64 Bit Words might be bigger than you think.

Every once in a while I’ve witnessed someone worrying about a counter overflowing. While those bugs do certainly happen. With things that are counted one at a time on hardware this is basically impossible.

Thesis: If you increment one at a time, on hardware, a Word64 is basically infinite.

From an engineering point of view if the hardware is guaranteed to die or your program to terminate before you exceed 2^64 you can treat a 64bit Words as infinite. Which is terribly convenient.

It’s hard to grasp how much leeway that actually gives us. So here are some examples.

How long can you count?

Incrementing in steps of one. How long can you count using a 64bit Word?

Cars

You write a program counting cars passing by. You expect an average of one car per second to go by. You will be able to count cars for ~40x the age of the universe. Do not worry about it.

CPU Cycles

A average high end CPU runs at ~4GHz. If we count the number of cycles one at a time we can count cycles for ~150 years. Don’t worry about it.

Water drops in the Danube

The danube has a throughput of ~6450m³/s. That is about 0.13 Trillion drops of water per second. If we count each drop one at a time we can count water drops for 43 Months. You probably don’t need to worry about it.

Photons hitting earth.

It seems ~10^20 Photons hit every m² of earth every seconding. If you count them one at a time then … wait what hardware are you running this one. Are you running our simulation. Why is my screen turning into a matrix screen saver.

Jokes aside there is no hardware that could count photons hitting earth one at a time. So don’t worry about it.

Word64 is not infinite

Things escalate quickly if you aggregate counters. While we can count cycles for longer than almost all hardware will last. Counting instructions on a Server might run into roll over territory. E.g. 192 cores * 2.5GHz * 3 (IPC) would give you a lower bound of 148 days before roll over.

But if you are counting things one at a time, on hardware, without adding up counters? Don’t worry about it.