What is the size limit for numbers in LC? -- and multiplying really large numbers
Jerry Jensen
jhj at jhj.com
Thu Sep 5 19:06:33 EDT 2013
I think LC uses IEEE binary64 floating point format which can represent integers to 15+ digits exactly (52+1 bit mantissa). However, last time this came up somebody made an example that gave inconclusive if not downright confusing results. Its probably platform specific as well.
.Jerry
On Sep 5, 2013, at 3:54 PM, Geoff Canyon <gcanyon at gmail.com> wrote:
> I've written bignum routines for addition and multiplication several times
> when solving project euler problems. Generally my multiplication functions
> bog down at about 200 digits -- i.e. take more than a second to run.
>
> I decided to optimize, and about a dozen iterations later, the below is the
> result. It will multiply two 5,000-digit numbers in about a second on my
> machine, and even 20,000 digit multiplication seems to work in about 15
> seconds or so (woot!).
>
> Here's the weird part. I would have said that LC numbers are 32 bit, and
> lose their minds at about 2 billion. The temp variable S in this function
> gets large, and I wrote many lines of code working around that. Then I ran
> some tests, and seemingly when multiplying a string of 20,0000 nines --
> 99999999...999999 -- even though S gets up to 499,949,990,000, all is well,
> and the result is correct. I wonder how large S can get before it
> overflows? I did some quick experiments without hitting a conclusive
> answer, and I don't see it in the docs or online.
>
> In the meantime, multiply really big integers here:
>
> function bigTimes X,Y
> if char 1 of X is "-" then
> put "-" into leadChar
> delete char 1 of X
> end if
> if char 1 of Y is "-" then
> if leadChar is "-" then put empty into leadChar else put "-" into
> leadChar
> delete char 1 of Y
> end if
> put (3 + length(X)) div 4 * 4 into XL
> put char 1 to XL - length(X) of "000" before X
> put (3 + length(Y)) div 4 * 4 into YL
> put char 1 to YL - length(y) of "000" before y
> repeat with N = XL + YL down to 9 step -4
> repeat with M = max(4,N - YL) to min(XL,N - 4) step 4
> add (char M - 3 to M of X) * (char N - M - 3 to N - M of Y) to S
> end repeat
> put char -4 to -1 of S before R
> delete char -4 to -1 of S
> end repeat
> if S is 0 then put empty into S
> return leadChar & S & R
> end bigTimes
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