>>

>> >> All,

>> >> About two months ago I posted a patch that hoisted the hottest case

>> >> statement from a switch statement during ISelLowering.

>> >>

>> >> See: ⚙ D5786 [PGO] Hoist hot case statement from switches

>> >>

>> >> Sean was rather adamant about using a Huffman tree (and I agree this

>> is

>> >> a

>> >> more complete solution), so I'd like to put a patch together.

>> >

>> > I think this sounds really cool!

>> >

>> >> That being

>> >> said, I have a few questions.

>> >>

>> >> The current switch lowering code sorts based on case values and is

>> >> lowered

>> >> with a combination of binary trees, lookup tables, bit tests and

>> magic.

>> >> If we lower the switch based on branch probabilities, I think the

>> most

>> >> reasonable approach would be to disable the lookup tables and stick

>> with

>> >> a

>> >> purely tree structure. Does anyone object or have opinions on this

>> >> matter?

>> >

>> > Spontaneously I would have thought the Huffman tree would just replace

>> > the binary trees, i.e. we'd use the branch probabilities to build the

>> > tree differently.

>>

>> The current implementation selects the pivot in such a way that it

>> optimizes

>> for lookup tables.

>

>

> This seems like a potential point of friction: for lookup tables (and

> other

> techniques) you want to inherently keep the cases sorted by their values,

> but a Huffman tree does not care about the actual values; it only cares

> about their relative probabilities.

Exactly! I can think of lots of ways to deal with this "friction", but

none of them sit well. As you mentioned, building a Huffman tree and then

dealing with corner cases would be one approach. Another, which was

Owen's suggestion, would be to peel the hot cases and then fall-back to

the current logic.

Another possibility might be to use a hybrid approach.

For example, while building the Huffman tree, propagate various information

up the tree as you build it. Then you can very easily start at the top of

the huffman tree and have all this information available to you (e.g. "peel

off the most probable cases until the relative probabilty has some relation

to the subtree case density").

On the other hand (more likely), you could keep the cases ordered (i.e. not

a Huffman tree) and integrate the branch probability info as the extra data

propagated up the tree (along with other stuff); e.g. the max probability

of any node in the subtree, the total probability sum in the subtree. This

would also allow some highly non-trivial properties, like "maximum number

of consecutive cases observed in each subtree" to be maintained, along with

O(1) access to the root of the subtree containing the consecutive cases

(and if we keep the tree balanced, O(log n) time to extract the consecutive

cases and update all data we are propagating up the tree). This would allow

a really clean lowering algorithm like:

while (we have subtrees with property X)

extract and handle subtree in a particular way

while (we have subtrees with property Y)

extract and handle subtree in a different way

etc.

A prototype of this can be done really easily with a non-balanced binary

tree. In order to make it reliably fast the binary tree with need to be

upgraded to a balanced binary tree (red-black, AVL, treap, etc.), which I

will go ahead and volunteer to do (I've actually spent more time than I

care to admit investigating balanced binary trees and their implementation).

For a textbook reference on maintaining extra data in a tree, see e.g.

section 14.2 of CLRS.

-- Sean Silva