fftsg_h.c

This is a package to calculate Discrete Fourier/Cosine/Sine Transforms of 1-dimensional sequences of

            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);
        }
    }
}


void bitrv2conj(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;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            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;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            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;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            j1 += m;
            k1 += m;
            a[j1 - 1] = -a[j1 - 1];
            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;
            a[k1 + 3] = -a[k1 + 3];
            for (i = nh >> 1; i > (j0 ^= i); i >>= 1);
        }
    }
}


void bitrv216(double *a)
{
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, 
        x5r, x5i, x7r, x7i, x8r, x8i, x10r, x10i, 
        x11r, x11i, x12r, x12i, x13r, x13i, x14r, x14i;
    
    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    a[2] = x8r;
    a[3] = x8i;
    a[4] = x4r;
    a[5] = x4i;
    a[6] = x12r;
    a[7] = x12i;
    a[8] = x2r;
    a[9] = x2i;
    a[10] = x10r;
    a[11] = x10i;
    a[14] = x14r;
    a[15] = x14i;
    a[16] = x1r;
    a[17] = x1i;
    a[20] = x5r;
    a[21] = x5i;
    a[22] = x13r;
    a[23] = x13i;
    a[24] = x3r;
    a[25] = x3i;
    a[26] = x11r;
    a[27] = x11i;
    a[28] = x7r;
    a[29] = x7i;
}


void bitrv216neg(double *a)
{
    double x1r, x1i, x2r, x2i, x3r, x3i, x4r, x4i, 
        x5r, x5i, x6r, x6i, x7r, x7i, x8r, x8i, 
        x9r, x9i, x10r, x10i, x11r, x11i, x12r, x12i, 
        x13r, x13i, x14r, x14i, x15r, x15i;
    
    x1r = a[2];
    x1i = a[3];
    x2r = a[4];
    x2i = a[5];
    x3r = a[6];
    x3i = a[7];
    x4r = a[8];
    x4i = a[9];
    x5r = a[10];
    x5i = a[11];
    x6r = a[12];
    x6i = a[13];
    x7r = a[14];
    x7i = a[15];
    x8r = a[16];
    x8i = a[17];
    x9r = a[18];
    x9i = a[19];
    x10r = a[20];
    x10i = a[21];
    x11r = a[22];
    x11i = a[23];
    x12r = a[24];
    x12i = a[25];
    x13r = a[26];
    x13i = a[27];
    x14r = a[28];
    x14i = a[29];
    x15r = a[30];
    x15i = a[31];
    a[2] = x15r;
    a[3] = x15i;
    a[4] = x7r;
    a[5] = x7i;
    a[6] = x11r;
    a[7] = x11i;
    a[8] = x3r;
    a[9] = x3i;
    a[10] = x13r;
    a[11] = x13i;
    a[12] = x5r;
    a[13] = x5i;
    a[14] = x9r;
    a[15] = x9i;
    a[16] = x1r;
    a[17] = x1i;
    a[18] = x14r;
    a[19] = x14i;
    a[20] = x6r;
    a[21] = x6i;
    a[22] = x10r;
    a[23] = x10i;
    a[24] = x2r;
    a[25] = x2i;
    a[26] = x12r;
    a[27] = x12i;
    a[28] = x4r;
    a[29] = x4i;
    a[30] = x8r;
    a[31] = x8i;