Update README.md

not-so-smart-contracts/cairo/incorrect_felt_comparison/README.md

@@ -1,6 +1,13 @@
 # Incorrect Felt Comparison
 
-In Cairo, there are two methods for the less than or equal to comparison operator: `assert_le` and `assert_nn_le`. `assert_le` asserts that a number `a` is less than or equal to `b`, regardless of the size of `a`, while `assert_nn_le` additionally asserts that `a` is [non-negative](https://github.com/starkware-libs/cairo-lang/blob/9889fbd522edc5eff603356e1912e20642ae20af/src/starkware/cairo/common/math.cairo#L71), i.e. not greater than or equal to the `RANGE_CHECK_BOUND` value of `2^128`. `assert_nn_le` works to compare unsigned integers but with a value less than `2^128` (e.g. an [Uint256](https://github.com/starkware-libs/cairo-lang/blob/9889fbd522edc5eff603356e1912e20642ae20af/src/starkware/cairo/common/uint256.cairo#L9-L14) field), to compare felts as unsigned integer over the entire range (0, P] use `assert_le_felt`. Note these functions exist also with the `is_` prefix where they return 1 (TRUE) or 0 (FALSE).
+In Cairo, there are two methods for the less than or equal to comparison operator: `assert_le` and `assert_nn_le`:
+- `assert_le` asserts that a number `a` is less than or equal to `b`, regardless of the size of `a`
+- `assert_nn_le` additionally asserts that `a` is [non-negative](https://github.com/starkware-libs/cairo-lang/blob/9889fbd522edc5eff603356e1912e20642ae20af/src/starkware/cairo/common/math.cairo#L71), i.e. not greater than or equal to the `RANGE_CHECK_BOUND` value of `2^128`. 
+
+`assert_nn_le` works to compare unsigned integers but with a value less than `2^128` (e.g. an [Uint256](https://github.com/starkware-libs/cairo-lang/blob/9889fbd522edc5eff603356e1912e20642ae20af/src/starkware/cairo/common/uint256.cairo#L9-L14) field). To compare felts as unsigned integer over the entire range (0, P], `assert_le_felt` should be used. Note these functions exist also with the `is_` prefix where they return 1 (TRUE) or 0 (FALSE).
+
+Due to the complexity of these assertions, a common mistake is to use `assert_le` when `assert_nn_le` should be used.
+
 # Example
 
 Suppose that a codebase uses the following checks regarding a hypothetical ERC20 token. In the first function, it may be possible that `value` is in fact greater than `max_supply`, yet because the function does not verify `value >= 0` the assertion will incorrectly pass. The second function, however, asserts that `0 <= value <= max_supply`, which will correctly not let an incorrect `value` go through the assertion.
@@ -36,4 +43,6 @@ func better_comparison{syscall_ptr : felt*, pedersen_ptr : HashBuiltin*, range_c
 
 
 # Mitigations
-Review all felt comparisons closely. Determine what sort of behavior the comparison should have, and if `assert_nn_le` or `assert_le_felt` is more appropriate.
+- Review all felt comparisons closely. 
+- Determine what sort of behavior the comparison should have, and if `assert_nn_le` or `assert_le_felt` is more appropriate. 
+- Use `assert_le` if you explicitly want to make comparison between signed integers - otherwise explicitely document why it is used over `assert_nn_le`