I am interested, did all Celeron processors support the FCOMIP instruction? I've made a compiler for my programming language and it uses FCOMIP for every floating-point comparison. I've noticed that causes the programs written in my programming language to crash when run on DosBox. So, I am interested how far in the past would I be able to go and still expect the programs my compiler outputs to work on an average computer.
Short Answer: Yes.
Celeron is a sales name, and does not specify a CPU architecture or instruction set.
Having said that, FCOMIP was introduced with the P6 Family, so essentially with the Pentium PRO (for workstation) and Pentium MMX for mainstream machines. IA-32 implementations before these CPUs do not feature this instruction. The first Celeron is essentially a Pentium II without the secondary cache, so it as well as all later CPUs carrying that name should support FCOMIP.
Compatible CPUs only if they as well support MMX. There were many, but today only AMD, VIA and DMP are left - plus maybe a some virtually unknown embedded implementations:
Other, no longer manufactured models with MMX (and FCOMIP) are: