transform4.cc

各种工程计算的库函数

            a[j2] = x0r - x2r;
            a[j2 + 1] = x0i - x2i;
            a[j1] = x1r - x3i;
            a[j1 + 1] = x1i + x3r;
            a[j3] = x1r + x3i;
            a[j3 + 1] = x1i - x3r;
        }
    } else {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            x0r = a[j] - a[j1];
            x0i = a[j + 1] - a[j1 + 1];
            a[j] += a[j1];
            a[j + 1] += a[j1 + 1];
            a[j1] = x0r;
            a[j1 + 1] = x0i;
        }
    }
}


T4_INLINE void clTransform4::cftbsub(long n, float *a, float *w)
{
    long j, j1, j2, j3, l;
    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    l = 2;
    if (n > 8) {
        cft1st(n, a, w);
        l = 8;
        while ((l << 2) < n) {
            cftmdl(n, l, a, w);
            l <<= 2;
        }
    }
    if ((l << 2) == n) {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = -a[j + 1] - a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = -a[j + 1] + a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i - x2i;
            a[j2] = x0r - x2r;
            a[j2 + 1] = x0i + x2i;
            a[j1] = x1r - x3i;
            a[j1 + 1] = x1i - x3r;
            a[j3] = x1r + x3i;
            a[j3 + 1] = x1i + x3r;
        }
    } else {
        for (j = 0; j < l; j += 2) {
            j1 = j + l;
            x0r = a[j] - a[j1];
            x0i = -a[j + 1] + a[j1 + 1];
            a[j] += a[j1];
            a[j + 1] = -a[j + 1] - a[j1 + 1];
            a[j1] = x0r;
            a[j1 + 1] = x0i;
        }
    }
}


T4_INLINE void clTransform4::cft1st(long n, float *a, float *w)
{
    long j, k1, k2;
    float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    x0r = a[0] + a[2];
    x0i = a[1] + a[3];
    x1r = a[0] - a[2];
    x1i = a[1] - a[3];
    x2r = a[4] + a[6];
    x2i = a[5] + a[7];
    x3r = a[4] - a[6];
    x3i = a[5] - a[7];
    a[0] = x0r + x2r;
    a[1] = x0i + x2i;
    a[4] = x0r - x2r;
    a[5] = x0i - x2i;
    a[2] = x1r - x3i;
    a[3] = x1i + x3r;
    a[6] = x1r + x3i;
    a[7] = x1i - x3r;
    wk1r = w[2];
    x0r = a[8] + a[10];
    x0i = a[9] + a[11];
    x1r = a[8] - a[10];
    x1i = a[9] - a[11];
    x2r = a[12] + a[14];
    x2i = a[13] + a[15];
    x3r = a[12] - a[14];
    x3i = a[13] - a[15];
    a[8] = x0r + x2r;
    a[9] = x0i + x2i;
    a[12] = x2i - x0i;
    a[13] = x0r - x2r;
    x0r = x1r - x3i;
    x0i = x1i + x3r;
    a[10] = wk1r * (x0r - x0i);
    a[11] = wk1r * (x0r + x0i);
    x0r = x3i + x1r;
    x0i = x3r - x1i;
    a[14] = wk1r * (x0i - x0r);
    a[15] = wk1r * (x0i + x0r);
    k1 = 0;
    for (j = 16; j < n; j += 16) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        x0r = a[j] + a[j + 2];
        x0i = a[j + 1] + a[j + 3];
        x1r = a[j] - a[j + 2];
        x1i = a[j + 1] - a[j + 3];
        x2r = a[j + 4] + a[j + 6];
        x2i = a[j + 5] + a[j + 7];
        x3r = a[j + 4] - a[j + 6];
        x3i = a[j + 5] - a[j + 7];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 4] = wk2r * x0r - wk2i * x0i;
        a[j + 5] = wk2r * x0i + wk2i * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 2] = wk1r * x0r - wk1i * x0i;
        a[j + 3] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 6] = wk3r * x0r - wk3i * x0i;
        a[j + 7] = wk3r * x0i + wk3i * x0r;
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        x0r = a[j + 8] + a[j + 10];
        x0i = a[j + 9] + a[j + 11];
        x1r = a[j + 8] - a[j + 10];
        x1i = a[j + 9] - a[j + 11];
        x2r = a[j + 12] + a[j + 14];
        x2i = a[j + 13] + a[j + 15];
        x3r = a[j + 12] - a[j + 14];
        x3i = a[j + 13] - a[j + 15];
        a[j + 8] = x0r + x2r;
        a[j + 9] = x0i + x2i;
        x0r -= x2r;
        x0i -= x2i;
        a[j + 12] = -wk2i * x0r - wk2r * x0i;
        a[j + 13] = -wk2i * x0i + wk2r * x0r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j + 10] = wk1r * x0r - wk1i * x0i;
        a[j + 11] = wk1r * x0i + wk1i * x0r;
        x0r = x1r + x3i;
        x0i = x1i - x3r;
        a[j + 14] = wk3r * x0r - wk3i * x0i;
        a[j + 15] = wk3r * x0i + wk3i * x0r;
    }
}


