| /* |
| Fast Fourier/Cosine/Sine Transform |
| dimension :one |
| data length :power of 2 |
| decimation :frequency |
| radix :8, 4, 2 |
| data :inplace |
| table :use |
| functions |
| cdft: Complex Discrete Fourier Transform |
| rdft: Real Discrete Fourier Transform |
| ddct: Discrete Cosine Transform |
| ddst: Discrete Sine Transform |
| dfct: Cosine Transform of RDFT (Real Symmetric DFT) |
| dfst: Sine Transform of RDFT (Real Anti-symmetric DFT) |
| function prototypes |
| void cdft(int, int, 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 *); |
| |
| |
| -------- 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 bitrv2(int n, int *ip, double *a); |
| void bitrv2conj(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, double *w); |
| void cftbsub(int n, double *a, double *w); |
| |
| if (n > (ip[0] << 2)) { |
| makewt(n >> 2, ip, w); |
| } |
| if (n > 4) { |
| if (isgn >= 0) { |
| bitrv2(n, ip + 2, a); |
| cftfsub(n, a, w); |
| } else { |
| bitrv2conj(n, ip + 2, a); |
| cftbsub(n, a, w); |
| } |
| } else if (n == 4) { |
| cftfsub(n, a, w); |
| } |
| } |
| |
| |
| 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 bitrv2(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, double *w); |
| void cftbsub(int n, double *a, 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) { |
| bitrv2(n, ip + 2, a); |
| cftfsub(n, a, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, 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); |
| bitrv2(n, ip + 2, a); |
| cftbsub(n, a, w); |
| } else if (n == 4) { |
| cftfsub(n, a, 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 bitrv2(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, double *w); |
| void cftbsub(int n, double *a, 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); |
| bitrv2(n, ip + 2, a); |
| cftbsub(n, a, w); |
| } else if (n == 4) { |
| cftfsub(n, a, w); |
| } |
| } |
| dctsub(n, a, nc, w + nw); |
| if (isgn >= 0) { |
| if (n > 4) { |
| bitrv2(n, ip + 2, a); |
| cftfsub(n, a, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, w); |
| } |
| xr = a[0] - a[1]; |
| a[0] += a[1]; |
| for (j = 2; j < n; j += 2) { |
| a[j - 1] = a[j] - a[j + 1]; |
| a[j] += a[j + 1]; |
| } |
| a[n - 1] = xr; |
| } |
| } |
| |
| |
| 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 bitrv2(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, double *w); |
| void cftbsub(int n, double *a, 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); |
| bitrv2(n, ip + 2, a); |
| cftbsub(n, a, w); |
| } else if (n == 4) { |
| cftfsub(n, a, w); |
| } |
| } |
| dstsub(n, a, nc, w + nw); |
| if (isgn >= 0) { |
| if (n > 4) { |
| bitrv2(n, ip + 2, a); |
| cftfsub(n, a, w); |
| rftfsub(n, a, nc, w + nw); |
| } else if (n == 4) { |
