blaze

Link to tutorial IPython noteboook

A reimplementation of STOKE in haskell.

STOKE is a superoptimizer that finds optimal instruction sequences to perform a particular task by using MCMC methods to explore the large search space.

High level algorithm

What we do is to "MCMC-sample the space of possible programs, with a scoring function based on program equivalence and performance". Broken down, the steps are:

• Start with the original program p
• Perturb it slightly to get a program q (add an instruction, remove some instructions, change an instruction)
• Assign a score to q by sending p and q random inputs, and checking how often they answer the same.
• If they answered the same for all random inputs, ask an SMT solver nicely if p and q are equivalent. If she's in a good mood and the universe is kind, the answer is yes.
• Now, score q based on the factors of:
  1. Are p and q semantically equivalent?
  2. On how many inputs p and q had the same answer?
  3. is q faster than p?
• Now, either pick q to be the new p or stay at p depending on q's score.
• Repeat ~10,000 times.
• Order best qs visited.

The results are quite impressive: Even with code as naive as what I've written, we are able to regain peephole optimisations that compilers perform essentially "for free".

Sample output

*** original: (nparams: 0 | [IPush 2,IPush 3,IAdd])***
[IPush 5] | score: 2.5 // constant folding
[IPush 2,IPush 3,IAdd] | score: 2.125
[IPush 2,IPush 3,ISwap,IAdd] | score: 2.0625

*** original: (nparams: 1 | [IPush 2,IMul])***
[IDup,IAdd] | score: 2.25 // strength reduction: 2 * x -> x + x
[IDup,ISwap,IAdd] | score: 2.125
[IDup,ISwap,ISwap,IAdd] | score: 2.0625
[IDup,ISwap,ISwap,ISwap,IAdd] | score: 2.03125

*** original: (nparams: 1 | progInsts = [IDup,IAnd])***
[] | score: 3.0 // constant folding: x & x == x
[IDup,IAnd] | score: 2.25
[IDup,ISwap,IAnd] | score: 2.125