/*
Fast Fourier/Cosine/Sine Transform
    dimension   :three
    data length :power of 2
    decimation  :frequency
    radix       :split-radix, row-column
    data        :inplace
    table       :use
functions
    cdft3d: Complex Discrete Fourier Transform
    rdft3d: Real Discrete Fourier Transform
    ddct3d: Discrete Cosine Transform
    ddst3d: Discrete Sine Transform
function prototypes
    void cdft3d(int, int, int, int, double ***, double *, int *, double *);
    void rdft3d(int, int, int, int, double ***, double *, int *, double *);
    void rdft3dsort(int, int, int, int, double ***);
    void ddct3d(int, int, int, int, double ***, double *, int *, double *);
    void ddst3d(int, int, int, int, double ***, double *, int *, double *);
necessary package
    fftsg.c  : 1D-FFT package
macro definitions
    USE_FFT3D_PTHREADS : default=not defined
        FFT3D_MAX_THREADS     : must be 2^N, default=4
        FFT3D_THREADS_BEGIN_N : default=65536
    USE_FFT3D_WINTHREADS : default=not defined
        FFT3D_MAX_THREADS     : must be 2^N, default=4
        FFT3D_THREADS_BEGIN_N : default=131072


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                x[j1][j2][j3] * 
                                exp(2*pi*i*j1*k1/n1) * 
                                exp(2*pi*i*j2*k2/n2) * 
                                exp(2*pi*i*j3*k3/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        <case2>
            X[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                x[j1][j2][j3] * 
                                exp(-2*pi*i*j1*k1/n1) * 
                                exp(-2*pi*i*j2*k2/n2) * 
                                exp(-2*pi*i*j3*k3/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            cdft3d(n1, n2, 2*n3, 1, a, t, ip, w);
        <case2>
            ip[0] = 0; // first time only
            cdft3d(n1, n2, 2*n3, -1, a, t, ip, w);
    [parameters]
        n1     :data length (int)
                n1 >= 1, n1 = power of 2
        n2     :data length (int)
                n2 >= 1, n2 = power of 2
        2*n3   :data length (int)
                n3 >= 1, n3 = power of 2
        a[0...n1-1][0...n2-1][0...2*n3-1]
               :input/output data (double ***)
                input data
                    a[j1][j2][2*j3] = Re(x[j1][j2][j3]), 
                    a[j1][j2][2*j3+1] = Im(x[j1][j2][j3]), 
                    0<=j1<n1, 0<=j2<n2, 0<=j3<n3
                output data
                    a[k1][k2][2*k3] = Re(X[k1][k2][k3]), 
                    a[k1][k2][2*k3+1] = Im(X[k1][k2][k3]), 
                    0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        t[0...*]
               :work area (double *)
                length of t >= max(8*n1, 8*n2),        if single thread, 
                length of t >= max(8*n1, 8*n2)*FFT3D_MAX_THREADS, 
                                                       if multi threads, 
                t is dynamically allocated, if t == NULL.
        ip[0...*]
               :work area for bit reversal (int *)
                length of ip >= 2+sqrt(n)
                (n = max(n1, n2, n3))
                ip[0],ip[1] are pointers of the cos/sin table.
        w[0...*]
               :cos/sin table (double *)
                length of w >= max(n1/2, n2/2, n3/2)
                w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            cdft3d(n1, n2, 2*n3, -1, a, t, ip, w);
        is 
            cdft3d(n1, n2, 2*n3, 1, a, t, ip, w);
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    for (j3 = 0; j3 <= 2 * n3 - 1; j3++) {
                        a[j1][j2][j3] *= 1.0 / n1 / n2 / n3;
                    }
                }
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                a[j1][j2][j3] * 
                                cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2 + 
                                    2*pi*j3*k3/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
            I[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                a[j1][j2][j3] * 
                                sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2 + 
                                    2*pi*j3*k3/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        <case2> IRDFT (excluding scale)
            a[k1][k2][k3] = (1/2) * sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                (R[j1][j2][j3] * 
                                cos(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2 + 
                                    2*pi*j3*k3/n3) + 
                                I[j1][j2][j3] * 
                                sin(2*pi*j1*k1/n1 + 2*pi*j2*k2/n2 + 
                                    2*pi*j3*k3/n3)), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        (notes: R[(n1-k1)%n1][(n2-k2)%n2][(n3-k3)%n3] = R[k1][k2][k3], 
                I[(n1-k1)%n1][(n2-k2)%n2][(n3-k3)%n3] = -I[k1][k2][k3], 
                0<=k1<n1, 0<=k2<n2, 0<=k3<n3)
    [usage]
        <case1>
            ip[0] = 0; // first time only
            rdft3d(n1, n2, n3, 1, a, t, ip, w);
        <case2>
            ip[0] = 0; // first time only
            rdft3d(n1, n2, n3, -1, a, t, ip, w);
    [parameters]
        n1     :data length (int)
                n1 >= 2, n1 = power of 2
        n2     :data length (int)
                n2 >= 2, n2 = power of 2
        n3     :data length (int)
                n3 >= 2, n3 = power of 2
        a[0...n1-1][0...n2-1][0...n3-1]
               :input/output data (double ***)
                <case1>
                    output data
                        a[k1][k2][2*k3] = R[k1][k2][k3]
                                        = R[(n1-k1)%n1][(n2-k2)%n2][n3-k3], 
                        a[k1][k2][2*k3+1] = I[k1][k2][k3]
                                          = -I[(n1-k1)%n1][(n2-k2)%n2][n3-k3], 
                            0<=k1<n1, 0<=k2<n2, 0<k3<n3/2, 
                            (n%m : n mod m), 
                        a[k1][k2][0] = R[k1][k2][0]
                                     = R[(n1-k1)%n1][n2-k2][0], 
                        a[k1][k2][1] = I[k1][k2][0]
                                     = -I[(n1-k1)%n1][n2-k2][0], 
                        a[k1][n2-k2][1] = R[(n1-k1)%n1][k2][n3/2]
                                        = R[k1][n2-k2][n3/2], 
                        a[k1][n2-k2][0] = -I[(n1-k1)%n1][k2][n3/2]
                                        = I[k1][n2-k2][n3/2], 
                            0<=k1<n1, 0<k2<n2/2, 
                        a[k1][0][0] = R[k1][0][0]
                                    = R[n1-k1][0][0], 
                        a[k1][0][1] = I[k1][0][0]
                                    = -I[n1-k1][0][0], 
                        a[k1][n2/2][0] = R[k1][n2/2][0]
                                       = R[n1-k1][n2/2][0], 
                        a[k1][n2/2][1] = I[k1][n2/2][0]
                                       = -I[n1-k1][n2/2][0], 
                        a[n1-k1][0][1] = R[k1][0][n3/2]
                                       = R[n1-k1][0][n3/2], 
                        a[n1-k1][0][0] = -I[k1][0][n3/2]
                                       = I[n1-k1][0][n3/2], 
                        a[n1-k1][n2/2][1] = R[k1][n2/2][n3/2]
                                          = R[n1-k1][n2/2][n3/2], 
                        a[n1-k1][n2/2][0] = -I[k1][n2/2][n3/2]
                                          = I[n1-k1][n2/2][n3/2], 
                            0<k1<n1/2, 
                        a[0][0][0] = R[0][0][0], 
                        a[0][0][1] = R[0][0][n3/2], 
                        a[0][n2/2][0] = R[0][n2/2][0], 
                        a[0][n2/2][1] = R[0][n2/2][n3/2], 
                        a[n1/2][0][0] = R[n1/2][0][0], 
                        a[n1/2][0][1] = R[n1/2][0][n3/2], 
                        a[n1/2][n2/2][0] = R[n1/2][n2/2][0], 
                        a[n1/2][n2/2][1] = R[n1/2][n2/2][n3/2]
                <case2>
                    input data
                        a[j1][j2][2*j3] = R[j1][j2][j3]
                                        = R[(n1-j1)%n1][(n2-j2)%n2][n3-j3], 
                        a[j1][j2][2*j3+1] = I[j1][j2][j3]
                                          = -I[(n1-j1)%n1][(n2-j2)%n2][n3-j3], 
                            0<=j1<n1, 0<=j2<n2, 0<j3<n3/2, 
                        a[j1][j2][0] = R[j1][j2][0]
                                     = R[(n1-j1)%n1][n2-j2][0], 
                        a[j1][j2][1] = I[j1][j2][0]
                                     = -I[(n1-j1)%n1][n2-j2][0], 
                        a[j1][n2-j2][1] = R[(n1-j1)%n1][j2][n3/2]
                                        = R[j1][n2-j2][n3/2], 
                        a[j1][n2-j2][0] = -I[(n1-j1)%n1][j2][n3/2]
                                        = I[j1][n2-j2][n3/2], 
                            0<=j1<n1, 0<j2<n2/2, 
                        a[j1][0][0] = R[j1][0][0]
                                    = R[n1-j1][0][0], 
                        a[j1][0][1] = I[j1][0][0]