| cftfsub(n, a, w); |
| } |
| xr = a[0] - a[1]; |
| a[0] += a[1]; |
| for (j = 2; j < n; j += 2) { |
| a[j - 1] = -a[j] - a[j + 1]; |
| a[j] -= a[j + 1]; |
| } |
| a[n - 1] = -xr; |
| } |
| } |
| |
| |
| 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 bitrv2(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, 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) { |
| bitrv2(m, ip + 2, a); |
| cftfsub(m, a, w); |
| rftfsub(m, a, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, a, w); |
| } |
| a[n - 1] = a[0] - a[1]; |
| a[1] = a[0] + a[1]; |
| for (j = m - 2; j >= 2; j -= 2) { |
| a[2 * j + 1] = a[j] + a[j + 1]; |
| a[2 * j - 1] = a[j] - a[j + 1]; |
| } |
| l = 2; |
| m = mh; |
| while (m >= 2) { |
| dctsub(m, t, nc, w + nw); |
| if (m > 4) { |
| bitrv2(m, ip + 2, t); |
| cftfsub(m, t, w); |
| rftfsub(m, t, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, t, w); |
| } |
| a[n - l] = t[0] - t[1]; |
| a[l] = t[0] + t[1]; |
| k = 0; |
| for (j = 2; j < m; j += 2) { |
| k += l << 2; |
| a[k - l] = t[j] - t[j + 1]; |
| a[k + l] = t[j] + t[j + 1]; |
| } |
| l <<= 1; |
| mh = m >> 1; |
| for (j = 0; j < mh; j++) { |
| k = m - j; |
| t[j] = t[m + k] - t[m + j]; |
| t[k] = t[m + k] + t[m + j]; |
| } |
| t[mh] = t[m + mh]; |
| m = mh; |
| } |
| a[l] = t[0]; |
| a[n] = t[2] - t[1]; |
| a[0] = t[2] + t[1]; |
| } else { |
| a[1] = a[0]; |
| a[2] = t[0]; |
| a[0] = t[1]; |
| } |
| } |
| |
| |
| 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 bitrv2(int n, int *ip, double *a); |
| void cftfsub(int n, double *a, 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) { |
| bitrv2(m, ip + 2, a); |
| cftfsub(m, a, w); |
| rftfsub(m, a, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, a, w); |
| } |
| a[n - 1] = a[1] - a[0]; |
| a[1] = a[0] + a[1]; |
| for (j = m - 2; j >= 2; j -= 2) { |
| a[2 * j + 1] = a[j] - a[j + 1]; |
| a[2 * j - 1] = -a[j] - a[j + 1]; |
| } |
| l = 2; |
| m = mh; |
| while (m >= 2) { |
| dstsub(m, t, nc, w + nw); |
| if (m > 4) { |
| bitrv2(m, ip + 2, t); |
| cftfsub(m, t, w); |
| rftfsub(m, t, nc, w + nw); |
| } else if (m == 4) { |
| cftfsub(m, t, w); |
| } |
| a[n - l] = t[1] - t[0]; |
| a[l] = t[0] + t[1]; |
| k = 0; |
| for (j = 2; j < m; j += 2) { |
| k += l << 2; |
| a[k - l] = -t[j] - t[j + 1]; |
| a[k + l] = t[j] - t[j + 1]; |
| } |
| l <<= 1; |
| mh = m >> 1; |
| for (j = 1; j < mh; j++) { |
| k = m - j; |
| t[j] = t[m + k] + t[m + j]; |
| t[k] = t[m + k] - t[m + j]; |
| } |
| t[0] = t[m + mh]; |
| m = mh; |
| } |
| a[l] = t[0]; |
| } |
| a[0] = 0; |
| } |
| |
| |
| /* -------- initializing routines -------- */ |
| |
| |
| #include <math.h> |
| |
| void makewt(int nw, int *ip, double *w) |
| { |
| void bitrv2(int n, int *ip, double *a); |
