[Haskell] for large x, log (x::Integer) :: Double

Graham Klyne GK at ninebynine.org
Wed Jun 30 15:06:50 EDT 2004

At 06:47 30/06/04 -0700, Hal Daume III wrote:
>i'm looking for an accurate way to take the log of a very large integer,

This may not help, but just in case... there is an effective (approximate) 
algorithm for computing a log-gamma function, documented in "Numerical 
Recipies" by Press/Flannery/Teukolsky/Vetterling.

If you want more info, I have an implementation in Mathematica somewhere, 
and could dig out a more specific reference.

The alternative way I'd consider involves building a power series of 
(2^(2^i))  and performing a compare-and-divide-and-sum so that you get n 
and x in 2^n*x, for x in the range (0.0..1.0) (or any other range that you 
may choose).


At 06:47 30/06/04 -0700, Hal Daume III wrote:
>i'm looking for an accurate way to take the log of a very large integer,
>for example:
>   let x :: Integer = 
> 1301427272151881160612765560226881966218101403436917787184856303672382623256898455416763978959067300249652773943715743032733292602624834984761739233232794619193611954735720284761058146899246611113236700853600891798968920775344491685185906922596026543915321367577774522912315930144523472702386240645993859368230855941019371447058664115974032571881072431604651385520393674840678811793554266595013773947434115579588912967969680150473258236727830867832149867100437142705476716669039640252677955201589378051836112800268367331455296715904387732836350613539218249950829555418397197909288345303407194983545308212828662999623279222913080214196287140117582811769188486693208227570257136851945943408206281672555558289460256867016896063334140640075708083581866297494610834545554864846306383014549439540479675828018496049574066533167553894586573246931377586176000
>this # is approximately 10^850.
>not surprisingly, if i do:
>   log (fromIntegral x) :: Double
>i get "Infinity".
>i can think of several ways to try to combat this: (1) divide x by
>something large (10^850) and then take the log of the integer part
>(requires finding that x ~ 10^850 by some search method); (2) multiply x
>by something large (10^10) and then take the log of this *as an Integer*
>and then convert that to a double.
>has anyone encountered this problem before?  surely there must be a "good
>way" to do this...
>  - hal
>  Hal Daume III                                   | hdaume at isi.edu
>  "Arrest this man, he talks in maths."           | www.isi.edu/~hdaume
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>Haskell at haskell.org

Graham Klyne
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