                                    = -I[n1-j1][0][0], 
                        a[j1][n2/2][0] = R[j1][n2/2][0]
                                       = R[n1-j1][n2/2][0], 
                        a[j1][n2/2][1] = I[j1][n2/2][0]
                                       = -I[n1-j1][n2/2][0], 
                        a[n1-j1][0][1] = R[j1][0][n3/2]
                                       = R[n1-j1][0][n3/2], 
                        a[n1-j1][0][0] = -I[j1][0][n3/2]
                                       = I[n1-j1][0][n3/2], 
                        a[n1-j1][n2/2][1] = R[j1][n2/2][n3/2]
                                          = R[n1-j1][n2/2][n3/2], 
                        a[n1-j1][n2/2][0] = -I[j1][n2/2][n3/2]
                                          = I[n1-j1][n2/2][n3/2], 
                            0<j1<n1/2, 
                        a[0][0][0] = R[0][0][0], 
                        a[0][0][1] = R[0][0][n3/2], 
                        a[0][n2/2][0] = R[0][n2/2][0], 
                        a[0][n2/2][1] = R[0][n2/2][n3/2], 
                        a[n1/2][0][0] = R[n1/2][0][0], 
                        a[n1/2][0][1] = R[n1/2][0][n3/2], 
                        a[n1/2][n2/2][0] = R[n1/2][n2/2][0], 
                        a[n1/2][n2/2][1] = R[n1/2][n2/2][n3/2]
                ---- output ordering ----
                    rdft3d(n1, n2, n3, 1, a, t, ip, w);
                    rdft3dsort(n1, n2, n3, 1, a);
                    // stored data is a[0...n1-1][0...n2-1][0...n3+1]:
                    // a[k1][k2][2*k3] = R[k1][k2][k3], 
                    // a[k1][k2][2*k3+1] = I[k1][k2][k3], 
                    // 0<=k1<n1, 0<=k2<n2, 0<=k3<=n3/2.
                    // the stored data is larger than the input data!
                ---- input ordering ----
                    rdft3dsort(n1, n2, n3, -1, a);
                    rdft3d(n1, n2, n3, -1, a, t, ip, w);
        t[0...*]
               :work area (double *)
                length of t >= max(8*n1, 8*n2),        if single thread, 
                length of t >= max(8*n1, 8*n2)*FFT3D_MAX_THREADS, 
                                                       if multi threads, 
                t is dynamically allocated, if t == NULL.
        ip[0...*]
               :work area for bit reversal (int *)
                length of ip >= 2+sqrt(n)
                (n = max(n1, n2, n3/2))
                ip[0],ip[1] are pointers of the cos/sin table.
        w[0...*]
               :cos/sin table (double *)
                length of w >= max(n1/2, n2/2, n3/4) + n3/4
                w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            rdft3d(n1, n2, n3, 1, a, t, ip, w);
        is 
            rdft3d(n1, n2, n3, -1, a, t, ip, w);
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    for (j3 = 0; j3 <= n3 - 1; j3++) {
                        a[j1][j2][j3] *= 2.0 / n1 / n2 / n3;
                    }
                }
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                a[j1][j2][j3] * 
                                cos(pi*j1*(k1+1/2)/n1) * 
                                cos(pi*j2*(k2+1/2)/n2) * 
                                cos(pi*j3*(k3+1/2)/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        <case2> DCT
            C[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                a[j1][j2][j3] * 
                                cos(pi*(j1+1/2)*k1/n1) * 
                                cos(pi*(j2+1/2)*k2/n2) * 
                                cos(pi*(j3+1/2)*k3/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddct3d(n1, n2, n3, 1, a, t, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddct3d(n1, n2, n3, -1, a, t, ip, w);
    [parameters]
        n1     :data length (int)
                n1 >= 2, n1 = power of 2
        n2     :data length (int)
                n2 >= 2, n2 = power of 2
        n3     :data length (int)
                n3 >= 2, n3 = power of 2
        a[0...n1-1][0...n2-1][0...n3-1]
               :input/output data (double ***)
                output data
                    a[k1][k2][k3] = C[k1][k2][k3], 
                        0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        t[0...*]
               :work area (double *)
                length of t >= max(4*n1, 4*n2),        if single thread, 
                length of t >= max(4*n1, 4*n2)*FFT3D_MAX_THREADS, 
                                                       if multi threads, 
                t is dynamically allocated, if t == NULL.
        ip[0...*]
               :work area for bit reversal (int *)
                length of ip >= 2+sqrt(n)
                (n = max(n1/2, n2/2, n3/2))
                ip[0],ip[1] are pointers of the cos/sin table.
        w[0...*]
               :cos/sin table (double *)
                length of w >= max(n1*3/2, n2*3/2, n3*3/2)
                w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            ddct3d(n1, n2, n3, -1, a, t, ip, w);
        is 
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    a[j1][j2][0] *= 0.5;
                }
                for (j3 = 0; j3 <= n3 - 1; j3++) {
                    a[j1][0][j3] *= 0.5;
                }
            }
            for (j2 = 0; j2 <= n2 - 1; j2++) {
                for (j3 = 0; j3 <= n3 - 1; j3++) {
                    a[0][j2][j3] *= 0.5;
                }
            }
            ddct3d(n1, n2, n3, 1, a, t, ip, w);
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    for (j3 = 0; j3 <= n3 - 1; j3++) {
                        a[j1][j2][j3] *= 8.0 / n1 / n2 / n3;
                    }
                }
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k1][k2][k3] = sum_j1=1^n1 sum_j2=1^n2 sum_j3=1^n3
                                A[j1][j2][j3] * 
                                sin(pi*j1*(k1+1/2)/n1) * 
                                sin(pi*j2*(k2+1/2)/n2) * 
                                sin(pi*j3*(k3+1/2)/n3), 
                                0<=k1<n1, 0<=k2<n2, 0<=k3<n3
        <case2> DST
            S[k1][k2][k3] = sum_j1=0^n1-1 sum_j2=0^n2-1 sum_j3=0^n3-1
                                a[j1][j2][j3] * 
                                sin(pi*(j1+1/2)*k1/n1) * 
                                sin(pi*(j2+1/2)*k2/n2) * 
                                sin(pi*(j3+1/2)*k3/n3), 
                                0<k1<=n1, 0<k2<=n2, 0<k3<=n3
    [usage]
        <case1>
            ip[0] = 0; // first time only
            ddst3d(n1, n2, n3, 1, a, t, ip, w);
        <case2>
            ip[0] = 0; // first time only
            ddst3d(n1, n2, n3, -1, a, t, ip, w);
    [parameters]
        n1     :data length (int)
                n1 >= 2, n1 = power of 2
        n2     :data length (int)
                n2 >= 2, n2 = power of 2
        n3     :data length (int)
                n3 >= 2, n3 = power of 2
        a[0...n1-1][0...n2-1][0...n3-1]
               :input/output data (double ***)
                <case1>
                    input data
                        a[j1%n1][j2%n2][j3%n3] = A[j1][j2][j3], 
                            0<j1<=n1, 0<j2<=n2, 0<j3<=n3, 
                            (n%m : n mod m)
                    output data
                        a[k1][k2][k3] = S[k1][k2][k3], 
                            0<=k1<n1, 0<=k2<n2, 0<=k3<n3
                <case2>
                    output data
                        a[k1%n1][k2%n2][k3%n3] = S[k1][k2][k3], 
                            0<k1<=n1, 0<k2<=n2, 0<k3<=n3
        t[0...*]
               :work area (double *)
                length of t >= max(4*n1, 4*n2),        if single thread, 
                length of t >= max(4*n1, 4*n2)*FFT3D_MAX_THREADS, 
                                                       if multi threads, 
                t is dynamically allocated, if t == NULL.
        ip[0...*]
               :work area for bit reversal (int *)
                length of ip >= 2+sqrt(n)
                (n = max(n1/2, n2/2, n3/2))
                ip[0],ip[1] are pointers of the cos/sin table.
        w[0...*]
               :cos/sin table (double *)
                length of w >= max(n1*3/2, n2*3/2, n3*3/2)
                w[],ip[] are initialized if ip[0] == 0.
    [remark]
        Inverse of 
            ddst3d(n1, n2, n3, -1, a, t, ip, w);
        is 
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    a[j1][j2][0] *= 0.5;
                }
                for (j3 = 0; j3 <= n3 - 1; j3++) {
                    a[j1][0][j3] *= 0.5;
                }
            }
            for (j2 = 0; j2 <= n2 - 1; j2++) {
                for (j3 = 0; j3 <= n3 - 1; j3++) {
                    a[0][j2][j3] *= 0.5;
                }
            }
            ddst3d(n1, n2, n3, 1, a, t, ip, w);
            for (j1 = 0; j1 <= n1 - 1; j1++) {
                for (j2 = 0; j2 <= n2 - 1; j2++) {
                    for (j3 = 0; j3 <= n3 - 1; j3++) {
                        a[j1][j2][j3] *= 8.0 / n1 / n2 / n3;
                    }
                }
            }
        .
*/


#include <stdio.h>
#include <stdlib.h>
#define fft3d_alloc_error_check(p) { \
    if ((p) == NULL) { \
        fprintf(stderr, "fft3d memory allocation error\n"); \
        exit(1); \
    } \
}


#ifdef USE_FFT3D_PTHREADS
#define USE_FFT3D_THREADS
#ifndef FFT3D_MAX_THREADS
#define FFT3D_MAX_THREADS 4
#endif
#ifndef FFT3D_THREADS_BEGIN_N
#define FFT3D_THREADS_BEGIN_N 65536
#endif
#include <pthread.h>
#define fft3d_thread_t pthread_t
#define fft3d_thread_create(thp,func,argp) { \
    if (pthread_create(thp, NULL, func, (void *) (argp)) != 0) { \
        fprintf(stderr, "fft3d thread error\n"); \
        exit(1); \
    } \
}
#define fft3d_thread_wait(th) { \
    if (pthread_join(th, NULL) != 0) { \
        fprintf(stderr, "fft3d thread error\n"); \
        exit(1); \
    } \
}
#endif /* USE_FFT3D_PTHREADS */


#ifdef USE_FFT3D_WINTHREADS
#define USE_FFT3D_THREADS
#ifndef FFT3D_MAX_THREADS
#define FFT3D_MAX_THREADS 4
#endif
#ifndef FFT3D_THREADS_BEGIN_N
#define FFT3D_THREADS_BEGIN_N 131072
#endif
#include <windows.h>
#define fft3d_thread_t HANDLE
#define fft3d_thread_create(thp,func,argp) { \
    DWORD thid; \
    *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) (func), (LPVOID) (argp), 0, &thid); \
    if (*(thp) == 0) { \
        fprintf(stderr, "fft3d thread error\n"); \
        exit(1); \
    } \
}
#define fft3d_thread_wait(th) { \
    WaitForSingleObject(th, INFINITE); \
    CloseHandle(th); \
}
#endif /* USE_FFT3D_WINTHREADS */


void cdft3d(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void xdft3da_sub(int n1, int n2, int n3, int icr, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void cdft3db_sub(int n1, int n2, int n3, int isgn, double ***a, 
        double *t, int *ip, double *w);
#ifdef USE_FFT3D_THREADS
    void xdft3da_subth(int n1, int n2, int n3, int icr, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void cdft3db_subth(int n1, int n2, int n3, int isgn, double ***a, 
        double *t, int *ip, double *w);
#endif /* USE_FFT3D_THREADS */
    int n, itnull, nt;
    
    n = n1;
    if (n < n2) {
        n = n2;
    }
    n <<= 1;
    if (n < n3) {
        n = n3;
    }
    if (n > (ip[0] << 2)) {
        makewt(n >> 2, ip, w);
    }
    itnull = 0;
    if (t == NULL) {
        itnull = 1;
        nt = n1;
        if (nt < n2) {
            nt = n2;
        }
        nt *= 8;
#ifdef USE_FFT3D_THREADS
        nt *= FFT3D_MAX_THREADS;
#endif /* USE_FFT3D_THREADS */
        if (n3 == 4) {
            nt >>= 1;
        } else if (n3 < 4) {
            nt >>= 2;
        }
        t = (double *) malloc(sizeof(double) * nt);
        fft3d_alloc_error_check(t);
    }
#ifdef USE_FFT3D_THREADS
    if ((double) n1 * n2 * n3 >= (double) FFT3D_THREADS_BEGIN_N) {
        xdft3da_subth(n1, n2, n3, 0, isgn, a, t, ip, w);
        cdft3db_subth(n1, n2, n3, isgn, a, t, ip, w);
    } else 
#endif /* USE_FFT3D_THREADS */
    {
        xdft3da_sub(n1, n2, n3, 0, isgn, a, t, ip, w);
        cdft3db_sub(n1, n2, n3, isgn, a, t, ip, w);
    }
    if (itnull != 0) {
        free(t);
    }
}


void rdft3d(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void xdft3da_sub(int n1, int n2, int n3, int icr, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void cdft3db_sub(int n1, int n2, int n3, int isgn, double ***a, 
        double *t, int *ip, double *w);
    void rdft3d_sub(int n1, int n2, int n3, int isgn, double ***a);
#ifdef USE_FFT3D_THREADS
    void xdft3da_subth(int n1, int n2, int n3, int icr, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void cdft3db_subth(int n1, int n2, int n3, int isgn, double ***a, 
        double *t, int *ip, double *w);
#endif /* USE_FFT3D_THREADS */
    int n, nw, nc, itnull, nt;
    
    n = n1;
    if (n < n2) {
        n = n2;
    }
    n <<= 1;
    if (n < n3) {
        n = n3;
    }
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n3 > (nc << 2)) {
        nc = n3 >> 2;
        makect(nc, ip, w + nw);
    }
    itnull = 0;
    if (t == NULL) {
        itnull = 1;
        nt = n1;
        if (nt < n2) {
            nt = n2;
        }
        nt *= 8;
#ifdef USE_FFT3D_THREADS
        nt *= FFT3D_MAX_THREADS;
#endif /* USE_FFT3D_THREADS */
        if (n3 == 4) {
            nt >>= 1;
        } else if (n3 < 4) {
            nt >>= 2;
        }
        t = (double *) malloc(sizeof(double) * nt);
        fft3d_alloc_error_check(t);
    }
#ifdef USE_FFT3D_THREADS
    if ((double) n1 * n2 * n3 >= (double) FFT3D_THREADS_BEGIN_N) {
        if (isgn < 0) {
            rdft3d_sub(n1, n2, n3, isgn, a);
            cdft3db_subth(n1, n2, n3, isgn, a, t, ip, w);
        }
        xdft3da_subth(n1, n2, n3, 1, isgn, a, t, ip, w);
        if (isgn >= 0) {
            cdft3db_subth(n1, n2, n3, isgn, a, t, ip, w);
            rdft3d_sub(n1, n2, n3, isgn, a);
        }
    } else 
#endif /* USE_FFT3D_THREADS */
    {
        if (isgn < 0) {
            rdft3d_sub(n1, n2, n3, isgn, a);
            cdft3db_sub(n1, n2, n3, isgn, a, t, ip, w);
        }
        xdft3da_sub(n1, n2, n3, 1, isgn, a, t, ip, w);
        if (isgn >= 0) {
            cdft3db_sub(n1, n2, n3, isgn, a, t, ip, w);
            rdft3d_sub(n1, n2, n3, isgn, a);
        }
    }
    if (itnull != 0) {
        free(t);
    }
}


