fft4g.c

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            cftbsub(n, a, w);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
    }
    dstsub(n, a, nc, w + nw);
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, ip + 2, a);
            cftfsub(n, a, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
        xr = a[0] - a[1];
        a[0] += a[1];
        for (j = 2; j < n; j += 2) {
            a[j - 1] = -a[j] - a[j + 1];
            a[j] -= a[j + 1];
        }
        a[n - 1] = -xr;
    }
}


void dfct(int n, float *a, float *t, int *ip, float *w)
{
    void makewt(int nw, int *ip, float *w);
    void makect(int nc, int *ip, float *c);
    void bitrv2(int n, int *ip, float *a);
    void cftfsub(int n, float *a, float *w);
    void rftfsub(int n, float *a, int nc, float *c);
    void dctsub(int n, float *a, int nc, float *c);
    int j, k, l, m, mh, nw, nc;
    float xr, xi, yr, yi;
    
    nw = ip[0];
    if (n > (nw << 3)) {
        nw = n >> 3;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
        nc = n >> 1;
        makect(nc, ip, w + nw);
    }
    m = n >> 1;
    yi = a[m];
    xi = a[0] + a[n];
    a[0] -= a[n];
    t[0] = xi - yi;
    t[m] = xi + yi;
    if (n > 2) {
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[j] - a[n - j];
            xi = a[j] + a[n - j];
            yr = a[k] - a[n - k];
            yi = a[k] + a[n - k];
            a[j] = xr;
            a[k] = yr;
            t[j] = xi - yi;
            t[k] = xi + yi;
        }
        t[mh] = a[mh] + a[n - mh];
        a[mh] -= a[n - mh];
        dctsub(m, a, nc, w + nw);
        if (m > 4) {
            bitrv2(m, ip + 2, a);
            cftfsub(m, a, w);
            rftfsub(m, a, nc, w + nw);
        } else if (m == 4) {
            cftfsub(m, a, w);
        }
        a[n - 1] = a[0] - a[1];
        a[1] = a[0] + a[1];
        for (j = m - 2; j >= 2; j -= 2) {
            a[2 * j + 1] = a[j] + a[j + 1];
            a[2 * j - 1] = a[j] - a[j + 1];
        }
        l = 2;
        m = mh;
        while (m >= 2) {
            dctsub(m, t, nc, w + nw);
            if (m > 4) {
                bitrv2(m, ip + 2, t);
                cftfsub(m, t, w);
                rftfsub(m, t, nc, w + nw);
            } else if (m == 4) {
                cftfsub(m, t, w);
            }
            a[n - l] = t[0] - t[1];
            a[l] = t[0] + t[1];
            k = 0;
            for (j = 2; j < m; j += 2) {
                k += l << 2;
                a[k - l] = t[j] - t[j + 1];
                a[k + l] = t[j] + t[j + 1];
            }
            l <<= 1;
            mh = m >> 1;
            for (j = 0; j < mh; j++) {
                k = m - j;
                t[j] = t[m + k] - t[m + j];
                t[k] = t[m + k] + t[m + j];
            }
            t[mh] = t[m + mh];
            m = mh;
        }
        a[l] = t[0];
        a[n] = t[2] - t[1];
        a[0] = t[2] + t[1];
    } else {
        a[1] = a[0];
        a[2] = t[0];
        a[0] = t[1];
    }
}


void dfst(int n, float *a, float *t, int *ip, float *w)
{
    void makewt(int nw, int *ip, float *w);
    void makect(int nc, int *ip, float *c);
    void bitrv2(int n, int *ip, float *a);
    void cftfsub(int n, float *a, float *w);
    void rftfsub(int n, float *a, int nc, float *c);
    void dstsub(int n, float *a, int nc, float *c);
    int j, k, l, m, mh, nw, nc;
    float xr, xi, yr, yi;
    
