jamie@149: /*
jamie@149: Fast Fourier/Cosine/Sine Transform
jamie@149:     dimension   :one
jamie@149:     data length :power of 2
jamie@149:     decimation  :frequency
jamie@149:     radix       :split-radix
jamie@149:     data        :inplace
jamie@149:     table       :use
jamie@149: functions
jamie@149:     cdft: Complex Discrete Fourier Transform
jamie@149:     rdft: Real Discrete Fourier Transform
jamie@149:     ddct: Discrete Cosine Transform
jamie@149:     ddst: Discrete Sine Transform
jamie@149:     dfct: Cosine Transform of RDFT (Real Symmetric DFT)
jamie@149:     dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
jamie@149: function prototypes
jamie@149:     void cdft(int, int, double *, int *, double *);
jamie@149:     void rdft(int, int, double *, int *, double *);
jamie@149:     void ddct(int, int, double *, int *, double *);
jamie@149:     void ddst(int, int, double *, int *, double *);
jamie@149:     void dfct(int, double *, double *, int *, double *);
jamie@149:     void dfst(int, double *, double *, int *, double *);
jamie@149: macro definitions
jamie@149:     USE_CDFT_PTHREADS : default=not defined
jamie@149:         CDFT_THREADS_BEGIN_N  : must be >= 512, default=8192
jamie@149:         CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
jamie@149:     USE_CDFT_WINTHREADS : default=not defined
jamie@149:         CDFT_THREADS_BEGIN_N  : must be >= 512, default=32768
jamie@149:         CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288
jamie@149: 
jamie@149: 
jamie@149: -------- Complex DFT (Discrete Fourier Transform) --------
jamie@149:     [definition]
jamie@149:         <case1>
jamie@149:             X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
jamie@149:         <case2>
jamie@149:             X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
jamie@149:         (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
jamie@149:     [usage]
jamie@149:         <case1>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             cdft(2*n, 1, a, ip, w);
jamie@149:         <case2>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             cdft(2*n, -1, a, ip, w);
jamie@149:     [parameters]
jamie@149:         2*n            :data length (int)
jamie@149:                         n >= 1, n = power of 2
jamie@149:         a[0...2*n-1]   :input/output data (double *)
jamie@149:                         input data
jamie@149:                             a[2*j] = Re(x[j]),
jamie@149:                             a[2*j+1] = Im(x[j]), 0<=j<n
jamie@149:                         output data
jamie@149:                             a[2*k] = Re(X[k]),
jamie@149:                             a[2*k+1] = Im(X[k]), 0<=k<n
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n/2-1]   :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             cdft(2*n, -1, a, ip, w);
jamie@149:         is
jamie@149:             cdft(2*n, 1, a, ip, w);
jamie@149:             for (j = 0; j <= 2 * n - 1; j++) {
jamie@149:                 a[j] *= 1.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: -------- Real DFT / Inverse of Real DFT --------
jamie@149:     [definition]
jamie@149:         <case1> RDFT
jamie@149:             R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
jamie@149:             I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
jamie@149:         <case2> IRDFT (excluding scale)
jamie@149:             a[k] = (R[0] + R[n/2]*cos(pi*k))/2 +
jamie@149:                    sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) +
jamie@149:                    sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
jamie@149:     [usage]
jamie@149:         <case1>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             rdft(n, 1, a, ip, w);
jamie@149:         <case2>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             rdft(n, -1, a, ip, w);
jamie@149:     [parameters]
jamie@149:         n              :data length (int)
jamie@149:                         n >= 2, n = power of 2
jamie@149:         a[0...n-1]     :input/output data (double *)
jamie@149:                         <case1>
jamie@149:                             output data
jamie@149:                                 a[2*k] = R[k], 0<=k<n/2
jamie@149:                                 a[2*k+1] = I[k], 0<k<n/2
jamie@149:                                 a[1] = R[n/2]
jamie@149:                         <case2>
jamie@149:                             input data
jamie@149:                                 a[2*j] = R[j], 0<=j<n/2
jamie@149:                                 a[2*j+1] = I[j], 0<j<n/2
jamie@149:                                 a[1] = R[n/2]
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n/2)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n/2+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n/2-1]   :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             rdft(n, 1, a, ip, w);
jamie@149:         is
jamie@149:             rdft(n, -1, a, ip, w);
jamie@149:             for (j = 0; j <= n - 1; j++) {
jamie@149:                 a[j] *= 2.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: -------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
jamie@149:     [definition]
jamie@149:         <case1> IDCT (excluding scale)
jamie@149:             C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
jamie@149:         <case2> DCT
jamie@149:             C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
jamie@149:     [usage]
jamie@149:         <case1>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             ddct(n, 1, a, ip, w);
jamie@149:         <case2>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             ddct(n, -1, a, ip, w);
jamie@149:     [parameters]
jamie@149:         n              :data length (int)
jamie@149:                         n >= 2, n = power of 2
jamie@149:         a[0...n-1]     :input/output data (double *)
jamie@149:                         output data
jamie@149:                             a[k] = C[k], 0<=k<n
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n/2)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n/2+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n*5/4-1] :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             ddct(n, -1, a, ip, w);
jamie@149:         is
jamie@149:             a[0] *= 0.5;
jamie@149:             ddct(n, 1, a, ip, w);
jamie@149:             for (j = 0; j <= n - 1; j++) {
jamie@149:                 a[j] *= 2.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: -------- DST (Discrete Sine Transform) / Inverse of DST --------
jamie@149:     [definition]
jamie@149:         <case1> IDST (excluding scale)
jamie@149:             S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
jamie@149:         <case2> DST
jamie@149:             S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
jamie@149:     [usage]
jamie@149:         <case1>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             ddst(n, 1, a, ip, w);
jamie@149:         <case2>
jamie@149:             ip[0] = 0; // first time only
jamie@149:             ddst(n, -1, a, ip, w);
jamie@149:     [parameters]
jamie@149:         n              :data length (int)
jamie@149:                         n >= 2, n = power of 2
jamie@149:         a[0...n-1]     :input/output data (double *)
jamie@149:                         <case1>
jamie@149:                             input data
jamie@149:                                 a[j] = A[j], 0<j<n
jamie@149:                                 a[0] = A[n]
jamie@149:                             output data
jamie@149:                                 a[k] = S[k], 0<=k<n
jamie@149:                         <case2>
jamie@149:                             output data
jamie@149:                                 a[k] = S[k], 0<k<n
jamie@149:                                 a[0] = S[n]
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n/2)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n/2+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n*5/4-1] :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             ddst(n, -1, a, ip, w);
jamie@149:         is
jamie@149:             a[0] *= 0.5;
jamie@149:             ddst(n, 1, a, ip, w);
jamie@149:             for (j = 0; j <= n - 1; j++) {
jamie@149:                 a[j] *= 2.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: -------- Cosine Transform of RDFT (Real Symmetric DFT) --------
jamie@149:     [definition]
jamie@149:         C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
jamie@149:     [usage]
jamie@149:         ip[0] = 0; // first time only
jamie@149:         dfct(n, a, t, ip, w);
jamie@149:     [parameters]
jamie@149:         n              :data length - 1 (int)
jamie@149:                         n >= 2, n = power of 2
jamie@149:         a[0...n]       :input/output data (double *)
jamie@149:                         output data
jamie@149:                             a[k] = C[k], 0<=k<=n
jamie@149:         t[0...n/2]     :work area (double *)
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n/4)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n/4+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n*5/8-1] :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             a[0] *= 0.5;
jamie@149:             a[n] *= 0.5;
jamie@149:             dfct(n, a, t, ip, w);
jamie@149:         is
jamie@149:             a[0] *= 0.5;
jamie@149:             a[n] *= 0.5;
jamie@149:             dfct(n, a, t, ip, w);
jamie@149:             for (j = 0; j <= n; j++) {
jamie@149:                 a[j] *= 2.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: -------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
jamie@149:     [definition]
jamie@149:         S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
jamie@149:     [usage]
jamie@149:         ip[0] = 0; // first time only
jamie@149:         dfst(n, a, t, ip, w);
jamie@149:     [parameters]
jamie@149:         n              :data length + 1 (int)
jamie@149:                         n >= 2, n = power of 2
jamie@149:         a[0...n-1]     :input/output data (double *)
jamie@149:                         output data
jamie@149:                             a[k] = S[k], 0<k<n
jamie@149:                         (a[0] is used for work area)
jamie@149:         t[0...n/2-1]   :work area (double *)
jamie@149:         ip[0...*]      :work area for bit reversal (int *)
jamie@149:                         length of ip >= 2+sqrt(n/4)
jamie@149:                         strictly,
jamie@149:                         length of ip >=
jamie@149:                             2+(1<<(int)(log(n/4+0.5)/log(2))/2).
jamie@149:                         ip[0],ip[1] are pointers of the cos/sin table.
jamie@149:         w[0...n*5/8-1] :cos/sin table (double *)
jamie@149:                         w[],ip[] are initialized if ip[0] == 0.
jamie@149:     [remark]
jamie@149:         Inverse of
jamie@149:             dfst(n, a, t, ip, w);
jamie@149:         is
jamie@149:             dfst(n, a, t, ip, w);
jamie@149:             for (j = 1; j <= n - 1; j++) {
jamie@149:                 a[j] *= 2.0 / n;
jamie@149:             }
jamie@149:         .
jamie@149: 
jamie@149: 
jamie@149: Appendix :
jamie@149:     The cos/sin table is recalculated when the larger table required.
jamie@149:     w[] and ip[] are compatible with all routines.
jamie@149: */
jamie@149: 
jamie@149: 
jamie@149: void cdft(int n, int isgn, double *a, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void cftbsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     int nw;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 2))
jamie@149:     {
jamie@149:         nw = n >> 2;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     if (isgn >= 0)
jamie@149:     {
jamie@149:         cftfsub(n, a, ip, nw, w);
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         cftbsub(n, a, ip, nw, w);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void rdft(int n, int isgn, double *a, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void makect(int nc, int *ip, double *c);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void cftbsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void rftfsub(int n, double *a, int nc, double *c);
jamie@149:     void rftbsub(int n, double *a, int nc, double *c);
jamie@149:     int nw, nc;
jamie@149:     double xi;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 2))
jamie@149:     {
