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131 lines
4.6 KiB
ReStructuredText
131 lines
4.6 KiB
ReStructuredText
================================
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LLVM Block Frequency Terminology
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================================
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.. contents::
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:local:
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Introduction
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============
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Block Frequency is a metric for estimating the relative frequency of different
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basic blocks. This document describes the terminology that the
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``BlockFrequencyInfo`` and ``MachineBlockFrequencyInfo`` analysis passes use.
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Branch Probability
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==================
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Blocks with multiple successors have probabilities associated with each
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outgoing edge. These are called branch probabilities. For a given block, the
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sum of its outgoing branch probabilities should be 1.0.
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Branch Weight
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=============
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Rather than storing fractions on each edge, we store an integer weight.
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Weights are relative to the other edges of a given predecessor block. The
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branch probability associated with a given edge is its own weight divided by
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the sum of the weights on the predecessor's outgoing edges.
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For example, consider this IR:
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.. code-block:: llvm
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define void @foo() {
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; ...
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A:
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br i1 %cond, label %B, label %C, !prof !0
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; ...
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}
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!0 = metadata !{metadata !"branch_weights", i32 7, i32 8}
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and this simple graph representation::
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A -> B (edge-weight: 7)
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A -> C (edge-weight: 8)
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The probability of branching from block A to block B is 7/15, and the
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probability of branching from block A to block C is 8/15.
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See :doc:`BranchWeightMetadata` for details about the branch weight IR
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representation.
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Block Frequency
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===============
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Block frequency is a relative metric that represents the number of times a
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block executes. The ratio of a block frequency to the entry block frequency is
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the expected number of times the block will execute per entry to the function.
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Block frequency is the main output of the ``BlockFrequencyInfo`` and
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``MachineBlockFrequencyInfo`` analysis passes.
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Implementation: a series of DAGs
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================================
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The implementation of the block frequency calculation analyses each loop,
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bottom-up, ignoring backedges; i.e., as a DAG. After each loop is processed,
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it's packaged up to act as a pseudo-node in its parent loop's (or the
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function's) DAG analysis.
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Block Mass
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==========
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For each DAG, the entry node is assigned a mass of ``UINT64_MAX`` and mass is
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distributed to successors according to branch weights. Block Mass uses a
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fixed-point representation where ``UINT64_MAX`` represents ``1.0`` and ``0``
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represents a number just above ``0.0``.
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After mass is fully distributed, in any cut of the DAG that separates the exit
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nodes from the entry node, the sum of the block masses of the nodes succeeded
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by a cut edge should equal ``UINT64_MAX``. In other words, mass is conserved
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as it "falls" through the DAG.
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If a function's basic block graph is a DAG, then block masses are valid block
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frequencies. This works poorly in practise though, since downstream users rely
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on adding block frequencies together without hitting the maximum.
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Loop Scale
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==========
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Loop scale is a metric that indicates how many times a loop iterates per entry.
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As mass is distributed through the loop's DAG, the (otherwise ignored) backedge
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mass is collected. This backedge mass is used to compute the exit frequency,
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and thus the loop scale.
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Implementation: Getting from mass and scale to frequency
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========================================================
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After analysing the complete series of DAGs, each block has a mass (local to
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its containing loop, if any), and each loop pseudo-node has a loop scale and
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its own mass (from its parent's DAG).
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We can get an initial frequency assignment (with entry frequency of 1.0) by
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multiplying these masses and loop scales together. A given block's frequency
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is the product of its mass, the mass of containing loops' pseudo nodes, and the
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containing loops' loop scales.
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Since downstream users need integers (not floating point), this initial
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frequency assignment is shifted as necessary into the range of ``uint64_t``.
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Block Bias
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==========
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Block bias is a proposed *absolute* metric to indicate a bias toward or away
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from a given block during a function's execution. The idea is that bias can be
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used in isolation to indicate whether a block is relatively hot or cold, or to
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compare two blocks to indicate whether one is hotter or colder than the other.
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The proposed calculation involves calculating a *reference* block frequency,
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where:
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* every branch weight is assumed to be 1 (i.e., every branch probability
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distribution is even) and
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* loop scales are ignored.
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This reference frequency represents what the block frequency would be in an
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unbiased graph.
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The bias is the ratio of the block frequency to this reference block frequency.
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