Checking that functions are constant time with Valgrind (2010)

Yes, especially as CPUs have got faster and put in more clever tricks to improve performance (bear in mind that this blog post is 15 years old). Modern architectures have introduced modes to allow you to turn this off so that for your crypto code you can get back the not-data-dependent timing you wanted. For instance on Arm that's FEAT_DIT:

https://developer.arm.com/documentation/ddi0601/2025-06/AArc...

and the set of instructions you can safely use is listed.

I believe Intel has a similar thing.

Partial solutions are still valuable. This valgrind hack lets you pose the question "Is this code constant time?"

It doesn't tell you "yes" or "no", but it does tell you "definitely not" or "maybe". This information is useful even if it's not the whole story.

There is a small bound for an integer of a given length.

It wasn't true back then, but should be common knowledge now: branches have variable timing.