From e98fc279e28de4817831a9d11ec99b83a3f49d02 Mon Sep 17 00:00:00 2001
From: Gabor Greif
The +User class provides a base for expressing the ownership of User +towards other +Values. The +Use helper class is employed to do the bookkeeping and facilitate O(1) +addition and removal.
+ ++ ----------------------------------------------------------------- + --- Interaction and relationship between User and Use objects --- + ----------------------------------------------------------------- + + +A subclass of User can choose between incorporating its Use objects +or refer to them out-of-line by means of a pointer. A mixed variant +(some Uses inline others hung off) is impractical and breaks the invariant +that the Use objects belonging to the same User form a contiguous array. + +We have 2 different layouts in the User (sub)classes: + +Layout a) +The Use object(s) are inside (resp. at fixed offset) of the User +object and there are a fixed number of them. + +Layout b) +The Use object(s) are referenced by a pointer to an +array from the User object and there may be a variable +number of them. + +Initially each layout will possess a direct pointer to the +start of the array of Uses. Though not mandatory for layout a), +we stick to this redundancy for the sake of simplicity. +The User object will also store the number of Use objects it +has. (Theoretically this information can also be calculated +given the scheme presented below.) + +Special forms of allocation operators (operator new) +will enforce the following memory layouts: + + +# Layout a) will be modelled by prepending the User object +# by the Use[] array. +# +# ...---.---.---.---.-------... +# | P | P | P | P | User +# '''---'---'---'---'-------''' + + +# Layout b) will be modelled by pointing at the Use[] array. +# +# .-------... +# | User +# '-------''' +# | +# v +# .---.---.---.---... +# | P | P | P | P | +# '---'---'---'---''' + + (In the above figures 'P' stands for the Use** that + is stored in each Use object in the member Use::Prev) + + +Since the Use objects will be deprived of the direct pointer to +their User objects, there must be a fast and exact method to +recover it. This is accomplished by the following scheme: + +A bit-encoding in the 2 LSBits of the Use::Prev will allow to find the +start of the User object: + +00 --> binary digit 0 +01 --> binary digit 1 +10 --> stop and calc (s) +11 --> full stop (S) + +Given a Use*, all we have to do is to walk till we get +a stop and we either have a User immediately behind or +we have to walk to the next stop picking up digits +and calculating the offset: + +.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---------------- +| 1 | s | 1 | 0 | 1 | 0 | s | 1 | 1 | 0 | s | 1 | 1 | s | 1 | S | User (or User*) +'---'---'---'---'---'---'---'---'---'---'---'---'---'---'---'---'---------------- + |+15 |+10 |+6 |+3 |+1 + | | | | |__> + | | | |__________> + | | |______________________> + | |______________________________________> + |__________________________________________________________> + + +Only the significant number of bits need to be stored between the +stops, so that the worst case is 20 memory accesses when there are +1000 Use objects. + +The following literate Haskell fragment demonstrates the concept: + +> import Test.QuickCheck +> +> digits :: Int -> [Char] -> [Char] +> digits 0 acc = '0' : acc +> digits 1 acc = '1' : acc +> digits n acc = digits (n `div` 2) $ digits (n `mod` 2) acc +> +> dist :: Int -> [Char] -> [Char] +> dist 0 [] = ['S'] +> dist 0 acc = acc +> dist 1 acc = let r = dist 0 acc in 's' : digits (length r) r +> dist n acc = dist (n - 1) $ dist 1 acc +> +> takeLast n ss = reverse $ take n $ reverse ss +> +> test = takeLast 40 $ dist 20 [] +> + +Printing+ +gives: "1s100000s11010s10100s1111s1010s110s11s1S" + +The reverse algorithm computes the +length of the string just by examining +a certain prefix: + +> pref :: [Char] -> Int +> pref "S" = 1 +> pref ('s':'1':rest) = decode 2 1 rest +> pref (_:rest) = 1 + pref rest +> +> decode walk acc ('0':rest) = decode (walk + 1) (acc * 2) rest +> decode walk acc ('1':rest) = decode (walk + 1) (acc * 2 + 1) rest +> decode walk acc _ = walk + acc +> + +Now, as expected, printing gives 40. + +We can quickCheck this with following property: + +> testcase = dist 2000 [] +> testcaseLength = length testcase +> +> identityProp n = n > 0 && n <= testcaseLength ==> length arr == pref arr +> where arr = takeLast n testcase + +As expected gives: + +*Main> quickCheck identityProp +OK, passed 100 tests. + +Let's be a bit more exhaustive: + +> +> deepCheck p = check (defaultConfig { configMaxTest = 500 }) p +> + +And here is the result of : + +*Main> deepCheck identityProp +OK, passed 500 tests. + + +To maintain the invariant that the 2 LSBits of each Use** in Use +never change after being set up, setters of Use::Prev must re-tag the +new Use** on every modification. Accordingly getters must strip the +tag bits. + +For layout b) instead of the User we will find a pointer (User* with LSBit set). +Following this pointer brings us to the User. A portable trick will ensure +that the first bytes of User (if interpreted as a pointer) will never have +the LSBit set. +