d_fftsg_h.c

/*
Fast Fourier/Cosine/Sine Transform
    dimension   :one
    data length :power of 2
    decimation  :frequency
    radix       :split-radix
    data        :inplace
    table       :not use
functions
    cdft: Complex Discrete Fourier Transform
    rdft: Real Discrete Fourier Transform
    ddct: Discrete Cosine Transform
    ddst: Discrete Sine Transform
    dfct: Cosine Transform of RDFT (Real Symmetric DFT)
    dfst: Sine Transform of RDFT (Real Anti-symmetric DFT)
function prototypes
    void cdft(int, int, double *);
    void rdft(int, int, double *);
    void ddct(int, int, double *);
    void ddst(int, int, double *);
    void dfct(int, double *);
    void dfst(int, double *);
macro definitions
    USE_CDFT_PTHREADS : default=not defined
        CDFT_THREADS_BEGIN_N  : must be >= 512, default=8192
        CDFT_4THREADS_BEGIN_N : must be >= 512, default=65536
    USE_CDFT_WINTHREADS : default=not defined
        CDFT_THREADS_BEGIN_N  : must be >= 512, default=32768
        CDFT_4THREADS_BEGIN_N : must be >= 512, default=524288


-------- Complex DFT (Discrete Fourier Transform) --------
    [definition]
        <case1>
            X[k] = sum_j=0^n-1 x[j]*exp(2*pi*i*j*k/n), 0<=k<n
        <case2>
            X[k] = sum_j=0^n-1 x[j]*exp(-2*pi*i*j*k/n), 0<=k<n
        (notes: sum_j=0^n-1 is a summation from j=0 to n-1)
    [usage]
        <case1>
            cdft(2*n, 1, a);
        <case2>
            cdft(2*n, -1, a);
    [parameters]
        2*n            :data length (int)
                        n >= 1, n = power of 2
        a[0...2*n-1]   :input/output data (double *)
                        input data
                            a[2*j] = Re(x[j]), 
                            a[2*j+1] = Im(x[j]), 0<=j<n
                        output data
                            a[2*k] = Re(X[k]), 
                            a[2*k+1] = Im(X[k]), 0<=k<n
    [remark]
        Inverse of 
            cdft(2*n, -1, a);
        is 
            cdft(2*n, 1, a);
            for (j = 0; j <= 2 * n - 1; j++) {
                a[j] *= 1.0 / n;
            }
        .


-------- Real DFT / Inverse of Real DFT --------
    [definition]
        <case1> RDFT
            R[k] = sum_j=0^n-1 a[j]*cos(2*pi*j*k/n), 0<=k<=n/2
            I[k] = sum_j=0^n-1 a[j]*sin(2*pi*j*k/n), 0<k<n/2
        <case2> IRDFT (excluding scale)
            a[k] = (R[0] + R[n/2]*cos(pi*k))/2 + 
                   sum_j=1^n/2-1 R[j]*cos(2*pi*j*k/n) + 
                   sum_j=1^n/2-1 I[j]*sin(2*pi*j*k/n), 0<=k<n
    [usage]
        <case1>
            rdft(n, 1, a);
        <case2>
            rdft(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            output data
                                a[2*k] = R[k], 0<=k<n/2
                                a[2*k+1] = I[k], 0<k<n/2
                                a[1] = R[n/2]
                        <case2>
                            input data
                                a[2*j] = R[j], 0<=j<n/2
                                a[2*j+1] = I[j], 0<j<n/2
                                a[1] = R[n/2]
    [remark]
        Inverse of 
            rdft(n, 1, a);
        is 
            rdft(n, -1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DCT (Discrete Cosine Transform) / Inverse of DCT --------
    [definition]
        <case1> IDCT (excluding scale)
            C[k] = sum_j=0^n-1 a[j]*cos(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DCT
            C[k] = sum_j=0^n-1 a[j]*cos(pi*(j+1/2)*k/n), 0<=k<n
    [usage]
        <case1>
            ddct(n, 1, a);
        <case2>
            ddct(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<n
    [remark]
        Inverse of 
            ddct(n, -1, a);
        is 
            a[0] *= 0.5;
            ddct(n, 1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- DST (Discrete Sine Transform) / Inverse of DST --------
    [definition]
        <case1> IDST (excluding scale)
            S[k] = sum_j=1^n A[j]*sin(pi*j*(k+1/2)/n), 0<=k<n
        <case2> DST
            S[k] = sum_j=0^n-1 a[j]*sin(pi*(j+1/2)*k/n), 0<k<=n
    [usage]
        <case1>
            ddst(n, 1, a);
        <case2>
            ddst(n, -1, a);
    [parameters]
        n              :data length (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        <case1>
                            input data
                                a[j] = A[j], 0<j<n
                                a[0] = A[n]
                            output data
                                a[k] = S[k], 0<=k<n
                        <case2>
                            output data
                                a[k] = S[k], 0<k<n
                                a[0] = S[n]
    [remark]
        Inverse of 
            ddst(n, -1, a);
        is 
            a[0] *= 0.5;
            ddst(n, 1, a);
            for (j = 0; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Cosine Transform of RDFT (Real Symmetric DFT) --------
    [definition]
        C[k] = sum_j=0^n a[j]*cos(pi*j*k/n), 0<=k<=n
    [usage]
        dfct(n, a);
    [parameters]
        n              :data length - 1 (int)
                        n >= 2, n = power of 2
        a[0...n]       :input/output data (double *)
                        output data
                            a[k] = C[k], 0<=k<=n
    [remark]
        Inverse of 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a);
        is 
            a[0] *= 0.5;
            a[n] *= 0.5;
            dfct(n, a);
            for (j = 0; j <= n; j++) {
                a[j] *= 2.0 / n;
            }
        .


