Least Recently Used (LRU) Approximations

1
Least Recently Used (LRU) Approximations

• Objective is to approximate Least Recently Used,
  as a predictor of future page use.
• Useful ideas for virtual memory and caching
  both replace pages
• Two Example Strategies
• Reference Bits
• use a set of bits to track the usage of a page,
  then make page replacement decisions based on the
  tracking data
• Second Chance Algorithm
• use a single bit to track usage

2
Reference Bits

• Implemented in hardware
• Uses a single bit to track recent access (per
  page)
• Uses a set of reference bits to store access
  history (per page)
• Every time a page is accessed, its accessed bit
  is set
• Periodically, the access bit is merged with the
  reference bits
• Shift reference bits to the right
• Add access bit in high-order bit position
• Reset the access bit
• The reference bits can be used to decide which
  page has been least recently accessed.
• High number is more recently access than low
  number

3
Second Chance Algorithm

• Pages are listed in a FIFO queue
• Each page has a single accessed bit
• When need to swap out a page To find the page
  to replace
• Start at top of list
• If pages reference bit is set, skip this page
  (but reset the bit to zero)
• If pages reference bit is reset, swap this page
• If reached the bottom of the list
• (all bits were set, but have now been reset),
• start over at the top (and replace that one)

4
Examples on Board

• Optimal
• FIFO
• Beladys Anomaly
• LRU
• Ref bits
• Second Chance FIFO

5
Work?

• The update of the reference bits can be done in
  hardware
• But what about the selection process finding
  the LRU
• Sequential search for ref bits? Order n O(n)
• Store pages in a binary tree? Order logn
  O(logn) (base 2)
• Second Chance FIFO
• Best case first one checked
• Worst case go around and start back at the top
  (n1)
• Average expected about n/2
• If n is large, then unacceptable
• Next a parallel implementation
• LRU reference bit compare by Self-Selection