How to handle precision and rounding errors in currency?

Question

Things I know from other SO questions:

• I must use either ints or Java's BigDecimal (Java is my case, though the question is broader), not floating point types.
• I must store at a minimum one more decimal place than what I want to show. In my case I want to show 2 decimal places. The convention is to use decimal(19,4) in the database (in my case it's Postgres, but again this question is broader)

When I have in memory a bill with 101 items each costing $1.00004999999999999 my calculated total from adding all BigDecimals of value $1.00004999999999999 (or all integers if I were to choose that representation) would be $101.005049999999999 which is rounded to $101.01.

If I store 4 decimal places in the DB, each item will be rounded and stored as $1.0000, and when I pull them from database and add them up I get $101.0000, rounded to $101.00.

If I increase the storage precision to decimal(19,5) I need 1001 items instead of 101 for that to happen, but it is still possible. It will always be something that can happen, though one possible solution is to increase storage precision so much that this error is less likely to happen than a lightning striking the computer.

So far my solution is to never use BigDecimal, but instead always use BigDecimal.setScale(4), which sets it to 4 decimal places. Would you suggest a different approach?

Things that I know won't work:

• Calculating the total after storage. I need to calculate it with JavaScript while the user is inputing the data.
• Never doing calculations with rounded values. I don't know of a way to store them without rounding them
• Never rounding up, always down. If I have a tax value of 1.005049999 it must be shown as 1.01. It's a business rule. I could challenge it, but there must be a way that doesn't impact the way the business works.

Other considerations:

• I don't care much about execution speed or memory usage.

Answer 1

Always use integer math for currency. Never store currency as a floating point value. Currency is a fixed point value. Store all currency values as an integer that represents the smallest denomination that matters to your system. For example, if you are using USD and the smallest denomination you care about is a penny ($0.01) then store currency values as a count of pennies. If you care about thousandths of a penny ($0.00001) then store that.

Answer 2

您可能需要考虑始终以完全精度存储BigDecimal值，以完全精度执行所有计算，并且仅在最后可能时刻舍入值。这样，您的舍入错误就不会累积。

但是，我必须质疑你的例子。您创建了一个正确答案为$ 101.005的情况。目前尚不清楚该值应该如何舍入。我们传统上总结为五，但这是因为，如果有任何其他数字，它更接近于较高的值而不是较低的数字。但是当它全为零时，它同样接近每个有效值，所以我不确定在这种情况下是否有正确的答案。