-------- Sine Transform of RDFT (Real Anti-symmetric DFT) --------
    [definition]
        S[k] = sum_j=1^n-1 a[j]*sin(pi*j*k/n), 0<k<n
    [usage]
        dfst(n, a);
    [parameters]
        n              :data length + 1 (int)
                        n >= 2, n = power of 2
        a[0...n-1]     :input/output data (double *)
                        output data
                            a[k] = S[k], 0<k<n
                        (a[0] is used for work area)
    [remark]
        Inverse of 
            dfst(n, a);
        is 
            dfst(n, a);
            for (j = 1; j <= n - 1; j++) {
                a[j] *= 2.0 / n;
            }
        .
*/


void cdft(int n, int isgn, double *a)
{
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    
    if (isgn >= 0) {
        cftfsub(n, a);
    } else {
        cftbsub(n, a);
    }
}


void rdft(int n, int isgn, double *a)
{
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    double xi;
    
    if (isgn >= 0) {
        if (n > 4) {
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xi = a[0] - a[1];
        a[0] += a[1];
        a[1] = xi;
    } else {
        a[1] = 0.5 * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4) {
            rftbsub(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftbsub(n, a);
        }
    }
}


void ddct(int n, int isgn, double *a)
{
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    void dctsub(int n, double *a);
    void dctsub4(int n, double *a);
    int j;
    double xr;
    
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = a[j] - a[j - 1];
            a[j] += a[j - 1];
        }
        a[1] = a[0] - xr;
        a[0] += xr;
        if (n > 4) {
            rftbsub(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftbsub(n, a);
        }
    }
    if (n > 4) {
        dctsub(n, a);
    } else {
        dctsub4(n, a);
    }
    if (isgn >= 0) {
        if (n > 4) {
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = a[j] - a[j + 1];
            a[j] += a[j + 1];
        }
        a[n - 1] = xr;
    }
}


void ddst(int n, int isgn, double *a)
{
    void cftfsub(int n, double *a);
    void cftbsub(int n, double *a);
    void rftfsub(int n, double *a);
    void rftbsub(int n, double *a);
    void dstsub(int n, double *a);
    void dstsub4(int n, double *a);
    int j;
    double xr;
    
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = -a[j] - a[j - 1];
            a[j] -= a[j - 1];
        }
        a[1] = a[0] + xr;
        a[0] -= xr;
        if (n > 4) {
            rftbsub(n, a);
            cftbsub(n, a);
        } else if (n == 4) {
            cftbsub(n, a);
        }
    }
    if (n > 4) {
        dstsub(n, a);
    } else {
        dstsub4(n, a);
    }
    if (isgn >= 0) {
        if (n > 4) {
            cftfsub(n, a);
            rftfsub(n, a);
        } else if (n == 4) {
            cftfsub(n, a);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = -a[j] - a[j + 1];
            a[j] -= a[j + 1];
        }
        a[n - 1] = -xr;
    }
}


void dfct(int n, double *a)
{
    void ddct(int n, int isgn, double *a);
    void bitrv1(int n, double *a);
    int j, k, m, mh;
    double xr, xi, yr, yi, an;
    
    m = n >> 1;
    for (j = 0; j < m; j++) {
        k = n - j;
        xr = a[j] + a[k];
        a[j] -= a[k];
        a[k] = xr;
    }
    an = a[n];
    while (m >= 2) {
        ddct(m, 1, a);
        if (m > 2) {
            bitrv1(m, a);
        }
        mh = m >> 1;
        xi = a[m];
        a[m] = a[0];
        a[0] = an - xi;
        an += xi;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[m + k];
            xi = a[m + j];
            yr = a[j];
            yi = a[k];
            a[m + j] = yr;
            a[m + k] = yi;
            a[j] = xr - xi;
            a[k] = xr + xi;
        }
        xr = a[mh];
        a[mh] = a[m + mh];
        a[m + mh] = xr;
        m = mh;
    }
    xi = a[1];
    a[1] = a[0];
    a[0] = an + xi;
    a[n] = an - xi;
    if (n > 2) {
        bitrv1(n, a);
    }
}