jamie@149:         nw = n >> 2;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     nc = ip[1];
jamie@149:     if (n > (nc << 2))
jamie@149:     {
jamie@149:         nc = n >> 2;
jamie@149:         makect(nc, ip, w + nw);
jamie@149:     }
jamie@149:     if (isgn >= 0)
jamie@149:     {
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:             rftfsub(n, a, nc, w + nw);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         xi = a[0] - a[1];
jamie@149:         a[0] += a[1];
jamie@149:         a[1] = xi;
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         a[1] = 0.5 * (a[0] - a[1]);
jamie@149:         a[0] -= a[1];
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             rftbsub(n, a, nc, w + nw);
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void ddct(int n, int isgn, double *a, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void makect(int nc, int *ip, double *c);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void cftbsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void rftfsub(int n, double *a, int nc, double *c);
jamie@149:     void rftbsub(int n, double *a, int nc, double *c);
jamie@149:     void dctsub(int n, double *a, int nc, double *c);
jamie@149:     int j, nw, nc;
jamie@149:     double xr;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 2))
jamie@149:     {
jamie@149:         nw = n >> 2;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     nc = ip[1];
jamie@149:     if (n > nc)
jamie@149:     {
jamie@149:         nc = n;
jamie@149:         makect(nc, ip, w + nw);
jamie@149:     }
jamie@149:     if (isgn < 0)
jamie@149:     {
jamie@149:         xr = a[n - 1];
jamie@149:         for (j = n - 2; j >= 2; j -= 2)
jamie@149:         {
jamie@149:             a[j + 1] = a[j] - a[j - 1];
jamie@149:             a[j] += a[j - 1];
jamie@149:         }
jamie@149:         a[1] = a[0] - xr;
jamie@149:         a[0] += xr;
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             rftbsub(n, a, nc, w + nw);
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:     }
jamie@149:     dctsub(n, a, nc, w + nw);
jamie@149:     if (isgn >= 0)
jamie@149:     {
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:             rftfsub(n, a, nc, w + nw);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         xr = a[0] - a[1];
jamie@149:         a[0] += a[1];
jamie@149:         for (j = 2; j < n; j += 2)
jamie@149:         {
jamie@149:             a[j - 1] = a[j] - a[j + 1];
jamie@149:             a[j] += a[j + 1];
jamie@149:         }
jamie@149:         a[n - 1] = xr;
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void ddst(int n, int isgn, double *a, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void makect(int nc, int *ip, double *c);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void cftbsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void rftfsub(int n, double *a, int nc, double *c);
jamie@149:     void rftbsub(int n, double *a, int nc, double *c);
jamie@149:     void dstsub(int n, double *a, int nc, double *c);
jamie@149:     int j, nw, nc;
jamie@149:     double xr;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 2))
jamie@149:     {
jamie@149:         nw = n >> 2;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     nc = ip[1];
jamie@149:     if (n > nc)
jamie@149:     {
jamie@149:         nc = n;
jamie@149:         makect(nc, ip, w + nw);
jamie@149:     }
jamie@149:     if (isgn < 0)
jamie@149:     {
jamie@149:         xr = a[n - 1];
jamie@149:         for (j = n - 2; j >= 2; j -= 2)
jamie@149:         {
jamie@149:             a[j + 1] = -a[j] - a[j - 1];
jamie@149:             a[j] -= a[j - 1];
jamie@149:         }
jamie@149:         a[1] = a[0] + xr;
jamie@149:         a[0] -= xr;
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             rftbsub(n, a, nc, w + nw);
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftbsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:     }
jamie@149:     dstsub(n, a, nc, w + nw);
jamie@149:     if (isgn >= 0)
jamie@149:     {
jamie@149:         if (n > 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:             rftfsub(n, a, nc, w + nw);
jamie@149:         }
jamie@149:         else if (n == 4)
jamie@149:         {
jamie@149:             cftfsub(n, a, ip, nw, w);
jamie@149:         }
jamie@149:         xr = a[0] - a[1];
jamie@149:         a[0] += a[1];
jamie@149:         for (j = 2; j < n; j += 2)
jamie@149:         {
jamie@149:             a[j - 1] = -a[j] - a[j + 1];
jamie@149:             a[j] -= a[j + 1];
jamie@149:         }
jamie@149:         a[n - 1] = -xr;
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void dfct(int n, double *a, double *t, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void makect(int nc, int *ip, double *c);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void rftfsub(int n, double *a, int nc, double *c);
jamie@149:     void dctsub(int n, double *a, int nc, double *c);
jamie@149:     int j, k, l, m, mh, nw, nc;
jamie@149:     double xr, xi, yr, yi;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 3))
jamie@149:     {
jamie@149:         nw = n >> 3;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     nc = ip[1];
jamie@149:     if (n > (nc << 1))
jamie@149:     {
jamie@149:         nc = n >> 1;
jamie@149:         makect(nc, ip, w + nw);
jamie@149:     }
jamie@149:     m = n >> 1;
jamie@149:     yi = a[m];
jamie@149:     xi = a[0] + a[n];
jamie@149:     a[0] -= a[n];
jamie@149:     t[0] = xi - yi;
jamie@149:     t[m] = xi + yi;
jamie@149:     if (n > 2)
jamie@149:     {
jamie@149:         mh = m >> 1;
jamie@149:         for (j = 1; j < mh; j++)
jamie@149:         {
jamie@149:             k = m - j;
jamie@149:             xr = a[j] - a[n - j];
jamie@149:             xi = a[j] + a[n - j];
jamie@149:             yr = a[k] - a[n - k];
jamie@149:             yi = a[k] + a[n - k];
jamie@149:             a[j] = xr;
jamie@149:             a[k] = yr;
jamie@149:             t[j] = xi - yi;
jamie@149:             t[k] = xi + yi;
jamie@149:         }
jamie@149:         t[mh] = a[mh] + a[n - mh];
jamie@149:         a[mh] -= a[n - mh];
jamie@149:         dctsub(m, a, nc, w + nw);
jamie@149:         if (m > 4)
jamie@149:         {
jamie@149:             cftfsub(m, a, ip, nw, w);
jamie@149:             rftfsub(m, a, nc, w + nw);
jamie@149:         }
jamie@149:         else if (m == 4)
jamie@149:         {
jamie@149:             cftfsub(m, a, ip, nw, w);
jamie@149:         }
jamie@149:         a[n - 1] = a[0] - a[1];
jamie@149:         a[1] = a[0] + a[1];
jamie@149:         for (j = m - 2; j >= 2; j -= 2)
jamie@149:         {
jamie@149:             a[2 * j + 1] = a[j] + a[j + 1];
jamie@149:             a[2 * j - 1] = a[j] - a[j + 1];
jamie@149:         }
jamie@149:         l = 2;
jamie@149:         m = mh;
jamie@149:         while (m >= 2)
jamie@149:         {
jamie@149:             dctsub(m, t, nc, w + nw);
jamie@149:             if (m > 4)
jamie@149:             {
jamie@149:                 cftfsub(m, t, ip, nw, w);
jamie@149:                 rftfsub(m, t, nc, w + nw);
jamie@149:             }
jamie@149:             else if (m == 4)
jamie@149:             {
jamie@149:                 cftfsub(m, t, ip, nw, w);
jamie@149:             }
jamie@149:             a[n - l] = t[0] - t[1];
jamie@149:             a[l] = t[0] + t[1];
jamie@149:             k = 0;
jamie@149:             for (j = 2; j < m; j += 2)
jamie@149:             {
jamie@149:                 k += l << 2;
jamie@149:                 a[k - l] = t[j] - t[j + 1];
jamie@149:                 a[k + l] = t[j] + t[j + 1];
jamie@149:             }
jamie@149:             l <<= 1;
jamie@149:             mh = m >> 1;
jamie@149:             for (j = 0; j < mh; j++)
jamie@149:             {
jamie@149:                 k = m - j;
jamie@149:                 t[j] = t[m + k] - t[m + j];
jamie@149:                 t[k] = t[m + k] + t[m + j];
jamie@149:             }
jamie@149:             t[mh] = t[m + mh];
jamie@149:             m = mh;
jamie@149:         }
jamie@149:         a[l] = t[0];
jamie@149:         a[n] = t[2] - t[1];
jamie@149:         a[0] = t[2] + t[1];
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         a[1] = a[0];
jamie@149:         a[2] = t[0];
jamie@149:         a[0] = t[1];
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void dfst(int n, double *a, double *t, int *ip, double *w)
jamie@149: {
jamie@149:     void makewt(int nw, int *ip, double *w);
jamie@149:     void makect(int nc, int *ip, double *c);
jamie@149:     void cftfsub(int n, double *a, int *ip, int nw, double *w);
jamie@149:     void rftfsub(int n, double *a, int nc, double *c);
jamie@149:     void dstsub(int n, double *a, int nc, double *c);
jamie@149:     int j, k, l, m, mh, nw, nc;
jamie@149:     double xr, xi, yr, yi;
jamie@149: 
jamie@149:     nw = ip[0];
jamie@149:     if (n > (nw << 3))
jamie@149:     {
jamie@149:         nw = n >> 3;
jamie@149:         makewt(nw, ip, w);
jamie@149:     }
jamie@149:     nc = ip[1];
jamie@149:     if (n > (nc << 1))
jamie@149:     {
jamie@149:         nc = n >> 1;
jamie@149:         makect(nc, ip, w + nw);
jamie@149:     }
jamie@149:     if (n > 2)
jamie@149:     {
jamie@149:         m = n >> 1;
jamie@149:         mh = m >> 1;
jamie@149:         for (j = 1; j < mh; j++)
jamie@149:         {
jamie@149:             k = m - j;
jamie@149:             xr = a[j] + a[n - j];
jamie@149:             xi = a[j] - a[n - j];
jamie@149:             yr = a[k] + a[n - k];
jamie@149:             yi = a[k] - a[n - k];
jamie@149:             a[j] = xr;
jamie@149:             a[k] = yr;
jamie@149:             t[j] = xi + yi;
jamie@149:             t[k] = xi - yi;
jamie@149:         }
jamie@149:         t[0] = a[mh] - a[n - mh];
jamie@149:         a[mh] += a[n - mh];
jamie@149:         a[0] = a[m];
jamie@149:         dstsub(m, a, nc, w + nw);
jamie@149:         if (m > 4)
jamie@149:         {
jamie@149:             cftfsub(m, a, ip, nw, w);
jamie@149:             rftfsub(m, a, nc, w + nw);
jamie@149:         }
jamie@149:         else if (m == 4)
jamie@149:         {
jamie@149:             cftfsub(m, a, ip, nw, w);
jamie@149:         }
jamie@149:         a[n - 1] = a[1] - a[0];
jamie@149:         a[1] = a[0] + a[1];
jamie@149:         for (j = m - 2; j >= 2; j -= 2)
jamie@149:         {
jamie@149:             a[2 * j + 1] = a[j] - a[j + 1];
jamie@149:             a[2 * j - 1] = -a[j] - a[j + 1];
jamie@149:         }
jamie@149:         l = 2;
jamie@149:         m = mh;
jamie@149:         while (m >= 2)
jamie@149:         {
jamie@149:             dstsub(m, t, nc, w + nw);
jamie@149:             if (m > 4)
jamie@149:             {
jamie@149:                 cftfsub(m, t, ip, nw, w);
jamie@149:                 rftfsub(m, t, nc, w + nw);
jamie@149:             }
jamie@149:             else if (m == 4)
jamie@149:             {
jamie@149:                 cftfsub(m, t, ip, nw, w);
jamie@149:             }
jamie@149:             a[n - l] = t[1] - t[0];
jamie@149:             a[l] = t[0] + t[1];
jamie@149:             k = 0;
jamie@149:             for (j = 2; j < m; j += 2)
jamie@149:             {
jamie@149:                 k += l << 2;
jamie@149:                 a[k - l] = -t[j] - t[j + 1];
jamie@149:                 a[k + l] = t[j] - t[j + 1];
jamie@149:             }
jamie@149:             l <<= 1;
jamie@149:             mh = m >> 1;
jamie@149:             for (j = 1; j < mh; j++)
jamie@149:             {
jamie@149:                 k = m - j;
jamie@149:                 t[j] = t[m + k] + t[m + j];
jamie@149:                 t[k] = t[m + k] - t[m + j];
jamie@149:             }
jamie@149:             t[0] = t[m + mh];
jamie@149:             m = mh;
jamie@149:         }
jamie@149:         a[l] = t[0];
jamie@149:     }
jamie@149:     a[0] = 0;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: /* -------- initializing routines -------- */
jamie@149: 
jamie@149: 
jamie@149: #include <math.h>
jamie@149: 
jamie@149: void makewt(int nw, int *ip, double *w)
jamie@149: {
jamie@149:     void makeipt(int nw, int *ip);
jamie@149:     int j, nwh, nw0, nw1;
jamie@149:     double delta, wn4r, wk1r, wk1i, wk3r, wk3i;
jamie@149: 
jamie@149:     ip[0] = nw;
jamie@149:     ip[1] = 1;
jamie@149:     if (nw > 2)
jamie@149:     {
jamie@149:         nwh = nw >> 1;
jamie@149:         delta = atan(1.0) / nwh;
jamie@149:         wn4r = cos(delta * nwh);
jamie@149:         w[0] = 1;
jamie@149:         w[1] = wn4r;
jamie@149:         if (nwh == 4)
jamie@149:         {
