Correcting Rounding Errors

In February, 2013, the patent office issued patent #8370226 to Patanjali Bhatt (Intuit) that describes a technique for correcting rounding errors. The example shown in the patent is:

  Financial value ($) Rounded financial values ($) Rounding error values ($)
  1.51 2 0.49
  1.51 2 0.49
  1.51 2 0.49
Total financial value - 6 -
Total error value - - 1.47
Rounded total error value - - 1
Corrected total financial value - 5 -

The “Total financial value” (6) is the sum of rounded numbers, and is called the pedantic sum in Whitebirch software as opposed to the accurate sum (5). The patent describes how to compute the accurate sum, as follows:

Abstract: A technique for performing a financial calculation is described. In this calculation technique, initial financial values are rounded based on a rounding criterion, and a total financial value is calculated by summing the rounded financial values. Based on the rounded financial values, associated rounding error values are computed. These rounding error values are then summed to determine a total error value. Moreover, the total error value is rounded based on the rounding criterion, and the resulting rounded total error value is used to correct a rounding error in the total financial value.



A more direct and obvious approach is to simply round the sum of initial financial values, an approach used by Excel as well as thousands of other programs over the past few decades. To be valid a patent must be non-obvious, so I suppose you could say this patent meets that criterion since it does not use the obvious approach. It is doubtful that this patent will ever go to court, because why would anyone use a convoluted patented computation, when the obvious prior art is so much better. Nevertheless, the patent office has awarded such a meaningless patent to Intuit. Fortunately, for Intuit, the patent is not funny enough to make any of the top 5 ridiculous patents lists.

Most people are more bothered by the reverse problem, that is, seeing 2+2+2 = 5, in a financial report, even though it is the more accurate answer. When these cases occur, there are three acceptable ways to “fix” (as oppose to “correct”) this issue:

  1. Use a pedantic sum; in other words, change the “5” to a “6”. This is acceptable as long as materiality is not compromised. (There are far more posts about how best to compute a pedantic sum than an accurate sum, suggesting that accurate sums are more obvious than pedantic sums, the opposite of what the patent asserts.)

  2. Add a footnote to the effect that totals may not equal the sum of components due to rounding, but be careful about how it is worded. One company mistakenly used the blooper phrase "fudge this" in their public financial statements instead of the standard phrase.

  3. Add an additional line item that includes rounding errors. The example above can be rewritten as
      2
      2
      2
    Rounding error -1
    Total 5

Finally, don’t be misled by this example and dismiss this as a “off by 1” trivial little problem. The difference between the accurate sum and pedantic sum can be quite large. If you spend 49 cents per day on a newspaper and sum up how much you spend in dollars over a year, the accurate sum is $179, but the pedantic sum is $0. Sometimes, companies will use deceptive rounding to exaggerate earnings.