void dfst(int n, double *a)
{
    void ddst(int n, int isgn, double *a);
    void bitrv1(int n, double *a);
    int j, k, m, mh;
    double xr, xi, yr, yi;
    
    m = n >> 1;
    for (j = 1; j < m; j++) {
        k = n - j;
        xr = a[j] - a[k];
        a[j] += a[k];
        a[k] = xr;
    }
    a[0] = a[m];
    while (m >= 2) {
        ddst(m, 1, a);
        if (m > 2) {
            bitrv1(m, a);
        }
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[m + k];
            xi = a[m + j];
            yr = a[j];
            yi = a[k];
            a[m + j] = yr;
            a[m + k] = yi;
            a[j] = xr + xi;
            a[k] = xr - xi;
        }
        a[m] = a[0];
        a[0] = a[m + mh];
        a[m + mh] = a[mh];
        m = mh;
    }
    a[1] = a[0];
    a[0] = 0;
    if (n > 2) {
        bitrv1(n, a);
    }
}


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


#include <math.h>
#ifndef M_PI_2
#define M_PI_2      1.570796326794896619231321691639751442098584699687
#endif
#ifndef WR5000  /* cos(M_PI_2*0.5000) */
#define WR5000      0.707106781186547524400844362104849039284835937688
#endif
#ifndef WR2500  /* cos(M_PI_2*0.2500) */
#define WR2500      0.923879532511286756128183189396788286822416625863
#endif
#ifndef WI2500  /* sin(M_PI_2*0.2500) */
#define WI2500      0.382683432365089771728459984030398866761344562485
#endif
#ifndef WR1250  /* cos(M_PI_2*0.1250) */
#define WR1250      0.980785280403230449126182236134239036973933730893
#endif
#ifndef WI1250  /* sin(M_PI_2*0.1250) */
#define WI1250      0.195090322016128267848284868477022240927691617751
#endif
#ifndef WR3750  /* cos(M_PI_2*0.3750) */
#define WR3750      0.831469612302545237078788377617905756738560811987
#endif
#ifndef WI3750  /* sin(M_PI_2*0.3750) */
#define WI3750      0.555570233019602224742830813948532874374937190754
#endif


#ifdef USE_CDFT_PTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 8192
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 65536
#endif
#include <pthread.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t pthread_t
#define cdft_thread_create(thp,func,argp) { \
    if (pthread_create(thp, NULL, func, (void *) argp) != 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#define cdft_thread_wait(th) { \
    if (pthread_join(th, NULL) != 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#endif /* USE_CDFT_PTHREADS */


#ifdef USE_CDFT_WINTHREADS
#define USE_CDFT_THREADS
#ifndef CDFT_THREADS_BEGIN_N
#define CDFT_THREADS_BEGIN_N 32768
#endif
#ifndef CDFT_4THREADS_BEGIN_N
#define CDFT_4THREADS_BEGIN_N 524288
#endif
#include <windows.h>
#include <stdio.h>
#include <stdlib.h>
#define cdft_thread_t HANDLE
#define cdft_thread_create(thp,func,argp) { \
    DWORD thid; \
    *(thp) = CreateThread(NULL, 0, (LPTHREAD_START_ROUTINE) func, (LPVOID) argp, 0, &thid); \
    if (*(thp) == 0) { \
        fprintf(stderr, "cdft thread error\n"); \
        exit(1); \
    } \
}
#define cdft_thread_wait(th) { \
    WaitForSingleObject(th, INFINITE); \
    CloseHandle(th); \
}
#endif /* USE_CDFT_WINTHREADS */


#ifndef CDFT_LOOP_DIV  /* control of the CDFT's speed & tolerance */
#define CDFT_LOOP_DIV 32
#endif

#ifndef RDFT_LOOP_DIV  /* control of the RDFT's speed & tolerance */
#define RDFT_LOOP_DIV 64
#endif

