What is the difference between the issue queue and lsq queue for memory instructions? Do memory instructions pass through both queues, or do they only pass through the lsq queue. If they pass through both queues what is their order?
Do memory instructions pass through the load-store queue and issue queue in the microarchitecture
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I'm assuming you use the arm-like nomenclature here so the issue queue is what Intel calls RS (reservation station) and by issue you mean sending a uop ready for execution.
The answer is that memory instructions need to pass both. All instructions need to be issued (except the ones that can be eliminated without execution, for example register moves, zero idioms, nops, etc..). Let's rephrase - all instructions that need to go through an ALU need to go through the issue process first. Memory instructions will simply use that step to calculate their addresses. This is true for loads, for stores there is usually an internal split into store-address and store-data, so the store-address will behave like a load in that sense and calculate its address during that step.
There is usually a dedicated execution port for that and dedicated execution units because the address calculation usually follows one of few specific addressing modes (each architecture has a different set of these), but aside from that the execution needs to follow the same rules like any other operation in the CPU - it needs to have its sources ready and read from the register file or bypassed from an in flight operation, it needs to get arbitrated when the execution port is free and prioritized by the same aging rules, so it makes sense that it uses the common path.
Once the memory operation has finished execution, it will be sent to the LSU (load-store unit, or the DCU, data-cache unit on Intel) and perform the actual memory access using the generated address. The LSU pipe will take care of the address translation, TLB lookups, the page walk if needed (though this is sometimes done in a dedicated unit), the address range and property checks, the cache lookup (if cacheable) and sending a miss to the next cache level or memory if needed. It may also trigger prefetches as part of the process.
For a load, when the LSU pipe has completed (which may require multiple passes and wakeups if the data was not available in the L1), the LSU will signal the issue queue again in order to wakeup anyone who was depended on the result. For a store, store-address may fetch the line to the cache in advance as an optimization but the actual next step is usually to wakeup after retirement (since stores may not be dispatched to memory while speculative, unless you have some tricks to handle that).
It's also worth to mention that some CPUs try to optimize loads that can forward the data directly from prior stores instead of fetching it from the cache/memory. This can include forwarding (very common) or memory renaming (less common). The former is usually handled by the LSU internally, but the latter can be done much earlier and without the LSU (though the LSU pipe is usually still activated to validate the result).