598 P.Eng. in a province with a population of 14 million. The odds of working with one without deliberately trying to work with one being close to none.

Computer engineer is something else. It is like an electrical engineer for computing

No, a computer engineering program typically offers a blended course of software and hardware. It is typically half way between computer science and electrical engineering. That being said, it all depends on the university. At some universities, you can pretty much take all comp sci classes as a computer engineering major. The major difference is that it is a "real engineering" degree in that it requires the engineering core curriculum.

I cannot to speak to all schools, but at Georgia Tech Computer Engineering was (circa 2005) EE with 3 CS courses, and instead of taking courses like power engineering the focus was on courses related to computer hardware design or applications.

Looking at it now, it seems they've dropped that 3 CS course requirement (at the time it was the same first 3 courses as CS majors) and replaced it with 1 required CS course: Computing for Engineers. Everything else, required, is ECE (electrical and computer engineering) with options to satisfy some major electives via CS courses (up to 7 by the hours, but no specific sequence, required to be 3xxx or above meaning a student would need to take at least 2 or 3, depending on present CS curriculum, to even qualify for them with prerequisites).

I picked this one as it seems like the quintessential CMPE program from what I've seen, and it's one of the top engineering schools in the US so it ends up influencing or setting the standard by which other US schools do things. And specifically, it's not halfway. It's often (from a perusal of other schools I'm familiar with) heavily biased towards the hardware side (by requirements, electives of course permit the student some leeway for individual breadth).

EDIT: I did misread the current GT requirements, seems they moved 2 of the programming courses into the ECE department and out of CS.

It was definitely a blend at Queen's University in Ontario. Computer engineers could choose between hardware and software specializations. All engineers shared a common first year. Then all electrical and computer engineers shared a common second year. Third and forth years focused more on the specialties, though there was still significant overlap.

Also worth noting, professional registrations may not line up exactly with degrees. You don't necessarily need a degree in computer engineering to be a computer engineer. The board would likely find a degree in electrical engineering and a few years of relevant work experience to be sufficient. (Though, this may vary by jurisdiction.)