#ifndef DCST_LOOP_DIV  /* control of the DCT,DST's speed & tolerance */
#define DCST_LOOP_DIV 64
#endif


void cftfsub(int n, double *a)
{
    void bitrv2(int n, double *a);
    void bitrv216(double *a);
    void bitrv208(double *a);
    void cftmdl1(int n, double *a);
    void cftrec4(int n, double *a);
    void cftleaf(int n, int isplt, double *a);
    void cftfx41(int n, double *a);
    void cftf161(double *a);
    void cftf081(double *a);
    void cftf040(double *a);
    void cftx020(double *a);
#ifdef USE_CDFT_THREADS
    void cftrec4_th(int n, double *a);
#endif /* USE_CDFT_THREADS */
    
    if (n > 8) {
        if (n > 32) {
            cftmdl1(n, a);
#ifdef USE_CDFT_THREADS
            if (n > CDFT_THREADS_BEGIN_N) {
                cftrec4_th(n, a);
            } else 
#endif /* USE_CDFT_THREADS */
            if (n > 512) {
                cftrec4(n, a);
            } else if (n > 128) {
                cftleaf(n, 1, a);
            } else {
                cftfx41(n, a);
            }
            bitrv2(n, a);
        } else if (n == 32) {
            cftf161(a);
            bitrv216(a);
        } else {
            cftf081(a);
            bitrv208(a);
        }
    } else if (n == 8) {
        cftf040(a);
    } else if (n == 4) {
        cftx020(a);
    }
}


void cftbsub(int n, double *a)
{
    void bitrv2conj(int n, double *a);
    void bitrv216neg(double *a);
    void bitrv208neg(double *a);
    void cftb1st(int n, double *a);
    void cftrec4(int n, double *a);
    void cftleaf(int n, int isplt, double *a);
    void cftfx41(int n, double *a);
    void cftf161(double *a);
    void cftf081(double *a);
    void cftb040(double *a);
    void cftx020(double *a);
#ifdef USE_CDFT_THREADS
    void cftrec4_th(int n, double *a);
#endif /* USE_CDFT_THREADS */
    
    if (n > 8) {
        if (n > 32) {
            cftb1st(n, a);
#ifdef USE_CDFT_THREADS
            if (n > CDFT_THREADS_BEGIN_N) {
                cftrec4_th(n, a);
            } else 
#endif /* USE_CDFT_THREADS */
            if (n > 512) {
                cftrec4(n, a);
            } else if (n > 128) {
                cftleaf(n, 1, a);
            } else {
                cftfx41(n, a);
            }
            bitrv2conj(n, a);
        } else if (n == 32) {
            cftf161(a);
            bitrv216neg(a);
        } else {
            cftf081(a);
            bitrv208neg(a);
        }
    } else if (n == 8) {
        cftb040(a);
    } else if (n == 4) {
        cftx020(a);
    }
}


void bitrv2(int n, double *a)
{
    int j0, k0, j1, k1, l, m, i, j, k, nh;
    double xr, xi, yr, yi;
    
    m = 4;
    for (l = n >> 2; l > 8; l >>= 2) {
        m <<= 1;
    }
    nh = n >> 1;
    if (l == 8) {
        j0 = 0;
        for (k0 = 0; k0 < m; k0 += 4) {
            k = k0;
            for (j = j0; j < j0 + k0; j += 4) {
                xr = a[j];
                xi = a[j + 1];
                yr = a[k];
                yi = a[k + 1];
                a[j] = yr;
                a[j + 1] = yi;
                a[k] = xr;
                a[k + 1] = xi;
                j1 = j + m;
                k1 = k + 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 -= m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 += 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += nh;
                k1 += 2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 += m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += 2;
                k1 += nh;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 += 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 -= m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 += 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= nh;
                k1 -= 2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 += m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= 2 * m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                for (i = nh >> 1; i > (k ^= i); i >>= 1);
            }
            k1 = j0 + k0;
            j1 = k1 + 2;
            k1 += nh;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m;
            k1 += 2 * m;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m;
            k1 -= m;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 -= 2;
            k1 -= nh;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += nh + 2;
            k1 += nh + 2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 -= nh - m;
            k1 += 2 * m - 2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
        }
    } else {
        j0 = 0;
        for (k0 = 0; k0 < m; k0 += 4) {
            k = k0;
            for (j = j0; j < j0 + k0; j += 4) {
                xr = a[j];
                xi = a[j + 1];
                yr = a[k];
                yi = a[k + 1];
                a[j] = yr;
                a[j + 1] = yi;
                a[k] = xr;
                a[k + 1] = xi;
                j1 = j + m;
                k1 = k + m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += nh;
                k1 += 2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += 2;
                k1 += nh;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m;
                k1 += m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= nh;
                k1 -= 2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 -= m;
                k1 -= m;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                for (i = nh >> 1; i > (k ^= i); i >>= 1);
            }
            k1 = j0 + k0;
            j1 = k1 + 2;
            k1 += nh;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            j1 += m;
            k1 += m;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
        }
    }
}