GH-118093: Don't lose confidence when tracing through 100% biased branches

[brandtbucher]

A 16/16 bias in one direction of a branch is a very strong indicator that we'll stay on trace in that direction. I don't think our current 10% confidence drop is helping us very much.

I originally tried a value closer to 6% (precisely, 1/18th), which follows from applying Laplace's rule of succession. But that still underperformed relative to this PR, which just takes the naive approach of not adjusting our confidence when encountering a highly-biased branch.

~1% faster, with a ~2% increase in uops executed and a ~3% decrease in traces executed (stats).

• Issue: Increase fraction of code executed by tier 2. #118093

[markshannon]

The original purpose of only assuming ~90% confidence was to avoid an exponential explosion of traces.
Take the following, highly contrived example code:

for i in range(1<<32): if i & 32: a if i & 64: b if i & 128: c if i & 256: d if i & 512: e if i & 1024: f if i & 2048: g if i & 4096: h

Which goes the same way on each branch for at least 16 iterations, but is unbiased and could produce 256 traces covering h.

If we do merge this, we need some alternative mechanism to avoid producing too many traces for a single piece of code.

[brandtbucher]

The original purpose of only assuming ~90% confidence was to avoid an exponential explosion of traces.
Take the following, highly contrived example code:

But the old code and the new code handle this highly contrived example the exact same. In fact, the current code accepts up to ten (0.9**10 > 0.333) highly-biased branches like this before bailing... two more than provided in your example.

I think the answer to pathological cases like this is probably tail fusion during trace compaction... not ending traces early, warming them up 64 hits later, and continuing to project. I think this PR probably handles "real world" code a tiny bit better though, as evidenced by the stats.

[brandtbucher]

And, to note, we already sort of fuse the tails. After four side exits in a chain, all traces that hit the next instruction will fuse anyways, since we stop projecting when we hit an ENTER_EXECUTOR.

[brandtbucher]

I just ran your example locally. On both main and this PR, only 66 traces are produced.

[markshannon]

So this is no worse than what we currently have in terms of generating excessive numbers of traces.
Which means:

• This should be OK to merge 🙂
• We have a problem with excessive numbers of traces 🙁

It sounds like you have ideas about how to limit the trace overlap. Could you make an issue for that?

[markshannon]

Maybe remove the comment. Otherwise, lgtm.