Factoring the constant
What about constants that aren't near a power of two at all? IDO factors them. If the constant is (something it knows how to build) × (a power of two), it builds the something, then shifts the whole result. Here's ×10, built as 5 × 2:
sll v0, a0, 2 # v0 = x * 4
addu v0, v0, a0 # v0 = x * 5
sll v0, v0, 1 # v0 = x*5 * 2 = x * 10
jr ra
nop
Lines one and two are last lesson's ×5 pattern, unchanged. Line three shifts the result — not the original argument — doubling everything built so far.
That distinction is the whole skill of reading long chains. An sll whose source is the original argument register starts a fresh "2^k times x" term. An sll whose source is the running result multiplies everything so far by a power of two. Track which one you're looking at, keep a running multiplier in the margin, and any chain decodes mechanically:
sll from the argument: start at 2^k.addu/subu with the argument: ±1.sll from the result: multiply the running total by 2^k.
The target chain below has the same three-instruction shape with different amounts. Run your margin math all the way to the bottom.
Your task
Write func_8024f390 to reproduce the target assembly.