How to find every combination of numbers that sum to a specific X given a large array of numbers?

I have a large array of integers (~3k items), and I want to find the indices of every combination of numbers where the sum of said numbers is equal to X. How to do this without the program taking years to execute?

I can find the first combination possible with the following Python code:

def find_numbers_that_sum_to(source_arr, target_number, return_index=True):
    result = []
    result_indices = []
    
    for idx, item in enumerate(source_arr):
        sum_list = sum(result)
        
        assert (sum_list + item) <= target_number
        result.append(item)
        result_indices.append(idx)
        
        if (sum_list + item) == target_number:
            break
    
    return result_indices

But I need every combination possible. At least a way of generating them dynamically. I only ever need one of them at a time, but if the indices it gave me don't match another criteria I need, I'll need the next set.

Solution

Unfortunately, this problem is NP-hard, meaning that there's no currently known polynomial time algorithm for this. If you want to benchmark your current code against other implementations, this SO question contains a bunch. Those implementations may be faster, but their runtimes will still be exponential.