jamie@149:             w[2] = cos(delta * 2);
jamie@149:             w[3] = sin(delta * 2);
jamie@149:         }
jamie@149:         else if (nwh > 4)
jamie@149:         {
jamie@149:             makeipt(nw, ip);
jamie@149:             w[2] = 0.5 / cos(delta * 2);
jamie@149:             w[3] = 0.5 / cos(delta * 6);
jamie@149:             for (j = 4; j < nwh; j += 4)
jamie@149:             {
jamie@149:                 w[j] = cos(delta * j);
jamie@149:                 w[j + 1] = sin(delta * j);
jamie@149:                 w[j + 2] = cos(3 * delta * j);
jamie@149:                 w[j + 3] = -sin(3 * delta * j);
jamie@149:             }
jamie@149:         }
jamie@149:         nw0 = 0;
jamie@149:         while (nwh > 2)
jamie@149:         {
jamie@149:             nw1 = nw0 + nwh;
jamie@149:             nwh >>= 1;
jamie@149:             w[nw1] = 1;
jamie@149:             w[nw1 + 1] = wn4r;
jamie@149:             if (nwh == 4)
jamie@149:             {
jamie@149:                 wk1r = w[nw0 + 4];
jamie@149:                 wk1i = w[nw0 + 5];
jamie@149:                 w[nw1 + 2] = wk1r;
jamie@149:                 w[nw1 + 3] = wk1i;
jamie@149:             }
jamie@149:             else if (nwh > 4)
jamie@149:             {
jamie@149:                 wk1r = w[nw0 + 4];
jamie@149:                 wk3r = w[nw0 + 6];
jamie@149:                 w[nw1 + 2] = 0.5 / wk1r;
jamie@149:                 w[nw1 + 3] = 0.5 / wk3r;
jamie@149:                 for (j = 4; j < nwh; j += 4)
jamie@149:                 {
jamie@149:                     wk1r = w[nw0 + 2 * j];
jamie@149:                     wk1i = w[nw0 + 2 * j + 1];
jamie@149:                     wk3r = w[nw0 + 2 * j + 2];
jamie@149:                     wk3i = w[nw0 + 2 * j + 3];
jamie@149:                     w[nw1 + j] = wk1r;
jamie@149:                     w[nw1 + j + 1] = wk1i;
jamie@149:                     w[nw1 + j + 2] = wk3r;
jamie@149:                     w[nw1 + j + 3] = wk3i;
jamie@149:                 }
jamie@149:             }
jamie@149:             nw0 = nw1;
jamie@149:         }
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void makeipt(int nw, int *ip)
jamie@149: {
jamie@149:     int j, l, m, m2, p, q;
jamie@149: 
jamie@149:     ip[2] = 0;
jamie@149:     ip[3] = 16;
jamie@149:     m = 2;
jamie@149:     for (l = nw; l > 32; l >>= 2)
jamie@149:     {
jamie@149:         m2 = m << 1;
jamie@149:         q = m2 << 3;
jamie@149:         for (j = m; j < m2; j++)
jamie@149:         {
jamie@149:             p = ip[j] << 2;
jamie@149:             ip[m + j] = p;
jamie@149:             ip[m2 + j] = p + q;
jamie@149:         }
jamie@149:         m = m2;
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void makect(int nc, int *ip, double *c)
jamie@149: {
jamie@149:     int j, nch;
jamie@149:     double delta;
jamie@149: 
jamie@149:     ip[1] = nc;
jamie@149:     if (nc > 1)
jamie@149:     {
jamie@149:         nch = nc >> 1;
jamie@149:         delta = atan(1.0) / nch;
jamie@149:         c[0] = cos(delta * nch);
jamie@149:         c[nch] = 0.5 * c[0];
jamie@149:         for (j = 1; j < nch; j++)
jamie@149:         {
jamie@149:             c[j] = 0.5 * cos(delta * j);
jamie@149:             c[nc - j] = 0.5 * sin(delta * j);
jamie@149:         }
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: /* -------- child routines -------- */
jamie@149: 
jamie@149: 
jamie@149: #ifdef USE_CDFT_PTHREADS
jamie@149: #define USE_CDFT_THREADS
jamie@149: #ifndef CDFT_THREADS_BEGIN_N
jamie@149: #define CDFT_THREADS_BEGIN_N 8192
jamie@149: #endif
jamie@149: #ifndef CDFT_4THREADS_BEGIN_N
jamie@149: #define CDFT_4THREADS_BEGIN_N 65536
jamie@149: #endif
jamie@149: #include <pthread.h>
jamie@149: #include <stdio.h>
jamie@149: #include <stdlib.h>
jamie@149: #define cdft_thread_t pthread_t
jamie@149: #define cdft_thread_create(thp,func,argp) { \
jamie@149:     if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
jamie@149:         fprintf(stderr, "cdft thread error\n"); \
jamie@149:         exit(1); \
jamie@149:     } \
jamie@149: }
jamie@149: #define cdft_thread_wait(th) { \
jamie@149:     if (pthread_join(th, NULL) != 0) { \
jamie@149:         fprintf(stderr, "cdft thread error\n"); \
jamie@149:         exit(1); \
jamie@149:     } \
jamie@149: }
jamie@149: #endif /* USE_CDFT_PTHREADS */
jamie@149: 
jamie@149: 
jamie@149: #ifdef USE_CDFT_WINTHREADS
jamie@149: #define USE_CDFT_THREADS
jamie@149: #ifndef CDFT_THREADS_BEGIN_N
jamie@149: #define CDFT_THREADS_BEGIN_N 32768
jamie@149: #endif
jamie@149: #ifndef CDFT_4THREADS_BEGIN_N
jamie@149: #define CDFT_4THREADS_BEGIN_N 524288
jamie@149: #endif
jamie@149: #include <windows.h>
jamie@149: #include <stdio.h>
jamie@149: #include <stdlib.h>
jamie@149: #define cdft_thread_t HANDLE
jamie@149: #define cdft_thread_create(thp,func,argp) { \
jamie@149:     DWORD thid; \
jamie@149:     *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
jamie@149:     if (*(thp) == 0) { \
jamie@149:         fprintf(stderr, "cdft thread error\n"); \
jamie@149:         exit(1); \
jamie@149:     } \
jamie@149: }
jamie@149: #define cdft_thread_wait(th) { \
jamie@149:     WaitForSingleObject(th, INFINITE); \
jamie@149:     CloseHandle(th); \
jamie@149: }
jamie@149: #endif /* USE_CDFT_WINTHREADS */
jamie@149: 
jamie@149: 
jamie@149: void cftfsub(int n, double *a, int *ip, int nw, double *w)
jamie@149: {
jamie@149:     void bitrv2(int n, int *ip, double *a);
jamie@149:     void bitrv216(double *a);
jamie@149:     void bitrv208(double *a);
jamie@149:     void cftf1st(int n, double *a, double *w);
jamie@149:     void cftrec4(int n, double *a, int nw, double *w);
jamie@149:     void cftleaf(int n, int isplt, double *a, int nw, double *w);
jamie@149:     void cftfx41(int n, double *a, int nw, double *w);
jamie@149:     void cftf161(double *a, double *w);
jamie@149:     void cftf081(double *a, double *w);
jamie@149:     void cftf040(double *a);
jamie@149:     void cftx020(double *a);
jamie@149: #ifdef USE_CDFT_THREADS
jamie@149:     void cftrec4_th(int n, double *a, int nw, double *w);
jamie@149: #endif /* USE_CDFT_THREADS */
jamie@149: 
jamie@149:     if (n > 8)
jamie@149:     {
jamie@149:         if (n > 32)
jamie@149:         {
jamie@149:             cftf1st(n, a, &w[nw - (n >> 2)]);
jamie@149: #ifdef USE_CDFT_THREADS
jamie@149:             if (n > CDFT_THREADS_BEGIN_N)
jamie@149:             {
jamie@149:                 cftrec4_th(n, a, nw, w);
jamie@149:             }
jamie@149:             else
jamie@149: #endif /* USE_CDFT_THREADS */
jamie@149:                 if (n > 512)
jamie@149:                 {
jamie@149:                     cftrec4(n, a, nw, w);
jamie@149:                 }
jamie@149:                 else if (n > 128)
jamie@149:                 {
jamie@149:                     cftleaf(n, 1, a, nw, w);
jamie@149:                 }
jamie@149:                 else
jamie@149:                 {
jamie@149:                     cftfx41(n, a, nw, w);
jamie@149:                 }
jamie@149:             bitrv2(n, ip, a);
jamie@149:         }
jamie@149:         else if (n == 32)
jamie@149:         {
jamie@149:             cftf161(a, &w[nw - 8]);
jamie@149:             bitrv216(a);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cftf081(a, w);
jamie@149:             bitrv208(a);
jamie@149:         }
jamie@149:     }
jamie@149:     else if (n == 8)
jamie@149:     {
jamie@149:         cftf040(a);
jamie@149:     }
jamie@149:     else if (n == 4)
jamie@149:     {
jamie@149:         cftx020(a);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftbsub(int n, double *a, int *ip, int nw, double *w)
jamie@149: {
jamie@149:     void bitrv2conj(int n, int *ip, double *a);
jamie@149:     void bitrv216neg(double *a);
jamie@149:     void bitrv208neg(double *a);
jamie@149:     void cftb1st(int n, double *a, double *w);
jamie@149:     void cftrec4(int n, double *a, int nw, double *w);
jamie@149:     void cftleaf(int n, int isplt, double *a, int nw, double *w);
jamie@149:     void cftfx41(int n, double *a, int nw, double *w);
jamie@149:     void cftf161(double *a, double *w);
jamie@149:     void cftf081(double *a, double *w);
jamie@149:     void cftb040(double *a);
jamie@149:     void cftx020(double *a);
jamie@149: #ifdef USE_CDFT_THREADS
jamie@149:     void cftrec4_th(int n, double *a, int nw, double *w);
jamie@149: #endif /* USE_CDFT_THREADS */
jamie@149: 
jamie@149:     if (n > 8)
jamie@149:     {
jamie@149:         if (n > 32)
jamie@149:         {
jamie@149:             cftb1st(n, a, &w[nw - (n >> 2)]);
jamie@149: #ifdef USE_CDFT_THREADS
jamie@149:             if (n > CDFT_THREADS_BEGIN_N)
jamie@149:             {
jamie@149:                 cftrec4_th(n, a, nw, w);
jamie@149:             }
jamie@149:             else
jamie@149: #endif /* USE_CDFT_THREADS */
jamie@149:                 if (n > 512)
jamie@149:                 {
jamie@149:                     cftrec4(n, a, nw, w);
jamie@149:                 }
jamie@149:                 else if (n > 128)
jamie@149:                 {
jamie@149:                     cftleaf(n, 1, a, nw, w);
jamie@149:                 }
jamie@149:                 else
jamie@149:                 {
jamie@149:                     cftfx41(n, a, nw, w);
jamie@149:                 }
jamie@149:             bitrv2conj(n, ip, a);
jamie@149:         }
jamie@149:         else if (n == 32)
jamie@149:         {
jamie@149:             cftf161(a, &w[nw - 8]);
jamie@149:             bitrv216neg(a);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cftf081(a, w);
jamie@149:             bitrv208neg(a);
jamie@149:         }
jamie@149:     }
jamie@149:     else if (n == 8)
jamie@149:     {
jamie@149:         cftb040(a);
jamie@149:     }
jamie@149:     else if (n == 4)
jamie@149:     {
jamie@149:         cftx020(a);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv2(int n, int *ip, double *a)
jamie@149: {
jamie@149:     int j, j1, k, k1, l, m, nh, nm;
jamie@149:     double xr, xi, yr, yi;
jamie@149: 
jamie@149:     m = 1;
jamie@149:     for (l = n >> 2; l > 8; l >>= 2)
jamie@149:     {
jamie@149:         m <<= 1;
jamie@149:     }
jamie@149:     nh = n >> 1;
jamie@149:     nm = 4 * m;
jamie@149:     if (l == 8)
jamie@149:     {
jamie@149:         for (k = 0; k < m; k++)
jamie@149:         {
jamie@149:             for (j = 0; j < k; j++)
jamie@149:             {
jamie@149:                 j1 = 4 * j + 2 * ip[m + k];
jamie@149:                 k1 = 4 * k + 2 * ip[m + j];
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nh;
jamie@149:                 k1 += 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += 2;
jamie@149:                 k1 += nh;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nh;
jamie@149:                 k1 -= 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:             }
jamie@149:             k1 = 4 * k + 2 * ip[m + k];
jamie@149:             j1 = k1 + 2;
jamie@149:             k1 += nh;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nm;
jamie@149:             k1 += 2 * nm;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nm;
jamie@149:             k1 -= nm;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 -= 2;
jamie@149:             k1 -= nh;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nh + 2;
jamie@149:             k1 += nh + 2;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 -= nh - nm;
jamie@149:             k1 += 2 * nm - 2;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:         }
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         for (k = 0; k < m; k++)
jamie@149:         {
jamie@149:             for (j = 0; j < k; j++)
jamie@149:             {
jamie@149:                 j1 = 4 * j + ip[m + k];
jamie@149:                 k1 = 4 * k + ip[m + j];
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nh;
jamie@149:                 k1 += 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += 2;
jamie@149:                 k1 += nh;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nh;
jamie@149:                 k1 -= 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:             }
jamie@149:             k1 = 4 * k + ip[m + k];
jamie@149:             j1 = k1 + 2;
jamie@149:             k1 += nh;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nm;
jamie@149:             k1 += nm;
jamie@149:             xr = a[j1];
jamie@149:             xi = a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:         }
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv2conj(int n, int *ip, double *a)
jamie@149: {