void rdft3dsort(int n1, int n2, int n3, int isgn, double ***a)
{
    int n1h, n2h, i, j;
    double x, y;
    
    n1h = n1 >> 1;
    n2h = n2 >> 1;
    if (isgn < 0) {
        for (i = 0; i < n1; i++) {
            for (j = n2h + 1; j < n2; j++) {
                a[i][j][0] = a[i][j][n3 + 1];
                a[i][j][1] = a[i][j][n3];
            }
        }
        for (i = n1h + 1; i < n1; i++) {
            a[i][0][0] = a[i][0][n3 + 1];
            a[i][0][1] = a[i][0][n3];
            a[i][n2h][0] = a[i][n2h][n3 + 1];
            a[i][n2h][1] = a[i][n2h][n3];
        }
        a[0][0][1] = a[0][0][n3];
        a[0][n2h][1] = a[0][n2h][n3];
        a[n1h][0][1] = a[n1h][0][n3];
        a[n1h][n2h][1] = a[n1h][n2h][n3];
    } else {
        for (j = n2h + 1; j < n2; j++) {
            y = a[0][j][0];
            x = a[0][j][1];
            a[0][j][n3] = x;
            a[0][j][n3 + 1] = y;
            a[0][n2 - j][n3] = x;
            a[0][n2 - j][n3 + 1] = -y;
            a[0][j][0] = a[0][n2 - j][0];
            a[0][j][1] = -a[0][n2 - j][1];
        }
        for (i = 1; i < n1; i++) {
            for (j = n2h + 1; j < n2; j++) {
                y = a[i][j][0];
                x = a[i][j][1];
                a[i][j][n3] = x;
                a[i][j][n3 + 1] = y;
                a[n1 - i][n2 - j][n3] = x;
                a[n1 - i][n2 - j][n3 + 1] = -y;
                a[i][j][0] = a[n1 - i][n2 - j][0];
                a[i][j][1] = -a[n1 - i][n2 - j][1];
            }
        }
        for (i = n1h + 1; i < n1; i++) {
            y = a[i][0][0];
            x = a[i][0][1];
            a[i][0][n3] = x;
            a[i][0][n3 + 1] = y;
            a[n1 - i][0][n3] = x;
            a[n1 - i][0][n3 + 1] = -y;
            a[i][0][0] = a[n1 - i][0][0];
            a[i][0][1] = -a[n1 - i][0][1];
            y = a[i][n2h][0];
            x = a[i][n2h][1];
            a[i][n2h][n3] = x;
            a[i][n2h][n3 + 1] = y;
            a[n1 - i][n2h][n3] = x;
            a[n1 - i][n2h][n3 + 1] = -y;
            a[i][n2h][0] = a[n1 - i][n2h][0];
            a[i][n2h][1] = -a[n1 - i][n2h][1];
        }
        a[0][0][n3] = a[0][0][1];
        a[0][0][n3 + 1] = 0;
        a[0][0][1] = 0;
        a[0][n2h][n3] = a[0][n2h][1];
        a[0][n2h][n3 + 1] = 0;
        a[0][n2h][1] = 0;
        a[n1h][0][n3] = a[n1h][0][1];
        a[n1h][0][n3 + 1] = 0;
        a[n1h][0][1] = 0;
        a[n1h][n2h][n3] = a[n1h][n2h][1];
        a[n1h][n2h][n3 + 1] = 0;
        a[n1h][n2h][1] = 0;
    }
}


void ddct3d(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void ddxt3da_sub(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void ddxt3db_sub(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
#ifdef USE_FFT3D_THREADS
    void ddxt3da_subth(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void ddxt3db_subth(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
#endif /* USE_FFT3D_THREADS */
    int n, nw, nc, itnull, nt;
    
    n = n1;
    if (n < n2) {
        n = n2;
    }
    if (n < n3) {
        n = n3;
    }
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
        nc = n;
        makect(nc, ip, w + nw);
    }
    itnull = 0;
    if (t == NULL) {
        itnull = 1;
        nt = n1;
        if (nt < n2) {
            nt = n2;
        }
        nt *= 4;
#ifdef USE_FFT3D_THREADS
        nt *= FFT3D_MAX_THREADS;
#endif /* USE_FFT3D_THREADS */
        if (n3 == 2) {
            nt >>= 1;
        }
        t = (double *) malloc(sizeof(double) * nt);
        fft3d_alloc_error_check(t);
    }
#ifdef USE_FFT3D_THREADS
    if ((double) n1 * n2 * n3 >= (double) FFT3D_THREADS_BEGIN_N) {
        ddxt3da_subth(n1, n2, n3, 0, isgn, a, t, ip, w);
        ddxt3db_subth(n1, n2, n3, 0, isgn, a, t, ip, w);
    } else 
#endif /* USE_FFT3D_THREADS */
    {
        ddxt3da_sub(n1, n2, n3, 0, isgn, a, t, ip, w);
        ddxt3db_sub(n1, n2, n3, 0, isgn, a, t, ip, w);
    }
    if (itnull != 0) {
        free(t);
    }
}


void ddst3d(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void makewt(int nw, int *ip, double *w);
    void makect(int nc, int *ip, double *c);
    void ddxt3da_sub(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void ddxt3db_sub(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
#ifdef USE_FFT3D_THREADS
    void ddxt3da_subth(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
    void ddxt3db_subth(int n1, int n2, int n3, int ics, int isgn, 
        double ***a, double *t, int *ip, double *w);
#endif /* USE_FFT3D_THREADS */
    int n, nw, nc, itnull, nt;
    
    n = n1;
    if (n < n2) {
        n = n2;
    }
    if (n < n3) {
        n = n3;
    }
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
        nc = n;
        makect(nc, ip, w + nw);
    }
    itnull = 0;
    if (t == NULL) {
        itnull = 1;
        nt = n1;
        if (nt < n2) {
            nt = n2;
        }
        nt *= 4;
#ifdef USE_FFT3D_THREADS
        nt *= FFT3D_MAX_THREADS;
#endif /* USE_FFT3D_THREADS */
        if (n3 == 2) {
            nt >>= 1;
        }
        t = (double *) malloc(sizeof(double) * nt);
        fft3d_alloc_error_check(t);
    }
#ifdef USE_FFT3D_THREADS
    if ((double) n1 * n2 * n3 >= (double) FFT3D_THREADS_BEGIN_N) {
        ddxt3da_subth(n1, n2, n3, 1, isgn, a, t, ip, w);
        ddxt3db_subth(n1, n2, n3, 1, isgn, a, t, ip, w);
    } else 
#endif /* USE_FFT3D_THREADS */
    {
        ddxt3da_sub(n1, n2, n3, 1, isgn, a, t, ip, w);
        ddxt3db_sub(n1, n2, n3, 1, isgn, a, t, ip, w);
    }
    if (itnull != 0) {
        free(t);
    }
}


