I just downloaded the Axiom book from
http://wiki.axiom-developer.org/public/book2.pdf
You can see in Ch. 2, "Using Axiom as a Pocket Calculator", how Axiom
does arithmetic with floats.
Kostas
Jay Belanger wrote:
> "Stavros Macrakis" <macrakis at alum.mit.edu> writes:
> ...
>> It may be worth noting that both Axiom and my pocket calculator give
>> the correct answer to 3*1.4^2.
>>
>> To how many digits? What are the results for (3*1.4^2)-5.88 or (5/9)*9-5? or sin
>> (3.1415926535897932385/4)-sqrt(1/2)?
>
>
> (1) -> (3*1.4^2) - 5.88
>
> (1) 0.0
> Type: Float
> (2) -> (5/9)*9-5
>
> (2) 0
> Type: Fraction Integer
> (3) -> sin(3.1415926535897932385/4)-sqrt(1/2)
>
> (3) 0.1 E -19
>
>> I don't know how Axiom operates. This may just be a rounding-on-display issue, or it
>> may actually calculate the answer differently internally (decimal floats? rationals?)
>
> I don't know much about the Axiom internals, either.
>
>> Your pocket calculator may operate in decimal floating-point, in which case it will
>> get exact answers for 3*1.4^2 and the like, but not for other calculations.
>
> Interesting. I realize that calculators typically only give
> approximations, but when does it give the wrong answer when you'd
> expect the right one? (I have no doubt such cases exist; I just don't
> know one offhand.)
>
>> Do you have any suggestions on how to improve things?
>
> No; I'm not being very helpful.
>
> Jay
>
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