RFR: 8282365: Consolidate and improve division by constant idealizations [v33]

[Kim Barrett]

On Tue, 24 Oct 2023 13:12:20 GMT, Quan Anh Mai <qamai at openjdk.org> wrote:

>> This patch implements idealisation for unsigned divisions to change a division by a constant into a series of multiplication and shift. I also change the idealisation of `DivI` to get a more efficient series when the magic constant overflows an int32.
>> 
>> In general, the idea behind a signed division transformation is that for a positive constant `d`, we would need to find constants `c` and `m` so that:
>> 
>>     floor(x / d) = floor(x * c / 2**m) for 0 < x < 2**(N - 1) (1)
>>     ceil(x / d) = floor(x * c / 2**m) + 1 for -2**(N - 1) <= x < 0 (2)
>> 
>> The implementation in the original book takes into consideration that the machine may not be able to perform the full multiplication `x * c`, so the constant overflow and we need to add back the dividend as in `DivLNode::Ideal` cases. However, for int32 division, `x * c` cannot overflow an int64. As a result, it is always feasible to just calculate the product and shift the result.
>> 
>> For unsigned multiplication, the situation is somewhat trickier because the condition needs to be twice as strong (the condition (1) and (2) above are mostly the same). This results in the magic constant `c` calculated based on the method presented in Hacker's Delight by Henry S. Warren, Jr. may overflow an uintN. For int division, we can depend on the theorem devised by Arch D. Robison in N-Bit Unsigned Division Via N-Bit Multiply-Add, which states that there exists either:
>> 
>>     c1 in uint32 and m1, such that floor(x / d) = floor(x * c1 / 2**m1) for 0 < x < 2**32 (3)
>>     c2 in uint32 and m2, such that floor(x / d) = floor((x + 1) * c2 / 2**m2) for 0 < x < 2**32 (4)
>> 
>> which means that either `x * c1` never overflows an uint64 or `(x + 1) * c2` never overflows an uint64. And we can perform a full multiplication.
>> 
>> For longs, there is no way to do a full multiplication so we do some basic transformations to achieve a computable formula. The details I have written as comments in the overflow case.
>> 
>> More tests are added to cover the possible patterns.
>> 
>> Please take a look and have some reviews. Thank you very much.
>
> Quan Anh Mai has updated the pull request with a new target base due to a merge or a rebase. The pull request now contains 74 commits:
> 
>  - fix proof
>  - Merge branch 'master' into unsignedDiv
>  - fix assert macro, benchmarks
>  - comment styles
>  - disable test with Xcomp
>  - remove verify
>  - fix x86 test
>  - more rigorous control
>  - verify the effectiveness of test
>  - require x64
>  - ... and 64 more: https://git.openjdk.org/jdk/compare/5224e979...529bd0f9

Not a review - mostly a comment for future development. I only became aware of
this PR recently (I don't track compiler PRs that closely), so didn't notice
the embedded separation of Java-semantics arithmetic from globalDefintions. I
strongly approve of that separation, but wish it had been done in it's own PR.
Kind of late for suggesting that now though. That change can (and hopefully
will) be followed by changes to remove the need to #include javaArithmetic.hpp
from globalDefinitons.hpp, since most code doesn't need javaArithmetic.hpp.
That's likely to take a while to accomplish, but would be a nice goal to
achieve. This goes along with the ongoing cleanup of replacing
unnecessary/inappropriate uses of JNI integral types with "native" types.

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PR Comment: https://git.openjdk.org/jdk/pull/9947#issuecomment-1828775134