| int j, nwh; |
| double delta, x, y; |
| |
| ip[0] = nw; |
| ip[1] = 1; |
| if (nw > 2) { |
| nwh = nw >> 1; |
| delta = atan(1.0) / nwh; |
| w[0] = 1; |
| w[1] = 0; |
| w[nwh] = cos(delta * nwh); |
| w[nwh + 1] = w[nwh]; |
| if (nwh > 2) { |
| for (j = 2; j < nwh; j += 2) { |
| x = cos(delta * j); |
| y = sin(delta * j); |
| w[j] = x; |
| w[j + 1] = y; |
| w[nw - j] = y; |
| w[nw - j + 1] = x; |
| } |
| for (j = nwh - 2; j >= 2; j -= 2) { |
| x = w[2 * j]; |
| y = w[2 * j + 1]; |
| w[nwh + j] = x; |
| w[nwh + j + 1] = y; |
| } |
| bitrv2(nw, ip + 2, w); |
| } |
| } |
| } |
| |
| |
| 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 -------- */ |
| |
| |
| void bitrv2(int n, int *ip, double *a) |
| { |
| int j, j1, k, k1, l, m, m2; |
| double xr, xi, yr, yi; |
| |
| ip[0] = 0; |
| l = n; |
| m = 1; |
| while ((m << 3) < l) { |
| l >>= 1; |
| for (j = 0; j < m; j++) { |
| ip[m + j] = ip[j] + l; |
| } |
| m <<= 1; |
| } |
| m2 = 2 * m; |
| if ((m << 3) == l) { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 2 * j + ip[k]; |
| k1 = 2 * k + ip[j]; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += 2 * m2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 -= m2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += 2 * m2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| j1 = 2 * k + m2 + ip[k]; |
| k1 = j1 + m2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| } else { |
| for (k = 1; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 2 * j + ip[k]; |
| k1 = 2 * k + ip[j]; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += m2; |
| xr = a[j1]; |
| xi = a[j1 + 1]; |
| yr = a[k1]; |
| yi = a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| } |
| } |
| } |
| |
| |
| void bitrv2conj(int n, int *ip, double *a) |
| { |
| int j, j1, k, k1, l, m, m2; |
| double xr, xi, yr, yi; |
| |
| ip[0] = 0; |
| l = n; |
| m = 1; |
| while ((m << 3) < l) { |
| l >>= 1; |
| for (j = 0; j < m; j++) { |
| ip[m + j] = ip[j] + l; |
| } |
| m <<= 1; |
| } |
| m2 = 2 * m; |
| if ((m << 3) == l) { |
| for (k = 0; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 2 * j + ip[k]; |
| k1 = 2 * k + ip[j]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += 2 * m2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 -= m2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += 2 * m2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 2 * k + ip[k]; |
| a[k1 + 1] = -a[k1 + 1]; |
| j1 = k1 + m2; |
| k1 = j1 + m2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| k1 += m2; |
| a[k1 + 1] = -a[k1 + 1]; |
| } |
| } else { |
| a[1] = -a[1]; |
| a[m2 + 1] = -a[m2 + 1]; |
| for (k = 1; k < m; k++) { |
| for (j = 0; j < k; j++) { |
| j1 = 2 * j + ip[k]; |
