This post links to a deep technical write-up on one of the oldest tricks in the compiler-optimization playbook: replacing integer division with multiplication by a precomputed "magic number." The article walks through how it's done on RISC-V, but the underlying technique applies anywhere — it's the same transformation that GCC, LLVM, and every serious compiler perform silently when you write x / 7 with a constant divisor.

The core idea: division is brutally slow on most CPUs (often 20–40+ cycles, often not pipelined), while multiplication is fast and pipelined (3–5 cycles). If the divisor is a known constant, you can mathematically rewrite n / d as (n * m) >> s, where m is a carefully chosen "multiplicative inverse" and s is a shift amount. The hard part is picking m and s so the result is exact for every possible n in the range — not just approximately right.

What makes this particularly interesting for r/asm readers:

• RISC-V is a great teaching vehicle for this. Its instruction set is small enough that you can see exactly which ops the trick depends on — mulh (high half of a multiply), arithmetic shift, and add. No hidden microcode magic.
• Signed vs. unsigned matters. The math for unsigned division is cleaner; signed requires an extra correction step because of how rounding-toward-zero interacts with arithmetic shifts of negative numbers.
• It's a window into what compilers do for you. Disassemble any optimized C code that divides by a constant and you'll see this pattern. Recognizing it makes reading optimized output much less mysterious.

The technique traces back to Granlund & Montgomery's 1994 paper "Division by Invariant Integers using Multiplication," and Hacker's Delight devotes a full chapter to it. But seeing it implemented in modern RISC-V assembly — with a working derivation rather than just the formula — is the clearest way to actually internalize why the magic numbers work, not just what they are.

If you've ever wondered why x / 10 compiles to a multiply followed by a shift, this is the explanation.