Assembly Loop Unrolling (GNU MP 6.3.0)
Description: How to install and use the GNU multiple precision arithmetic library, version 6.3.0.

#### 15.8.9 Loop Unrolling

Loop unrolling consists of replicating code so that several limbs are processed in each loop. At a minimum this reduces loop overheads by a corresponding factor, but it can also allow better register usage, for example alternately using one register combination and then another. Judicious use of `m4` macros can help avoid lots of duplication in the source code.

Any amount of unrolling can be handled with a loop counter that’s decremented by N each time, stopping when the remaining count is less than the further N the loop will process. Or by subtracting N at the start, the termination condition becomes when the counter C is less than 0 (and the count of remaining limbs is C+N).

Alternately for a power of 2 unroll the loop count and remainder can be established with a shift and mask. This is convenient if also making a computed jump into the middle of a large loop.

The limbs not a multiple of the unrolling can be handled in various ways, for example

- A simple loop at the end (or the start) to process the excess. Care will be wanted that it isn’t too much slower than the unrolled part.
- A set of binary tests, for example after an 8-limb unrolling, test for 4 more limbs to process, then a further 2 more or not, and finally 1 more or not. This will probably take more code space than a simple loop.
- A `switch` statement, providing separate code for each possible excess, for example an 8-limb unrolling would have separate code for 0 remaining, 1 remaining, etc, up to 7 remaining. This might take a lot of code, but may be the best way to optimize all cases in combination with a deep pipelined loop.
- A computed jump into the middle of the loop, thus making the first iteration handle the excess. This should make times smoothly increase with size, which is attractive, but setups for the jump and adjustments for pointers can be tricky and could become quite difficult in combination with deep pipelining.