| k1 = 2 * k + ip[j]; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| j1 += m2; |
| k1 += m2; |
| xr = a[j1]; |
| xi = -a[j1 + 1]; |
| yr = a[k1]; |
| yi = -a[k1 + 1]; |
| a[j1] = yr; |
| a[j1 + 1] = yi; |
| a[k1] = xr; |
| a[k1 + 1] = xi; |
| } |
| k1 = 2 * k + ip[k]; |
| a[k1 + 1] = -a[k1 + 1]; |
| a[k1 + m2 + 1] = -a[k1 + m2 + 1]; |
| } |
| } |
| } |
| |
| |
| void cftfsub(int n, double *a, double *w) |
| { |
| void cft1st(int n, double *a, double *w); |
| void cftmdl(int n, int l, double *a, double *w); |
| int j, j1, j2, j3, l; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i; |
| |
| l = 2; |
| if (n >= 16) { |
| cft1st(n, a, w); |
| l = 16; |
| while ((l << 3) <= n) { |
| cftmdl(n, l, a, w); |
| l <<= 3; |
| } |
| } |
| if ((l << 1) < n) { |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| x0r = a[j] + a[j1]; |
| x0i = a[j + 1] + a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = a[j + 1] - a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| a[j] = x0r + x2r; |
| a[j + 1] = x0i + x2i; |
| a[j2] = x0r - x2r; |
| a[j2 + 1] = x0i - x2i; |
| a[j1] = x1r - x3i; |
| a[j1 + 1] = x1i + x3r; |
| a[j3] = x1r + x3i; |
| a[j3 + 1] = x1i - x3r; |
| } |
| } else if ((l << 1) == n) { |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| x0r = a[j] - a[j1]; |
| x0i = a[j + 1] - a[j1 + 1]; |
| a[j] += a[j1]; |
| a[j + 1] += a[j1 + 1]; |
| a[j1] = x0r; |
| a[j1 + 1] = x0i; |
| } |
| } |
| } |
| |
| |
| void cftbsub(int n, double *a, double *w) |
| { |
| void cft1st(int n, double *a, double *w); |
| void cftmdl(int n, int l, double *a, double *w); |
| int j, j1, j2, j3, j4, j5, j6, j7, l; |
| 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; |
| |
| l = 2; |
| if (n > 16) { |
| cft1st(n, a, w); |
| l = 16; |
| while ((l << 3) < n) { |
| cftmdl(n, l, a, w); |
| l <<= 3; |
| } |
| } |
| if ((l << 2) < n) { |
| wn4r = w[2]; |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| j4 = j3 + l; |
| j5 = j4 + l; |
| j6 = j5 + l; |
| j7 = j6 + l; |
| x0r = a[j] + a[j1]; |
| x0i = -a[j + 1] - a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = -a[j + 1] + a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| 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[j4] + a[j5]; |
| x0i = a[j4 + 1] + a[j5 + 1]; |
| x1r = a[j4] - a[j5]; |
| x1i = a[j4 + 1] - a[j5 + 1]; |
| x2r = a[j6] + a[j7]; |
| x2i = a[j6 + 1] + a[j7 + 1]; |
| x3r = a[j6] - a[j7]; |
| x3i = a[j6 + 1] - a[j7 + 1]; |
| 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[j1] = y1r + y5r; |
| a[j1 + 1] = y1i - y5i; |
| a[j5] = y1r - y5r; |
| a[j5 + 1] = y1i + y5i; |
| a[j3] = y3r - y7i; |
| a[j3 + 1] = y3i - y7r; |
| a[j7] = y3r + y7i; |
| a[j7 + 1] = y3i + y7r; |
| a[j] = y0r + y4r; |
| a[j + 1] = y0i - y4i; |
| a[j4] = y0r - y4r; |
