On 3/6/2024 12:49 PM, Carl Linkletter via gnucash-user wrote:
OK, Found the bug. The problem is that the tax is totaled up using sub-penny
calculations. That causes a 1.004 + 1.004 to equal 2.008 which is then rounded
to 2.01. Each line should be rounded to the penny first, then rounded up. So
if 1.004 is first rounded to 1.00, then that would cause this calculation to
total 2.00, not 2.01.
If that makes any sense :-) Guess I will enter a bug on this.
Does NOT solve the problem (rounding to the penny first). It is simply
the case that rounded(A) + rounded(B) /= rounded(A+B).
You have given an example where 1.004 + 1.004 would give 2.00 if rounded
first and 2.01 if rounded after adding. But how about 1.004 + 1.004 +
1.004 which would give 3.00 if rounded before adding and 3.01 if rounded
after.
The problem is actually because of using "reals" to represent decimal
quantities. Now MY working days were spend with machines whose
architecture directly supported expressing decimals in BCD (binary coded
decimal). But the fact that our current CPUs don't directly support BCD
representation and arithmetic does not mean couldn't emulate that in
software (in our higher level language). Most of us using c++ are doing
that so we don't have to "roll our own" << c++ is actually a
"pre-processor" for c >> Somebody like me COULD come up with a BCD
arithmetic package and I assume existing developers could also.
The point is that people like the late Admr. Grace Murray Hopper (WWII
cryptologist, designer of COBOL) understood that using reals to express
decimals would have this problem and so used BCD for money amounts.
That's because intended for business and business implies money amounts.
THEN machine were made with architecture to directly support it.
Michael D Novack
PS --- BCD is essentially "integer" representation and math with the
"display amount" handling the editing to insert the decimal point. Now
the only arithmetic operation raising a rounding issue is division.
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