jamie@149:     int j, j1, k, k1, l, m, nh, nm;
jamie@149:     double xr, xi, yr, yi;
jamie@149: 
jamie@149:     m = 1;
jamie@149:     for (l = n >> 2; l > 8; l >>= 2)
jamie@149:     {
jamie@149:         m <<= 1;
jamie@149:     }
jamie@149:     nh = n >> 1;
jamie@149:     nm = 4 * m;
jamie@149:     if (l == 8)
jamie@149:     {
jamie@149:         for (k = 0; k < m; k++)
jamie@149:         {
jamie@149:             for (j = 0; j < k; j++)
jamie@149:             {
jamie@149:                 j1 = 4 * j + 2 * ip[m + k];
jamie@149:                 k1 = 4 * k + 2 * ip[m + j];
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nh;
jamie@149:                 k1 += 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += 2;
jamie@149:                 k1 += nh;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nh;
jamie@149:                 k1 -= 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= 2 * nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:             }
jamie@149:             k1 = 4 * k + 2 * ip[m + k];
jamie@149:             j1 = k1 + 2;
jamie@149:             k1 += nh;
jamie@149:             a[j1 - 1] = -a[j1 - 1];
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             a[k1 + 3] = -a[k1 + 3];
jamie@149:             j1 += nm;
jamie@149:             k1 += 2 * nm;
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nm;
jamie@149:             k1 -= nm;
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 -= 2;
jamie@149:             k1 -= nh;
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 += nh + 2;
jamie@149:             k1 += nh + 2;
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             j1 -= nh - nm;
jamie@149:             k1 += 2 * nm - 2;
jamie@149:             a[j1 - 1] = -a[j1 - 1];
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             a[k1 + 3] = -a[k1 + 3];
jamie@149:         }
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         for (k = 0; k < m; k++)
jamie@149:         {
jamie@149:             for (j = 0; j < k; j++)
jamie@149:             {
jamie@149:                 j1 = 4 * j + ip[m + k];
jamie@149:                 k1 = 4 * k + ip[m + j];
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nh;
jamie@149:                 k1 += 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += 2;
jamie@149:                 k1 += nh;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 += nm;
jamie@149:                 k1 += nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nh;
jamie@149:                 k1 -= 2;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:                 j1 -= nm;
jamie@149:                 k1 -= nm;
jamie@149:                 xr = a[j1];
jamie@149:                 xi = -a[j1 + 1];
jamie@149:                 yr = a[k1];
jamie@149:                 yi = -a[k1 + 1];
jamie@149:                 a[j1] = yr;
jamie@149:                 a[j1 + 1] = yi;
jamie@149:                 a[k1] = xr;
jamie@149:                 a[k1 + 1] = xi;
jamie@149:             }
jamie@149:             k1 = 4 * k + ip[m + k];
jamie@149:             j1 = k1 + 2;
jamie@149:             k1 += nh;
jamie@149:             a[j1 - 1] = -a[j1 - 1];
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             a[k1 + 3] = -a[k1 + 3];
jamie@149:             j1 += nm;
jamie@149:             k1 += nm;
jamie@149:             a[j1 - 1] = -a[j1 - 1];
jamie@149:             xr = a[j1];
jamie@149:             xi = -a[j1 + 1];
jamie@149:             yr = a[k1];
jamie@149:             yi = -a[k1 + 1];
jamie@149:             a[j1] = yr;
jamie@149:             a[j1 + 1] = yi;
jamie@149:             a[k1] = xr;
jamie@149:             a[k1 + 1] = xi;
jamie@149:             a[k1 + 3] = -a[k1 + 3];
jamie@149:         }
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv216(double *a)
jamie@149: {
jamie@149:     double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
jamie@149:            x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i,
jamie@149:            x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
jamie@149: 
jamie@149:     x1r = a[2];
jamie@149:     x1i = a[3];
jamie@149:     x2r = a[4];
jamie@149:     x2i = a[5];
jamie@149:     x3r = a[6];
jamie@149:     x3i = a[7];
jamie@149:     x4r = a[8];
jamie@149:     x4i = a[9];
jamie@149:     x5r = a[10];
jamie@149:     x5i = a[11];
jamie@149:     x7r = a[14];
jamie@149:     x7i = a[15];
jamie@149:     x8r = a[16];
jamie@149:     x8i = a[17];
jamie@149:     x10r = a[20];
jamie@149:     x10i = a[21];
jamie@149:     x11r = a[22];
jamie@149:     x11i = a[23];
jamie@149:     x12r = a[24];
jamie@149:     x12i = a[25];
jamie@149:     x13r = a[26];
jamie@149:     x13i = a[27];
jamie@149:     x14r = a[28];
jamie@149:     x14i = a[29];
jamie@149:     a[2] = x8r;
jamie@149:     a[3] = x8i;
jamie@149:     a[4] = x4r;
jamie@149:     a[5] = x4i;
jamie@149:     a[6] = x12r;
jamie@149:     a[7] = x12i;
jamie@149:     a[8] = x2r;
jamie@149:     a[9] = x2i;
jamie@149:     a[10] = x10r;
jamie@149:     a[11] = x10i;
jamie@149:     a[14] = x14r;
jamie@149:     a[15] = x14i;
jamie@149:     a[16] = x1r;
jamie@149:     a[17] = x1i;
jamie@149:     a[20] = x5r;
jamie@149:     a[21] = x5i;
jamie@149:     a[22] = x13r;
jamie@149:     a[23] = x13i;
jamie@149:     a[24] = x3r;
jamie@149:     a[25] = x3i;
jamie@149:     a[26] = x11r;
jamie@149:     a[27] = x11i;
jamie@149:     a[28] = x7r;
jamie@149:     a[29] = x7i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv216neg(double *a)
jamie@149: {
jamie@149:     double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
jamie@149:            x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i,
jamie@149:            x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i,
jamie@149:            x13r, x13i, x14r, x14i, x15r, x15i;
jamie@149: 
jamie@149:     x1r = a[2];
jamie@149:     x1i = a[3];
jamie@149:     x2r = a[4];
jamie@149:     x2i = a[5];
jamie@149:     x3r = a[6];
jamie@149:     x3i = a[7];
jamie@149:     x4r = a[8];
jamie@149:     x4i = a[9];
jamie@149:     x5r = a[10];
jamie@149:     x5i = a[11];
jamie@149:     x6r = a[12];
jamie@149:     x6i = a[13];
jamie@149:     x7r = a[14];
jamie@149:     x7i = a[15];
jamie@149:     x8r = a[16];
jamie@149:     x8i = a[17];
jamie@149:     x9r = a[18];
jamie@149:     x9i = a[19];
jamie@149:     x10r = a[20];
jamie@149:     x10i = a[21];
jamie@149:     x11r = a[22];
jamie@149:     x11i = a[23];
jamie@149:     x12r = a[24];
jamie@149:     x12i = a[25];
jamie@149:     x13r = a[26];
jamie@149:     x13i = a[27];
jamie@149:     x14r = a[28];
jamie@149:     x14i = a[29];
jamie@149:     x15r = a[30];
jamie@149:     x15i = a[31];
jamie@149:     a[2] = x15r;
jamie@149:     a[3] = x15i;
jamie@149:     a[4] = x7r;
jamie@149:     a[5] = x7i;
jamie@149:     a[6] = x11r;
jamie@149:     a[7] = x11i;
jamie@149:     a[8] = x3r;
jamie@149:     a[9] = x3i;
jamie@149:     a[10] = x13r;
jamie@149:     a[11] = x13i;
jamie@149:     a[12] = x5r;
jamie@149:     a[13] = x5i;
jamie@149:     a[14] = x9r;
jamie@149:     a[15] = x9i;
jamie@149:     a[16] = x1r;
jamie@149:     a[17] = x1i;
jamie@149:     a[18] = x14r;
jamie@149:     a[19] = x14i;
jamie@149:     a[20] = x6r;
jamie@149:     a[21] = x6i;
jamie@149:     a[22] = x10r;
jamie@149:     a[23] = x10i;
jamie@149:     a[24] = x2r;
jamie@149:     a[25] = x2i;
jamie@149:     a[26] = x12r;
jamie@149:     a[27] = x12i;
jamie@149:     a[28] = x4r;
jamie@149:     a[29] = x4i;
jamie@149:     a[30] = x8r;
jamie@149:     a[31] = x8i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv208(double *a)
jamie@149: {
jamie@149:     double x1r, x1i, x3r, x3i, x4r, x4i, x6r, x6i;
jamie@149: 
jamie@149:     x1r = a[2];
jamie@149:     x1i = a[3];
jamie@149:     x3r = a[6];
jamie@149:     x3i = a[7];
jamie@149:     x4r = a[8];
jamie@149:     x4i = a[9];
jamie@149:     x6r = a[12];
jamie@149:     x6i = a[13];
jamie@149:     a[2] = x4r;
jamie@149:     a[3] = x4i;
jamie@149:     a[6] = x6r;
jamie@149:     a[7] = x6i;
jamie@149:     a[8] = x1r;
jamie@149:     a[9] = x1i;
jamie@149:     a[12] = x3r;
jamie@149:     a[13] = x3i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void bitrv208neg(double *a)
jamie@149: {
jamie@149:     double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i,
jamie@149:            x5r, x5i, x6r, x6i, x7r, x7i;
jamie@149: 
jamie@149:     x1r = a[2];
jamie@149:     x1i = a[3];
jamie@149:     x2r = a[4];
jamie@149:     x2i = a[5];
jamie@149:     x3r = a[6];
jamie@149:     x3i = a[7];
jamie@149:     x4r = a[8];
jamie@149:     x4i = a[9];
jamie@149:     x5r = a[10];
jamie@149:     x5i = a[11];
jamie@149:     x6r = a[12];
jamie@149:     x6i = a[13];
jamie@149:     x7r = a[14];
jamie@149:     x7i = a[15];
jamie@149:     a[2] = x7r;
jamie@149:     a[3] = x7i;
jamie@149:     a[4] = x3r;
jamie@149:     a[5] = x3i;
jamie@149:     a[6] = x5r;
jamie@149:     a[7] = x5i;
jamie@149:     a[8] = x1r;
jamie@149:     a[9] = x1i;
jamie@149:     a[10] = x6r;
jamie@149:     a[11] = x6i;
jamie@149:     a[12] = x2r;
jamie@149:     a[13] = x2i;
jamie@149:     a[14] = x4r;
jamie@149:     a[15] = x4i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf1st(int n, double *a, double *w)
jamie@149: {
jamie@149:     int j, j0, j1, j2, j3, k, m, mh;
jamie@149:     double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
jamie@149:            wd1r, wd1i, wd3r, wd3i;
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
jamie@149: 
jamie@149:     mh = n >> 3;
jamie@149:     m = 2 * mh;
jamie@149:     j1 = m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[0] + a[j2];
jamie@149:     x0i = a[1] + a[j2 + 1];
jamie@149:     x1r = a[0] - a[j2];
jamie@149:     x1i = a[1] - a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i + x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i - x2i;
jamie@149:     a[j2] = x1r - x3i;
jamie@149:     a[j2 + 1] = x1i + x3r;
jamie@149:     a[j3] = x1r + x3i;
jamie@149:     a[j3 + 1] = x1i - x3r;
jamie@149:     wn4r = w[1];
jamie@149:     csc1 = w[2];
jamie@149:     csc3 = w[3];
jamie@149:     wd1r = 1;
jamie@149:     wd1i = 0;
jamie@149:     wd3r = 1;
jamie@149:     wd3i = 0;
jamie@149:     k = 0;
jamie@149:     for (j = 2; j < mh - 2; j += 4)
jamie@149:     {
jamie@149:         k += 4;
jamie@149:         wk1r = csc1 * (wd1r + w[k]);
jamie@149:         wk1i = csc1 * (wd1i + w[k + 1]);
jamie@149:         wk3r = csc3 * (wd3r + w[k + 2]);
jamie@149:         wk3i = csc3 * (wd3i + w[k + 3]);
jamie@149:         wd1r = w[k];
jamie@149:         wd1i = w[k + 1];
jamie@149:         wd3r = w[k + 2];
jamie@149:         wd3i = w[k + 3];
jamie@149:         j1 = j + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j] + a[j2];
jamie@149:         x0i = a[j + 1] + a[j2 + 1];
jamie@149:         x1r = a[j] - a[j2];
jamie@149:         x1i = a[j + 1] - a[j2 + 1];
jamie@149:         y0r = a[j + 2] + a[j2 + 2];
jamie@149:         y0i = a[j + 3] + a[j2 + 3];
jamie@149:         y1r = a[j + 2] - a[j2 + 2];
jamie@149:         y1i = a[j + 3] - a[j2 + 3];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         y2r = a[j1 + 2] + a[j3 + 2];
jamie@149:         y2i = a[j1 + 3] + a[j3 + 3];
jamie@149:         y3r = a[j1 + 2] - a[j3 + 2];
jamie@149:         y3i = a[j1 + 3] - a[j3 + 3];
jamie@149:         a[j] = x0r + x2r;
jamie@149:         a[j + 1] = x0i + x2i;
jamie@149:         a[j + 2] = y0r + y2r;
jamie@149:         a[j + 3] = y0i + y2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i - x2i;
jamie@149:         a[j1 + 2] = y0r - y2r;
jamie@149:         a[j1 + 3] = y0i - y2i;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1r * x0r - wk1i * x0i;
jamie@149:         a[j2 + 1] = wk1r * x0i + wk1i * x0r;
jamie@149:         x0r = y1r - y3i;
jamie@149:         x0i = y1i + y3r;
jamie@149:         a[j2 + 2] = wd1r * x0r - wd1i * x0i;
jamie@149:         a[j2 + 3] = wd1r * x0i + wd1i * x0r;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3r * x0r + wk3i * x0i;
jamie@149:         a[j3 + 1] = wk3r * x0i - wk3i * x0r;
jamie@149:         x0r = y1r + y3i;
jamie@149:         x0i = y1i - y3r;
jamie@149:         a[j3 + 2] = wd3r * x0r + wd3i * x0i;
jamie@149:         a[j3 + 3] = wd3r * x0i - wd3i * x0r;
jamie@149:         j0 = m - j;
jamie@149:         j1 = j0 + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j0] + a[j2];
jamie@149:         x0i = a[j0 + 1] + a[j2 + 1];
jamie@149:         x1r = a[j0] - a[j2];
jamie@149:         x1i = a[j0 + 1] - a[j2 + 1];
jamie@149:         y0r = a[j0 - 2] + a[j2 - 2];
jamie@149:         y0i = a[j0 - 1] + a[j2 - 1];