| a[j4 + 1] = y0i + y4i; |
| a[j2] = y2r - y6i; |
| a[j2 + 1] = y2i - y6r; |
| a[j6] = y2r + y6i; |
| a[j6 + 1] = y2i + y6r; |
| } |
| } else if ((l << 2) == n) { |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| x0r = a[j] + a[j1]; |
| x0i = -a[j + 1] - a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = -a[j + 1] + a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| a[j] = x0r + x2r; |
| a[j + 1] = x0i - x2i; |
| a[j2] = x0r - x2r; |
| a[j2 + 1] = x0i + x2i; |
| a[j1] = x1r - x3i; |
| a[j1 + 1] = x1i - x3r; |
| a[j3] = x1r + x3i; |
| a[j3 + 1] = x1i + x3r; |
| } |
| } else { |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| x0r = a[j] - a[j1]; |
| x0i = -a[j + 1] + a[j1 + 1]; |
| a[j] += a[j1]; |
| a[j + 1] = -a[j + 1] - a[j1 + 1]; |
| a[j1] = x0r; |
| a[j1 + 1] = x0i; |
| } |
| } |
| } |
| |
| |
| void cft1st(int n, double *a, double *w) |
| { |
| int j, k1; |
| double wn4r, wtmp, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, |
| wk4r, wk4i, wk5r, wk5i, wk6r, wk6i, wk7r, wk7i; |
| double 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[2]; |
| x0r = a[0] + a[2]; |
| x0i = a[1] + a[3]; |
| x1r = a[0] - a[2]; |
| x1i = a[1] - a[3]; |
| x2r = a[4] + a[6]; |
| x2i = a[5] + a[7]; |
| x3r = a[4] - a[6]; |
| x3i = a[5] - a[7]; |
| 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[8] + a[10]; |
| x0i = a[9] + a[11]; |
| x1r = a[8] - a[10]; |
| x1i = a[9] - a[11]; |
| x2r = a[12] + a[14]; |
| x2i = a[13] + a[15]; |
| x3r = a[12] - a[14]; |
| x3i = a[13] - a[15]; |
| 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[2] = y1r + y5r; |
| a[3] = y1i + y5i; |
| a[10] = y1r - y5r; |
| a[11] = y1i - y5i; |
| a[6] = y3r - y7i; |
| a[7] = y3i + y7r; |
| a[14] = y3r + y7i; |
| a[15] = y3i - y7r; |
| a[0] = y0r + y4r; |
| a[1] = y0i + y4i; |
| a[8] = y0r - y4r; |
| a[9] = y0i - y4i; |
| a[4] = y2r - y6i; |
| a[5] = y2i + y6r; |
| a[12] = y2r + y6i; |
| a[13] = y2i - y6r; |
| if (n > 16) { |
| wk1r = w[4]; |
| wk1i = w[5]; |
| x0r = a[16] + a[18]; |
| x0i = a[17] + a[19]; |
| x1r = a[16] - a[18]; |
| x1i = a[17] - a[19]; |
| x2r = a[20] + a[22]; |
| x2i = a[21] + a[23]; |
| x3r = a[20] - a[22]; |
| x3i = a[21] - a[23]; |
| 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[24] + a[26]; |
| x0i = a[25] + a[27]; |
| x1r = a[24] - a[26]; |
| x1i = a[25] - a[27]; |
| x2r = a[28] + a[30]; |
| x2i = a[29] + a[31]; |
| x3r = a[28] - a[30]; |
| x3i = a[29] - a[31]; |
| y4r = x0r + x2r; |
| y4i = x0i + x2i; |
| y6r = x0r - x2r; |
| y6i = x0i - x2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| x2r = x1r + x3i; |
| x2i = x3r - x1i; |
| y5r = wk1i * x0r - wk1r * x0i; |
| y5i = wk1i * x0i + wk1r * x0r; |
| y7r = wk1r * x2r + wk1i * x2i; |
| y7i = wk1r * x2i - wk1i * x2r; |