    nw = ip[0];
    if (n > (nw << 3)) {
        nw = n >> 3;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 1)) {
        nc = n >> 1;
        makect(nc, ip, w + nw);
    }
    if (n > 2) {
        m = n >> 1;
        mh = m >> 1;
        for (j = 1; j < mh; j++) {
            k = m - j;
            xr = a[j] + a[n - j];
            xi = a[j] - a[n - j];
            yr = a[k] + a[n - k];
            yi = a[k] - a[n - k];
            a[j] = xr;
            a[k] = yr;
            t[j] = xi + yi;
            t[k] = xi - yi;
        }
        t[0] = a[mh] - a[n - mh];
        a[mh] += a[n - mh];
        a[0] = a[m];
        dstsub(m, a, nc, w + nw);
        if (m > 4) {
            bitrv2(m, ip + 2, a);
            cftfsub(m, a, w);
            rftfsub(m, a, nc, w + nw);
        } else if (m == 4) {
            cftfsub(m, a, w);
        }
        a[n - 1] = a[1] - a[0];
        a[1] = a[0] + a[1];
        for (j = m - 2; j >= 2; j -= 2) {
            a[2 * j + 1] = a[j] - a[j + 1];
            a[2 * j - 1] = -a[j] - a[j + 1];
        }
        l = 2;
        m = mh;
        while (m >= 2) {
            dstsub(m, t, nc, w + nw);
            if (m > 4) {
                bitrv2(m, ip + 2, t);
                cftfsub(m, t, w);
                rftfsub(m, t, nc, w + nw);
            } else if (m == 4) {
                cftfsub(m, t, w);
            }
            a[n - l] = t[1] - t[0];
            a[l] = t[0] + t[1];
            k = 0;
            for (j = 2; j < m; j += 2) {
                k += l << 2;
                a[k - l] = -t[j] - t[j + 1];
                a[k + l] = t[j] - t[j + 1];
            }
            l <<= 1;
            mh = m >> 1;
            for (j = 1; j < mh; j++) {
                k = m - j;
                t[j] = t[m + k] + t[m + j];
                t[k] = t[m + k] - t[m + j];
            }
            t[0] = t[m + mh];
            m = mh;
        }
        a[l] = t[0];
    }
    a[0] = 0;
}


/* -------- initializing routines -------- */


#include <math.h>

void makewt(int nw, int *ip, float *w)
{
    void bitrv2(int n, int *ip, float *a);
    int j, nwh;
    float delta, x, y;
    
    ip[0] = nw;
    ip[1] = 1;
    if (nw > 2) {
        nwh = nw >> 1;
        delta = atan(1.0) / nwh;
        w[0] = 1;
        w[1] = 0;
        w[nwh] = cos(delta * nwh);
        w[nwh + 1] = w[nwh];
        if (nwh > 2) {
            for (j = 2; j < nwh; j += 2) {
                x = cos(delta * j);
                y = sin(delta * j);
                w[j] = x;
                w[j + 1] = y;
                w[nw - j] = y;
                w[nw - j + 1] = x;
            }
            bitrv2(nw, ip + 2, w);
        }
    }
}


void makect(int nc, int *ip, float *c)
{
    int j, nch;
    float delta;
    
    ip[1] = nc;
    if (nc > 1) {
        nch = nc >> 1;
        delta = atan(1.0) / nch;
        c[0] = cos(delta * nch);
        c[nch] = 0.5 * c[0];
        for (j = 1; j < nch; j++) {
            c[j] = 0.5 * cos(delta * j);
            c[nc - j] = 0.5 * sin(delta * j);
        }
    }
}


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


void bitrv2(int n, int *ip, float *a)
{
    int j, j1, k, k1, l, m, m2;
    float xr, xi, yr, yi;
    
    ip[0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
            ip[m + j] = ip[j] + l;
        }
        m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 -= m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
            j1 = 2 * k + m2 + ip[k];
            k1 = j1 + m2;
            xr = a[j1];
            xi = a[j1 + 1];
            yr = a[k1];
            yi = a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
        }
    } else {
        for (k = 1; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += m2;
                xr = a[j1];
                xi = a[j1 + 1];
                yr = a[k1];
                yi = a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
        }
    }
}


void bitrv2conj(int n, int *ip, float *a)
{
    int j, j1, k, k1, l, m, m2;
    float xr, xi, yr, yi;
    
    ip[0] = 0;
    l = n;
    m = 1;
    while ((m << 3) < l) {
        l >>= 1;
        for (j = 0; j < m; j++) {
            ip[m + j] = ip[j] + l;
        }
        m <<= 1;
    }
    m2 = 2 * m;
    if ((m << 3) == l) {
        for (k = 0; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 -= m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
                j1 += m2;
                k1 += 2 * m2;
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;
                a[k1] = xr;
                a[k1 + 1] = xi;
            }
            k1 = 2 * k + ip[k];
            a[k1 + 1] = -a[k1 + 1];
            j1 = k1 + m2;
            k1 = j1 + m2;
            xr = a[j1];
            xi = -a[j1 + 1];
            yr = a[k1];
            yi = -a[k1 + 1];
            a[j1] = yr;
            a[j1 + 1] = yi;
            a[k1] = xr;
            a[k1 + 1] = xi;
            k1 += m2;
            a[k1 + 1] = -a[k1 + 1];
        }
    } else {
        a[1] = -a[1];
        a[m2 + 1] = -a[m2 + 1];
        for (k = 1; k < m; k++) {
            for (j = 0; j < k; j++) {
                j1 = 2 * j + ip[k];
                k1 = 2 * k + ip[j];
                xr = a[j1];
                xi = -a[j1 + 1];
                yr = a[k1];
                yi = -a[k1 + 1];
                a[j1] = yr;
                a[j1 + 1] = yi;