jamie@149:         y1r = a[j0 - 2] - a[j2 - 2];
jamie@149:         y1i = a[j0 - 1] - a[j2 - 1];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         y2r = a[j1 - 2] + a[j3 - 2];
jamie@149:         y2i = a[j1 - 1] + a[j3 - 1];
jamie@149:         y3r = a[j1 - 2] - a[j3 - 2];
jamie@149:         y3i = a[j1 - 1] - a[j3 - 1];
jamie@149:         a[j0] = x0r + x2r;
jamie@149:         a[j0 + 1] = x0i + x2i;
jamie@149:         a[j0 - 2] = y0r + y2r;
jamie@149:         a[j0 - 1] = y0i + y2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i - x2i;
jamie@149:         a[j1 - 2] = y0r - y2r;
jamie@149:         a[j1 - 1] = y0i - y2i;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1i * x0r - wk1r * x0i;
jamie@149:         a[j2 + 1] = wk1i * x0i + wk1r * x0r;
jamie@149:         x0r = y1r - y3i;
jamie@149:         x0i = y1i + y3r;
jamie@149:         a[j2 - 2] = wd1i * x0r - wd1r * x0i;
jamie@149:         a[j2 - 1] = wd1i * x0i + wd1r * x0r;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3i * x0r + wk3r * x0i;
jamie@149:         a[j3 + 1] = wk3i * x0i - wk3r * x0r;
jamie@149:         x0r = y1r + y3i;
jamie@149:         x0i = y1i - y3r;
jamie@149:         a[j3 - 2] = wd3i * x0r + wd3r * x0i;
jamie@149:         a[j3 - 1] = wd3i * x0i - wd3r * x0r;
jamie@149:     }
jamie@149:     wk1r = csc1 * (wd1r + wn4r);
jamie@149:     wk1i = csc1 * (wd1i + wn4r);
jamie@149:     wk3r = csc3 * (wd3r - wn4r);
jamie@149:     wk3i = csc3 * (wd3i - wn4r);
jamie@149:     j0 = mh;
jamie@149:     j1 = j0 + m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[j0 - 2] + a[j2 - 2];
jamie@149:     x0i = a[j0 - 1] + a[j2 - 1];
jamie@149:     x1r = a[j0 - 2] - a[j2 - 2];
jamie@149:     x1i = a[j0 - 1] - a[j2 - 1];
jamie@149:     x2r = a[j1 - 2] + a[j3 - 2];
jamie@149:     x2i = a[j1 - 1] + a[j3 - 1];
jamie@149:     x3r = a[j1 - 2] - a[j3 - 2];
jamie@149:     x3i = a[j1 - 1] - a[j3 - 1];
jamie@149:     a[j0 - 2] = x0r + x2r;
jamie@149:     a[j0 - 1] = x0i + x2i;
jamie@149:     a[j1 - 2] = x0r - x2r;
jamie@149:     a[j1 - 1] = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2 - 2] = wk1r * x0r - wk1i * x0i;
jamie@149:     a[j2 - 1] = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3 - 2] = wk3r * x0r + wk3i * x0i;
jamie@149:     a[j3 - 1] = wk3r * x0i - wk3i * x0r;
jamie@149:     x0r = a[j0] + a[j2];
jamie@149:     x0i = a[j0 + 1] + a[j2 + 1];
jamie@149:     x1r = a[j0] - a[j2];
jamie@149:     x1i = a[j0 + 1] - a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[j0] = x0r + x2r;
jamie@149:     a[j0 + 1] = x0i + x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2] = wn4r * (x0r - x0i);
jamie@149:     a[j2 + 1] = wn4r * (x0i + x0r);
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3] = -wn4r * (x0r + x0i);
jamie@149:     a[j3 + 1] = -wn4r * (x0i - x0r);
jamie@149:     x0r = a[j0 + 2] + a[j2 + 2];
jamie@149:     x0i = a[j0 + 3] + a[j2 + 3];
jamie@149:     x1r = a[j0 + 2] - a[j2 + 2];
jamie@149:     x1i = a[j0 + 3] - a[j2 + 3];
jamie@149:     x2r = a[j1 + 2] + a[j3 + 2];
jamie@149:     x2i = a[j1 + 3] + a[j3 + 3];
jamie@149:     x3r = a[j1 + 2] - a[j3 + 2];
jamie@149:     x3i = a[j1 + 3] - a[j3 + 3];
jamie@149:     a[j0 + 2] = x0r + x2r;
jamie@149:     a[j0 + 3] = x0i + x2i;
jamie@149:     a[j1 + 2] = x0r - x2r;
jamie@149:     a[j1 + 3] = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2 + 2] = wk1i * x0r - wk1r * x0i;
jamie@149:     a[j2 + 3] = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3 + 2] = wk3i * x0r + wk3r * x0i;
jamie@149:     a[j3 + 3] = wk3i * x0i - wk3r * x0r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftb1st(int n, double *a, double *w)
jamie@149: {
jamie@149:     int j, j0, j1, j2, j3, k, m, mh;
jamie@149:     double wn4r, csc1, csc3, wk1r, wk1i, wk3r, wk3i,
jamie@149:            wd1r, wd1i, wd3r, wd3i;
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i;
jamie@149: 
jamie@149:     mh = n >> 3;
jamie@149:     m = 2 * mh;
jamie@149:     j1 = m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[0] + a[j2];
jamie@149:     x0i = -a[1] - a[j2 + 1];
jamie@149:     x1r = a[0] - a[j2];
jamie@149:     x1i = -a[1] + a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i - x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i + x2i;
jamie@149:     a[j2] = x1r + x3i;
jamie@149:     a[j2 + 1] = x1i + x3r;
jamie@149:     a[j3] = x1r - x3i;
jamie@149:     a[j3 + 1] = x1i - x3r;
jamie@149:     wn4r = w[1];
jamie@149:     csc1 = w[2];
jamie@149:     csc3 = w[3];
jamie@149:     wd1r = 1;
jamie@149:     wd1i = 0;
jamie@149:     wd3r = 1;
jamie@149:     wd3i = 0;
jamie@149:     k = 0;
jamie@149:     for (j = 2; j < mh - 2; j += 4)
jamie@149:     {
jamie@149:         k += 4;
jamie@149:         wk1r = csc1 * (wd1r + w[k]);
jamie@149:         wk1i = csc1 * (wd1i + w[k + 1]);
jamie@149:         wk3r = csc3 * (wd3r + w[k + 2]);
jamie@149:         wk3i = csc3 * (wd3i + w[k + 3]);
jamie@149:         wd1r = w[k];
jamie@149:         wd1i = w[k + 1];
jamie@149:         wd3r = w[k + 2];
jamie@149:         wd3i = w[k + 3];
jamie@149:         j1 = j + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j] + a[j2];
jamie@149:         x0i = -a[j + 1] - a[j2 + 1];
jamie@149:         x1r = a[j] - a[j2];
jamie@149:         x1i = -a[j + 1] + a[j2 + 1];
jamie@149:         y0r = a[j + 2] + a[j2 + 2];
jamie@149:         y0i = -a[j + 3] - a[j2 + 3];
jamie@149:         y1r = a[j + 2] - a[j2 + 2];
jamie@149:         y1i = -a[j + 3] + a[j2 + 3];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         y2r = a[j1 + 2] + a[j3 + 2];
jamie@149:         y2i = a[j1 + 3] + a[j3 + 3];
jamie@149:         y3r = a[j1 + 2] - a[j3 + 2];
jamie@149:         y3i = a[j1 + 3] - a[j3 + 3];
jamie@149:         a[j] = x0r + x2r;
jamie@149:         a[j + 1] = x0i - x2i;
jamie@149:         a[j + 2] = y0r + y2r;
jamie@149:         a[j + 3] = y0i - y2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i + x2i;
jamie@149:         a[j1 + 2] = y0r - y2r;
jamie@149:         a[j1 + 3] = y0i + y2i;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1r * x0r - wk1i * x0i;
jamie@149:         a[j2 + 1] = wk1r * x0i + wk1i * x0r;
jamie@149:         x0r = y1r + y3i;
jamie@149:         x0i = y1i + y3r;
jamie@149:         a[j2 + 2] = wd1r * x0r - wd1i * x0i;
jamie@149:         a[j2 + 3] = wd1r * x0i + wd1i * x0r;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3r * x0r + wk3i * x0i;
jamie@149:         a[j3 + 1] = wk3r * x0i - wk3i * x0r;
jamie@149:         x0r = y1r - y3i;
jamie@149:         x0i = y1i - y3r;
jamie@149:         a[j3 + 2] = wd3r * x0r + wd3i * x0i;
jamie@149:         a[j3 + 3] = wd3r * x0i - wd3i * x0r;
jamie@149:         j0 = m - j;
jamie@149:         j1 = j0 + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j0] + a[j2];
jamie@149:         x0i = -a[j0 + 1] - a[j2 + 1];
jamie@149:         x1r = a[j0] - a[j2];
jamie@149:         x1i = -a[j0 + 1] + a[j2 + 1];
jamie@149:         y0r = a[j0 - 2] + a[j2 - 2];
jamie@149:         y0i = -a[j0 - 1] - a[j2 - 1];
jamie@149:         y1r = a[j0 - 2] - a[j2 - 2];
jamie@149:         y1i = -a[j0 - 1] + a[j2 - 1];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         y2r = a[j1 - 2] + a[j3 - 2];
jamie@149:         y2i = a[j1 - 1] + a[j3 - 1];
jamie@149:         y3r = a[j1 - 2] - a[j3 - 2];
jamie@149:         y3i = a[j1 - 1] - a[j3 - 1];
jamie@149:         a[j0] = x0r + x2r;
jamie@149:         a[j0 + 1] = x0i - x2i;
jamie@149:         a[j0 - 2] = y0r + y2r;
jamie@149:         a[j0 - 1] = y0i - y2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i + x2i;
jamie@149:         a[j1 - 2] = y0r - y2r;
jamie@149:         a[j1 - 1] = y0i + y2i;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1i * x0r - wk1r * x0i;
jamie@149:         a[j2 + 1] = wk1i * x0i + wk1r * x0r;
jamie@149:         x0r = y1r + y3i;
jamie@149:         x0i = y1i + y3r;
jamie@149:         a[j2 - 2] = wd1i * x0r - wd1r * x0i;
jamie@149:         a[j2 - 1] = wd1i * x0i + wd1r * x0r;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3i * x0r + wk3r * x0i;
jamie@149:         a[j3 + 1] = wk3i * x0i - wk3r * x0r;
jamie@149:         x0r = y1r - y3i;
jamie@149:         x0i = y1i - y3r;
jamie@149:         a[j3 - 2] = wd3i * x0r + wd3r * x0i;
jamie@149:         a[j3 - 1] = wd3i * x0i - wd3r * x0r;
jamie@149:     }
jamie@149:     wk1r = csc1 * (wd1r + wn4r);
jamie@149:     wk1i = csc1 * (wd1i + wn4r);
jamie@149:     wk3r = csc3 * (wd3r - wn4r);
jamie@149:     wk3i = csc3 * (wd3i - wn4r);
jamie@149:     j0 = mh;
jamie@149:     j1 = j0 + m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[j0 - 2] + a[j2 - 2];
jamie@149:     x0i = -a[j0 - 1] - a[j2 - 1];
jamie@149:     x1r = a[j0 - 2] - a[j2 - 2];
jamie@149:     x1i = -a[j0 - 1] + a[j2 - 1];
jamie@149:     x2r = a[j1 - 2] + a[j3 - 2];
jamie@149:     x2i = a[j1 - 1] + a[j3 - 1];
jamie@149:     x3r = a[j1 - 2] - a[j3 - 2];
jamie@149:     x3i = a[j1 - 1] - a[j3 - 1];
jamie@149:     a[j0 - 2] = x0r + x2r;
jamie@149:     a[j0 - 1] = x0i - x2i;
jamie@149:     a[j1 - 2] = x0r - x2r;
jamie@149:     a[j1 - 1] = x0i + x2i;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2 - 2] = wk1r * x0r - wk1i * x0i;
jamie@149:     a[j2 - 1] = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3 - 2] = wk3r * x0r + wk3i * x0i;
jamie@149:     a[j3 - 1] = wk3r * x0i - wk3i * x0r;
jamie@149:     x0r = a[j0] + a[j2];
jamie@149:     x0i = -a[j0 + 1] - a[j2 + 1];
jamie@149:     x1r = a[j0] - a[j2];
jamie@149:     x1i = -a[j0 + 1] + a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[j0] = x0r + x2r;
jamie@149:     a[j0 + 1] = x0i - x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i + x2i;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2] = wn4r * (x0r - x0i);
jamie@149:     a[j2 + 1] = wn4r * (x0i + x0r);
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3] = -wn4r * (x0r + x0i);
jamie@149:     a[j3 + 1] = -wn4r * (x0i - x0r);
jamie@149:     x0r = a[j0 + 2] + a[j2 + 2];
jamie@149:     x0i = -a[j0 + 3] - a[j2 + 3];
jamie@149:     x1r = a[j0 + 2] - a[j2 + 2];
jamie@149:     x1i = -a[j0 + 3] + a[j2 + 3];
jamie@149:     x2r = a[j1 + 2] + a[j3 + 2];
jamie@149:     x2i = a[j1 + 3] + a[j3 + 3];
jamie@149:     x3r = a[j1 + 2] - a[j3 + 2];
jamie@149:     x3i = a[j1 + 3] - a[j3 + 3];
jamie@149:     a[j0 + 2] = x0r + x2r;
jamie@149:     a[j0 + 3] = x0i - x2i;
jamie@149:     a[j1 + 2] = x0r - x2r;
jamie@149:     a[j1 + 3] = x0i + x2i;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2 + 2] = wk1i * x0r - wk1r * x0i;
jamie@149:     a[j2 + 3] = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3 + 2] = wk3i * x0r + wk3r * x0i;
jamie@149:     a[j3 + 3] = wk3i * x0i - wk3r * x0r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: #ifdef USE_CDFT_THREADS
jamie@149: struct cdft_arg_st
jamie@149: {
jamie@149:     int n0;
jamie@149:     int n;
jamie@149:     double *a;
jamie@149:     int nw;
jamie@149:     double *w;
jamie@149: };
jamie@149: typedef struct cdft_arg_st cdft_arg_t;
jamie@149: 
jamie@149: 
jamie@149: void cftrec4_th(int n, double *a, int nw, double *w)
jamie@149: {
jamie@149:     void *cftrec1_th(void *p);
jamie@149:     void *cftrec2_th(void *p);
jamie@149:     int i, idiv4, m, nthread;
jamie@149:     cdft_thread_t th[4];
jamie@149:     cdft_arg_t ag[4];
jamie@149: 
jamie@149:     nthread = 2;
jamie@149:     idiv4 = 0;
jamie@149:     m = n >> 1;
jamie@149:     if (n > CDFT_4THREADS_BEGIN_N)
jamie@149:     {
jamie@149:         nthread = 4;
jamie@149:         idiv4 = 1;
jamie@149:         m >>= 1;
jamie@149:     }
jamie@149:     for (i = 0; i < nthread; i++)
jamie@149:     {
jamie@149:         ag[i].n0 = n;
jamie@149:         ag[i].n = m;
jamie@149:         ag[i].a = &a[i * m];
jamie@149:         ag[i].nw = nw;
jamie@149:         ag[i].w = w;
jamie@149:         if (i != idiv4)
jamie@149:         {
jamie@149:             cdft_thread_create(&th[i], cftrec1_th, &ag[i]);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cdft_thread_create(&th[i], cftrec2_th, &ag[i]);
jamie@149:         }
jamie@149:     }
jamie@149:     for (i = 0; i < nthread; i++)
jamie@149:     {
jamie@149:         cdft_thread_wait(th[i]);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void *cftrec1_th(void *p)
jamie@149: {
jamie@149:     int cfttree(int n, int j, int k, double *a, int nw, double *w);
jamie@149:     void cftleaf(int n, int isplt, double *a, int nw, double *w);
jamie@149:     void cftmdl1(int n, double *a, double *w);
jamie@149:     int isplt, j, k, m, n, n0, nw;
jamie@149:     double *a, *w;
jamie@149: 
jamie@149:     n0 = ((cdft_arg_t *) p)->n0;
