Forensic Financial Analysis of First National Bank

The forensic team has completed its analysis of the financial computing software for First National Bank. Our findings indicate that "siphoning" (or "skimming") was occurring.

The software takes a list of 10,000 credit transactions and 10,000 debit transactions and calculates the net balance

However, the calculations were carried out using the IEEE single-precision floating-point number system, which maintains approximately 8 significant digits.

The net was computed by the software using 3 different methods.

Method A simply calculates the sum of the credits, and subtracts from it the sum of the debits.

Method B calculates the sum of the credits, and then subtracts the debits, one at a time, from smallest in size to the largest.

Method C sorts both the credits and debits, from smallest in size to largest, and incorporates them into the net in credit/debit pairs, starting with the smallest.

Finally, the program returns the minimum of the 3 values.

Mathematically, these three methods are equivalent. However, they can result in drastic differences when round-off error is present.

Our analysis indicates that Method C is the most accurate because it results in much smaller intermediate values. Using Method A or B, intermediate values can be larger in size than $100,000,000, which means the round-off error (for IEEE single-precision) would be around the "tens" digit. These round-off errors can accumulate.

Since the function returns the minimum of the three methods, we conclude that the author of the code intended the software to under-report the net value of the calculation, and "skim" the unreported dollars into their own bank account.