Laura Creighton <l...@openend.se> writes: > In a message of Mon, 01 Jun 2015 19:45:31 +1000, Chris Angelico writes: >>On Mon, Jun 1, 2015 at 5:58 PM, Laura Creighton <l...@openend.se> wrote: >>> If you are giving a talk about Decimal -- and trying to stamp out the >>> inappropriate use of floats you have to first inform people that >>> what they learned as 'decimals' as children was not floating point, >>> despite the fact that we write them the same way.
That may be focusing on the wrong aspect because what you learn in school (at least in the UK) is not so dissimilar to floating point arithmetic. The differences between that and machine floating point are that (a) machines typically use base 2 (so the set of fractions that can be represented exactly is a surprise); (b) machines use fixed-size floating point whereas at school the representation, whilst always finite, is more elastic; and (c) the base you calculate in is the base you are given the data in and also the base you have to give the result in. For example, when a pupil is asked to "calculate 1.5 x 10^3 + 1.01 x 10^2 to two decimal places" what they will do is very similar to what a machine would do if it had decimal floating point. The surprises that come from using typical machine floating point come from two base conversions and (possibly) from rounding at every stage rather than just at the end. <snip> > You have missed my point. What I want is for floats never to be > represented as '.' or ',' notation. That way, when each naive > user writes his or her first program that deals with money, when > they look at their computer manual they will come to the section on > floating point numbers and they will all look like something they > have never seen before. I agree that the key in to learn enough about what is going on. Maybe the solution is to teach people fixed-width binary floating point arithmetic in schools! > So they will read the section carefully > to see if this is what they want or need, and the section can nicely > say NEVER USE THIS FOR MONEY and they will know they are in the wrong > place. I know what you mean by this but it still bothers me a bit! My first job was writing programs for an economist. It was all about money but, being macro economics, was all in floating-point. (In those days you could not solve sets of non-linear differential equations in reasonable time using anything else, but even if you could there would be no point.) Even some kinds of accounting can be done using floating point. You can use "scaled integers" in floating point to get some advantages over integer arithmetic. You might get a wider range (~53 bits rather than 32 say) and you get very simple checks for many overflow conditions. You can also arrange for a simple check that you've failed to round correctly at some step -- any non-integer fractional part will usually indicate this. I'm not averse to a blanket warning as the simplest way to get the message across to beginners, but it's slowly becoming a "fact" that nothing to do with money can be done correctly using floating point. <snip> -- Ben. -- https://mail.python.org/mailman/listinfo/python-list