| x0r = wk1r * y1r - wk1i * y1i; |
| x0i = wk1r * y1i + wk1i * y1r; |
| a[18] = x0r + y5r; |
| a[19] = x0i + y5i; |
| a[26] = y5i - x0i; |
| a[27] = x0r - y5r; |
| x0r = wk1i * y3r - wk1r * y3i; |
| x0i = wk1i * y3i + wk1r * y3r; |
| a[22] = x0r - y7r; |
| a[23] = x0i + y7i; |
| a[30] = y7i - x0i; |
| a[31] = x0r + y7r; |
| a[16] = y0r + y4r; |
| a[17] = y0i + y4i; |
| a[24] = y4i - y0i; |
| a[25] = y0r - y4r; |
| x0r = y2r - y6i; |
| x0i = y2i + y6r; |
| a[20] = wn4r * (x0r - x0i); |
| a[21] = wn4r * (x0i + x0r); |
| x0r = y6r - y2i; |
| x0i = y2r + y6i; |
| a[28] = wn4r * (x0r - x0i); |
| a[29] = wn4r * (x0i + x0r); |
| k1 = 4; |
| for (j = 32; j < n; j += 16) { |
| k1 += 4; |
| wk1r = w[k1]; |
| wk1i = w[k1 + 1]; |
| wk2r = w[k1 + 2]; |
| wk2i = w[k1 + 3]; |
| wtmp = 2 * wk2i; |
| wk3r = wk1r - wtmp * wk1i; |
| wk3i = wtmp * wk1r - wk1i; |
| wk4r = 1 - wtmp * wk2i; |
| wk4i = wtmp * wk2r; |
| wtmp = 2 * wk4i; |
| wk5r = wk3r - wtmp * wk1i; |
| wk5i = wtmp * wk1r - wk3i; |
| wk6r = wk2r - wtmp * wk2i; |
| wk6i = wtmp * wk2r - wk2i; |
| wk7r = wk1r - wtmp * wk3i; |
| wk7i = wtmp * wk3r - wk1i; |
| x0r = a[j] + a[j + 2]; |
| x0i = a[j + 1] + a[j + 3]; |
| x1r = a[j] - a[j + 2]; |
| x1i = a[j + 1] - a[j + 3]; |
| x2r = a[j + 4] + a[j + 6]; |
| x2i = a[j + 5] + a[j + 7]; |
| x3r = a[j + 4] - a[j + 6]; |
| x3i = a[j + 5] - a[j + 7]; |
| 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[j + 8] + a[j + 10]; |
| x0i = a[j + 9] + a[j + 11]; |
| x1r = a[j + 8] - a[j + 10]; |
| x1i = a[j + 9] - a[j + 11]; |
| x2r = a[j + 12] + a[j + 14]; |
| x2i = a[j + 13] + a[j + 15]; |
| x3r = a[j + 12] - a[j + 14]; |
| x3i = a[j + 13] - a[j + 15]; |
| 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); |
| x0r = y1r + y5r; |
| x0i = y1i + y5i; |
| a[j + 2] = wk1r * x0r - wk1i * x0i; |
| a[j + 3] = wk1r * x0i + wk1i * x0r; |
| x0r = y1r - y5r; |
| x0i = y1i - y5i; |
| a[j + 10] = wk5r * x0r - wk5i * x0i; |
| a[j + 11] = wk5r * x0i + wk5i * x0r; |
| x0r = y3r - y7i; |
| x0i = y3i + y7r; |
| a[j + 6] = wk3r * x0r - wk3i * x0i; |
| a[j + 7] = wk3r * x0i + wk3i * x0r; |
| x0r = y3r + y7i; |
| x0i = y3i - y7r; |
| a[j + 14] = wk7r * x0r - wk7i * x0i; |
| a[j + 15] = wk7r * x0i + wk7i * x0r; |
| a[j] = y0r + y4r; |
| a[j + 1] = y0i + y4i; |
| x0r = y0r - y4r; |
| x0i = y0i - y4i; |
| a[j + 8] = wk4r * x0r - wk4i * x0i; |
| a[j + 9] = wk4r * x0i + wk4i * x0r; |
| x0r = y2r - y6i; |
| x0i = y2i + y6r; |
| a[j + 4] = wk2r * x0r - wk2i * x0i; |
| a[j + 5] = wk2r * x0i + wk2i * x0r; |
| x0r = y2r + y6i; |
| x0i = y2i - y6r; |
| a[j + 12] = wk6r * x0r - wk6i * x0i; |
| a[j + 13] = wk6r * x0i + wk6i * x0r; |
| } |
| } |
| } |
| |
| |
| void cftmdl(int n, int l, double *a, double *w) |
| { |
