The sll amount is the element size
Change the element type and exactly one number changes in the indexing trio: the shift amount. A u16 array strides by 2, so the index is scaled with sll … 1:
s32 hw_at(u16 *t, s32 i) {
return t[i];
}
sll t6, a1, 1 # i * 2 (stride of a halfword)
addu t7, a0, t6 # &t[i]
lhu v0, 0(t7) # t[i], zero-extended
jr ra
nop
The trio now carries two pieces of type information at once, and they have to agree:
sll … 1 says the elements are 2 bytes wide;lhu says each element is an unsigned halfword.
That agreement is your cross-check. A sll … 2 feeding an lhu would be nonsense (4-byte stride, 2-byte load) — if you ever think you're seeing that, re-read the registers, because one of the two belongs to a different computation. And as always, the load mnemonic is the type oracle from last chapter: lhu here forced the u16 in the C.
The target indexes a halfword array too, but its load is the signed flavor, and the loaded value gets one piece of arithmetic done to it before heading out — an idiom from the very start of this tier.
Your task
Write func_800aa190 to reproduce the target assembly.