; |
| a[j2] = x1r + x3i; |
| a[j2 + 1] = x1i + x3r; |
| a[j3] = x1r - x3i; |
| a[j3 + 1] = x1i - x3r; |
| wn4r = w[1]; |
| csc1 = w[2]; |
| csc3 = w[3]; |
| wd1r = 1; |
| wd1i = 0; |
| wd3r = 1; |
| wd3i = 0; |
| k = 0; |
| for (j = 2; j < mh - 2; j += 4) { |
| k += 4; |
| wk1r = csc1 * (wd1r + w[k]); |
| wk1i = csc1 * (wd1i + w[k + 1]); |
| wk3r = csc3 * (wd3r + w[k + 2]); |
| wk3i = csc3 * (wd3i + w[k + 3]); |
| wd1r = w[k]; |
| wd1i = w[k + 1]; |
| wd3r = w[k + 2]; |
| wd3i = w[k + 3]; |
| j1 = j + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j] + a[j2]; |
| x0i = -a[j + 1] - a[j2 + 1]; |
| x1r = a[j] - a[j2]; |
| x1i = -a[j + 1] + a[j2 + 1]; |
| y0r = a[j + 2] + a[j2 + 2]; |
| y0i = -a[j + 3] - a[j2 + 3]; |
| y1r = a[j + 2] - a[j2 + 2]; |
| y1i = -a[j + 3] + a[j2 + 3]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| y2r = a[j1 + 2] + a[j3 + 2]; |
| y2i = a[j1 + 3] + a[j3 + 3]; |
| y3r = a[j1 + 2] - a[j3 + 2]; |
| y3i = a[j1 + 3] - a[j3 + 3]; |
| a[j] = x0r + x2r; |
| a[j + 1] = x0i - x2i; |
| a[j + 2] = y0r + y2r; |
| a[j + 3] = y0i - y2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i + x2i; |
| a[j1 + 2] = y0r - y2r; |
| a[j1 + 3] = y0i + y2i; |
| x0r = x1r + x3i; |
| x0i = x1i + x3r; |
| a[j2] = wk1r * x0r - wk1i * x0i; |
| a[j2 + 1] = wk1r * x0i + wk1i * x0r; |
| x0r = y1r + y3i; |
| x0i = y1i + y3r; |
| a[j2 + 2] = wd1r * x0r - wd1i * x0i; |
| a[j2 + 3] = wd1r * x0i + wd1i * x0r; |
| x0r = x1r - x3i; |
| x0i = x1i - x3r; |
| a[j3] = wk3r * x0r + wk3i * x0i; |
| a[j3 + 1] = wk3r * x0i - wk3i * x0r; |
| x0r = y1r - y3i; |
| x0i = y1i - y3r; |
| a[j3 + 2] = wd3r * x0r + wd3i * x0i; |
| a[j3 + 3] = wd3r * x0i - wd3i * x0r; |
| j0 = m - j; |
| j1 = j0 + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j0] + a[j2]; |
| x0i = -a[j0 + 1] - a[j2 + 1]; |
| x1r = a[j0] - a[j2]; |
| x1i = -a[j0 + 1] + a[j2 + 1]; |
| y0r = a[j0 - 2] + a[j2 - 2]; |
| y0i = -a[j0 - 1] - a[j2 - 1]; |
| y1r = a[j0 - 2] - a[j2 - 2]; |
| y1i = -a[j0 - 1] + a[j2 - 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 1]; |
| y2r = a[j1 - 2] + a[j3 - 2]; |
| y2i = a[j1 - 1] + a[j3 - 1]; |
| y3r = a[j1 - 2] - a[j3 - 2]; |
| y3i = a[j1 - 1] - a[j3 - 1]; |
| a[j0] = x0r + x2r; |
| a[j0 + 1] = x0i - x2i; |
| a[j0 - 2] = y0r + y2r; |
| a[j0 - 1] = y0i - y2i; |
| a[j1] = x0r - x2r; |
| a[j1 + 1] = x0i + x2i; |
| a[j1 - 2] = y0r - y2r; |
| a[j1 - 1] = y0i + y2i; |
| x0r = x1r + x3i; |
| x0i = x1i + x3r; |
| a[j2] = wk1i * x0r - wk1r * x0i; |
| a[j2 + 1] = wk1i * x0i + wk1r * x0r; |
| x0r = y1r + y3i; |
| x0i = y1i + y3r; |
| a[j2 - 2] = wd1i * x0r - wd1r * x0i; |
| a[j2 - 1] = wd1i * x0i + wd1r * x0r; |
| x0r = x1r - x3i; |
| x0i = x1i - x3r; |
| a[j3] = wk3i * x0r + wk3r * x0i; |
| a[j3 + 1] = wk3i * x0i - wk3r * x0r; |
| x0r = y1r - y3i; |
| x0i = y1i - y3r; |
| a[j3 - 2] = wd3i * x0r + wd3r * x0i; |
| a[j3 - 1] = wd3i * x0i - wd3r * x0r; |
| } |
| wk1r = csc1 * (wd1r + wn4r); |
| wk1i = csc1 * (wd1i + wn4r); |
| wk3r = csc3 * (wd3r - wn4r); |
| wk3i = csc3 * (wd3i - wn4r); |
| j0 = mh; |
| j1 = j0 + m; |
| j2 = j1 + m; |
| j3 = j2 + m; |
| x0r = a[j0 - 2] + a[j2 - 2]; |
| x0i = -a[j0 - 1] - a[j2 - 1]; |
| x1r = a[j0 - 2] - a[j2 - 2]; |
| x1i = -a[j0 - 1] + a[j2 - 1]; |
| x2r = a[j1 - 2] + a[j3 - 2]; |
| x2i = a[j1 - 1] + a[j3 - 1]; |
| x3r = a[j1 - 2] - a[j3 - 2]; |
| x3i = a[j1 - 1] - a[j3 - 1]; |
| a[j0 - 2] = x0r + x2r; |
| a[j0 - 1] = x0i - x2i; |
| a[j1 - 2] = x0r - x2r; |
| a[j1 - 1] = x0i + x2i; |
| x0r = x1r + x3i; |
| x0i = x1i + x3r; |
| a[j2 - 2] = wk1r * x0r - wk1i * x0i; |
| a[j2 - 1] = wk1r * x0i + wk1i * x0r; |
| x0r = x1r - x3i; |
| x0i = x1i - x3r; |
| a[j3 - 2] = wk3r * x0r + wk3i * x0i; |
| a[j3 - 1] = wk3r * x0i - wk3i * x0r; |
| x0r = a[j0] + a[j2]; |
| x0i = -a[j0 + 1] - a[j2 + 1]; |
| x1r = a[j0] - a[j2]; |
| x1i = -a[j0 + 1] + a[j2 + 1]; |
| x2r = a[j1] + a[j3]; |
| x2i = a[j1 + 1] + a[j3 + 1]; |
| x3r = a[j1] - a[j3]; |
| x3i = a[j1 + 1] - a[j3 + 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]; |
| } |
| |