/* -------- child routines -------- */


void xdft3da_sub(int n1, int n2, int n3, int icr, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void cdft(int n, int isgn, double *a, int *ip, double *w);
    void rdft(int n, int isgn, double *a, int *ip, double *w);
    int i, j, k;
    
    for (i = 0; i < n1; i++) {
        if (icr == 0) {
            for (j = 0; j < n2; j++) {
                cdft(n3, isgn, a[i][j], ip, w);
            }
        } else if (isgn >= 0) {
            for (j = 0; j < n2; j++) {
                rdft(n3, isgn, a[i][j], ip, w);
            }
        }
        if (n3 > 4) {
            for (k = 0; k < n3; k += 8) {
                for (j = 0; j < n2; j++) {
                    t[2 * j] = a[i][j][k];
                    t[2 * j + 1] = a[i][j][k + 1];
                    t[2 * n2 + 2 * j] = a[i][j][k + 2];
                    t[2 * n2 + 2 * j + 1] = a[i][j][k + 3];
                    t[4 * n2 + 2 * j] = a[i][j][k + 4];
                    t[4 * n2 + 2 * j + 1] = a[i][j][k + 5];
                    t[6 * n2 + 2 * j] = a[i][j][k + 6];
                    t[6 * n2 + 2 * j + 1] = a[i][j][k + 7];
                }
                cdft(2 * n2, isgn, t, ip, w);
                cdft(2 * n2, isgn, &t[2 * n2], ip, w);
                cdft(2 * n2, isgn, &t[4 * n2], ip, w);
                cdft(2 * n2, isgn, &t[6 * n2], ip, w);
                for (j = 0; j < n2; j++) {
                    a[i][j][k] = t[2 * j];
                    a[i][j][k + 1] = t[2 * j + 1];
                    a[i][j][k + 2] = t[2 * n2 + 2 * j];
                    a[i][j][k + 3] = t[2 * n2 + 2 * j + 1];
                    a[i][j][k + 4] = t[4 * n2 + 2 * j];
                    a[i][j][k + 5] = t[4 * n2 + 2 * j + 1];
                    a[i][j][k + 6] = t[6 * n2 + 2 * j];
                    a[i][j][k + 7] = t[6 * n2 + 2 * j + 1];
                }
            }
        } else if (n3 == 4) {
            for (j = 0; j < n2; j++) {
                t[2 * j] = a[i][j][0];
                t[2 * j + 1] = a[i][j][1];
                t[2 * n2 + 2 * j] = a[i][j][2];
                t[2 * n2 + 2 * j + 1] = a[i][j][3];
            }
            cdft(2 * n2, isgn, t, ip, w);
            cdft(2 * n2, isgn, &t[2 * n2], ip, w);
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[2 * j];
                a[i][j][1] = t[2 * j + 1];
                a[i][j][2] = t[2 * n2 + 2 * j];
                a[i][j][3] = t[2 * n2 + 2 * j + 1];
            }
        } else if (n3 == 2) {
            for (j = 0; j < n2; j++) {
                t[2 * j] = a[i][j][0];
                t[2 * j + 1] = a[i][j][1];
            }
            cdft(2 * n2, isgn, t, ip, w);
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[2 * j];
                a[i][j][1] = t[2 * j + 1];
            }
        }
        if (icr != 0 && isgn < 0) {
            for (j = 0; j < n2; j++) {
                rdft(n3, isgn, a[i][j], ip, w);
            }
        }
    }
}


void cdft3db_sub(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void cdft(int n, int isgn, double *a, int *ip, double *w);
    int i, j, k;
    
    if (n3 > 4) {
        for (j = 0; j < n2; j++) {
            for (k = 0; k < n3; k += 8) {
                for (i = 0; i < n1; i++) {
                    t[2 * i] = a[i][j][k];
                    t[2 * i + 1] = a[i][j][k + 1];
                    t[2 * n1 + 2 * i] = a[i][j][k + 2];
                    t[2 * n1 + 2 * i + 1] = a[i][j][k + 3];
                    t[4 * n1 + 2 * i] = a[i][j][k + 4];
                    t[4 * n1 + 2 * i + 1] = a[i][j][k + 5];
                    t[6 * n1 + 2 * i] = a[i][j][k + 6];
                    t[6 * n1 + 2 * i + 1] = a[i][j][k + 7];
                }
                cdft(2 * n1, isgn, t, ip, w);
                cdft(2 * n1, isgn, &t[2 * n1], ip, w);
                cdft(2 * n1, isgn, &t[4 * n1], ip, w);
                cdft(2 * n1, isgn, &t[6 * n1], ip, w);
                for (i = 0; i < n1; i++) {
                    a[i][j][k] = t[2 * i];
                    a[i][j][k + 1] = t[2 * i + 1];
                    a[i][j][k + 2] = t[2 * n1 + 2 * i];
                    a[i][j][k + 3] = t[2 * n1 + 2 * i + 1];
                    a[i][j][k + 4] = t[4 * n1 + 2 * i];
                    a[i][j][k + 5] = t[4 * n1 + 2 * i + 1];
                    a[i][j][k + 6] = t[6 * n1 + 2 * i];
                    a[i][j][k + 7] = t[6 * n1 + 2 * i + 1];
                }
            }
        }
    } else if (n3 == 4) {
        for (j = 0; j < n2; j++) {
            for (i = 0; i < n1; i++) {
                t[2 * i] = a[i][j][0];
                t[2 * i + 1] = a[i][j][1];
                t[2 * n1 + 2 * i] = a[i][j][2];
                t[2 * n1 + 2 * i + 1] = a[i][j][3];
            }
            cdft(2 * n1, isgn, t, ip, w);
            cdft(2 * n1, isgn, &t[2 * n1], ip, w);
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[2 * i];
                a[i][j][1] = t[2 * i + 1];
                a[i][j][2] = t[2 * n1 + 2 * i];
                a[i][j][3] = t[2 * n1 + 2 * i + 1];
            }
        }
    } else if (n3 == 2) {
        for (j = 0; j < n2; j++) {
            for (i = 0; i < n1; i++) {
                t[2 * i] = a[i][j][0];
                t[2 * i + 1] = a[i][j][1];
            }
            cdft(2 * n1, isgn, t, ip, w);
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[2 * i];
                a[i][j][1] = t[2 * i + 1];
            }
        }
    }
}


void rdft3d_sub(int n1, int n2, int n3, int isgn, double ***a)
{
    int n1h, n2h, i, j, k, l;
    double xi;
    
    n1h = n1 >> 1;
    n2h = n2 >> 1;
    if (isgn < 0) {
        for (i = 1; i < n1h; i++) {
            j = n1 - i;
            xi = a[i][0][0] - a[j][0][0];
            a[i][0][0] += a[j][0][0];
            a[j][0][0] = xi;
            xi = a[j][0][1] - a[i][0][1];
            a[i][0][1] += a[j][0][1];
            a[j][0][1] = xi;
            xi = a[i][n2h][0] - a[j][n2h][0];
            a[i][n2h][0] += a[j][n2h][0];
            a[j][n2h][0] = xi;
            xi = a[j][n2h][1] - a[i][n2h][1];
            a[i][n2h][1] += a[j][n2h][1];
            a[j][n2h][1] = xi;
            for (k = 1; k < n2h; k++) {
                l = n2 - k;
                xi = a[i][k][0] - a[j][l][0];
                a[i][k][0] += a[j][l][0];
                a[j][l][0] = xi;
                xi = a[j][l][1] - a[i][k][1];
                a[i][k][1] += a[j][l][1];
                a[j][l][1] = xi;
                xi = a[j][k][0] - a[i][l][0];
                a[j][k][0] += a[i][l][0];
                a[i][l][0] = xi;
                xi = a[i][l][1] - a[j][k][1];
                a[j][k][1] += a[i][l][1];
                a[i][l][1] = xi;
            }
        }
        for (k = 1; k < n2h; k++) {
            l = n2 - k;
            xi = a[0][k][0] - a[0][l][0];
            a[0][k][0] += a[0][l][0];
            a[0][l][0] = xi;
            xi = a[0][l][1] - a[0][k][1];
            a[0][k][1] += a[0][l][1];
            a[0][l][1] = xi;
            xi = a[n1h][k][0] - a[n1h][l][0];
            a[n1h][k][0] += a[n1h][l][0];
            a[n1h][l][0] = xi;
            xi = a[n1h][l][1] - a[n1h][k][1];
            a[n1h][k][1] += a[n1h][l][1];
            a[n1h][l][1] = xi;
        }
    } else {
        for (i = 1; i < n1h; i++) {
            j = n1 - i;
            a[j][0][0] = 0.5 * (a[i][0][0] - a[j][0][0]);
            a[i][0][0] -= a[j][0][0];
            a[j][0][1] = 0.5 * (a[i][0][1] + a[j][0][1]);
            a[i][0][1] -= a[j][0][1];
            a[j][n2h][0] = 0.5 * (a[i][n2h][0] - a[j][n2h][0]);
            a[i][n2h][0] -= a[j][n2h][0];
            a[j][n2h][1] = 0.5 * (a[i][n2h][1] + a[j][n2h][1]);
            a[i][n2h][1] -= a[j][n2h][1];
            for (k = 1; k < n2h; k++) {
                l = n2 - k;
                a[j][l][0] = 0.5 * (a[i][k][0] - a[j][l][0]);
                a[i][k][0] -= a[j][l][0];
                a[j][l][1] = 0.5 * (a[i][k][1] + a[j][l][1]);
                a[i][k][1] -= a[j][l][1];
                a[i][l][0] = 0.5 * (a[j][k][0] - a[i][l][0]);
                a[j][k][0] -= a[i][l][0];
                a[i][l][1] = 0.5 * (a[j][k][1] + a[i][l][1]);
                a[j][k][1] -= a[i][l][1];
            }
        }
        for (k = 1; k < n2h; k++) {
            l = n2 - k;
            a[0][l][0] = 0.5 * (a[0][k][0] - a[0][l][0]);
            a[0][k][0] -= a[0][l][0];
            a[0][l][1] = 0.5 * (a[0][k][1] + a[0][l][1]);
            a[0][k][1] -= a[0][l][1];
            a[n1h][l][0] = 0.5 * (a[n1h][k][0] - a[n1h][l][0]);
            a[n1h][k][0] -= a[n1h][l][0];
            a[n1h][l][1] = 0.5 * (a[n1h][k][1] + a[n1h][l][1]);
            a[n1h][k][1] -= a[n1h][l][1];
        }
    }
}


