[ANN] New version of the MasterLibrary is available

[Geoff Canyon]

I couldn't resist. __nCombFactors is slower than __nCombFloor, although
faster than the original function (slightly, in my testing), but it offers
the advantage that any result that is within the number limits of LC will
be returned correctly, regardless of how large the intermediate values
would be if they were calculated. For example, __nCombFactors is the only
one that (I think) returns the correct value for 80 c 40

The next step (obviously) would be to add a bignum * function, so that
nearly any combination could be calculated.

function __factorialFloor x,f
   if x <= f then return 1
   return x * __factorialFloor(x-1,f)
end __factorialFloor

function __nCombFloor n, r
   if (r > 0) or (r <= n) then \
         return __factorialFloor(n,max(r,n-r))/__factorial(min(r,n-r))
   Answer "nComb error:" && r && "is not between 0 and" && n
   exit to top
end __nCombFloor

function __nCombFactors n, r
   if (r <= 0) or (r > n) then
      Answer "nComb error:" && r && "is not between 0 and" && n
      exit to top
   end if
   put __factorialFactors(n,max(r,n-r)+1) into tNum
   put __factorialFactors(min(r,n-r)) into tDen
   put __removeItems(tNum,tDen) into c
   replace comma with "*" in c
   if c is empty then return 1 else return value(c)
end __nCombFactors

function __removeItems N,D
   repeat until D is empty
      if item 1 of D > item 1 of N then
         put item 1 of N & comma after R
         delete item 1 of N
      else
         delete item 1 of N
         delete item 1 of D
      end if
   end repeat
   if N is empty then return char 1 to -2 of R else return R & N
end __removeItems

function __factorialFactors x,f
   if f is empty then put 2 into f
   repeat with i = f to x
      put __primeFactors(i),"" after R
   end repeat
   sort items of R numeric
   return char 2 to -1 of R
end __factorialFactors


function __primeFactors x
   repeat with i = 2 to x div 2
      repeat until x mod i <> 0
         put i,"" after R
         put x div i into x
         if x = 1 then return char 1 to -2 of R
      end repeat
   end repeat
   return x
end __primeFactors

On Sun, Feb 1, 2015 at 2:08 PM, Geoff Canyon <gcanyon at gmail.com> wrote:

> You could handle (some) larger combinatorials (and speed up the code) by
> modifying like so:
>
> function __factorialFloor x,f
>    if x <= f then return 1
>    return x * __factorialFloor(x-1,f)
> end __factorialFloor
>
> function __nCombFloor n, r
>    if (r > 0) or (r <= n) then \
>          return __factorialFloor(n,max(r,n-r))/__factorial(min(r,n-r))
>    Answer "nComb error:" && r && "is not between 0 and" && n
>    exit to top
> end __nCombFloor
>
> Of course, to handle even more/larger possible values you could decompose
> the arguments to their prime factors and eliminate dupes rather than
> divide, but this was a fairly easy optimization.
>
> On Sun, Feb 1, 2015 at 12:02 PM, Michael Doub <mikedoub at gmail.com> wrote:
>
>> Release 24
>> *    added:
>>     __Zap - a function that returns only POSIX printable characters,
>> space, tab and return from a
>>        string
>>     __GetRegexMatches - Finds all the matches of pregex in ptext and
>> returns a list of the
>>        start,end char positions
>>     __deleteExtraTokens - This fuction witll remove sequences of the
>> specified token that are greater than
>>        one.
>>    __combinatorial - returns all possible subsets of a set, where n = #
>> of objects in the set
>>    __nComb - Returns the # of combinations of n objects taken r at a time
>>    __factorial - Returns x!
>>    __latLongDist - Finds distances  between two points based on Latitude
>> and Longitude
>>    __dd2dms - Converts a digital longitude or Latitude into degrees,
>> minutes, seconds, direction format.
>>    __dms2dd - Converts a degrees, minutes, seconds, direction longitude
>> or latitude to digital format
>>
>> https://www.dropbox.com/s/3wpwn3hfbmpl7sk/MasterLibrary.livecode?dl=0
>>
>> Enjoy...
>>
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>
>