scalar evolution to determine access functions in arays


How can I compute the functions on the loop iterators used as array indices?

For example:

for i = 0, N
for j = 0, M
A[2*i + j - 10] = …

Can I obtain that this instruction A[2i + j - 10]= … always accesses memory using a function f(i,j) = 2i + j - 10 + base_address_of_A

If I run the scalar evolution pass on this code I obtain:

%arrayidx = getelementptr inbounds [200 x i32]* @main.A, i32 0, i64 %idxprom

→ ((4 * (sext i32 (-10 + (2 * %tmp6) + %tmp7) to i64)) + @main.A)

Could you please offer an insight on how can I obtain the function from the internals of the scalar evolution pass?
Thank you.


Hello Alexandra,

The scalar evolution pass doesn’t to anything when it runs except initialize some empty maps. The important one is the Value->SCEV map. SCEV is the class that holds an expression tree. Scalar evolution populates this map on-demand when the client asks for an expression via ScalarEvolution::getSCEV(Value).

IndVarSimplify and LoopStrengthReduce are example SCEV clients.

Just be careful to invalidate SCEV entries when you mutate the IR.


Hi Alexandra,

sorry for the delay, I was a little bit busy.

In general your approach is correct, but scalar evolution is in your case not able to derive an access function that is defined in terms of loop iterators. (If it would you would have something like {0, + 1}<loop_1> in your scev expression).

What I suspect is that you need to run some canonicalization passes before you actually run the scalar evolution pass. Most of the time these passes should be sufficient:
-correlated-propagation -mem2reg -instcombine -loop-simplify -indvars

But in Polly we use e.g.:
-basicaa -mem2reg -simplify-libcalls -simplifycfg -instcombine -tailcallelim -loop-simplify -lcssa -loop-rotate -lcssa -loop-unswitch -instcombine -loop-simplify -lcssa -indvars -loop-deletion -instcombine -polly-prepare -polly-region-simplify -indvars

If you send me the .ll file you run your tool on, I could take a closer look.

Cheers and all the best

Hello Tobi,

You are right, we need to run some other passes before running the scalar evolution pass. The sequence that I run for this example is -O3 -loop-simplify -reg2mem. This is why I did not obtain the expressions depending on the loop indices. So I removed the reg2mem pass and scalar evolution computes the correct functions.

However, I need to run the reg2mem pass (or any other that would eliminate the phi nodes) before calling my own passes. So probably we are going to run the scalar evolution on the code containing the phi nodes, run reg2mem and try to identify the original variables in the new code built after reg2mem.

Thanks for your advice,

Just out of interest. Why do you need to run the reg2mem pass?


Only because in my next passes I change the CFG significantly and it is very hard to maintain the values of the Phi nodes.


OK. In Polly we developed a pass called, 'independent-blocks-pass'. It basically creates basic blocks, that can easily be rescheduled without stopping the scalar evolution analysis to work. Maybe something similar can help you. Details about this pass are available in my thesis.


Ok, thank you, I will have a look and reply with questions if necessary. Does it take into consideration the existing phi nodes?


It is extremely polyhedral. The basic idea is that all calculations that scalar evolution can analyze (including canonical induction variables), are kept in registers. Any other values are promoted to memory.

As we keep the information about operations scalar evolution can express in our polyhedral data structures, we do not care about them while reworking the CFG. When generating the changed structure, we create new expressions that calculate loop bounds and access functions.

In respect of PHI nodes, we keep the canonical induction variables as PHI nodes. Those are ignored during reworking the CFG and regenerated from the polyhedral description. All other PHI-node (are promoted to memory. Those are basically the inter basic block, scalar dependences.