void ddxt3da_sub(int n1, int n2, int n3, int ics, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void ddct(int n, int isgn, double *a, int *ip, double *w);
    void ddst(int n, int isgn, double *a, int *ip, double *w);
    int i, j, k;
    
    for (i = 0; i < n1; i++) {
        if (ics == 0) {
            for (j = 0; j < n2; j++) {
                ddct(n3, isgn, a[i][j], ip, w);
            }
        } else {
            for (j = 0; j < n2; j++) {
                ddst(n3, isgn, a[i][j], ip, w);
            }
        }
        if (n3 > 2) {
            for (k = 0; k < n3; k += 4) {
                for (j = 0; j < n2; j++) {
                    t[j] = a[i][j][k];
                    t[n2 + j] = a[i][j][k + 1];
                    t[2 * n2 + j] = a[i][j][k + 2];
                    t[3 * n2 + j] = a[i][j][k + 3];
                }
                if (ics == 0) {
                    ddct(n2, isgn, t, ip, w);
                    ddct(n2, isgn, &t[n2], ip, w);
                    ddct(n2, isgn, &t[2 * n2], ip, w);
                    ddct(n2, isgn, &t[3 * n2], ip, w);
                } else {
                    ddst(n2, isgn, t, ip, w);
                    ddst(n2, isgn, &t[n2], ip, w);
                    ddst(n2, isgn, &t[2 * n2], ip, w);
                    ddst(n2, isgn, &t[3 * n2], ip, w);
                }
                for (j = 0; j < n2; j++) {
                    a[i][j][k] = t[j];
                    a[i][j][k + 1] = t[n2 + j];
                    a[i][j][k + 2] = t[2 * n2 + j];
                    a[i][j][k + 3] = t[3 * n2 + j];
                }
            }
        } else if (n3 == 2) {
            for (j = 0; j < n2; j++) {
                t[j] = a[i][j][0];
                t[n2 + j] = a[i][j][1];
            }
            if (ics == 0) {
                ddct(n2, isgn, t, ip, w);
                ddct(n2, isgn, &t[n2], ip, w);
            } else {
                ddst(n2, isgn, t, ip, w);
                ddst(n2, isgn, &t[n2], ip, w);
            }
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[j];
                a[i][j][1] = t[n2 + j];
            }
        }
    }
}


void ddxt3db_sub(int n1, int n2, int n3, int ics, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void ddct(int n, int isgn, double *a, int *ip, double *w);
    void ddst(int n, int isgn, double *a, int *ip, double *w);
    int i, j, k;
    
    if (n3 > 2) {
        for (j = 0; j < n2; j++) {
            for (k = 0; k < n3; k += 4) {
                for (i = 0; i < n1; i++) {
                    t[i] = a[i][j][k];
                    t[n1 + i] = a[i][j][k + 1];
                    t[2 * n1 + i] = a[i][j][k + 2];
                    t[3 * n1 + i] = a[i][j][k + 3];
                }
                if (ics == 0) {
                    ddct(n1, isgn, t, ip, w);
                    ddct(n1, isgn, &t[n1], ip, w);
                    ddct(n1, isgn, &t[2 * n1], ip, w);
                    ddct(n1, isgn, &t[3 * n1], ip, w);
                } else {
                    ddst(n1, isgn, t, ip, w);
                    ddst(n1, isgn, &t[n1], ip, w);
                    ddst(n1, isgn, &t[2 * n1], ip, w);
                    ddst(n1, isgn, &t[3 * n1], ip, w);
                }
                for (i = 0; i < n1; i++) {
                    a[i][j][k] = t[i];
                    a[i][j][k + 1] = t[n1 + i];
                    a[i][j][k + 2] = t[2 * n1 + i];
                    a[i][j][k + 3] = t[3 * n1 + i];
                }
            }
        }
    } else if (n3 == 2) {
        for (j = 0; j < n2; j++) {
            for (i = 0; i < n1; i++) {
                t[i] = a[i][j][0];
                t[n1 + i] = a[i][j][1];
            }
            if (ics == 0) {
                ddct(n1, isgn, t, ip, w);
                ddct(n1, isgn, &t[n1], ip, w);
            } else {
                ddst(n1, isgn, t, ip, w);
                ddst(n1, isgn, &t[n1], ip, w);
            }
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[i];
                a[i][j][1] = t[n1 + i];
            }
        }
    }
}


#ifdef USE_FFT3D_THREADS
struct fft3d_arg_st {
    int nthread;
    int n0;
    int n1;
    int n2;
    int n3;
    int ic;
    int isgn;
    double ***a;
    double *t;
    int *ip;
    double *w;
};
typedef struct fft3d_arg_st fft3d_arg_t;


void xdft3da_subth(int n1, int n2, int n3, int icr, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void *xdft3da_th(void *p);
    fft3d_thread_t th[FFT3D_MAX_THREADS];
    fft3d_arg_t ag[FFT3D_MAX_THREADS];
    int nthread, nt, i;
    
    nthread = FFT3D_MAX_THREADS;
    if (nthread > n1) {
        nthread = n1;
    }
    nt = 8 * n2;
    if (n3 == 4) {
        nt >>= 1;
    } else if (n3 < 4) {
        nt >>= 2;
    }
    for (i = 0; i < nthread; i++) {
        ag[i].nthread = nthread;
        ag[i].n0 = i;
        ag[i].n1 = n1;
        ag[i].n2 = n2;
        ag[i].n3 = n3;
        ag[i].ic = icr;
        ag[i].isgn = isgn;
        ag[i].a = a;
        ag[i].t = &t[nt * i];
        ag[i].ip = ip;
        ag[i].w = w;
        fft3d_thread_create(&th[i], xdft3da_th, &ag[i]);
    }
    for (i = 0; i < nthread; i++) {
        fft3d_thread_wait(th[i]);
    }
}


void cdft3db_subth(int n1, int n2, int n3, int isgn, double ***a, 
    double *t, int *ip, double *w)
{
    void *cdft3db_th(void *p);
    fft3d_thread_t th[FFT3D_MAX_THREADS];
    fft3d_arg_t ag[FFT3D_MAX_THREADS];
    int nthread, nt, i;
    
    nthread = FFT3D_MAX_THREADS;
    if (nthread > n2) {
        nthread = n2;
    }
    nt = 8 * n1;
    if (n3 == 4) {
        nt >>= 1;
    } else if (n3 < 4) {
        nt >>= 2;
    }
    for (i = 0; i < nthread; i++) {
        ag[i].nthread = nthread;
        ag[i].n0 = i;
        ag[i].n1 = n1;
        ag[i].n2 = n2;
        ag[i].n3 = n3;
        ag[i].isgn = isgn;
        ag[i].a = a;
        ag[i].t = &t[nt * i];
        ag[i].ip = ip;
        ag[i].w = w;
        fft3d_thread_create(&th[i], cdft3db_th, &ag[i]);
    }
    for (i = 0; i < nthread; i++) {
        fft3d_thread_wait(th[i]);
    }
}


