The bit twiddling office called. They want a function to compute a sequence of ARM64 instructions that fills a register with an arbitrary constant 64-bit number.

Zeros in positive number

All ARM64 instructions are 32 bits long, so one instruction can’t possibly handle all 64-bit patterns. One straightforward way to assemble the desired bit pattern is to use MOVK which sets any one of the four 16-bit chunks of the register without touching any other chunks. So, four MOVK instructions can assemble any 64-bit pattern.

Adding MOVZ to the mix improves this strategy. Small numbers have many zeros in the pattern, so we’d rather start by zeroing the whole register than zeroing out one 16-bit chunk at a time with MOVK. In one go, MOVZ sets one 16-bit chunk to the desired value and also zeros out all other chunks. For small numbers like 7, all we need is one MOVZ.

The negative ones

Another instruction in the same family is MOVN. It sets the register like MOVZ, but with all bits inverted. So, MOVN sets the three chunks that are not directly encoded in the instruction to all ones. Why would you want so many ones? Negative numbers!

The most significant bit of a two’s complement number contributes negatively to the value tally unlike the rest of the bits. Adding a leading one to the bit string makes the old most significant bit at position K go from having a value of -2^K to 2^K, adding 2•2^K=2^K+1 to the balance. The new leading one at K+1 has value -2^K+1 , though, so adding a leading one preserves the numeric value of the encoded number. This is one way to see why -1 is encoded as all bits ones. Start with a single one and add leading ones.

Leading ones are to negative numbers what leading zeros are to positive numbers. ¹

Strategy using MOVN

Using MOVN and MOVK gives a pretty good strategy for negative numbers. Sometimes, the whole sequence takes fewer than 64 bits. That’s shorter than movabs from x86-64, which encodes all 64 bits of the constant into the instruction.

Pick a 16-bit chunk in the constant that is not all bits set and use a MOVN to set the chunk, filling all other chunks with ones as well. If no such chunk exists, then all bits are set, and a single MOVN finishes the job. Otherwise, set other chunks with MOVK.

If there is even a single 16-bit chunk of ones, the initial MOVN finishes setting two chunks or more in one go, beating out the one-chunk-at-a-time MOVK. MOVZ fills zeros and MOVN fills ones.

This strategy is not limited to negative numbers. For example, it sets 0x7000_ffff_cafe_ffff with just two instructions.

Play with it!

On a browser with WASM support, there should be an interactive toy below that implements the MOVN strategy. It only uses MOVN and MOVK, so don’t expect the shortest possible sequence for all inputs. (For one, it doesn’t attempt to use a bitmask immediate.) It’s made with capstone-rs compiled through wasm32-unknown-emscripten.² It assembles the machine code bytes only to run it through a disassembler as an elaborate way of verification.