6. HW6: Data Flow Analysis and Optimizations

6.1. Getting Started

Many of the files in this project are taken from the earlier projects. The new files (only) and their uses are listed below. Only those preceeded with an asterisk will need to be modified for this assignment.:

llprograms/*.ll    - example .ll programs used in testing
hw4programs/*.oat  - example .oat programs used in testing
hw5programs/*.oat  - example .oat programs used in testing
hw6programs/*.oat  - long-running .oat programs for benchmarking your optimisations

  datastructures.ml - set and map modules (enhanced with printing)
  cfg.ml            - "view" of LL control-flow graphs as dataflow graphs

  analysis.ml       - helper functions for propagating dataflow facts

  *solver.ml        - the general-purpose iterative dataflow analysis solver
  *alias.ml         - alias analysis
  *dce.ml           - dead code elimination optimization
  *constprop.ml     - constant propagation analysis & optimization

  liveness.ml       - provided liveness analysis code
  analysistests.ml  - test cases (for liveness, constprop, alias)

  opt.ml            - optimizer that runs dce and constprop

  *backend.ml       - you will implement register allocation heuristics here
  registers.ml      - collects statistics about register usage

  printanalysis.ml  - a standalone program to print the results of an analysis


As usual, running main.native –test will run the test suite. main.native also now supports several new flags having to do with optimizations:

  • -O1 runs two iterations of (constprop followed by dce)
  • --liveness {trivial|dataflow} select which liveness analysis to use for register allocation
  • --regalloc {none|greedy|better} select which register allocator to use
  • --print-regs print a histogram of the registers used

6.2. Overview

The Oat compiler we have developed so far produces very inefficient code, since it performs no optimizations at any stage of the compilation pipeline. In this project, you will implement several simple dataflow analyses and some optimizations at the level of our LLVMlite intermediate representation in order to improve code size and speed.

Provided Code

The provided code makes extensive use of modules, module signatures, and functors. These aid in code reuse and abstraction. If you need a refresher on OCaml functors, we recommend reading through the Chapter on Functors of Real World OCaml.

In datastructures.ml, we provide you with a number of useful modules, module signatures, and functors for the assignment, including:

  • OrdPrintT: A module signature for a type which is both comparable and can be converted to a string for printing. This is used in conjunction with some of our other custom modules described below. Wrapper modules Lbl and Uid satisfying this signature are defined later in the file for the Ll.lbl and Ll.uid types.
  • SetS: A module signature that extends OCaml’s built-in set to include string conversion and printing capabilities.
  • MakeSet: A functor which creates an extended set (SetS) from a type which satisfies the OrdPrintT module signature. This is applied to the Lbl and Uid wrapper modules to create a label set module LblS and a UID set module UidS.
  • MapS: A module signature that extends OCaml’s built-in maps to include string conversion and printing capabilities. Three additional helper functions are also included: update for updating the value associated with a particular key, find_or for performing a map look-up with a default value to be supplied when the key is not present, and update_or for updating the value associated with a key if it is present, or adding an entry with a default value if not.
  • MakeMap: A functor which creates an extended map (MapS) from a type which satisfies the OrdPrintT module signature. This is applied to the Lbl and Uid wrapper modules to create a label map module LblM and a UID map module UidM. These map modules have fixed key types, but are polymorphic in the types of their values.

6.3. Task I: Dataflow Analysis

Your first task is to implement a version of the worklist algorithm for solving dataflow flow equations presented in lecture. Since we plan to implement several analyses, we’d like to reuse as much code as possible between each one. In lecture, we saw that each analysis differs only in the choice of the lattice, “gen” and “kill” sets, the direction of the analysis, and how to compute the meet of facts flowing into a node. We can take advantage of this by writing a generic solver as an OCaml functor and instantiating it with these parameters.

The Algorithm

Assuming only that we have a directed graph where each node is labeled with a dataflow fact and a flow function, we can compute a fixpoint of the flow on the graph as follows (described in pseudocode):

let w = new set with all nodes
repeat until w is empty
  let n = w.pop()
  old_out = out[n]
  let in = combine(preds[n])
  out[n] := flow[n](in)
  if (!equal old_out out[n]),
    for all m in succs[n], w.add(m)

Here equal, combine and flow are abstract operations that will be instantiated with lattice equality, the meet operation and the flow function (e.g., defined by the gen and kill sets of the analysis), respectively. Similarly, preds and succs are the node predecessors and successors in the flow graph, and do not correspond to the control flow of the program. They can be instantiated appropriately to create a forwards or backwards analysis.


Don’t try to use OCaml’s polymorphic equality operator (=) to compare old_out and out[n] – that’s reference equality, not structural equality. Use the supplied Fact.compare instead.

