But it's still surprising that that LLM doesn't work on iPhone 16 at all. After all LLMs are known for their tolerance to quantization.
But, what got me about this is that:
* every other Apple device delivered the same results
* Apple's own LLM silently failed on this device
to me that behavior suggests an unexpected failure rather than a fundamental issue; it seems Bad (TM) that Apple would ship devices where their own LLM didn't work.
It is commutative (except for NaN). It isn't associative though.
Why? This is well specified by IEEE 754. Many runtimes (e.g. for Javascript) use NaN boxing. Treating floats as a semi-arbitrary selection of rational numbers plus a handful of special values is /more/ correct than treating them as real numbers, but treating them as actually specified does give more flexibility and power.
My understanding is the exact opposite - that it allows implementations to return any NaN value at all. It need not be any that were inputs.
It may be that JavaScript relies on it and that has become more binding than the actual spec, but I don't think the spec actually guarantees this.
Edit: actually it turns out nan-boxing does not involve arithmetic, which is why it works. I think my original point stands, if you are doing something that relies on how bit values of NaNs are propagated during arithmetic, you are on shaky ground.
https://rust-lang.github.io/rfcs/3514-float-semantics.html
See also this section of wikipedia https://en.wikipedia.org/wiki/NaN#Canonical_NaN
"On RISC-V, most floating-point operations only ever generate the canonical NaN, even if a NaN is given as the operand (the payload is not propagated)."
And from the same article:
"IEEE 754-2008 recommends, but does not require, propagation of the NaN payload." (Emphasis mine)
I call bullshit on the statement "specifically binary operations combining two NaN inputs must result in one of the input NaNs." It is definitely not in the spec.