Example on FFT from Numerical Recipes book results in runtime error

I am trying to implement the FFT algorithm on C. I wrote a code based on the function "four1" from the book "Numerical Recipes in C". I know that using external libraries such as FFTW would be more efficient, but I just wanted to try this as a first approach. But I am getting an error at runtime.

After trying to debug for a while, I have decided to copy the exact same function provided in the book, but I still have the same problem. The problem seems to be in the following commands:

tempr = wr * data[j] - wi * data[j + 1];
tempi = wr * data[j + 1] + wi * data[j];

and

data[j + 1] = data[i + 1] - tempi;

the j is sometimes as high as the last index of the array, so you cannot add one when indexing.

As I said, I didnĀ“t change anything from the code, so I am very surprised that it is not working for me; it is a well-known reference for numerical methods in C, and I doubt there are errors in it. Also, I have found some questions regarding the same code example but none of them seemed to have the same issue (see C: Numerical Recipies (FFT), for example). What am I doing wrong?

Here is the code:

#include <iostream>
#include <stdio.h>
using namespace std;

#define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr
void four1(double* data, unsigned long nn, int isign)
{
    unsigned long n, mmax, m, j, istep, i;
    double wtemp, wr, wpr, wpi, wi, theta;
    double tempr, tempi;

    n = nn << 1;
    j = 1;
    for (i = 1; i < n; i += 2) {
        if (j > i) {
            SWAP(data[j], data[i]);
            SWAP(data[j + 1], data[i + 1]);
        }
        m = n >> 1;
        while (m >= 2 && j > m) {
            j -= m;
            m >>= 1;
        }
        j += m;
    }
    mmax = 2;
    while (n > mmax) {
        istep = mmax << 1;
        theta = isign * (6.28318530717959 / mmax);
        wtemp = sin(0.5 * theta);
        wpr = -2.0 * wtemp * wtemp;
        wpi = sin(theta);
        wr = 1.0;
        wi = 0.0;
        for (m = 1; m < mmax; m += 2) {
            for (i = m; i <= n; i += istep) {
                j = i + mmax;

                tempr = wr * data[j] - wi * data[j + 1];
                tempi = wr * data[j + 1] + wi * data[j];
                data[j] = data[i] - tempr;
                data[j + 1] = data[i + 1] - tempi;
                data[i] += tempr;
                data[i + 1] += tempi;
            }
            wr = (wtemp = wr) * wpr - wi * wpi + wr;
            wi = wi * wpr + wtemp * wpi + wi;
        }
        mmax = istep;
    }
}
#undef SWAP


int main()
{
    // Testing with random data
    double data[] = {1, 1, 2, 0, 1, 3, 4, 0};

    four1(data, 4, 1);

    for (int i = 0; i < 7; i++) {
        cout << data[i] << " ";
    }

}

>Solution :

The first 2 editions of Numerical Recipes in C use the unusual (for C) convention that arrays are 1-based. (This was probably because the Fortran (1-based) version came first and the translation to C was done without regard to conventions.)

You should read section 1.2 Some C Conventions for Scientific
Computing
, specifically the paragraphs on Vectors and One-Dimensional Arrays. As well as trying to justify their 1-based decision, this section does explain how to adapt pointers appropriately to match their code.

In your case, this should work –

int main()
{
    // Testing with random data
    double data[] = {1, 1, 2, 0, 1, 3, 4, 0};
    double *data1based = data - 1;

    four1(data1based, 4, 1);

    for (int i = 0; i < 7; i++) {
        cout << data[i] << " ";
    }

}

The third edition tacitly recognised this ‘mistake’ and, as part of supporting C++ and standard library collections, switched to use the C & C++ conventions of zero-based arrays.

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