#8898: Overall improvement for randomIvalInteger -------------------------------------+------------------------------------- Reporter: novadenizen | Owner: Type: bug | Status: new Priority: normal | Milestone: Component: libraries/random | Version: 7.9 Resolution: | Keywords: Operating System: Unknown/Multiple | Architecture: Unknown/Multiple Type of failure: Incorrect result | Difficulty: Easy (less than 1 at runtime | hour) Test Case: | Blocked By: Blocking: | Related Tickets: #5278 #5280 #1120 -------------------------------------+------------------------------------- Changes (by hvr): * related: 5278 5280 1120 => #5278 #5280 #1120 Old description:
The current randomIvalInteger implementation uses repeated div operations to approximate the size of the desired random output, then generates that number of random values from the given RandomGen. It does not compensate for the "mod base" uniformity problem. It also assumes that all RandomGen implementations produce the same range of random values as StdGen.
My new implementation addresses all these correctness issues, with potentially a slight performance improvement.
Instead of performing repeated div base operations to determine the size of the desired range, this uses faster (* base) operations. An equivalent set of intermediate Integers is generated still.
To compensate for the "`mod` base" uniformity problem, the desired range size is multiplied by the q factor (1000 in my code). When k is the desired range and b^(n) is the range of numbers generated, and d = b^(n) div k, some elements will have probability d/b^(n) and others will have probability (d+1)/b^(n), resulting in significant nonuniformity when d is very small. When you extend the generated range beyond the minimum by a factor of q, you are guaranteeed that d will be at least q, so the nonuniformity will be much less consequential.
This implementation also works with any RandomGen, even ones that produce as little as a single bit of entropy per next call or have a minimum bound other than zero.
New description: The current `randomIvalInteger` implementation uses repeated `div` operations to approximate the size of the desired random output, then generates that number of random values from the given `RandomGen`. It does not compensate for the {{{`mod` base}}} uniformity problem. It also assumes that all `RandomGen` implementations produce the same range of random values as `StdGen`. My new implementation addresses all these correctness issues, with potentially a slight performance improvement. Instead of performing repeated div base operations to determine the size of the desired range, this uses faster `(* base)` operations. An equivalent set of intermediate `Integer`s is generated still. To compensate for the {{{`mod` base}}} uniformity problem, the desired range size is multiplied by the ''q'' factor (1000 in my code). When ''k'' is the desired range and ''b^n^'' is the range of numbers generated, and ''d = b^n^ div k'', some elements will have probability ''d/b^n^'' and others will have probability ''(d+1)/b^n^'', resulting in significant non- uniformity when ''d'' is very small. When you extend the generated range beyond the minimum by a factor of ''q'', you are guaranteed that ''d'' will be at least ''q'', so the non-uniformity will be much less consequential. This implementation also works with any `RandomGen`, even ones that produce as little as a single bit of entropy per next call or have a minimum bound other than zero. -- Comment: fixup wiki-markup in description -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/8898#comment:1 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler