[erlang-questions] why do I see a message about area of a square
Roelof Wobben
<>
Tue Jan 27 14:14:20 CET 2015
schreef op 27-1-2015 om 13:03:
>> As I understand it right. The eror message is on all functions so on the
>> square, circle and triangle functions.
>> And if not so, why also not a error functions on the other two.
> You have ONE area/1 function; the error message applies to it.
>
> By the way, you are -import+ing math:sqrt/1.
> I like that; I appreciate seeing in one place which external
> functions are used. But the actual point of -import in Erlang
> is to let you call the imported function *without* a module
> prefix. That's considered a bad idea, and indeed, you do use
> a module prefix. But that means the -import directive was
> pointless. You are calling math:pi() without any -import
> directive, after all.
>
> I know this is a toy exercise, but I do think I should point out
> for the unwary that
>
>>>> area({triangle, A, B, C}) ->
>>>> S = (A + B + C)/2,
>>>> math:sqrt(S*(S-A)*(S-B)*(S-C));
> is a poor way to calculate the area of a triangle.
> It's great mathematics, but Kahan ("Dr IEEE floats") has
> explained that it is very bad *computationally*.
> Let's see if I can approximate his explanation.
>
> Suppose we have a tall skinny triangle, so that A and B are nearly
> equal, and C is quite small in comparison. Then S is very nearly
> A (and so very nearly B). This means that S-A involves
> *catastrophic cancellation*, where the result has a lot fewer
> significant digits than you expect.
>
> For example, suppose we have 7 decimal digits of precision,
> and A = B = 1000.0, C = 1.0. Then S = 1000.5.
> A = 1.000000e3
> S = 1.000500e3
> S-A = #.###500e3 (using # for 0 to highlight lost significance)
> and the result has 3 digits of precision, not 7.
>
> Ah. Here's Kahan's paper: www.cs.berkeley.edu/~wkahan/Triangle.pdf
>
> area({triangle, A, B, C}) ->
> 0.25*math:sqrt((A+(B+C))*(C-(A-B))*(C+(A-B))*(A+(B-C)));
>
> is an Erlang version of Kahan's improved formula -- assuming,
> which I would not advise, that I have not made any mistakes in copying it.
>
>
Thanks for the explanation.
Roelof
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