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.

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.

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:

```
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 *LLVM Branch Weight Metadata* for details about the branch weight IR
representation.

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.

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.

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 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.

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 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.