1================================ 2LLVM Block Frequency Terminology 3================================ 4 5.. contents:: 6 :local: 7 8Introduction 9============ 10 11Block Frequency is a metric for estimating the relative frequency of different 12basic blocks. This document describes the terminology that the 13``BlockFrequencyInfo`` and ``MachineBlockFrequencyInfo`` analysis passes use. 14 15Branch Probability 16================== 17 18Blocks with multiple successors have probabilities associated with each 19outgoing edge. These are called branch probabilities. For a given block, the 20sum of its outgoing branch probabilities should be 1.0. 21 22Branch Weight 23============= 24 25Rather than storing fractions on each edge, we store an integer weight. 26Weights are relative to the other edges of a given predecessor block. The 27branch probability associated with a given edge is its own weight divided by 28the sum of the weights on the predecessor's outgoing edges. 29 30For example, consider this IR: 31 32.. code-block:: llvm 33 34 define void @foo() { 35 ; ... 36 A: 37 br i1 %cond, label %B, label %C, !prof !0 38 ; ... 39 } 40 !0 = metadata !{metadata !"branch_weights", i32 7, i32 8} 41 42and this simple graph representation:: 43 44 A -> B (edge-weight: 7) 45 A -> C (edge-weight: 8) 46 47The probability of branching from block A to block B is 7/15, and the 48probability of branching from block A to block C is 8/15. 49 50See :doc:`BranchWeightMetadata` for details about the branch weight IR 51representation. 52 53Block Frequency 54=============== 55 56Block frequency is a relative metric that represents the number of times a 57block executes. The ratio of a block frequency to the entry block frequency is 58the expected number of times the block will execute per entry to the function. 59 60Block frequency is the main output of the ``BlockFrequencyInfo`` and 61``MachineBlockFrequencyInfo`` analysis passes. 62 63Implementation: a series of DAGs 64================================ 65 66The implementation of the block frequency calculation analyses each loop, 67bottom-up, ignoring backedges; i.e., as a DAG. After each loop is processed, 68it's packaged up to act as a pseudo-node in its parent loop's (or the 69function's) DAG analysis. 70 71Block Mass 72========== 73 74For each DAG, the entry node is assigned a mass of ``UINT64_MAX`` and mass is 75distributed to successors according to branch weights. Block Mass uses a 76fixed-point representation where ``UINT64_MAX`` represents ``1.0`` and ``0`` 77represents a number just above ``0.0``. 78 79After mass is fully distributed, in any cut of the DAG that separates the exit 80nodes from the entry node, the sum of the block masses of the nodes succeeded 81by a cut edge should equal ``UINT64_MAX``. In other words, mass is conserved 82as it "falls" through the DAG. 83 84If a function's basic block graph is a DAG, then block masses are valid block 85frequencies. This works poorly in practice though, since downstream users rely 86on adding block frequencies together without hitting the maximum. 87 88Loop Scale 89========== 90 91Loop scale is a metric that indicates how many times a loop iterates per entry. 92As mass is distributed through the loop's DAG, the (otherwise ignored) backedge 93mass is collected. This backedge mass is used to compute the exit frequency, 94and thus the loop scale. 95 96Implementation: Getting from mass and scale to frequency 97======================================================== 98 99After analysing the complete series of DAGs, each block has a mass (local to 100its containing loop, if any), and each loop pseudo-node has a loop scale and 101its own mass (from its parent's DAG). 102 103We can get an initial frequency assignment (with entry frequency of 1.0) by 104multiplying these masses and loop scales together. A given block's frequency 105is the product of its mass, the mass of containing loops' pseudo nodes, and the 106containing loops' loop scales. 107 108Since downstream users need integers (not floating point), this initial 109frequency assignment is shifted as necessary into the range of ``uint64_t``. 110 111Block Bias 112========== 113 114Block bias is a proposed *absolute* metric to indicate a bias toward or away 115from a given block during a function's execution. The idea is that bias can be 116used in isolation to indicate whether a block is relatively hot or cold, or to 117compare two blocks to indicate whether one is hotter or colder than the other. 118 119The proposed calculation involves calculating a *reference* block frequency, 120where: 121 122* every branch weight is assumed to be 1 (i.e., every branch probability 123 distribution is even) and 124 125* loop scales are ignored. 126 127This reference frequency represents what the block frequency would be in an 128unbiased graph. 129 130The bias is the ratio of the block frequency to this reference block frequency. 131