Getting Started and Testing

Be sure to review the comments in the DFA_GRAPH (data flow analysis graph) and FACT module signatures in solver.ml, which define the parameters of the solver. Make sure you understand what each declaration the signature does – your solver will need to use each one (other than the printing functions)! It will also be helpful for you to understand the way that cfg.ml connects to the solver. Read the commentary there for more information.

Now implement the solver

Your first task is to fill in the solve function in the Solver.Make functor in solver.ml. The input to the function is a flow graph labeled with the initial facts. It should compute the fixpoint and return a graph with the corresponding labeling. You will find the set datatype from datastructures.ml useful for manipulating sets of nodes.

To test your solver, we have provided a full implementation of a liveness analysis in liveness.ml. Once you’ve completed the solver, the liveness tests in the test suite should all be passing. These tests compare the output of your solver on a number of programs with pre-computed solutions in analysistest.ml. Each entry in this file describes the set of uids that are live-in at a label in a program from ./llprograms. To debug, you can compare these with the output of the Graph.to_string function on the flow graphs you will be manipulating.


The stand-alone executable printanalysis.native (built via make) can print out the results of a dataflow analysis for a given .ll program. It takes flags for each analysis (run with --h for a list).

6.4. Task II: Alias Analysis and Dead Code Elimination

The goal of this task is to implement a simple dead code elimination optimization that can also remove store instructions when we can prove that they have no effect on the result of the program. Though we already have a liveness analysis, it doesn’t give us enough information to eliminate store instructions: even if we know the UID of the destination pointer is dead after a store and is not used in a load in the rest of the program, we can not remove a store instruction because of aliasing. The problem is that there may be different UIDs that name the same stack slot, and we need to ensure that removing a store operation does not affect the data those UIDs refer to. There are a number of ways this can happen after a pointer is returned by alloca:

  • The pointer is used as an argument to a getelementptr or bitcast instruction
  • The pointer is stored into memory and then later loaded
  • The pointer is passed as an argument to a function, which can manipulate it in arbitrary ways

Some pointers are never aliased. For example, the code generated by the Oat frontend for local variables never creates aliases because the Oat language itself doesn’t have an “address of” operator. We can find such uses of alloca by applying a simple version of an alias analysis.

Alias Analysis

We have provided some code to get you started in alias.ml. You will have to fill in the flow function and lattice operations. The type of lattice elements, fact is a map from UIDs to symbolic pointers of type SymPtr.t. Your analysis should compute, at every program point, the set of UIDs of pointer type that are in scope and, additionally, whether that pointer is the unique name for a stack slot according to the rules above. See the comments in alias.ml for details.

  1. Alias.insn_flow: the flow function over instructions
  2. Alias.fact.combine: the combine function for alias facts

Dead Code Elimination

Now we can use our liveness and alias analyses to implement a dead code elimination pass. We will simply compute the results of the analysis at each program point, then iterate over the blocks of the CFG removing any instructions that do not contribute to the output of the program.

  • For all instructions except store and call, the instruction can be removed if the UID it defines is not live-out at the point of definition
  • A store instruction can be removed if we know the UID of the destination pointer is not aliased and not live-out at the program point of the store
  • A call instruction can never be removed

Complete the dead-code elimination optimization in dce.ml, where you will only need to fill out the dce_block function that implements these rules.

6.5. Task III: Constant Propagation

Programmers don’t often write dead code directly. However, dead code is often produced as a result of other optimizations that execute parts of the original program at compile time, for instance constant propagation. In this section you’ll implement a simple constant propagation analysis and constant folding optimization.

Start by reading through the constprop.ml. Constant propagation is similar to the alias analysis from the previous section. Dataflow facts will be maps from UIDs to the type SymConst.t, which corresponds to the lattice from the lecture slides. Your analysis will compute the set of UIDs in scope at each program point, and the integer value of any UID that is computed as a result of a series of binop and icmp instructions on constant operands. More specifically:

  • The flow out of any binop or icmp whose operands have been determined to be constants is the incoming flow with the defined UID to Const with the expected constant value
  • The flow out of any binop or icmp with a NonConst operand sets the defined UID to NonConst
  • Similarly, the flow out of any binop or icmp with a UndefConst operand sets the defined UID to UndefConst
  • A store or call of type Void sets the defined UID to UndefConst
  • All other instructions set the defined UID to NonConst

(At this point we could also include some arithmetic identities, for instance optimizing multiplication by 0, but we’ll keep the specification simple.)

Next, you will have to implement the constant folding optimization itself, which just traverses the blocks of the CFG and replaces operands whose values we have computed with the appropriate constants. The structure of the code is very similar to that in the previous section. You will have to fill in:

  1. Constprop.insn_flow with the rules defined above
  2. Constprop.Fact.combine with the combine operation for the analysis
  3. Constprop.cp_block (inside the run function) with the code needed to perform the constant propagation transformation


Once you have implemented constant folding and dead-code elimination, the compiler’s -O1 option will optimize your .ll code by doing 2 iterations of (constant prop followed by dce). See opt.ml. The -O1 optimizations are not used for testing except that they are always performed in the register-allocation quality tests – these optimizations improve register allocation (see below).

