And for associative and commutative functions it doesn’t matter what order they’re executed in the final result is always the same.
Not directed at you specifically, but just a reminder for anyone who hasn’t been burned by it yet: floating point addition is not associative. (a+b)+c != a+(b+c). It’s close, but if you’re not careful you can get bad results where the accumulated small errors turn into wrong answers.
Not just floating point maths either. The built-in "integers" in your computer don't behave like the integers taught in school either but that's how we tend to think about them. This is why I argue trapping is the most acceptable choice for arithmetic problems in general purpose languages, if the program tries to add 150 to 150 in an unsigned 8-bit integer, that's a programming error. By all means offer wrapping arithmetic, sometimes it's what the programmer actually wanted and they benefit from being able to clarify that - but most often they didn't want that and would be astonished that 150 + 150 = 44.
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Not directed at you specifically, but just a reminder for anyone who hasn’t been burned by it yet: floating point addition is not associative. (a+b)+c != a+(b+c). It’s close, but if you’re not careful you can get bad results where the accumulated small errors turn into wrong answers.
Not just floating point maths either. The built-in "integers" in your computer don't behave like the integers taught in school either but that's how we tend to think about them. This is why I argue trapping is the most acceptable choice for arithmetic problems in general purpose languages, if the program tries to add 150 to 150 in an unsigned 8-bit integer, that's a programming error. By all means offer wrapping arithmetic, sometimes it's what the programmer actually wanted and they benefit from being able to clarify that - but most often they didn't want that and would be astonished that 150 + 150 = 44.
It can overflow, but integer math is associative and commutative still, isn’t? It’s just modulo the biggest representable number (if unsigned).