[PATCH] D147305: [LoongArch] Optimize multiplication with immediates

[Ben Shi via Phabricator via llvm-commits]

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In D147305#4236071 <https://reviews.llvm.org/D147305#4236071>, @xen0n wrote:

> This is good strength reduction overall, thanks for the insight!
>
> Though maybe the exact patterns can be automatically generated with nested loops, for reduced mental burden to prove correctness? I've sketched something and it seems doable:
>
>   >>> alsl = lambda j, k, imm: (j << imm) + k
>   >>> a = [alsl(alsl(1, 1, i), alsl(1, 1, i), j) for j in range(1,5) for i in range(1,5)]
>   >>> a
>   [9, 15, 27, 51, 15, 25, 45, 85, 27, 45, 81, 153, 51, 85, 153, 289]
>   >>> list(sorted(set(a)))
>   [9, 15, 25, 27, 45, 51, 81, 85, 153, 289]
>   >>> b = [alsl(alsl(1, 1, i), 1, j) for j in range(1,5) for i in range(1,5)]
>   >>> b
>   [7, 11, 19, 35, 13, 21, 37, 69, 25, 41, 73, 137, 49, 81, 145, 273]
>   >>> ab = set(a).union(set(b))
>   >>> len(ab)
>   24
>   >>> list(sorted(set(a).intersection(set(b))))
>   [25, 81]
>   
>   >>> c = [alsl(1, alsl(1, 1, i), j) for j in range(1,5) for i in range(1,5)]
>   >>> c
>   [5, 7, 11, 19, 7, 9, 13, 21, 11, 13, 17, 25, 19, 21, 25, 33]
>   >>> list(sorted(set(c)))
>   [5, 7, 9, 11, 13, 17, 19, 21, 25, 33]
>   
>   >>> set(c).difference(ab)
>   {33, 5, 17}
>   >>> all = set(c).union(ab).difference({3, 5, 9, 17})
>   >>> len(all)
>   24
>   >>> list(sorted(all))
>   [7, 11, 13, 15, 19, 21, 25, 27, 33, 35, 37, 41, 45, 49, 51, 69, 73, 81, 85, 137, 145, 153, 273, 289]
>
> So basically, we can strength-reduce a total of 24 different constant-multiplications with two `alsl`'s:
>
> - case 1: `alsl T, X, X, i; alsl Y, T, T, j`: 15, 25, 27, 45, 51, 81, 85, 153, 289
> - case 2: `alsl T, X, X, i; alsl Y, T, X, j`: 7, 11, 13, 19, 21, 25, 35, 37, 41, 49, 69, 73, 81, 137, 145, 273
> - case 3: `alsl T, X, X, i; alsl Y, X, T, j`: 7, 11, 13, 19, 21, 25, 33
>
> Problem is that there are some overlaps between the 3 possible combinations, and some inside case 1 and 3. If we could somehow avoid producing conflicting rules then probably leveraging TableGen's loop and computation abilities would produce code that's easier to maintain. Otherwise, simplifying the code with some macros could also be beneficial.

Thanks for your suggestion! Using foreach really makes the code more clear!

BTW: ALSL only accepts shift amount 1,2,3,4, the value 5 is not supported.


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