ref: 5941f9e98c6b1b8986acae9308de6e3359d617f3
dir: /src/spectral/ooura_fft8g.c/
/* 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]; }