| int j, j1, j2, j3, j4, j5, j6, j7, k, k1, m; |
| double wn4r, wtmp, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i, |
| wk4r, wk4i, wk5r, wk5i, wk6r, wk6i, wk7r, wk7i; |
| double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, |
| y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i, |
| y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i; |
| |
| m = l << 3; |
| wn4r = w[2]; |
| for (j = 0; j < l; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| j4 = j3 + l; |
| j5 = j4 + l; |
| j6 = j5 + l; |
| j7 = j6 + l; |
| x0r = a[j] + a[j1]; |
| x0i = a[j + 1] + a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = a[j + 1] - a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| 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[j4] + a[j5]; |
| x0i = a[j4 + 1] + a[j5 + 1]; |
| x1r = a[j4] - a[j5]; |
| x1i = a[j4 + 1] - a[j5 + 1]; |
| x2r = a[j6] + a[j7]; |
| x2i = a[j6 + 1] + a[j7 + 1]; |
| x3r = a[j6] - a[j7]; |
| x3i = a[j6 + 1] - a[j7 + 1]; |
| 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[j1] = y1r + y5r; |
| a[j1 + 1] = y1i + y5i; |
| a[j5] = y1r - y5r; |
| a[j5 + 1] = y1i - y5i; |
| a[j3] = y3r - y7i; |
| a[j3 + 1] = y3i + y7r; |
| a[j7] = y3r + y7i; |
| a[j7 + 1] = y3i - y7r; |
| a[j] = y0r + y4r; |
| a[j + 1] = y0i + y4i; |
| a[j4] = y0r - y4r; |
| a[j4 + 1] = y0i - y4i; |
| a[j2] = y2r - y6i; |
| a[j2 + 1] = y2i + y6r; |
| a[j6] = y2r + y6i; |
| a[j6 + 1] = y2i - y6r; |
| } |
| if (m < n) { |
| wk1r = w[4]; |
| wk1i = w[5]; |
| for (j = m; j < l + m; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| j4 = j3 + l; |
| j5 = j4 + l; |
| j6 = j5 + l; |
| j7 = j6 + l; |
| x0r = a[j] + a[j1]; |
| x0i = a[j + 1] + a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = a[j + 1] - a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| 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[j4] + a[j5]; |
| x0i = a[j4 + 1] + a[j5 + 1]; |
| x1r = a[j4] - a[j5]; |
| x1i = a[j4 + 1] - a[j5 + 1]; |
| x2r = a[j6] + a[j7]; |
| x2i = a[j6 + 1] + a[j7 + 1]; |
| x3r = a[j6] - a[j7]; |
| x3i = a[j6 + 1] - a[j7 + 1]; |
| y4r = x0r + x2r; |
| y4i = x0i + x2i; |
| y6r = x0r - x2r; |
| y6i = x0i - x2i; |
| x0r = x1r - x3i; |
| x0i = x1i + x3r; |
| x2r = x1r + x3i; |
| x2i = x3r - x1i; |
| y5r = wk1i * x0r - wk1r * x0i; |
| y5i = wk1i * x0i + wk1r * x0r; |
| y7r = wk1r * x2r + wk1i * x2i; |
| y7i = wk1r * x2i - wk1i * x2r; |
| x0r = wk1r * y1r - wk1i * y1i; |
| x0i = wk1r * y1i + wk1i * y1r; |
| a[j1] = x0r + y5r; |
| a[j1 + 1] = x0i + y5i; |
| a[j5] = y5i - x0i; |
| a[j5 + 1] = x0r - y5r; |
| x0r = wk1i * y3r - wk1r * y3i; |
| x0i = wk1i * y3i + wk1r * y3r; |
| a[j3] = x0r - y7r; |
| a[j3 + 1] = x0i + y7i; |
| a[j7] = y7i - x0i; |
| a[j7 + 1] = x0r + y7r; |
| a[j] = y0r + y4r; |
