Re: [boost] Interest in an arbitrary precision library?

From: Lucas Galfaso (lgalfaso_at_[hidden])
Date: 2005-09-03 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.)  Built-in 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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