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From: Lucas Galfaso (lgalfaso_at_[hidden])
Date: 20050903 15:08:53
Hi,
"Joel Eidsath" <jeidsath_at_[hidden]> wrote in message
news:431931ED.7060901_at_gmail.com...
>
>>
>>Do not agree. You should have ease of use _and_ efficiency. Modern C++
>>techniques allow for this.
>>
>>
> I was trying to give myself wiggle room, but I pretty much agree with
> you. I don't expect anything as fast as GMP, but I imagine that a plain
> C++ library could still do very well.
>
Agree, I do not want to compete with GMP on performance, but, without
sacrificing ease of use, have the best performance that a fully conformant
C++ implementation allows.
>>It is not clear to me what you mean by "useful for number theory". You
>>want
>>the library to handle Z[sqrt(2)](log(2)) arbitrarily good? (this question
>>is
>>not rhetoric)
>>
>>
> You would set the precision of your calculations with a function call.
> (Specify the number of digits of accuracy.)
>
> Example:
> set_precision(3);
> cout << arbitrary_sqrt(2) << endl;
> set_precision(10);
> cout << arbitrary_sqrt(2);
>
> Output:
> 1.414
> 1.4142135624
>
Ahh, ok I was thinking about a lazy evaluated, arbitrary precision, FP/big
int library.
>>>3) As well as arbitrary precision, it should provide error range math:
>>>2.00 * 2.00 is not generally the same thing as 2.0 * 2.0
>>>
>>>
>>
>>Do not fully understand, please expand this idea.
>>
>>
>>
> For example:
> 1.0 + 1.00 = 2.0 (plus or minus .05)
> 1.00 + 1.00 = 2.00 (plus or minus .005)
>
Ok, understood.
>>I do not fully like the idea of exceptions on the middle of my
>>computations,
>>I prefer to set the 'state' of the object to Nan. Even for big ints.
>>
>>
>>
> That would work too. Whatever the solution is though, I don't want it
> to attempt a normal int division by zero internally if asked to do a big
> int division by zero. There is no way to handle that sort of error at
> run time.
>
Agree.
>>>9) Precision for rational numbers may be set as a static member
>>>variable or it may not. In the second case, expressions involving
>>>rational numbers of different.
>>>
>>>
>>
>>I see no point in using rational numbers, but maybe I am missing
>>something.
>>
>>
>>
> By rational, I a type that is "more than just integers." (Mathematics
> is my field, not CS.) Builtin types like float and double hold
> rational numbers. So I am not talking about a struct that holds a
> numerator and a denominator, if that's what you were thinking.
>
Maths my field too (I thought you might figure that out of the expression
'Z[sqrt(2)])(log(2))' ) but now I do not understand your original point (9)
Anyway I can say I agree with you on almost everything. Do you want to move
forward with this idea?
> Joel Eidsath
Lucas Galfaso
>
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