>> because the software workaround for detecting integer overflow, which is mandatory for any program that claims to be written in a safe way, lowers the attainable performance much more than the workarounds for not having carry
That's absurd. A better way is to ensure that your algorithms don't overflow. Detecting an overflow just means your code has to STOP which is usually not safe. It'd be insane to have conditionally executed code trying to figure out how to handle an overflow anywhere in code. Another problem is that flags are not even accessible from any language higher level then ASM. From a C perspective there are no flags.
While there is no direct access to flags in standard C, you can nevertheless on gcc and clang compile with -ftrapv and get your signed integer arithmetic be overflow-checked. Or you can use __builtin_add_overflow & co and get access to the overflow flags that way. Rust debug builds trap on signed and unsigned integer overflow, and you can make release builds do so too.
While it'd be nice to have a formal proof that every single `a+b`, `a-b`, `a*b` in every codebase doesn't overflow, I'm sure you understand that that is rather impractical. (and really, it'd be nice! I've thought about having some compile-time-bounded-size integers where each addition increases the size, but multiplication is much less suitable for that, and it also means you can't have a loop adding to an accumulator. It's a rather non-trivial problem really - you might think that it'd be fine to have a loop over a list of objects and sum their sizes, but that can relatively easily overflow if the list references the same massive object many times, so can't even really abstract that)
Oh, also, C23 added standard ckd_add & ckd_sub & ckd_mul for getting a boolean of whether the operation overflows (i.e. standard equivalent to __builtin_add_overflow)!
That's absurd. A better way is to ensure that your algorithms don't overflow. Detecting an overflow just means your code has to STOP which is usually not safe. It'd be insane to have conditionally executed code trying to figure out how to handle an overflow anywhere in code. Another problem is that flags are not even accessible from any language higher level then ASM. From a C perspective there are no flags.