> Decimal is also not a solution to floating point approximation.
Then what is the solution?
As someone whose worked with finance where floating point approximation lead to one being attacked by auditor's chasing 1 cent error that somehow crept in over millions of operations, what other choices are there?
Floating point introduces the worst sort of error. If you are expecting exact results floating point gets it right with almost no effort 99.999% of the time. The remaining 0.001% it gets it wrong, and it happens at seemingly random. A heisenbug in other words. But if you force programmers to use integers, all those missing fractions of cents suddenly become glaringly obvious.
Decimals / fixed point / integers don't "solve" the approximation problem. They just make it plain, forcing programmers to think about it, code for it, and test for it. If you care about what happens to every last bit, then there is no other solution.
Or to put it another way, if you don't particularly care what happens to the lsb, then fine use floating point. Problems happen because people really do care, but are seduced by floating points 99.999% success rate and use it anyway. Hint: if you are comparing for the equality of two numbers computed in two different ways, you absolutely care.
I should have specified ‘decimal floating point’ for clarity, since that is what Python's Decimal is. I agree that non-floating representations often are the solution, depending on what problem you have.
Then what is the solution?
As someone whose worked with finance where floating point approximation lead to one being attacked by auditor's chasing 1 cent error that somehow crept in over millions of operations, what other choices are there?
Floating point introduces the worst sort of error. If you are expecting exact results floating point gets it right with almost no effort 99.999% of the time. The remaining 0.001% it gets it wrong, and it happens at seemingly random. A heisenbug in other words. But if you force programmers to use integers, all those missing fractions of cents suddenly become glaringly obvious.
Decimals / fixed point / integers don't "solve" the approximation problem. They just make it plain, forcing programmers to think about it, code for it, and test for it. If you care about what happens to every last bit, then there is no other solution.
Or to put it another way, if you don't particularly care what happens to the lsb, then fine use floating point. Problems happen because people really do care, but are seduced by floating points 99.999% success rate and use it anyway. Hint: if you are comparing for the equality of two numbers computed in two different ways, you absolutely care.