| a[j + 1] = y0i + y4i; |
| a[j4] = y4i - y0i; |
| a[j4 + 1] = y0r - y4r; |
| x0r = y2r - y6i; |
| x0i = y2i + y6r; |
| a[j2] = wn4r * (x0r - x0i); |
| a[j2 + 1] = wn4r * (x0i + x0r); |
| x0r = y6r - y2i; |
| x0i = y2r + y6i; |
| a[j6] = wn4r * (x0r - x0i); |
| a[j6 + 1] = wn4r * (x0i + x0r); |
| } |
| k1 = 4; |
| for (k = 2 * m; k < n; k += m) { |
| k1 += 4; |
| wk1r = w[k1]; |
| wk1i = w[k1 + 1]; |
| wk2r = w[k1 + 2]; |
| wk2i = w[k1 + 3]; |
| wtmp = 2 * wk2i; |
| wk3r = wk1r - wtmp * wk1i; |
| wk3i = wtmp * wk1r - wk1i; |
| wk4r = 1 - wtmp * wk2i; |
| wk4i = wtmp * wk2r; |
| wtmp = 2 * wk4i; |
| wk5r = wk3r - wtmp * wk1i; |
| wk5i = wtmp * wk1r - wk3i; |
| wk6r = wk2r - wtmp * wk2i; |
| wk6i = wtmp * wk2r - wk2i; |
| wk7r = wk1r - wtmp * wk3i; |
| wk7i = wtmp * wk3r - wk1i; |
| for (j = k; j < l + k; j += 2) { |
| j1 = j + l; |
| j2 = j1 + l; |
| j3 = j2 + l; |
| j4 = j3 + l; |
| j5 = j4 + l; |
| j6 = j5 + l; |
| j7 = j6 + l; |
| x0r = a[j] + a[j1]; |
| x0i = a[j + 1] + a[j1 + 1]; |
| x1r = a[j] - a[j1]; |
| x1i = a[j + 1] - a[j1 + 1]; |
| x2r = a[j2] + a[j3]; |
| x2i = a[j2 + 1] + a[j3 + 1]; |
| x3r = a[j2] - a[j3]; |
| x3i = a[j2 + 1] - a[j3 + 1]; |
| 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[j4] + a[j5]; |
| x0i = a[j4 + 1] + a[j5 + 1]; |
| x1r = a[j4] - a[j5]; |
| x1i = a[j4 + 1] - a[j5 + 1]; |
| x2r = a[j6] + a[j7]; |
| x2i = a[j6 + 1] + a[j7 + 1]; |
| x3r = a[j6] - a[j7]; |
| x3i = a[j6 + 1] - a[j7 + 1]; |
| 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); |
| x0r = y1r + y5r; |
| x0i = y1i + y5i; |
| a[j1] = wk1r * x0r - wk1i * x0i; |
| a[j1 + 1] = wk1r * x0i + wk1i * x0r; |
| x0r = y1r - y5r; |
| x0i = y1i - y5i; |
| a[j5] = wk5r * x0r - wk5i * x0i; |
| a[j5 + 1] = wk5r * x0i + wk5i * x0r; |
| x0r = y3r - y7i; |
| x0i = y3i + y7r; |
| a[j3] = wk3r * x0r - wk3i * x0i; |
| a[j3 + 1] = wk3r * x0i + wk3i * x0r; |
| x0r = y3r + y7i; |
| x0i = y3i - y7r; |
| a[j7] = wk7r * x0r - wk7i * x0i; |
| a[j7 + 1] = wk7r * x0i + wk7i * x0r; |
| a[j] = y0r + y4r; |
| a[j + 1] = y0i + y4i; |
| x0r = y0r - y4r; |
| x0i = y0i - y4i; |
| a[j4] = wk4r * x0r - wk4i * x0i; |
| a[j4 + 1] = wk4r * x0i + wk4i * x0r; |
| x0r = y2r - y6i; |
| x0i = y2i + y6r; |
| a[j2] = wk2r * x0r - wk2i * x0i; |
| a[j2 + 1] = wk2r * x0i + wk2i * x0r; |
| x0r = y2r + y6i; |
| x0i = y2i - y6r; |
| a[j6] = wk6r * x0r - wk6i * x0i; |
| a[j6 + 1] = wk6r * x0i + wk6i * x0r; |
| } |
| } |
| } |
| } |
| |
| |
| 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; |
| |
| a[1] = -a[1]; |
| 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[j + 1]; |
| a[k] += yr; |
| a[k + 1] = yi - a[k + 1]; |
| } |
| a[m + 1] = -a[m + 1]; |
| } |
| |
| |
| 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]; |
| } |
| |