void ddxt3da_subth(int n1, int n2, int n3, int ics, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void *ddxt3da_th(void *p);
    fft3d_thread_t th[FFT3D_MAX_THREADS];
    fft3d_arg_t ag[FFT3D_MAX_THREADS];
    int nthread, nt, i;
    
    nthread = FFT3D_MAX_THREADS;
    if (nthread > n1) {
        nthread = n1;
    }
    nt = 4 * n2;
    if (n3 == 2) {
        nt >>= 1;
    }
    for (i = 0; i < nthread; i++) {
        ag[i].nthread = nthread;
        ag[i].n0 = i;
        ag[i].n1 = n1;
        ag[i].n2 = n2;
        ag[i].n3 = n3;
        ag[i].ic = ics;
        ag[i].isgn = isgn;
        ag[i].a = a;
        ag[i].t = &t[nt * i];
        ag[i].ip = ip;
        ag[i].w = w;
        fft3d_thread_create(&th[i], ddxt3da_th, &ag[i]);
    }
    for (i = 0; i < nthread; i++) {
        fft3d_thread_wait(th[i]);
    }
}


void ddxt3db_subth(int n1, int n2, int n3, int ics, int isgn, 
    double ***a, double *t, int *ip, double *w)
{
    void *ddxt3db_th(void *p);
    fft3d_thread_t th[FFT3D_MAX_THREADS];
    fft3d_arg_t ag[FFT3D_MAX_THREADS];
    int nthread, nt, i;
    
    nthread = FFT3D_MAX_THREADS;
    if (nthread > n2) {
        nthread = n2;
    }
    nt = 4 * n1;
    if (n3 == 2) {
        nt >>= 1;
    }
    for (i = 0; i < nthread; i++) {
        ag[i].nthread = nthread;
        ag[i].n0 = i;
        ag[i].n1 = n1;
        ag[i].n2 = n2;
        ag[i].n3 = n3;
        ag[i].ic = ics;
        ag[i].isgn = isgn;
        ag[i].a = a;
        ag[i].t = &t[nt * i];
        ag[i].ip = ip;
        ag[i].w = w;
        fft3d_thread_create(&th[i], ddxt3db_th, &ag[i]);
    }
    for (i = 0; i < nthread; i++) {
        fft3d_thread_wait(th[i]);
    }
}


void *xdft3da_th(void *p)
{
    void cdft(int n, int isgn, double *a, int *ip, double *w);
    void rdft(int n, int isgn, double *a, int *ip, double *w);
    int nthread, n0, n1, n2, n3, icr, isgn, *ip, i, j, k;
    double ***a, *t, *w;
    
    nthread = ((fft3d_arg_t *) p)->nthread;
    n0 = ((fft3d_arg_t *) p)->n0;
    n1 = ((fft3d_arg_t *) p)->n1;
    n2 = ((fft3d_arg_t *) p)->n2;
    n3 = ((fft3d_arg_t *) p)->n3;
    icr = ((fft3d_arg_t *) p)->ic;
    isgn = ((fft3d_arg_t *) p)->isgn;
    a = ((fft3d_arg_t *) p)->a;
    t = ((fft3d_arg_t *) p)->t;
    ip = ((fft3d_arg_t *) p)->ip;
    w = ((fft3d_arg_t *) p)->w;
    for (i = n0; i < n1; i += nthread) {
        if (icr == 0) {
            for (j = 0; j < n2; j++) {
                cdft(n3, isgn, a[i][j], ip, w);
            }
        } else if (isgn >= 0) {
            for (j = 0; j < n2; j++) {
                rdft(n3, isgn, a[i][j], ip, w);
            }
        }
        if (n3 > 4) {
            for (k = 0; k < n3; k += 8) {
                for (j = 0; j < n2; j++) {
                    t[2 * j] = a[i][j][k];
                    t[2 * j + 1] = a[i][j][k + 1];
                    t[2 * n2 + 2 * j] = a[i][j][k + 2];
                    t[2 * n2 + 2 * j + 1] = a[i][j][k + 3];
                    t[4 * n2 + 2 * j] = a[i][j][k + 4];
                    t[4 * n2 + 2 * j + 1] = a[i][j][k + 5];
                    t[6 * n2 + 2 * j] = a[i][j][k + 6];
                    t[6 * n2 + 2 * j + 1] = a[i][j][k + 7];
                }
                cdft(2 * n2, isgn, t, ip, w);
                cdft(2 * n2, isgn, &t[2 * n2], ip, w);
                cdft(2 * n2, isgn, &t[4 * n2], ip, w);
                cdft(2 * n2, isgn, &t[6 * n2], ip, w);
                for (j = 0; j < n2; j++) {
                    a[i][j][k] = t[2 * j];
                    a[i][j][k + 1] = t[2 * j + 1];
                    a[i][j][k + 2] = t[2 * n2 + 2 * j];
                    a[i][j][k + 3] = t[2 * n2 + 2 * j + 1];
                    a[i][j][k + 4] = t[4 * n2 + 2 * j];
                    a[i][j][k + 5] = t[4 * n2 + 2 * j + 1];
                    a[i][j][k + 6] = t[6 * n2 + 2 * j];
                    a[i][j][k + 7] = t[6 * n2 + 2 * j + 1];
                }
            }
        } else if (n3 == 4) {
            for (j = 0; j < n2; j++) {
                t[2 * j] = a[i][j][0];
                t[2 * j + 1] = a[i][j][1];
                t[2 * n2 + 2 * j] = a[i][j][2];
                t[2 * n2 + 2 * j + 1] = a[i][j][3];
            }
            cdft(2 * n2, isgn, t, ip, w);
            cdft(2 * n2, isgn, &t[2 * n2], ip, w);
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[2 * j];
                a[i][j][1] = t[2 * j + 1];
                a[i][j][2] = t[2 * n2 + 2 * j];
                a[i][j][3] = t[2 * n2 + 2 * j + 1];
            }
        } else if (n3 == 2) {
            for (j = 0; j < n2; j++) {
                t[2 * j] = a[i][j][0];
                t[2 * j + 1] = a[i][j][1];
            }
            cdft(2 * n2, isgn, t, ip, w);
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[2 * j];
                a[i][j][1] = t[2 * j + 1];
            }
        }
        if (icr != 0 && isgn < 0) {
            for (j = 0; j < n2; j++) {
                rdft(n3, isgn, a[i][j], ip, w);
            }
        }
    }
    return (void *) 0;
}


void *cdft3db_th(void *p)
{
    void cdft(int n, int isgn, double *a, int *ip, double *w);
    int nthread, n0, n1, n2, n3, isgn, *ip, i, j, k;
    double ***a, *t, *w;
    
