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