jamie@149:     n = ((cdft_arg_t *) p)->n;
jamie@149:     a = ((cdft_arg_t *) p)->a;
jamie@149:     nw = ((cdft_arg_t *) p)->nw;
jamie@149:     w = ((cdft_arg_t *) p)->w;
jamie@149:     m = n0;
jamie@149:     while (m > 512)
jamie@149:     {
jamie@149:         m >>= 2;
jamie@149:         cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
jamie@149:     }
jamie@149:     cftleaf(m, 1, &a[n - m], nw, w);
jamie@149:     k = 0;
jamie@149:     for (j = n - m; j > 0; j -= m)
jamie@149:     {
jamie@149:         k++;
jamie@149:         isplt = cfttree(m, j, k, a, nw, w);
jamie@149:         cftleaf(m, isplt, &a[j - m], nw, w);
jamie@149:     }
jamie@149:     return (void *) 0;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void *cftrec2_th(void *p)
jamie@149: {
jamie@149:     int cfttree(int n, int j, int k, double *a, int nw, double *w);
jamie@149:     void cftleaf(int n, int isplt, double *a, int nw, double *w);
jamie@149:     void cftmdl2(int n, double *a, double *w);
jamie@149:     int isplt, j, k, m, n, n0, nw;
jamie@149:     double *a, *w;
jamie@149: 
jamie@149:     n0 = ((cdft_arg_t *) p)->n0;
jamie@149:     n = ((cdft_arg_t *) p)->n;
jamie@149:     a = ((cdft_arg_t *) p)->a;
jamie@149:     nw = ((cdft_arg_t *) p)->nw;
jamie@149:     w = ((cdft_arg_t *) p)->w;
jamie@149:     k = 1;
jamie@149:     m = n0;
jamie@149:     while (m > 512)
jamie@149:     {
jamie@149:         m >>= 2;
jamie@149:         k <<= 2;
jamie@149:         cftmdl2(m, &a[n - m], &w[nw - m]);
jamie@149:     }
jamie@149:     cftleaf(m, 0, &a[n - m], nw, w);
jamie@149:     k >>= 1;
jamie@149:     for (j = n - m; j > 0; j -= m)
jamie@149:     {
jamie@149:         k++;
jamie@149:         isplt = cfttree(m, j, k, a, nw, w);
jamie@149:         cftleaf(m, isplt, &a[j - m], nw, w);
jamie@149:     }
jamie@149:     return (void *) 0;
jamie@149: }
jamie@149: #endif /* USE_CDFT_THREADS */
jamie@149: 
jamie@149: 
jamie@149: void cftrec4(int n, double *a, int nw, double *w)
jamie@149: {
jamie@149:     int cfttree(int n, int j, int k, double *a, int nw, double *w);
jamie@149:     void cftleaf(int n, int isplt, double *a, int nw, double *w);
jamie@149:     void cftmdl1(int n, double *a, double *w);
jamie@149:     int isplt, j, k, m;
jamie@149: 
jamie@149:     m = n;
jamie@149:     while (m > 512)
jamie@149:     {
jamie@149:         m >>= 2;
jamie@149:         cftmdl1(m, &a[n - m], &w[nw - (m >> 1)]);
jamie@149:     }
jamie@149:     cftleaf(m, 1, &a[n - m], nw, w);
jamie@149:     k = 0;
jamie@149:     for (j = n - m; j > 0; j -= m)
jamie@149:     {
jamie@149:         k++;
jamie@149:         isplt = cfttree(m, j, k, a, nw, w);
jamie@149:         cftleaf(m, isplt, &a[j - m], nw, w);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: int cfttree(int n, int j, int k, double *a, int nw, double *w)
jamie@149: {
jamie@149:     void cftmdl1(int n, double *a, double *w);
jamie@149:     void cftmdl2(int n, double *a, double *w);
jamie@149:     int i, isplt, m;
jamie@149: 
jamie@149:     if ((k & 3) != 0)
jamie@149:     {
jamie@149:         isplt = k & 1;
jamie@149:         if (isplt != 0)
jamie@149:         {
jamie@149:             cftmdl1(n, &a[j - n], &w[nw - (n >> 1)]);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cftmdl2(n, &a[j - n], &w[nw - n]);
jamie@149:         }
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         m = n;
jamie@149:         for (i = k; (i & 3) == 0; i >>= 2)
jamie@149:         {
jamie@149:             m <<= 2;
jamie@149:         }
jamie@149:         isplt = i & 1;
jamie@149:         if (isplt != 0)
jamie@149:         {
jamie@149:             while (m > 128)
jamie@149:             {
jamie@149:                 cftmdl1(m, &a[j - m], &w[nw - (m >> 1)]);
jamie@149:                 m >>= 2;
jamie@149:             }
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             while (m > 128)
jamie@149:             {
jamie@149:                 cftmdl2(m, &a[j - m], &w[nw - m]);
jamie@149:                 m >>= 2;
jamie@149:             }
jamie@149:         }
jamie@149:     }
jamie@149:     return isplt;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftleaf(int n, int isplt, double *a, int nw, double *w)
jamie@149: {
jamie@149:     void cftmdl1(int n, double *a, double *w);
jamie@149:     void cftmdl2(int n, double *a, double *w);
jamie@149:     void cftf161(double *a, double *w);
jamie@149:     void cftf162(double *a, double *w);
jamie@149:     void cftf081(double *a, double *w);
jamie@149:     void cftf082(double *a, double *w);
jamie@149: 
jamie@149:     if (n == 512)
jamie@149:     {
jamie@149:         cftmdl1(128, a, &w[nw - 64]);
jamie@149:         cftf161(a, &w[nw - 8]);
jamie@149:         cftf162(&a[32], &w[nw - 32]);
jamie@149:         cftf161(&a[64], &w[nw - 8]);
jamie@149:         cftf161(&a[96], &w[nw - 8]);
jamie@149:         cftmdl2(128, &a[128], &w[nw - 128]);
jamie@149:         cftf161(&a[128], &w[nw - 8]);
jamie@149:         cftf162(&a[160], &w[nw - 32]);
jamie@149:         cftf161(&a[192], &w[nw - 8]);
jamie@149:         cftf162(&a[224], &w[nw - 32]);
jamie@149:         cftmdl1(128, &a[256], &w[nw - 64]);
jamie@149:         cftf161(&a[256], &w[nw - 8]);
jamie@149:         cftf162(&a[288], &w[nw - 32]);
jamie@149:         cftf161(&a[320], &w[nw - 8]);
jamie@149:         cftf161(&a[352], &w[nw - 8]);
jamie@149:         if (isplt != 0)
jamie@149:         {
jamie@149:             cftmdl1(128, &a[384], &w[nw - 64]);
jamie@149:             cftf161(&a[480], &w[nw - 8]);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cftmdl2(128, &a[384], &w[nw - 128]);
jamie@149:             cftf162(&a[480], &w[nw - 32]);
jamie@149:         }
jamie@149:         cftf161(&a[384], &w[nw - 8]);
jamie@149:         cftf162(&a[416], &w[nw - 32]);
jamie@149:         cftf161(&a[448], &w[nw - 8]);
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         cftmdl1(64, a, &w[nw - 32]);
jamie@149:         cftf081(a, &w[nw - 8]);
jamie@149:         cftf082(&a[16], &w[nw - 8]);
jamie@149:         cftf081(&a[32], &w[nw - 8]);
jamie@149:         cftf081(&a[48], &w[nw - 8]);
jamie@149:         cftmdl2(64, &a[64], &w[nw - 64]);
jamie@149:         cftf081(&a[64], &w[nw - 8]);
jamie@149:         cftf082(&a[80], &w[nw - 8]);
jamie@149:         cftf081(&a[96], &w[nw - 8]);
jamie@149:         cftf082(&a[112], &w[nw - 8]);
jamie@149:         cftmdl1(64, &a[128], &w[nw - 32]);
jamie@149:         cftf081(&a[128], &w[nw - 8]);
jamie@149:         cftf082(&a[144], &w[nw - 8]);
jamie@149:         cftf081(&a[160], &w[nw - 8]);
jamie@149:         cftf081(&a[176], &w[nw - 8]);
jamie@149:         if (isplt != 0)
jamie@149:         {
jamie@149:             cftmdl1(64, &a[192], &w[nw - 32]);
jamie@149:             cftf081(&a[240], &w[nw - 8]);
jamie@149:         }
jamie@149:         else
jamie@149:         {
jamie@149:             cftmdl2(64, &a[192], &w[nw - 64]);
jamie@149:             cftf082(&a[240], &w[nw - 8]);
jamie@149:         }
jamie@149:         cftf081(&a[192], &w[nw - 8]);
jamie@149:         cftf082(&a[208], &w[nw - 8]);
jamie@149:         cftf081(&a[224], &w[nw - 8]);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftmdl1(int n, double *a, double *w)
jamie@149: {
jamie@149:     int j, j0, j1, j2, j3, k, m, mh;
jamie@149:     double wn4r, wk1r, wk1i, wk3r, wk3i;
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
jamie@149: 
jamie@149:     mh = n >> 3;
jamie@149:     m = 2 * mh;
jamie@149:     j1 = m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[0] + a[j2];
jamie@149:     x0i = a[1] + a[j2 + 1];
jamie@149:     x1r = a[0] - a[j2];
jamie@149:     x1i = a[1] - a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i + x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i - x2i;
jamie@149:     a[j2] = x1r - x3i;
jamie@149:     a[j2 + 1] = x1i + x3r;
jamie@149:     a[j3] = x1r + x3i;
jamie@149:     a[j3 + 1] = x1i - x3r;
jamie@149:     wn4r = w[1];
jamie@149:     k = 0;
jamie@149:     for (j = 2; j < mh; j += 2)
jamie@149:     {
jamie@149:         k += 4;
jamie@149:         wk1r = w[k];
jamie@149:         wk1i = w[k + 1];
jamie@149:         wk3r = w[k + 2];
jamie@149:         wk3i = w[k + 3];
jamie@149:         j1 = j + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j] + a[j2];
jamie@149:         x0i = a[j + 1] + a[j2 + 1];
jamie@149:         x1r = a[j] - a[j2];
jamie@149:         x1i = a[j + 1] - a[j2 + 1];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         a[j] = x0r + x2r;
jamie@149:         a[j + 1] = x0i + x2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i - x2i;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1r * x0r - wk1i * x0i;
jamie@149:         a[j2 + 1] = wk1r * x0i + wk1i * x0r;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3r * x0r + wk3i * x0i;
jamie@149:         a[j3 + 1] = wk3r * x0i - wk3i * x0r;
jamie@149:         j0 = m - j;
jamie@149:         j1 = j0 + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j0] + a[j2];
jamie@149:         x0i = a[j0 + 1] + a[j2 + 1];
jamie@149:         x1r = a[j0] - a[j2];
jamie@149:         x1i = a[j0 + 1] - a[j2 + 1];
jamie@149:         x2r = a[j1] + a[j3];
jamie@149:         x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:         x3r = a[j1] - a[j3];
jamie@149:         x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:         a[j0] = x0r + x2r;
jamie@149:         a[j0 + 1] = x0i + x2i;
jamie@149:         a[j1] = x0r - x2r;
jamie@149:         a[j1 + 1] = x0i - x2i;
jamie@149:         x0r = x1r - x3i;
jamie@149:         x0i = x1i + x3r;
jamie@149:         a[j2] = wk1i * x0r - wk1r * x0i;
jamie@149:         a[j2 + 1] = wk1i * x0i + wk1r * x0r;
jamie@149:         x0r = x1r + x3i;
jamie@149:         x0i = x1i - x3r;
jamie@149:         a[j3] = wk3i * x0r + wk3r * x0i;
jamie@149:         a[j3 + 1] = wk3i * x0i - wk3r * x0r;
jamie@149:     }
jamie@149:     j0 = mh;
jamie@149:     j1 = j0 + m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[j0] + a[j2];
jamie@149:     x0i = a[j0 + 1] + a[j2 + 1];
jamie@149:     x1r = a[j0] - a[j2];
jamie@149:     x1i = a[j0 + 1] - a[j2 + 1];
jamie@149:     x2r = a[j1] + a[j3];
jamie@149:     x2i = a[j1 + 1] + a[j3 + 1];
jamie@149:     x3r = a[j1] - a[j3];
jamie@149:     x3i = a[j1 + 1] - a[j3 + 1];
jamie@149:     a[j0] = x0r + x2r;
jamie@149:     a[j0 + 1] = x0i + x2i;
jamie@149:     a[j1] = x0r - x2r;
jamie@149:     a[j1 + 1] = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     a[j2] = wn4r * (x0r - x0i);
jamie@149:     a[j2 + 1] = wn4r * (x0i + x0r);
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     a[j3] = -wn4r * (x0r + x0i);
jamie@149:     a[j3 + 1] = -wn4r * (x0i - x0r);
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftmdl2(int n, double *a, double *w)
jamie@149: {
jamie@149:     int j, j0, j1, j2, j3, k, kr, m, mh;
jamie@149:     double wn4r, wk1r, wk1i, wk3r, wk3i, wd1r, wd1i, wd3r, wd3i;
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i, y0r, y0i, y2r, y2i;
jamie@149: 
jamie@149:     mh = n >> 3;
jamie@149:     m = 2 * mh;
jamie@149:     wn4r = w[1];
jamie@149:     j1 = m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[0] - a[j2 + 1];
jamie@149:     x0i = a[1] + a[j2];
jamie@149:     x1r = a[0] + a[j2 + 1];
jamie@149:     x1i = a[1] - a[j2];
jamie@149:     x2r = a[j1] - a[j3 + 1];
jamie@149:     x2i = a[j1 + 1] + a[j3];
jamie@149:     x3r = a[j1] + a[j3 + 1];
jamie@149:     x3i = a[j1 + 1] - a[j3];
jamie@149:     y0r = wn4r * (x2r - x2i);
jamie@149:     y0i = wn4r * (x2i + x2r);
jamie@149:     a[0] = x0r + y0r;
jamie@149:     a[1] = x0i + y0i;
jamie@149:     a[j1] = x0r - y0r;
jamie@149:     a[j1 + 1] = x0i - y0i;
jamie@149:     y0r = wn4r * (x3r - x3i);
jamie@149:     y0i = wn4r * (x3i + x3r);
jamie@149:     a[j2] = x1r - y0i;
jamie@149:     a[j2 + 1] = x1i + y0r;
jamie@149:     a[j3] = x1r + y0i;
jamie@149:     a[j3 + 1] = x1i - y0r;
jamie@149:     k = 0;
jamie@149:     kr = 2 * m;
jamie@149:     for (j = 2; j < mh; j += 2)
jamie@149:     {
jamie@149:         k += 4;
jamie@149:         wk1r = w[k];
jamie@149:         wk1i = w[k + 1];
jamie@149:         wk3r = w[k + 2];
jamie@149:         wk3i = w[k + 3];
jamie@149:         kr -= 4;
jamie@149:         wd1i = w[kr];
jamie@149:         wd1r = w[kr + 1];
jamie@149:         wd3i = w[kr + 2];
jamie@149:         wd3r = w[kr + 3];
jamie@149:         j1 = j + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j] - a[j2 + 1];
jamie@149:         x0i = a[j + 1] + a[j2];
jamie@149:         x1r = a[j] + a[j2 + 1];
jamie@149:         x1i = a[j + 1] - a[j2];