    nthread = ((fft3d_arg_t *) p)->nthread;
    n0 = ((fft3d_arg_t *) p)->n0;
    n1 = ((fft3d_arg_t *) p)->n1;
    n2 = ((fft3d_arg_t *) p)->n2;
    n3 = ((fft3d_arg_t *) p)->n3;
    isgn = ((fft3d_arg_t *) p)->isgn;
    a = ((fft3d_arg_t *) p)->a;
    t = ((fft3d_arg_t *) p)->t;
    ip = ((fft3d_arg_t *) p)->ip;
    w = ((fft3d_arg_t *) p)->w;
    if (n3 > 4) {
        for (j = n0; j < n2; j += nthread) {
            for (k = 0; k < n3; k += 8) {
                for (i = 0; i < n1; i++) {
                    t[2 * i] = a[i][j][k];
                    t[2 * i + 1] = a[i][j][k + 1];
                    t[2 * n1 + 2 * i] = a[i][j][k + 2];
                    t[2 * n1 + 2 * i + 1] = a[i][j][k + 3];
                    t[4 * n1 + 2 * i] = a[i][j][k + 4];
                    t[4 * n1 + 2 * i + 1] = a[i][j][k + 5];
                    t[6 * n1 + 2 * i] = a[i][j][k + 6];
                    t[6 * n1 + 2 * i + 1] = a[i][j][k + 7];
                }
                cdft(2 * n1, isgn, t, ip, w);
                cdft(2 * n1, isgn, &t[2 * n1], ip, w);
                cdft(2 * n1, isgn, &t[4 * n1], ip, w);
                cdft(2 * n1, isgn, &t[6 * n1], ip, w);
                for (i = 0; i < n1; i++) {
                    a[i][j][k] = t[2 * i];
                    a[i][j][k + 1] = t[2 * i + 1];
                    a[i][j][k + 2] = t[2 * n1 + 2 * i];
                    a[i][j][k + 3] = t[2 * n1 + 2 * i + 1];
                    a[i][j][k + 4] = t[4 * n1 + 2 * i];
                    a[i][j][k + 5] = t[4 * n1 + 2 * i + 1];
                    a[i][j][k + 6] = t[6 * n1 + 2 * i];
                    a[i][j][k + 7] = t[6 * n1 + 2 * i + 1];
                }
            }
        }
    } else if (n3 == 4) {
        for (j = n0; j < n2; j += nthread) {
            for (i = 0; i < n1; i++) {
                t[2 * i] = a[i][j][0];
                t[2 * i + 1] = a[i][j][1];
                t[2 * n1 + 2 * i] = a[i][j][2];
                t[2 * n1 + 2 * i + 1] = a[i][j][3];
            }
            cdft(2 * n1, isgn, t, ip, w);
            cdft(2 * n1, isgn, &t[2 * n1], ip, w);
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[2 * i];
                a[i][j][1] = t[2 * i + 1];
                a[i][j][2] = t[2 * n1 + 2 * i];
                a[i][j][3] = t[2 * n1 + 2 * i + 1];
            }
        }
    } else if (n3 == 2) {
        for (j = n0; j < n2; j += nthread) {
            for (i = 0; i < n1; i++) {
                t[2 * i] = a[i][j][0];
                t[2 * i + 1] = a[i][j][1];
            }
            cdft(2 * n1, isgn, t, ip, w);
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[2 * i];
                a[i][j][1] = t[2 * i + 1];
            }
        }
    }
    return (void *) 0;
}


void *ddxt3da_th(void *p)
{
    void ddct(int n, int isgn, double *a, int *ip, double *w);
    void ddst(int n, int isgn, double *a, int *ip, double *w);
    int nthread, n0, n1, n2, n3, ics, isgn, *ip, i, j, k;
    double ***a, *t, *w;
    
    nthread = ((fft3d_arg_t *) p)->nthread;
    n0 = ((fft3d_arg_t *) p)->n0;
    n1 = ((fft3d_arg_t *) p)->n1;
    n2 = ((fft3d_arg_t *) p)->n2;
    n3 = ((fft3d_arg_t *) p)->n3;
    ics = ((fft3d_arg_t *) p)->ic;
    isgn = ((fft3d_arg_t *) p)->isgn;
    a = ((fft3d_arg_t *) p)->a;
    t = ((fft3d_arg_t *) p)->t;
    ip = ((fft3d_arg_t *) p)->ip;
    w = ((fft3d_arg_t *) p)->w;
    for (i = n0; i < n1; i += nthread) {
        if (ics == 0) {
            for (j = 0; j < n2; j++) {
                ddct(n3, isgn, a[i][j], ip, w);
            }
        } else {
            for (j = 0; j < n2; j++) {
                ddst(n3, isgn, a[i][j], ip, w);
            }
        }
        if (n3 > 2) {
            for (k = 0; k < n3; k += 4) {
                for (j = 0; j < n2; j++) {
                    t[j] = a[i][j][k];
                    t[n2 + j] = a[i][j][k + 1];
                    t[2 * n2 + j] = a[i][j][k + 2];
                    t[3 * n2 + j] = a[i][j][k + 3];
                }
                if (ics == 0) {
                    ddct(n2, isgn, t, ip, w);
                    ddct(n2, isgn, &t[n2], ip, w);
                    ddct(n2, isgn, &t[2 * n2], ip, w);
                    ddct(n2, isgn, &t[3 * n2], ip, w);
                } else {
                    ddst(n2, isgn, t, ip, w);
                    ddst(n2, isgn, &t[n2], ip, w);
                    ddst(n2, isgn, &t[2 * n2], ip, w);
                    ddst(n2, isgn, &t[3 * n2], ip, w);
                }
                for (j = 0; j < n2; j++) {
                    a[i][j][k] = t[j];
                    a[i][j][k + 1] = t[n2 + j];
                    a[i][j][k + 2] = t[2 * n2 + j];
                    a[i][j][k + 3] = t[3 * n2 + j];
                }
            }
        } else if (n3 == 2) {
            for (j = 0; j < n2; j++) {
                t[j] = a[i][j][0];
                t[n2 + j] = a[i][j][1];
            }
            if (ics == 0) {
                ddct(n2, isgn, t, ip, w);
                ddct(n2, isgn, &t[n2], ip, w);
            } else {
                ddst(n2, isgn, t, ip, w);
                ddst(n2, isgn, &t[n2], ip, w);
            }
            for (j = 0; j < n2; j++) {
                a[i][j][0] = t[j];
                a[i][j][1] = t[n2 + j];
            }
        }
    }
    return (void *) 0;
}


void *ddxt3db_th(void *p)
{
    void ddct(int n, int isgn, double *a, int *ip, double *w);
    void ddst(int n, int isgn, double *a, int *ip, double *w);
    int nthread, n0, n1, n2, n3, ics, isgn, *ip, i, j, k;
    double ***a, *t, *w;
    
    nthread = ((fft3d_arg_t *) p)->nthread;
    n0 = ((fft3d_arg_t *) p)->n0;
    n1 = ((fft3d_arg_t *) p)->n1;
    n2 = ((fft3d_arg_t *) p)->n2;
    n3 = ((fft3d_arg_t *) p)->n3;
    ics = ((fft3d_arg_t *) p)->ic;
    isgn = ((fft3d_arg_t *) p)->isgn;
    a = ((fft3d_arg_t *) p)->a;
    t = ((fft3d_arg_t *) p)->t;
    ip = ((fft3d_arg_t *) p)->ip;
    w = ((fft3d_arg_t *) p)->w;
    if (n3 > 2) {
        for (j = n0; j < n2; j += nthread) {
            for (k = 0; k < n3; k += 4) {
                for (i = 0; i < n1; i++) {
                    t[i] = a[i][j][k];
                    t[n1 + i] = a[i][j][k + 1];
                    t[2 * n1 + i] = a[i][j][k + 2];
                    t[3 * n1 + i] = a[i][j][k + 3];
                }
                if (ics == 0) {
                    ddct(n1, isgn, t, ip, w);
                    ddct(n1, isgn, &t[n1], ip, w);
                    ddct(n1, isgn, &t[2 * n1], ip, w);
                    ddct(n1, isgn, &t[3 * n1], ip, w);
                } else {
                    ddst(n1, isgn, t, ip, w);
                    ddst(n1, isgn, &t[n1], ip, w);
                    ddst(n1, isgn, &t[2 * n1], ip, w);
                    ddst(n1, isgn, &t[3 * n1], ip, w);
                }
                for (i = 0; i < n1; i++) {
                    a[i][j][k] = t[i];
                    a[i][j][k + 1] = t[n1 + i];
                    a[i][j][k + 2] = t[2 * n1 + i];
                    a[i][j][k + 3] = t[3 * n1 + i];
                }
            }
        }
    } else if (n3 == 2) {
        for (j = n0; j < n2; j += nthread) {
            for (i = 0; i < n1; i++) {
                t[i] = a[i][j][0];
                t[n1 + i] = a[i][j][1];
            }
            if (ics == 0) {
                ddct(n1, isgn, t, ip, w);
                ddct(n1, isgn, &t[n1], ip, w);
            } else {
                ddst(n1, isgn, t, ip, w);
                ddst(n1, isgn, &t[n1], ip, w);
            }
            for (i = 0; i < n1; i++) {
                a[i][j][0] = t[i];
                a[i][j][1] = t[n1 + i];
            }
        }
    }
    return (void *) 0;
}
#endif /* USE_FFT3D_THREADS */