This coupling means that if you have a faulty optimization pass, it might cause the quality of your register allocator to degrade. And it might make getting a high score harder.

6.6. Task IV: Register Allocation

The backend implementation that we have given you provides two basic register allocation strategies: none - spills all uids to the stack; greedy - uses register and a greedy linear-scan algorithm.

For this task, you will implement a better register allocation strategy that makes use of the liveness information that you compute in Task I. Most of the instructions for this part of the assignment are found in backend.ml, where we have modified the code generation strategy to be able to make use of liveness information. The task is to implement a single function better_layout that beats our example “greedy” register allocation strategy. We recommend familiarizing yourself with the way that the simple strategies work before attempting to write your own allocator. Also, take a look at the graph definitions we provided.

The compiler now also supports several additional command-line switches that can be used to select among different analysis and code generation options for testing purposes:

--print-regs prints the register usage statistics for x86 code
--liveness {trivial|dataflow} use the specified liveness analysis
--regalloc {none|greedy|better} use the specified register allocator

The flags above do not imply the -O1 flag (despite the fact that we always turn on optimization for testing purposes when running with --test). You should enable it explicitly.

For testing purposes, you can run the compiler with the -v verbose flag and/or use the --print-regs flag to get more information about how your algorithm is performing. It is also useful to sprinkle your own verbose output into the backend.

The goal for this part of the homework is to create a strategy such that code generated with the --regalloc better --liveness dataflow flags is “better” than code generated using the simple settings, which are --regalloc greedy --liveness dataflow. See the discussion about how we compare register allocation strategies in backend.ml. The “quality” test cases report the results of these comparisons.

Of course your register allocation strategy should produce correct code, so we still perform all of the correctness tests that we have used in previous version of the compiler. Your allocation strategy should not break any of these tests – and you cannot earn points for the “quality” tests unless all of the correctness tests also pass.

6.7. Task V: Experimentation / Validation

Of course we want to understand how much of an impact your register allocation strategy has on actual execution time. For the final task, you will create a new Oat program that highlights the difference. There are two parts to this task.

Create a test case

Post an Oat program to GitHub. This program should exhibit significantly different performance when compiled using the “greedy” register allocation strategy vs. using your “better” register allocation strategy with dataflow information. See the file hw4programs/regalloctest.oat and hw4programs/regalloctest2.oat for uninspired examples of such a program. Yours should be more interesting (or at least as interesting as programs in hw6programs).

Post your running time

Use the unix time command to test the performance of your register allocation algorithm. This should take the form of a simple table of timing information for several test cases, including the one you create and those mentioned below. You should test the performance in several configurations:

  1. using the --liveness trivial --regalloc none flags (baseline)
  2. using the --liveness dataflow --regalloc greedy flags (greedy)
  3. using the --liveness dataflow --regalloc better flags (better)
  4. using the --clang flag (clang)

And also with all of the above plus the -O1 flag.

Test your compiler on these programs:

  • llprograms/matmul.ll
  • hw6programs/*.oat
  • your own test case

Please, keep your table concise. In addition to the results, report the processor and OS version that you use to test. For best results, use a “lightly loaded” machine (close all other applications, including the browser) and average the timing over several trial runs.

The example below shows one interaction used to test the matmul.ll file in several configurations from the command line:

> ./main.native --liveness trivial --regalloc none llprograms/matmul.ll
> time ./a.out

real   0m1.647s
user   0m1.639s
sys    0m0.002s

> ./main.native --liveness dataflow --regalloc greedy llprograms/matmul.ll
> time ./a.out

real   0m1.127s
user   0m1.123s
sys    0m0.002s

> ./main.native --liveness dataflow --regalloc better llprograms/matmul.ll
> time ./a.out

real   0m0.500s
user   0m0.496s
sys    0m0.002s

> ./main.native --clang llprograms/matmul.ll
> time ./a.out

real   0m0.061s
user   0m0.053s
sys    0m0.004s


Don’t get too discouraged when clang beats your compiler’s performance by orders of magnitude. It uses register promotion and many other optimizations to get high-quality code!

6.8. Grading

Projects that do not compile will receive no credit!

Your team’s grade for this project will be based on:

  • 90 Points: the various automated tests that we provide. Note that the register-allocator quality points cannot be earned with an allocator that generates incorrect code.
  • 5 Points for posting an interesting test case to GitHub. (Graded manually)
  • 5 Points for posting your timing analysis to GitHub. (Graded manually.)