jamie@149:         x2r = a[j1] - a[j3 + 1];
jamie@149:         x2i = a[j1 + 1] + a[j3];
jamie@149:         x3r = a[j1] + a[j3 + 1];
jamie@149:         x3i = a[j1 + 1] - a[j3];
jamie@149:         y0r = wk1r * x0r - wk1i * x0i;
jamie@149:         y0i = wk1r * x0i + wk1i * x0r;
jamie@149:         y2r = wd1r * x2r - wd1i * x2i;
jamie@149:         y2i = wd1r * x2i + wd1i * x2r;
jamie@149:         a[j] = y0r + y2r;
jamie@149:         a[j + 1] = y0i + y2i;
jamie@149:         a[j1] = y0r - y2r;
jamie@149:         a[j1 + 1] = y0i - y2i;
jamie@149:         y0r = wk3r * x1r + wk3i * x1i;
jamie@149:         y0i = wk3r * x1i - wk3i * x1r;
jamie@149:         y2r = wd3r * x3r + wd3i * x3i;
jamie@149:         y2i = wd3r * x3i - wd3i * x3r;
jamie@149:         a[j2] = y0r + y2r;
jamie@149:         a[j2 + 1] = y0i + y2i;
jamie@149:         a[j3] = y0r - y2r;
jamie@149:         a[j3 + 1] = y0i - y2i;
jamie@149:         j0 = m - j;
jamie@149:         j1 = j0 + m;
jamie@149:         j2 = j1 + m;
jamie@149:         j3 = j2 + m;
jamie@149:         x0r = a[j0] - a[j2 + 1];
jamie@149:         x0i = a[j0 + 1] + a[j2];
jamie@149:         x1r = a[j0] + a[j2 + 1];
jamie@149:         x1i = a[j0 + 1] - a[j2];
jamie@149:         x2r = a[j1] - a[j3 + 1];
jamie@149:         x2i = a[j1 + 1] + a[j3];
jamie@149:         x3r = a[j1] + a[j3 + 1];
jamie@149:         x3i = a[j1 + 1] - a[j3];
jamie@149:         y0r = wd1i * x0r - wd1r * x0i;
jamie@149:         y0i = wd1i * x0i + wd1r * x0r;
jamie@149:         y2r = wk1i * x2r - wk1r * x2i;
jamie@149:         y2i = wk1i * x2i + wk1r * x2r;
jamie@149:         a[j0] = y0r + y2r;
jamie@149:         a[j0 + 1] = y0i + y2i;
jamie@149:         a[j1] = y0r - y2r;
jamie@149:         a[j1 + 1] = y0i - y2i;
jamie@149:         y0r = wd3i * x1r + wd3r * x1i;
jamie@149:         y0i = wd3i * x1i - wd3r * x1r;
jamie@149:         y2r = wk3i * x3r + wk3r * x3i;
jamie@149:         y2i = wk3i * x3i - wk3r * x3r;
jamie@149:         a[j2] = y0r + y2r;
jamie@149:         a[j2 + 1] = y0i + y2i;
jamie@149:         a[j3] = y0r - y2r;
jamie@149:         a[j3 + 1] = y0i - y2i;
jamie@149:     }
jamie@149:     wk1r = w[m];
jamie@149:     wk1i = w[m + 1];
jamie@149:     j0 = mh;
jamie@149:     j1 = j0 + m;
jamie@149:     j2 = j1 + m;
jamie@149:     j3 = j2 + m;
jamie@149:     x0r = a[j0] - a[j2 + 1];
jamie@149:     x0i = a[j0 + 1] + a[j2];
jamie@149:     x1r = a[j0] + a[j2 + 1];
jamie@149:     x1i = a[j0 + 1] - a[j2];
jamie@149:     x2r = a[j1] - a[j3 + 1];
jamie@149:     x2i = a[j1 + 1] + a[j3];
jamie@149:     x3r = a[j1] + a[j3 + 1];
jamie@149:     x3i = a[j1 + 1] - a[j3];
jamie@149:     y0r = wk1r * x0r - wk1i * x0i;
jamie@149:     y0i = wk1r * x0i + wk1i * x0r;
jamie@149:     y2r = wk1i * x2r - wk1r * x2i;
jamie@149:     y2i = wk1i * x2i + wk1r * x2r;
jamie@149:     a[j0] = y0r + y2r;
jamie@149:     a[j0 + 1] = y0i + y2i;
jamie@149:     a[j1] = y0r - y2r;
jamie@149:     a[j1 + 1] = y0i - y2i;
jamie@149:     y0r = wk1i * x1r - wk1r * x1i;
jamie@149:     y0i = wk1i * x1i + wk1r * x1r;
jamie@149:     y2r = wk1r * x3r - wk1i * x3i;
jamie@149:     y2i = wk1r * x3i + wk1i * x3r;
jamie@149:     a[j2] = y0r - y2r;
jamie@149:     a[j2 + 1] = y0i - y2i;
jamie@149:     a[j3] = y0r + y2r;
jamie@149:     a[j3 + 1] = y0i + y2i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftfx41(int n, double *a, int nw, double *w)
jamie@149: {
jamie@149:     void cftf161(double *a, double *w);
jamie@149:     void cftf162(double *a, double *w);
jamie@149:     void cftf081(double *a, double *w);
jamie@149:     void cftf082(double *a, double *w);
jamie@149: 
jamie@149:     if (n == 128)
jamie@149:     {
jamie@149:         cftf161(a, &w[nw - 8]);
jamie@149:         cftf162(&a[32], &w[nw - 32]);
jamie@149:         cftf161(&a[64], &w[nw - 8]);
jamie@149:         cftf161(&a[96], &w[nw - 8]);
jamie@149:     }
jamie@149:     else
jamie@149:     {
jamie@149:         cftf081(a, &w[nw - 8]);
jamie@149:         cftf082(&a[16], &w[nw - 8]);
jamie@149:         cftf081(&a[32], &w[nw - 8]);
jamie@149:         cftf081(&a[48], &w[nw - 8]);
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf161(double *a, double *w)
jamie@149: {
jamie@149:     double wn4r, wk1r, wk1i,
jamie@149:            x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
jamie@149:            y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
jamie@149:            y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
jamie@149:            y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
jamie@149: 
jamie@149:     wn4r = w[1];
jamie@149:     wk1r = w[2];
jamie@149:     wk1i = w[3];
jamie@149:     x0r = a[0] + a[16];
jamie@149:     x0i = a[1] + a[17];
jamie@149:     x1r = a[0] - a[16];
jamie@149:     x1i = a[1] - a[17];
jamie@149:     x2r = a[8] + a[24];
jamie@149:     x2i = a[9] + a[25];
jamie@149:     x3r = a[8] - a[24];
jamie@149:     x3i = a[9] - a[25];
jamie@149:     y0r = x0r + x2r;
jamie@149:     y0i = x0i + x2i;
jamie@149:     y4r = x0r - x2r;
jamie@149:     y4i = x0i - x2i;
jamie@149:     y8r = x1r - x3i;
jamie@149:     y8i = x1i + x3r;
jamie@149:     y12r = x1r + x3i;
jamie@149:     y12i = x1i - x3r;
jamie@149:     x0r = a[2] + a[18];
jamie@149:     x0i = a[3] + a[19];
jamie@149:     x1r = a[2] - a[18];
jamie@149:     x1i = a[3] - a[19];
jamie@149:     x2r = a[10] + a[26];
jamie@149:     x2i = a[11] + a[27];
jamie@149:     x3r = a[10] - a[26];
jamie@149:     x3i = a[11] - a[27];
jamie@149:     y1r = x0r + x2r;
jamie@149:     y1i = x0i + x2i;
jamie@149:     y5r = x0r - x2r;
jamie@149:     y5i = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     y9r = wk1r * x0r - wk1i * x0i;
jamie@149:     y9i = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     y13r = wk1i * x0r - wk1r * x0i;
jamie@149:     y13i = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = a[4] + a[20];
jamie@149:     x0i = a[5] + a[21];
jamie@149:     x1r = a[4] - a[20];
jamie@149:     x1i = a[5] - a[21];
jamie@149:     x2r = a[12] + a[28];
jamie@149:     x2i = a[13] + a[29];
jamie@149:     x3r = a[12] - a[28];
jamie@149:     x3i = a[13] - a[29];
jamie@149:     y2r = x0r + x2r;
jamie@149:     y2i = x0i + x2i;
jamie@149:     y6r = x0r - x2r;
jamie@149:     y6i = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     y10r = wn4r * (x0r - x0i);
jamie@149:     y10i = wn4r * (x0i + x0r);
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     y14r = wn4r * (x0r + x0i);
jamie@149:     y14i = wn4r * (x0i - x0r);
jamie@149:     x0r = a[6] + a[22];
jamie@149:     x0i = a[7] + a[23];
jamie@149:     x1r = a[6] - a[22];
jamie@149:     x1i = a[7] - a[23];
jamie@149:     x2r = a[14] + a[30];
jamie@149:     x2i = a[15] + a[31];
jamie@149:     x3r = a[14] - a[30];
jamie@149:     x3i = a[15] - a[31];
jamie@149:     y3r = x0r + x2r;
jamie@149:     y3i = x0i + x2i;
jamie@149:     y7r = x0r - x2r;
jamie@149:     y7i = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     y11r = wk1i * x0r - wk1r * x0i;
jamie@149:     y11i = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = x1r + x3i;
jamie@149:     x0i = x1i - x3r;
jamie@149:     y15r = wk1r * x0r - wk1i * x0i;
jamie@149:     y15i = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = y12r - y14r;
jamie@149:     x0i = y12i - y14i;
jamie@149:     x1r = y12r + y14r;
jamie@149:     x1i = y12i + y14i;
jamie@149:     x2r = y13r - y15r;
jamie@149:     x2i = y13i - y15i;
jamie@149:     x3r = y13r + y15r;
jamie@149:     x3i = y13i + y15i;
jamie@149:     a[24] = x0r + x2r;
jamie@149:     a[25] = x0i + x2i;
jamie@149:     a[26] = x0r - x2r;
jamie@149:     a[27] = x0i - x2i;
jamie@149:     a[28] = x1r - x3i;
jamie@149:     a[29] = x1i + x3r;
jamie@149:     a[30] = x1r + x3i;
jamie@149:     a[31] = x1i - x3r;
jamie@149:     x0r = y8r + y10r;
jamie@149:     x0i = y8i + y10i;
jamie@149:     x1r = y8r - y10r;
jamie@149:     x1i = y8i - y10i;
jamie@149:     x2r = y9r + y11r;
jamie@149:     x2i = y9i + y11i;
jamie@149:     x3r = y9r - y11r;
jamie@149:     x3i = y9i - y11i;
jamie@149:     a[16] = x0r + x2r;
jamie@149:     a[17] = x0i + x2i;
jamie@149:     a[18] = x0r - x2r;
jamie@149:     a[19] = x0i - x2i;
jamie@149:     a[20] = x1r - x3i;
jamie@149:     a[21] = x1i + x3r;
jamie@149:     a[22] = x1r + x3i;
jamie@149:     a[23] = x1i - x3r;
jamie@149:     x0r = y5r - y7i;
jamie@149:     x0i = y5i + y7r;
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     x0r = y5r + y7i;
jamie@149:     x0i = y5i - y7r;
jamie@149:     x3r = wn4r * (x0r - x0i);
jamie@149:     x3i = wn4r * (x0i + x0r);
jamie@149:     x0r = y4r - y6i;
jamie@149:     x0i = y4i + y6r;
jamie@149:     x1r = y4r + y6i;
jamie@149:     x1i = y4i - y6r;
jamie@149:     a[8] = x0r + x2r;
jamie@149:     a[9] = x0i + x2i;
jamie@149:     a[10] = x0r - x2r;
jamie@149:     a[11] = x0i - x2i;
jamie@149:     a[12] = x1r - x3i;
jamie@149:     a[13] = x1i + x3r;
jamie@149:     a[14] = x1r + x3i;
jamie@149:     a[15] = x1i - x3r;
jamie@149:     x0r = y0r + y2r;
jamie@149:     x0i = y0i + y2i;
jamie@149:     x1r = y0r - y2r;
jamie@149:     x1i = y0i - y2i;
jamie@149:     x2r = y1r + y3r;
jamie@149:     x2i = y1i + y3i;
jamie@149:     x3r = y1r - y3r;
jamie@149:     x3i = y1i - y3i;
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i + x2i;
jamie@149:     a[2] = x0r - x2r;
jamie@149:     a[3] = x0i - x2i;
jamie@149:     a[4] = x1r - x3i;
jamie@149:     a[5] = x1i + x3r;
jamie@149:     a[6] = x1r + x3i;
jamie@149:     a[7] = x1i - x3r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf162(double *a, double *w)
jamie@149: {
jamie@149:     double wn4r, wk1r, wk1i, wk2r, wk2i, wk3r, wk3i,
jamie@149:            x0r, x0i, x1r, x1i, x2r, x2i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
jamie@149:            y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i,
jamie@149:            y8r, y8i, y9r, y9i, y10r, y10i, y11r, y11i,
jamie@149:            y12r, y12i, y13r, y13i, y14r, y14i, y15r, y15i;
jamie@149: 
jamie@149:     wn4r = w[1];
jamie@149:     wk1r = w[4];
jamie@149:     wk1i = w[5];
jamie@149:     wk3r = w[6];
jamie@149:     wk3i = -w[7];
jamie@149:     wk2r = w[8];
jamie@149:     wk2i = w[9];
jamie@149:     x1r = a[0] - a[17];
jamie@149:     x1i = a[1] + a[16];
jamie@149:     x0r = a[8] - a[25];
jamie@149:     x0i = a[9] + a[24];
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     y0r = x1r + x2r;
jamie@149:     y0i = x1i + x2i;
jamie@149:     y4r = x1r - x2r;
jamie@149:     y4i = x1i - x2i;
jamie@149:     x1r = a[0] + a[17];
jamie@149:     x1i = a[1] - a[16];
jamie@149:     x0r = a[8] + a[25];
jamie@149:     x0i = a[9] - a[24];
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     y8r = x1r - x2i;
jamie@149:     y8i = x1i + x2r;
jamie@149:     y12r = x1r + x2i;
jamie@149:     y12i = x1i - x2r;
jamie@149:     x0r = a[2] - a[19];
jamie@149:     x0i = a[3] + a[18];
jamie@149:     x1r = wk1r * x0r - wk1i * x0i;
jamie@149:     x1i = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = a[10] - a[27];
jamie@149:     x0i = a[11] + a[26];
jamie@149:     x2r = wk3i * x0r - wk3r * x0i;
jamie@149:     x2i = wk3i * x0i + wk3r * x0r;
jamie@149:     y1r = x1r + x2r;
jamie@149:     y1i = x1i + x2i;
jamie@149:     y5r = x1r - x2r;
jamie@149:     y5i = x1i - x2i;
jamie@149:     x0r = a[2] + a[19];
jamie@149:     x0i = a[3] - a[18];
jamie@149:     x1r = wk3r * x0r - wk3i * x0i;
jamie@149:     x1i = wk3r * x0i + wk3i * x0r;
jamie@149:     x0r = a[10] + a[27];
jamie@149:     x0i = a[11] - a[26];
jamie@149:     x2r = wk1r * x0r + wk1i * x0i;
jamie@149:     x2i = wk1r * x0i - wk1i * x0r;
jamie@149:     y9r = x1r - x2r;
jamie@149:     y9i = x1i - x2i;
jamie@149:     y13r = x1r + x2r;
jamie@149:     y13i = x1i + x2i;
jamie@149:     x0r = a[4] - a[21];
jamie@149:     x0i = a[5] + a[20];
jamie@149:     x1r = wk2r * x0r - wk2i * x0i;
jamie@149:     x1i = wk2r * x0i + wk2i * x0r;
jamie@149:     x0r = a[12] - a[29];
jamie@149:     x0i = a[13] + a[28];
jamie@149:     x2r = wk2i * x0r - wk2r * x0i;
jamie@149:     x2i = wk2i * x0i + wk2r * x0r;
jamie@149:     y2r = x1r + x2r;
jamie@149:     y2i = x1i + x2i;
jamie@149:     y6r = x1r - x2r;
jamie@149:     y6i = x1i - x2i;
jamie@149:     x0r = a[4] + a[21];
jamie@149:     x0i = a[5] - a[20];
jamie@149:     x1r = wk2i * x0r - wk2r * x0i;
jamie@149:     x1i = wk2i * x0i + wk2r * x0r;
jamie@149:     x0r = a[12] + a[29];
jamie@149:     x0i = a[13] - a[28];
jamie@149:     x2r = wk2r * x0r - wk2i * x0i;
jamie@149:     x2i = wk2r * x0i + wk2i * x0r;
jamie@149:     y10r = x1r - x2r;
jamie@149:     y10i = x1i - x2i;
jamie@149:     y14r = x1r + x2r;