T4_INLINE void clTransform4::cftmdl(long n, long l, float *a, float *w)
{
    long j, j1, j2, j3, k, k1, k2, m, m2;
    float wk1r, wk1i, wk2r, wk2i, wk3r, wk3i;
    float x0r, x0i, x1r, x1i, x2r, x2i, x3r, x3i;
    
    m = l << 2;
    for (j = 0; j < l; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x0r - x2r;
        a[j2 + 1] = x0i - x2i;
        a[j1] = x1r - x3i;
        a[j1 + 1] = x1i + x3r;
        a[j3] = x1r + x3i;
        a[j3 + 1] = x1i - x3r;
    }
    wk1r = w[2];
    for (j = m; j < l + m; j += 2) {
        j1 = j + l;
        j2 = j1 + l;
        j3 = j2 + l;
        x0r = a[j] + a[j1];
        x0i = a[j + 1] + a[j1 + 1];
        x1r = a[j] - a[j1];
        x1i = a[j + 1] - a[j1 + 1];
        x2r = a[j2] + a[j3];
        x2i = a[j2 + 1] + a[j3 + 1];
        x3r = a[j2] - a[j3];
        x3i = a[j2 + 1] - a[j3 + 1];
        a[j] = x0r + x2r;
        a[j + 1] = x0i + x2i;
        a[j2] = x2i - x0i;
        a[j2 + 1] = x0r - x2r;
        x0r = x1r - x3i;
        x0i = x1i + x3r;
        a[j1] = wk1r * (x0r - x0i);
        a[j1 + 1] = wk1r * (x0r + x0i);
        x0r = x3i + x1r;
        x0i = x3r - x1i;
        a[j3] = wk1r * (x0i - x0r);
        a[j3 + 1] = wk1r * (x0i + x0r);
    }
    k1 = 0;
    m2 = 2 * m;
    for (k = m2; k < n; k += m2) {
        k1 += 2;
        k2 = 2 * k1;
        wk2r = w[k1];
        wk2i = w[k1 + 1];
        wk1r = w[k2];
        wk1i = w[k2 + 1];
        wk3r = wk1r - 2 * wk2i * wk1i;
        wk3i = 2 * wk2i * wk1r - wk1i;
        for (j = k; j < l + k; j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = a[j + 1] + a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = a[j + 1] - a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i + x2i;
            x0r -= x2r;
            x0i -= x2i;
            a[j2] = wk2r * x0r - wk2i * x0i;
            a[j2 + 1] = wk2r * x0i + wk2i * x0r;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[j1] = wk1r * x0r - wk1i * x0i;
            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[j3] = wk3r * x0r - wk3i * x0i;
            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
        wk1r = w[k2 + 2];
        wk1i = w[k2 + 3];
        wk3r = wk1r - 2 * wk2r * wk1i;
        wk3i = 2 * wk2r * wk1r - wk1i;
        for (j = k + m; j < l + (k + m); j += 2) {
            j1 = j + l;
            j2 = j1 + l;
            j3 = j2 + l;
            x0r = a[j] + a[j1];
            x0i = a[j + 1] + a[j1 + 1];
            x1r = a[j] - a[j1];
            x1i = a[j + 1] - a[j1 + 1];
            x2r = a[j2] + a[j3];
            x2i = a[j2 + 1] + a[j3 + 1];
            x3r = a[j2] - a[j3];
            x3i = a[j2 + 1] - a[j3 + 1];
            a[j] = x0r + x2r;
            a[j + 1] = x0i + x2i;
            x0r -= x2r;
            x0i -= x2i;
            a[j2] = -wk2i * x0r - wk2r * x0i;
            a[j2 + 1] = -wk2i * x0i + wk2r * x0r;
            x0r = x1r - x3i;
            x0i = x1i + x3r;
            a[j1] = wk1r * x0r - wk1i * x0i;
            a[j1 + 1] = wk1r * x0i + wk1i * x0r;
            x0r = x1r + x3i;
            x0i = x1i - x3r;
            a[j3] = wk3r * x0r - wk3i * x0i;
            a[j3 + 1] = wk3r * x0i + wk3i * x0r;
        }
    }
}


T4_INLINE void clTransform4::rftfsub(long n, float *a, long nc, float *c)
{
    long j, k, kk, ks, m;
    float wkr, wki, xr, xi, yr, yi;
    
    m = n >> 1;
    ks = 2 * nc / m;
    kk = 0;
    for (j = 2; j < m; j += 2) {
        k = n - j;
        kk += ks;
        wkr = 0.5f - c[nc - kk];
        wki = c[kk];
        xr = a[j] - a[k];
        xi = a[j + 1] + a[k + 1];
        yr = wkr * xr - wki * xi;
        yi = wkr * xi + wki * xr;
        a[j] -= yr;
        a[j + 1] -= yi;
        a[k] += yr;
        a[k + 1] -= yi;
    }
}


T4_INLINE void clTransform4::rftbsub(long n, float *a, long nc, float *c)
{
    long j, k, kk, ks, m;
    float wkr, wki, xr, xi, yr, yi;
    
    a[1] = -a[1];
    m = n >> 1;
    ks = 2 * nc / m;
    kk = 0;
    for (j = 2; j < m; j += 2) {
        k = n - j;
        kk += ks;
        wkr = 0.5f - c[nc - kk];
        wki = c[kk];
        xr = a[j] - a[k];
        xi = a[j + 1] + a[k + 1];
        yr = wkr * xr + wki * xi;
        yi = wkr * xi - wki * xr;
        a[j] -= yr;
        a[j + 1] = yi - a[j + 1];
        a[k] += yr;
        a[k + 1] = yi - a[k + 1];
    }
    a[m + 1] = -a[m + 1];
}


T4_INLINE void clTransform4::dctsub(long n, float *a, long nc, float *c)
{
    long j, k, kk, ks, m;
    float wkr, wki, xr;
    
    m = n >> 1;
    ks = nc / n;
    kk = 0;
    for (j = 1; j < m; j++) {
        k = n - j;
        kk += ks;
        wkr = c[kk] - c[nc - kk];
        wki = c[kk] + c[nc - kk];
        xr = wki * a[j] - wkr * a[k];
        a[j] = wkr * a[j] + wki * a[k];
        a[k] = xr;
    }
    a[m] *= c[0];
}


T4_INLINE void clTransform4::dstsub(long n, float *a, long nc, float *c)
{
    long j, k, kk, ks, m;
    float wkr, wki, xr;
    
    m = n >> 1;
    ks = nc / n;
    kk = 0;
    for (j = 1; j < m; j++) {
        k = n - j;
        kk += ks;
        wkr = c[kk] - c[nc - kk];
        wki = c[kk] + c[nc - kk];
        xr = wki * a[k] - wkr * a[j];
        a[k] = wkr * a[k] + wki * a[j];
        a[j] = xr;
    }
    a[m] *= c[0];
}


// ----- double versions start here!


void clTransform4::cdft(long n, long isgn, double *a, long *ip, double *w)
{
    if (n > (ip[0] << 2)) {
        makewt(n >> 2, ip, w);
    }
    if (n > 4) {
        if (isgn >= 0) {
            bitrv2(n, ip + 2, a);
            cftfsub(n, a, w);
        } else {
            bitrv2conj(n, ip + 2, a);
            cftbsub(n, a, w);
        }
    } else if (n == 4) {
        cftfsub(n, a, w);
    }
}


void clTransform4::rdft(long n, long isgn, double *a, long *ip, double *w)
{
    long nw, nc;
    double xi;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > (nc << 2)) {
        nc = n >> 2;
        makect(nc, ip, w + nw);
    }
    if (isgn >= 0) {
        if (n > 4) {
            bitrv2(n, ip + 2, a);
            cftfsub(n, a, w);
            rftfsub(n, a, nc, w + nw);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
        xi = a[0] - a[1];
        a[0] += a[1];
        a[1] = xi;
    } else {
        a[1] = 0.5 * (a[0] - a[1]);
        a[0] -= a[1];
        if (n > 4) {
            rftbsub(n, a, nc, w + nw);
            bitrv2(n, ip + 2, a);
            cftbsub(n, a, w);
        } else if (n == 4) {
            cftfsub(n, a, w);
        }
    }
}


void clTransform4::ddct(long n, long isgn, double *a, long *ip, double *w)
{
    long j, nw, nc;
    double xr;
    
    nw = ip[0];
    if (n > (nw << 2)) {
        nw = n >> 2;
        makewt(nw, ip, w);
    }
    nc = ip[1];
    if (n > nc) {
        nc = n;
        makect(nc, ip, w + nw);
    }
    if (isgn < 0) {
        xr = a[n - 1];
        for (j = n - 2; j >= 2; j -= 2) {
            a[j + 1] = a[j] - a[j - 1];
            a[j] += a[j - 1];
        }
        a[1] = a[0] - xr;
        a[0] += xr;