# Going past the float size limits?

Steven D'Aprano steve at REMOVE-THIS-cybersource.com.au
Sat Oct 27 03:35:28 CEST 2007

```On Fri, 26 Oct 2007 16:29:34 -0700, jimmy.musselwhite wrote:

> On Oct 26, 6:56 pm, "Chris Mellon" <arka... at gmail.com> wrote:
>> On 10/26/07, jimmy.musselwh... at gmail.com <jimmy.musselwh... at gmail.com>
>> wrote:
>>
>> > Hello all
>> > It would be great if I could make a number that can go beyond current
>> > size limitations. Is there any sort of external library that can have
>> > infinitely huge numbers? Way way way way beyond say 5x10^350 or
>> > whatever it is?
>>
>> > I'm hitting that "inf" boundary rather fast and I can't seem to work
>> > around it.
>>
>> What in the world are you trying to count?
>
> The calculation looks like this
>
> A = 0.35
> T = 0.30
> C = 0.25
> G = 0.10
>
> and then I basically continually multiply those numbers together. I need
> to do it like 200,000+ times but that's nuts.

Because this is homework, I'm not going to give you the answer. But I
will give you *almost* the answer:

(A*T*C*G)**200000 = ?.03?10875*10**-51?194

Some of the digits in the above have been deliberately changed to
question marks, to keep you honest.

> I can't even do it 1000
> times or the number rounds off to 0.0. I tried taking the inverse of
> these numbers as I go but then it just shoots up to "inf".

Hint:

If we multiply A*T*C*G, we get 0.002625.

That's the same as 0.2625 with a (negative) scale factor of 2.

Another hint: for calculations of this nature, you can't rely on floating
point because it isn't exact. You need to do everything in integer maths.

A third hint: don't re-scale the product too often.

Enough clues?

--
Steven.

```