token-2022: [I-03] Clarify calculate_inverse_fee math (#6874)

#### Problem

According to the Certora audit report:

> Description: The function calculate_inverse_fee is not exactly an
inverse operation of calculate_fee. That is, it is not the case that
calculate_inverse_fee(x + calculate_fee(x)) == calculate_fee(x).
> Recommendation: Document that calculate_inverse_fee is not an exact
inverse and instead that only the relationship calculate_fee(x) <=
calculate_inverse_fee(x + calculate_fee(x)) holds in order to avoid
confusion with the potential users of calculate_inverse_fee.

#### Solution

Do the recommended thing. I don't think the math in the comment is
correct, so I've added a test to make sure the relationship is correct.

Author: joncinque

token/program-2022/src/extension/transfer_fee/mod.rs

@@ -113,6 +113,15 @@ impl TransferFee {
     }
 
     /// Calculate the fee that would produce the given output
+    ///
+    /// Note: this function is not an exact inverse operation of
+    /// `calculate_fee`. Meaning, it is not the case that:
+    ///
+    /// `calculate_fee(x) == calculate_inverse_fee(x - calculate_fee(x))`
+    ///
+    /// Only the following relationship holds:
+    ///
+    /// `calculate_fee(x) >= calculate_inverse_fee(x - calculate_fee(x))`
     pub fn calculate_inverse_fee(&self, post_fee_amount: u64) -> Option<u64> {
         let pre_fee_amount = self.calculate_pre_fee_amount(post_fee_amount)?;
         self.calculate_fee(pre_fee_amount)
@@ -444,4 +453,23 @@ pub(crate) mod test {
             assert!(diff < precision, "diff is {} for precision {}", diff, precision);
         }
     }
+
+    proptest! {
+        #[test]
+        fn inverse_fee_relationship(
+            transfer_fee_basis_points in 0u16..MAX_FEE_BASIS_POINTS,
+            maximum_fee in u64::MIN..=u64::MAX,
+            amount_in in 0..=u64::MAX
+        ) {
+            let transfer_fee = TransferFee {
+                epoch: PodU64::from(0),
+                maximum_fee: PodU64::from(maximum_fee),
+                transfer_fee_basis_points: PodU16::from(transfer_fee_basis_points),
+            };
+            let fee = transfer_fee.calculate_fee(amount_in).unwrap();
+            let amount_out = amount_in.checked_sub(fee).unwrap();
+            let fee_exact_out = transfer_fee.calculate_inverse_fee(amount_out).unwrap();
+            assert!(fee >= fee_exact_out);
+        }
+    }
 }