Consider the following IR:

define half @f(half %a, half %b, half %c) {
    %d = fadd half %a, %b
    %e = fadd half %d, %c
    ret half %e
}

On backends without native half support, LLVM generally lowers half by converting to float, performing the desired operation, and then converting back to half. For this to be a valid lowering, a conversion back to f16 must occur after each operation, otherwise the excess precision of float will affect the result. For example 65504.0 + 65504.0 + -65504.0 equals infinity if each operation is done at half precision, but will result in 65504.0 if the intermediate value is not rounded to a half but instead kept as a float. This excess runtime precision can lead to miscompilations similar to #89885.

However, it appears that on several backends LLVM will fail to round the intermediate result of consecutive half operations, leading to these kind of bugs. I'm filing this as a single issue rather than a separate issue for each backend as I believe this is an issue with LLVM's default handling of half operations rather than a problem in any specific backend (for instance, AFAIK the only backend-specific code LoongArch has for handling half was added in #94456).

By inspecting the assembly LLVM emits, I've discovered that at least the following backends appear to be affected (in brackets are a specific target triple that I've checked):

• AVR (avr-unknown-unknown)
• C-SKY (csky-unknown-linux-gnuabiv2)
• Hexagon (hexagon-unknown-linux-musl)
• LoongArch (loongarch64-unknown-linux-gnu): Fixed by [loongarch][DAG][FREEZE] Fix crash when FREEZE a half(f16) type on loongarch #107791
• M68k (m68k-unknown-linux-gnu)
• MIPS (mips64el-unknown-linux-gnuabi64): Fixed by [MIPS] Use softPromoteHalf legalization for fp16 rather than PromoteFloat #110199
• MSP430 (msp430-none-elf)
• PowerPC (powerpc64le-unknown-linux-gnu)
• SPARC (sparc64-unknown-linux-gnu)
• WASM (wasm32-unknown-wasi): Already reported in On wasm32, half operation results aren't correctly rounded between each operation #96437
• Xtensa (xtensa-none-elf)

I also noticed that 32-bit ARM has this problem in LLVM 18 but not on the main branch. Looking through the issue tracker, it seems it's likely that this was fixed by #80440.

Related to #97981.