Is it possible that in MIPS an instruction's certain steps come before that of its predecessor in a pipelined structure?

Question

For issue 1, in a simple, scalar pipeline, a stall introduces a pipeline bubble which cannot be "popped". To allow an instruction later in program order to fill a pipeline bubble, that instruction would have to go past the stalled instruction. Supporting such reordering of instructions increases the complexity of the pipeline, which tends to increase design and production costs and to increase either pipeline depth or cycle time (as well as use more energy per active cycle [out-of-order execution can be more energy efficient in total even when more energy is used when active]). The mechanisms needed to support such reordering also increases the complexity of explaining pipelines.

For issue 2, with a more complex pipeline it is possible to begin execution of more than one instruction at the same time. Such processors are called superscalar. With in-order execution, only instructions in a consecutive sequence (in program order) can begin execution at the same time, and this requires that the instructions do not have data dependencies and that sufficient hardware resources are available to execute the instructions and handle their results. For an in-order microarchitecture, the width of the earlier pipeline stages is typically the same as the width of later pipeline stages, though buffering would allow multiple instructions to accumulate behind a stall.

(Even at only two-wide execution, there are usually additional restrictions on what kinds of instructions can be executed in parallel. E.g., one execution port might not handle memory accesses or branches while the other execution port might handle those instructions but not shifts or multiplies. Having two copies of hardware for relatively expensive operations [like shifts and multiplies] increases size and limiting the data paths for memory accesses and branches can simplify design and potentially reduce delay.)

For issue 3, out-of-order execution allows the reordering of instructions, so an instruction later in program order could execute and writeback results to the register file before an earlier instruction. With some additional complexity in handling exceptions/interrupts and arbitrating register write port use (or increasing the number of write ports), it is also possible for an in-order processor to writeback results out of program order. The Motorola 88110 (from the early 1990s) is an example of a processor which did such. In order to handle exceptions, the 88110 had a history buffer to hold data that is overwritten by instructions that are later in program order than where the exception is. The 88110 had two additional read ports to each of the register files to read the data in the destination registers and write such to the history buffer.

For issue 4, I am guessing that you mean the case where the body of the loop is composed on only one instruction. For a typical RISC instruction set the branch instruction controlling the loop is a separate instruction from the instruction performing a computation or memory access, so the loop would actually contain two instructions. (Power, formerly PowerPC, could have a one instruction delay loop using branch on counter which decrements the special counter register, but optimizing instruction fetch for a simple implementation for such peculiar code would be foolish.)

For the simple classic 5-stage pipeline with delayed branches, it does not make sense from a performance perspective to avoid an instruction cache access since the loop branch does not introduce a pipeline bubble even when taken. This means that there is no opportunity to execute more instructions. However, in some microarchitectures where redirecting instruction fetch to a non-sequential address introduces a pipeline bubble (particularly if from instruction fetch taking more than one cycle), providing a small fast-access buffer can improve performance. (Instruction fetch bandwidth limitations could also justify a buffer for performance; a small buffer could provide higher bandwidth than a large cache or an off-chip memory.) In addition, to reduce energy use, the use of a loop buffer makes considerable sense, but one would almost certainly not want to limit the size of the buffer to only two instructions (the branch plus one "body" instruction) because such tiny loops are rare and even increasing the buffer size to eight instructions would only add a modest amount of hardware.

In order to specially handle the case of small bodied loops, such loops must be detected. While the buffer could always be filled with the last N instructions (to avoid the first encounter of the short backward branch not "hitting" in the loop buffer--and such a buffer could also even out variations in instruction fetch which might be caused by crossing cache line boundaries, cache misses, fetch redirection delays, etc.), it would be necessary to check each branch instruction to see if it targeted an instruction within the buffer. (It would even be possible to provide a special storage for the loop branch instruction since storage is only needed for the condition checked, a small index into the loop buffer and an indication of where the branch is, but short loops are probably not sufficiently common for such specialized hardware.) In effect, a loop buffer can be a very small Level 0 instruction cache

(A branch target instruction cache [BTIC] is a mechanism similar to a loop buffer, but instead of caching instructions only from the target of the most recent loop branch a BTIC caches instructions from the targets of a number of recent branches. BTICs are primarily used to hide instruction fetch latency.)

When teaching pipelines, such complicating factors are usually avoided initially.