How do I store lookup tables in magic numbers?

Question

I have seen something interesting here, saying you can store lookup tables at magic numbers.

I have tried using brute-force to find the magic number, but all the results are incorrect.

How do I find the correct magic number for a certain lookup table? Thank you.

Answer 1

As the author of that answer puts it:

The magic number stores the table as a bitstring, with the n-th digit (from the end) corresponding to the nth table entry

Here's a really simple example:

Entry   Value   Bit
-----   -----   ---
  0     True     1
  1     False    0
  2     False    0
  3     True     1
                 b  # needed to indicate
                 0  # 'binary number'

So the "magic number" for this lookup table, reading up from the bottom, is:

>>> 0b1001  # (1 * 8) + (0 * 4) + (0 * 2) + (1 * 1)
9

Or, to rotate it:

              3      2      1      0      | Entry
              True   False  False  True   | Value
0      b      1      0      0      1      | Bit    # -> 0b1001

---

In terms of extracting the output, the right-shift binary operator x >> y moves all bits in x right by y places, truncating the last y bits:

>>> for x in range(4):
        print(x, '0b{:04b}'.format(9>>x))


0 0b1001
1 0b0100
2 0b0010
3 0b0001

and the bitwise AND & 1 tells you the value of the last bit. Getting the results back out:

>>> for x in range(4):
    print(x, 9>>x&1)


0 1
1 0
2 0
3 1

---

Another example:

Entry   Value   Bit
-----   -----   ---
  0     True     1
  1     False    0
  2     True     1
  3     False    0
                 b  # needed to indicate
                 0  # 'binary number'

So the "magic number" for this lookup table, reading up from the bottom, is:

>>> 0b0101  # (0 * 8) + (1 * 4) + (0 * 2) + (1 * 1)
5

Or, to rotate it:

              3      2      1      0      | Entry
              False  True   False  True   | Value
0      b      0      1      0      1      | Bit    # -> 0b0101