mirror of
https://github.com/RPCS3/llvm-mirror.git
synced 2024-11-22 10:42:39 +01:00
131 lines
4.6 KiB
ReStructuredText
131 lines
4.6 KiB
ReStructuredText
================================
|
|
LLVM Block Frequency Terminology
|
|
================================
|
|
|
|
.. contents::
|
|
:local:
|
|
|
|
Introduction
|
|
============
|
|
|
|
Block Frequency is a metric for estimating the relative frequency of different
|
|
basic blocks. This document describes the terminology that the
|
|
``BlockFrequencyInfo`` and ``MachineBlockFrequencyInfo`` analysis passes use.
|
|
|
|
Branch Probability
|
|
==================
|
|
|
|
Blocks with multiple successors have probabilities associated with each
|
|
outgoing edge. These are called branch probabilities. For a given block, the
|
|
sum of its outgoing branch probabilities should be 1.0.
|
|
|
|
Branch Weight
|
|
=============
|
|
|
|
Rather than storing fractions on each edge, we store an integer weight.
|
|
Weights are relative to the other edges of a given predecessor block. The
|
|
branch probability associated with a given edge is its own weight divided by
|
|
the sum of the weights on the predecessor's outgoing edges.
|
|
|
|
For example, consider this IR:
|
|
|
|
.. code-block:: llvm
|
|
|
|
define void @foo() {
|
|
; ...
|
|
A:
|
|
br i1 %cond, label %B, label %C, !prof !0
|
|
; ...
|
|
}
|
|
!0 = metadata !{metadata !"branch_weights", i32 7, i32 8}
|
|
|
|
and this simple graph representation::
|
|
|
|
A -> B (edge-weight: 7)
|
|
A -> C (edge-weight: 8)
|
|
|
|
The probability of branching from block A to block B is 7/15, and the
|
|
probability of branching from block A to block C is 8/15.
|
|
|
|
See :doc:`BranchWeightMetadata` for details about the branch weight IR
|
|
representation.
|
|
|
|
Block Frequency
|
|
===============
|
|
|
|
Block frequency is a relative metric that represents the number of times a
|
|
block executes. The ratio of a block frequency to the entry block frequency is
|
|
the expected number of times the block will execute per entry to the function.
|
|
|
|
Block frequency is the main output of the ``BlockFrequencyInfo`` and
|
|
``MachineBlockFrequencyInfo`` analysis passes.
|
|
|
|
Implementation: a series of DAGs
|
|
================================
|
|
|
|
The implementation of the block frequency calculation analyses each loop,
|
|
bottom-up, ignoring backedges; i.e., as a DAG. After each loop is processed,
|
|
it's packaged up to act as a pseudo-node in its parent loop's (or the
|
|
function's) DAG analysis.
|
|
|
|
Block Mass
|
|
==========
|
|
|
|
For each DAG, the entry node is assigned a mass of ``UINT64_MAX`` and mass is
|
|
distributed to successors according to branch weights. Block Mass uses a
|
|
fixed-point representation where ``UINT64_MAX`` represents ``1.0`` and ``0``
|
|
represents a number just above ``0.0``.
|
|
|
|
After mass is fully distributed, in any cut of the DAG that separates the exit
|
|
nodes from the entry node, the sum of the block masses of the nodes succeeded
|
|
by a cut edge should equal ``UINT64_MAX``. In other words, mass is conserved
|
|
as it "falls" through the DAG.
|
|
|
|
If a function's basic block graph is a DAG, then block masses are valid block
|
|
frequencies. This works poorly in practise though, since downstream users rely
|
|
on adding block frequencies together without hitting the maximum.
|
|
|
|
Loop Scale
|
|
==========
|
|
|
|
Loop scale is a metric that indicates how many times a loop iterates per entry.
|
|
As mass is distributed through the loop's DAG, the (otherwise ignored) backedge
|
|
mass is collected. This backedge mass is used to compute the exit frequency,
|
|
and thus the loop scale.
|
|
|
|
Implementation: Getting from mass and scale to frequency
|
|
========================================================
|
|
|
|
After analysing the complete series of DAGs, each block has a mass (local to
|
|
its containing loop, if any), and each loop pseudo-node has a loop scale and
|
|
its own mass (from its parent's DAG).
|
|
|
|
We can get an initial frequency assignment (with entry frequency of 1.0) by
|
|
multiplying these masses and loop scales together. A given block's frequency
|
|
is the product of its mass, the mass of containing loops' pseudo nodes, and the
|
|
containing loops' loop scales.
|
|
|
|
Since downstream users need integers (not floating point), this initial
|
|
frequency assignment is shifted as necessary into the range of ``uint64_t``.
|
|
|
|
Block Bias
|
|
==========
|
|
|
|
Block bias is a proposed *absolute* metric to indicate a bias toward or away
|
|
from a given block during a function's execution. The idea is that bias can be
|
|
used in isolation to indicate whether a block is relatively hot or cold, or to
|
|
compare two blocks to indicate whether one is hotter or colder than the other.
|
|
|
|
The proposed calculation involves calculating a *reference* block frequency,
|
|
where:
|
|
|
|
* every branch weight is assumed to be 1 (i.e., every branch probability
|
|
distribution is even) and
|
|
|
|
* loop scales are ignored.
|
|
|
|
This reference frequency represents what the block frequency would be in an
|
|
unbiased graph.
|
|
|
|
The bias is the ratio of the block frequency to this reference block frequency.
|