LLVM Loop Terminology (and Canonical Forms)

Introduction

Loops are a core concept in any optimizer. This page spells out some of the common terminology used within LLVM code to describe loop structures.

First, let's start with the basics. In LLVM, a Loop is a maximal set of basic blocks that form a strongly connected component (SCC) in the Control Flow Graph (CFG) where there exists a dedicated entry/header block that dominates all other blocks within the loop. Thus, without leaving the loop, one can reach every block in the loop from the header block and the header block from every block in the loop.

Note that there are some important implications of this definition:

• Not all SCCs are loops. There exist SCCs that do not meet the dominance requirement and such are not considered loops.
• Loops can contain non-loop SCCs and non-loop SCCs may contain loops. Loops may also contain sub-loops.
• A header block is uniquely associated with one loop. There can be multiple SCC within that loop, but the strongly connected component (SCC) formed from their union must always be unique.
• Given the use of dominance in the definition, all loops are statically reachable from the entry of the function.
• Every loop must have a header block, and some set of predecessors outside the loop. A loop is allowed to be statically infinite, so there need not be any exiting edges.
• Any two loops are either fully disjoint (no intersecting blocks), or one must be a sub-loop of the other.

A loop may have an arbitrary number of exits, both explicit (via control flow) and implicit (via throwing calls which transfer control out of the containing function). There is no special requirement on the form or structure of exit blocks (the block outside the loop which is branched to). They may have multiple predecessors, phis, etc...

Key Terminology

Header Block - The basic block which dominates all other blocks contained within the loop. As such, it is the first one executed if the loop executes at all. Note that a block can be the header of two separate loops at the same time, but only if one is a sub-loop of the other.

Exiting Block - A basic block contained within a given loop which has at least one successor outside of the loop and one successor inside the loop. (The latter is a consequence of the block being contained within an SCC which is part of the loop.) That is, it has a successor which is an Exit Block.

Exit Block - A basic block outside of the associated loop which has a predecessor inside the loop. That is, it has a predecessor which is an Exiting Block.

Latch Block - A basic block within the loop whose successors include the header block of the loop. Thus, a latch is a source of backedge. A loop may have multiple latch blocks. A latch block may be either conditional or unconditional.

Backedge(s) - The edge(s) in the CFG from latch blocks to the header block. Note that there can be multiple such edges, and even multiple such edges leaving a single latch block.

Loop Predecessor - The predecessor blocks of the loop header which are not contained by the loop itself. These are the only blocks through which execution can enter the loop. When used in the singular form implies that there is only one such unique block.

Preheader Block - A preheader is a (singular) loop predecessor which ends in an unconditional transfer of control to the loop header. Note that not all loops have such blocks.

Backedge Taken Count - The number of times the backedge will execute before some interesting event happens. Commonly used without qualification of the event as a shorthand for when some exiting block branches to some exit block. May be zero, or not statically computable.

Iteration Count - The number of times the header will execute before some interesting event happens. Commonly used without qualification to refer to the iteration count at which the loop exits. Will always be one greater than the backedge taken count. Warning: Preceding statement is true in the integer domain; if you're dealing with fixed width integers (such as LLVM Values or SCEVs), you need to be cautious of overflow when converting one to the other.

It's important to note that the same basic block can play multiple roles in the same loop, or in different loops at once. For example, a single block can be the header for two nested loops at once, while also being an exiting block for the inner one only, and an exit block for a sibling loop. Example:

while (..) {
  for (..) {}
  do {
    do {
      // <-- block of interest
      if (exit) break;
    } while (..);
  } while (..)
}

LoopInfo

LoopInfo is the core analysis for obtaining information about loops. There are few key implications of the definitions given above which are important for working successfully with this interface.

• LoopInfo does not contain information about non-loop cycles. As a result, it is not suitable for any algorithm which requires complete cycle detection for correctness.
• LoopInfo provides an interface for enumerating all top level loops (e.g. those not contained in any other loop). From there, you may walk the tree of sub-loops rooted in that top level loop.
• Loops which become statically unreachable during optimization must be removed from LoopInfo. If this can not be done for some reason, then the optimization is required to preserve the static reachability of the loop.

Loop Simplify Form

TBD

Loop Closed SSA (LCSSA)

TBD

"More Canonical" Loops

TBD