jamie@149:     y14i = x1i + x2i;
jamie@149:     x0r = a[6] - a[23];
jamie@149:     x0i = a[7] + a[22];
jamie@149:     x1r = wk3r * x0r - wk3i * x0i;
jamie@149:     x1i = wk3r * x0i + wk3i * x0r;
jamie@149:     x0r = a[14] - a[31];
jamie@149:     x0i = a[15] + a[30];
jamie@149:     x2r = wk1i * x0r - wk1r * x0i;
jamie@149:     x2i = wk1i * x0i + wk1r * x0r;
jamie@149:     y3r = x1r + x2r;
jamie@149:     y3i = x1i + x2i;
jamie@149:     y7r = x1r - x2r;
jamie@149:     y7i = x1i - x2i;
jamie@149:     x0r = a[6] + a[23];
jamie@149:     x0i = a[7] - a[22];
jamie@149:     x1r = wk1i * x0r + wk1r * x0i;
jamie@149:     x1i = wk1i * x0i - wk1r * x0r;
jamie@149:     x0r = a[14] + a[31];
jamie@149:     x0i = a[15] - a[30];
jamie@149:     x2r = wk3i * x0r - wk3r * x0i;
jamie@149:     x2i = wk3i * x0i + wk3r * x0r;
jamie@149:     y11r = x1r + x2r;
jamie@149:     y11i = x1i + x2i;
jamie@149:     y15r = x1r - x2r;
jamie@149:     y15i = x1i - x2i;
jamie@149:     x1r = y0r + y2r;
jamie@149:     x1i = y0i + y2i;
jamie@149:     x2r = y1r + y3r;
jamie@149:     x2i = y1i + y3i;
jamie@149:     a[0] = x1r + x2r;
jamie@149:     a[1] = x1i + x2i;
jamie@149:     a[2] = x1r - x2r;
jamie@149:     a[3] = x1i - x2i;
jamie@149:     x1r = y0r - y2r;
jamie@149:     x1i = y0i - y2i;
jamie@149:     x2r = y1r - y3r;
jamie@149:     x2i = y1i - y3i;
jamie@149:     a[4] = x1r - x2i;
jamie@149:     a[5] = x1i + x2r;
jamie@149:     a[6] = x1r + x2i;
jamie@149:     a[7] = x1i - x2r;
jamie@149:     x1r = y4r - y6i;
jamie@149:     x1i = y4i + y6r;
jamie@149:     x0r = y5r - y7i;
jamie@149:     x0i = y5i + y7r;
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     a[8] = x1r + x2r;
jamie@149:     a[9] = x1i + x2i;
jamie@149:     a[10] = x1r - x2r;
jamie@149:     a[11] = x1i - x2i;
jamie@149:     x1r = y4r + y6i;
jamie@149:     x1i = y4i - y6r;
jamie@149:     x0r = y5r + y7i;
jamie@149:     x0i = y5i - y7r;
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     a[12] = x1r - x2i;
jamie@149:     a[13] = x1i + x2r;
jamie@149:     a[14] = x1r + x2i;
jamie@149:     a[15] = x1i - x2r;
jamie@149:     x1r = y8r + y10r;
jamie@149:     x1i = y8i + y10i;
jamie@149:     x2r = y9r - y11r;
jamie@149:     x2i = y9i - y11i;
jamie@149:     a[16] = x1r + x2r;
jamie@149:     a[17] = x1i + x2i;
jamie@149:     a[18] = x1r - x2r;
jamie@149:     a[19] = x1i - x2i;
jamie@149:     x1r = y8r - y10r;
jamie@149:     x1i = y8i - y10i;
jamie@149:     x2r = y9r + y11r;
jamie@149:     x2i = y9i + y11i;
jamie@149:     a[20] = x1r - x2i;
jamie@149:     a[21] = x1i + x2r;
jamie@149:     a[22] = x1r + x2i;
jamie@149:     a[23] = x1i - x2r;
jamie@149:     x1r = y12r - y14i;
jamie@149:     x1i = y12i + y14r;
jamie@149:     x0r = y13r + y15i;
jamie@149:     x0i = y13i - y15r;
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     a[24] = x1r + x2r;
jamie@149:     a[25] = x1i + x2i;
jamie@149:     a[26] = x1r - x2r;
jamie@149:     a[27] = x1i - x2i;
jamie@149:     x1r = y12r + y14i;
jamie@149:     x1i = y12i - y14r;
jamie@149:     x0r = y13r - y15i;
jamie@149:     x0i = y13i + y15r;
jamie@149:     x2r = wn4r * (x0r - x0i);
jamie@149:     x2i = wn4r * (x0i + x0r);
jamie@149:     a[28] = x1r - x2i;
jamie@149:     a[29] = x1i + x2r;
jamie@149:     a[30] = x1r + x2i;
jamie@149:     a[31] = x1i - x2r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf081(double *a, double *w)
jamie@149: {
jamie@149:     double wn4r, x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
jamie@149:            y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
jamie@149: 
jamie@149:     wn4r = w[1];
jamie@149:     x0r = a[0] + a[8];
jamie@149:     x0i = a[1] + a[9];
jamie@149:     x1r = a[0] - a[8];
jamie@149:     x1i = a[1] - a[9];
jamie@149:     x2r = a[4] + a[12];
jamie@149:     x2i = a[5] + a[13];
jamie@149:     x3r = a[4] - a[12];
jamie@149:     x3i = a[5] - a[13];
jamie@149:     y0r = x0r + x2r;
jamie@149:     y0i = x0i + x2i;
jamie@149:     y2r = x0r - x2r;
jamie@149:     y2i = x0i - x2i;
jamie@149:     y1r = x1r - x3i;
jamie@149:     y1i = x1i + x3r;
jamie@149:     y3r = x1r + x3i;
jamie@149:     y3i = x1i - x3r;
jamie@149:     x0r = a[2] + a[10];
jamie@149:     x0i = a[3] + a[11];
jamie@149:     x1r = a[2] - a[10];
jamie@149:     x1i = a[3] - a[11];
jamie@149:     x2r = a[6] + a[14];
jamie@149:     x2i = a[7] + a[15];
jamie@149:     x3r = a[6] - a[14];
jamie@149:     x3i = a[7] - a[15];
jamie@149:     y4r = x0r + x2r;
jamie@149:     y4i = x0i + x2i;
jamie@149:     y6r = x0r - x2r;
jamie@149:     y6i = x0i - x2i;
jamie@149:     x0r = x1r - x3i;
jamie@149:     x0i = x1i + x3r;
jamie@149:     x2r = x1r + x3i;
jamie@149:     x2i = x1i - x3r;
jamie@149:     y5r = wn4r * (x0r - x0i);
jamie@149:     y5i = wn4r * (x0r + x0i);
jamie@149:     y7r = wn4r * (x2r - x2i);
jamie@149:     y7i = wn4r * (x2r + x2i);
jamie@149:     a[8] = y1r + y5r;
jamie@149:     a[9] = y1i + y5i;
jamie@149:     a[10] = y1r - y5r;
jamie@149:     a[11] = y1i - y5i;
jamie@149:     a[12] = y3r - y7i;
jamie@149:     a[13] = y3i + y7r;
jamie@149:     a[14] = y3r + y7i;
jamie@149:     a[15] = y3i - y7r;
jamie@149:     a[0] = y0r + y4r;
jamie@149:     a[1] = y0i + y4i;
jamie@149:     a[2] = y0r - y4r;
jamie@149:     a[3] = y0i - y4i;
jamie@149:     a[4] = y2r - y6i;
jamie@149:     a[5] = y2i + y6r;
jamie@149:     a[6] = y2r + y6i;
jamie@149:     a[7] = y2i - y6r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf082(double *a, double *w)
jamie@149: {
jamie@149:     double wn4r, wk1r, wk1i, x0r, x0i, x1r, x1i,
jamie@149:            y0r, y0i, y1r, y1i, y2r, y2i, y3r, y3i,
jamie@149:            y4r, y4i, y5r, y5i, y6r, y6i, y7r, y7i;
jamie@149: 
jamie@149:     wn4r = w[1];
jamie@149:     wk1r = w[2];
jamie@149:     wk1i = w[3];
jamie@149:     y0r = a[0] - a[9];
jamie@149:     y0i = a[1] + a[8];
jamie@149:     y1r = a[0] + a[9];
jamie@149:     y1i = a[1] - a[8];
jamie@149:     x0r = a[4] - a[13];
jamie@149:     x0i = a[5] + a[12];
jamie@149:     y2r = wn4r * (x0r - x0i);
jamie@149:     y2i = wn4r * (x0i + x0r);
jamie@149:     x0r = a[4] + a[13];
jamie@149:     x0i = a[5] - a[12];
jamie@149:     y3r = wn4r * (x0r - x0i);
jamie@149:     y3i = wn4r * (x0i + x0r);
jamie@149:     x0r = a[2] - a[11];
jamie@149:     x0i = a[3] + a[10];
jamie@149:     y4r = wk1r * x0r - wk1i * x0i;
jamie@149:     y4i = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = a[2] + a[11];
jamie@149:     x0i = a[3] - a[10];
jamie@149:     y5r = wk1i * x0r - wk1r * x0i;
jamie@149:     y5i = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = a[6] - a[15];
jamie@149:     x0i = a[7] + a[14];
jamie@149:     y6r = wk1i * x0r - wk1r * x0i;
jamie@149:     y6i = wk1i * x0i + wk1r * x0r;
jamie@149:     x0r = a[6] + a[15];
jamie@149:     x0i = a[7] - a[14];
jamie@149:     y7r = wk1r * x0r - wk1i * x0i;
jamie@149:     y7i = wk1r * x0i + wk1i * x0r;
jamie@149:     x0r = y0r + y2r;
jamie@149:     x0i = y0i + y2i;
jamie@149:     x1r = y4r + y6r;
jamie@149:     x1i = y4i + y6i;
jamie@149:     a[0] = x0r + x1r;
jamie@149:     a[1] = x0i + x1i;
jamie@149:     a[2] = x0r - x1r;
jamie@149:     a[3] = x0i - x1i;
jamie@149:     x0r = y0r - y2r;
jamie@149:     x0i = y0i - y2i;
jamie@149:     x1r = y4r - y6r;
jamie@149:     x1i = y4i - y6i;
jamie@149:     a[4] = x0r - x1i;
jamie@149:     a[5] = x0i + x1r;
jamie@149:     a[6] = x0r + x1i;
jamie@149:     a[7] = x0i - x1r;
jamie@149:     x0r = y1r - y3i;
jamie@149:     x0i = y1i + y3r;
jamie@149:     x1r = y5r - y7r;
jamie@149:     x1i = y5i - y7i;
jamie@149:     a[8] = x0r + x1r;
jamie@149:     a[9] = x0i + x1i;
jamie@149:     a[10] = x0r - x1r;
jamie@149:     a[11] = x0i - x1i;
jamie@149:     x0r = y1r + y3i;
jamie@149:     x0i = y1i - y3r;
jamie@149:     x1r = y5r + y7r;
jamie@149:     x1i = y5i + y7i;
jamie@149:     a[12] = x0r - x1i;
jamie@149:     a[13] = x0i + x1r;
jamie@149:     a[14] = x0r + x1i;
jamie@149:     a[15] = x0i - x1r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftf040(double *a)
jamie@149: {
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
jamie@149: 
jamie@149:     x0r = a[0] + a[4];
jamie@149:     x0i = a[1] + a[5];
jamie@149:     x1r = a[0] - a[4];
jamie@149:     x1i = a[1] - a[5];
jamie@149:     x2r = a[2] + a[6];
jamie@149:     x2i = a[3] + a[7];
jamie@149:     x3r = a[2] - a[6];
jamie@149:     x3i = a[3] - a[7];
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i + x2i;
jamie@149:     a[2] = x1r - x3i;
jamie@149:     a[3] = x1i + x3r;
jamie@149:     a[4] = x0r - x2r;
jamie@149:     a[5] = x0i - x2i;
jamie@149:     a[6] = x1r + x3i;
jamie@149:     a[7] = x1i - x3r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftb040(double *a)
jamie@149: {
jamie@149:     double x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
jamie@149: 
jamie@149:     x0r = a[0] + a[4];
jamie@149:     x0i = a[1] + a[5];
jamie@149:     x1r = a[0] - a[4];
jamie@149:     x1i = a[1] - a[5];
jamie@149:     x2r = a[2] + a[6];
jamie@149:     x2i = a[3] + a[7];
jamie@149:     x3r = a[2] - a[6];
jamie@149:     x3i = a[3] - a[7];
jamie@149:     a[0] = x0r + x2r;
jamie@149:     a[1] = x0i + x2i;
jamie@149:     a[2] = x1r + x3i;
jamie@149:     a[3] = x1i - x3r;
jamie@149:     a[4] = x0r - x2r;
jamie@149:     a[5] = x0i - x2i;
jamie@149:     a[6] = x1r - x3i;
jamie@149:     a[7] = x1i + x3r;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void cftx020(double *a)
jamie@149: {
jamie@149:     double x0r, x0i;
jamie@149: 
jamie@149:     x0r = a[0] - a[2];
jamie@149:     x0i = a[1] - a[3];
jamie@149:     a[0] += a[2];
jamie@149:     a[1] += a[3];
jamie@149:     a[2] = x0r;
jamie@149:     a[3] = x0i;
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void rftfsub(int n, double *a, int nc, double *c)
jamie@149: {
jamie@149:     int j, k, kk, ks, m;
jamie@149:     double wkr, wki, xr, xi, yr, yi;
jamie@149: 
jamie@149:     m = n >> 1;
jamie@149:     ks = 2 * nc / m;
jamie@149:     kk = 0;
jamie@149:     for (j = 2; j < m; j += 2)
jamie@149:     {
jamie@149:         k = n - j;
jamie@149:         kk += ks;
jamie@149:         wkr = 0.5 - c[nc - kk];
jamie@149:         wki = c[kk];
jamie@149:         xr = a[j] - a[k];
jamie@149:         xi = a[j + 1] + a[k + 1];
jamie@149:         yr = wkr * xr - wki * xi;
jamie@149:         yi = wkr * xi + wki * xr;
jamie@149:         a[j] -= yr;
jamie@149:         a[j + 1] -= yi;
jamie@149:         a[k] += yr;
jamie@149:         a[k + 1] -= yi;
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void rftbsub(int n, double *a, int nc, double *c)
jamie@149: {
jamie@149:     int j, k, kk, ks, m;
jamie@149:     double wkr, wki, xr, xi, yr, yi;
jamie@149: 
jamie@149:     m = n >> 1;
jamie@149:     ks = 2 * nc / m;
jamie@149:     kk = 0;
jamie@149:     for (j = 2; j < m; j += 2)
jamie@149:     {
jamie@149:         k = n - j;
jamie@149:         kk += ks;
jamie@149:         wkr = 0.5 - c[nc - kk];
jamie@149:         wki = c[kk];
jamie@149:         xr = a[j] - a[k];
jamie@149:         xi = a[j + 1] + a[k + 1];
jamie@149:         yr = wkr * xr + wki * xi;
jamie@149:         yi = wkr * xi - wki * xr;
jamie@149:         a[j] -= yr;
jamie@149:         a[j + 1] -= yi;
jamie@149:         a[k] += yr;
jamie@149:         a[k + 1] -= yi;
jamie@149:     }
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void dctsub(int n, double *a, int nc, double *c)
jamie@149: {
jamie@149:     int j, k, kk, ks, m;
jamie@149:     double wkr, wki, xr;
jamie@149: 
jamie@149:     m = n >> 1;
jamie@149:     ks = nc / n;
jamie@149:     kk = 0;
jamie@149:     for (j = 1; j < m; j++)
jamie@149:     {
jamie@149:         k = n - j;
jamie@149:         kk += ks;
jamie@149:         wkr = c[kk] - c[nc - kk];
jamie@149:         wki = c[kk] + c[nc - kk];
jamie@149:         xr = wki * a[j] - wkr * a[k];
jamie@149:         a[j] = wkr * a[j] + wki * a[k];
jamie@149:         a[k] = xr;
jamie@149:     }
jamie@149:     a[m] *= c[0];
jamie@149: }
jamie@149: 
jamie@149: 
jamie@149: void dstsub(int n, double *a, int nc, double *c)
jamie@149: {
jamie@149:     int j, k, kk, ks, m;
jamie@149:     double wkr, wki, xr;
jamie@149: 
jamie@149:     m = n >> 1;
jamie@149:     ks = nc / n;
jamie@149:     kk = 0;
jamie@149:     for (j = 1; j < m; j++)
jamie@149:     {
jamie@149:         k = n - j;
jamie@149:         kk += ks;
jamie@149:         wkr = c[kk] - c[nc - kk];
jamie@149:         wki = c[kk] + c[nc - kk];
jamie@149:         xr = wki * a[k] - wkr * a[j];
jamie@149:         a[k] = wkr * a[k] + wki * a[j];
jamie@149:         a[j] = xr;
jamie@149:     }
jamie@149:     a[m] *= c[0];
jamie@149: }
jamie@149: