Incorrect in-place FFT Code (in CP4 Book)

[BrandonTang89]

In CP4 Page 517, code for an in-place FFT is written. However, it contains (multiple) errors. Here is a working version of the same function.

typedef complex<long double> cd;
const double PI = acos(-1.0);

int reverseBit(int x, int m) {  // m is the binary length A.size()-1
    int ret = 0;
    for (int k = 0; k < m; k++) {
        if (x & (1 << k)) ret |= (1 << (m - 1 - k));
    }
    return ret;
}

void FFT(vector<cd> &A) {  // evaulates A at the nth roots of unity for n = 2^k >= A.size()
    int m = 0;
    while ((1 << m) < (int)A.size()) m++;
    A.resize(1 << m, 0);                       // size of A should be a power of 2, resizes A
    for (int k = 0; k < (int)A.size(); k++) {  // sort to bit-reversal permutation
        if (k < reverseBit(k, m)) swap(A[k], A[reverseBit(k, m)]);
    }

    for (int n = 2; n <= (int)A.size(); n <<= 1) {
        for (int k = 0; 2 * k < n; k++) {
            // we are going to get the kth and k+n/2th element of each length n block
            cd x = cd(cos(2 * PI * k / n), sin(2 * PI * k / n));  // nth root of unity
            for (int j = 0; j < (int)A.size(); j += n) {  // apply to every sub-array of length n
                cd A0k = A[k + j];                        // previously computed
                cd A1k = A[k + j + n / 2];                // previously computed
                A[k + j] = A0k + x * A1k;
                A[k + j + n / 2] = A0k - x * A1k;
            }
        }
    }
}