OT: PHP 32 bit numbers security issue

[Uri Even-Chen]

On Wed, Jan 5, 2011 at 13:07, Tzafrir Cohen <tzafrir at cohens.org.il> wrote:
> On Wed, Jan 05, 2011 at 12:40:14PM +0200, Uri Even-Chen wrote:
>> I hate floating point. if you search Google for 2^1023,
>
>
>
>> you get this result:
>>
>> 2^1023 = 8.98846567 × 10^307
>>
>> However if you search for 2^1024, you don't get a number at all.
>
> Do you prefer to do that in fixed-point?
>
> It's actually neat to be able to use a relatively low number of bits and
> still say something meaningfull about 2^1023 .

Actually since long time ago I am thinking about better representation
of numbers. I think numbers should be 100% accurate, at least with
rational numbers. Using many bits is not a problem now, and also the
time it takes to calculate mathematical expressions is much much less
than the time it takes to run graphical software, so I think a
rational number can be represented by a division of two integers;
integers can be represented in binary form and if floating point is
used - there should not be any limit to both the accuracy and the
exponent. for example if a number needs 1024 bits for accuracy, I
think it's not too much, and the exponent should be at least 32 bits
long. Many times I want to calculate specific expressions, such as the
square root of googolplex, and I think we should move to represent
numbers in a way that such calculations will be possible.  Anyway I
think googol^4 and even googol^10000 should always return a result in
any calculator.  For example ln(googol^10000) is a small number, I
don't think I have to switch to 10000*ln(googol) if I want to
calculate it (of course with irrational numbers, we need to define the
precision. this should also be user-defined parameter and not fixed).

>
> --
> Tzafrir Cohen         | tzafrir at jabber.org | VIM is
> http://tzafrir.org.il |                    | a Mutt's
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>
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Uri Even-Chen
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E-mail: uri at speedy.net
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