[_TestSupport] Fix DoubleWidth think-o that trips an assert

[xwu]

If lhs and rhs have the same number of leading zero bits (and we know rhs < lhs), then we can't call _divide to divide a triple-width magnitude by a double-width magnitude (this trips the assert on line 634), but rather we know that the quotient is one. Additionally, we must use >> instead of &>> when computing the high word because in this scenario the leading zero bits may be zero.

Since it turns out there's more than one calling site for _divide that doesn't ensure the invariant asserted on line 634, we should actually deal with this in one place by replacing the assertion with a guard that handles the special case.

Additionally, fix a third think-o related to full-width multiplication where a carry isn't accounted for, causing unintended overflow with certain inputs.

This type now gives correct output verified for addition/subtraction/multiplication/nonzero-division-with-overflow for every pair of 16-bit unsigned integers using DoubleWidth<DoubleWidth<UInt4>> (with a custom UInt4 implementation).

Resolves https://github.com/apple/swift-numerics/issues/272

[LiarPrincess]

I updated dem issue with more of dem details:

• merged both comments
• 1 new test

Current status after this PR:

Test	Status	Comment
test_a	🟢 Works	Test 1 from the original issue.
test_b	🔴 Incorrect quotient and remainder	Test 2 from the original issue. Still failing.
test_c	🔴 Assertion failure	New test.

[xwu]

@LiarPrincess Thank you for providing more detail in the bug report regarding related edge cases!
All are now addressed in this PR.

[xwu]

@swift-ci test

[LiarPrincess]

Added test_d and test_e to the issue.

Current status:

Test	Status	Comment
test_a	🟢 Works
test_b	🟢 Works
test_c	🟢 Works
test_d	🔴 Assertion failure	New UInt256 test.
test_e	🔴 Assertion failure	New UInt256 test.

EDIT:

Ooo… Interesting!

In the original issue I added the "hint" (the if self.leadingZeroBitCount == rhs.leadingZeroBitCount thingie). Even pasting this code into DoubleWidth will not solve test_d and test_e (the new tests). It seems that the error is somewhere else, but I have not debugged your code.

[xwu]

@LiarPrincess, have you provided all of the failing test cases in the bug report? It would be good to see all of them in one go instead of iteratively expanding the bug.

[LiarPrincess]

In the issue I mentioned:

Those tests come from Oh-my-decimal:

• UInt128Tests and UInt256Tests - you may need to modify them to compile with DoubleWidth - see "Tests" section below.
• Python script to generate tests - the quality of the test cases is not that great - just some random numbers smashed together -> they will not excise edge cases for min/max etc. Only use unsigned types, so you have check any signed types yourself.

To run those tests on DoubleWidth you need to:

1. add this inside every class:

   typealias UInt128 = DoubleWidth<UInt64>
   typealias UInt256 = DoubleWidth<UInt128>
   typealias Word = UInt64

2. customize the create method - copy from the test classes that I provided in the issue

3. comment the "multiply by half" section - compiler error, just comment the red squigglies.

EDIT:

I created gists, so you can just copy-paste them (note that the 2nd one is quite big):

• UInt128 - https://gist.github.com/LiarPrincess/54bbaaf3589e55ee25783fe9f6648c55
• UInt256 - https://gist.github.com/LiarPrincess/8b4d2891e0f8c557a9543d054790ad7b

[xwu]

@LiarPrincess, that's a lot of tests! Can you specifically list the failing ones in the bug report?

[LiarPrincess]

You can just run them: copy the code from the gist and run it. They should finish execution in ~1 second. If there is a failure then Xcode will point you to an exact line. If there is a crash then it will automatically jump into a debugger.

In the issue I added 2 examples: test_d and test_e. I hope that resolving them will make all tests pass, but since I have not debugged your code it may be possible that there is some other bug hiding in there.

[LiarPrincess]

Test	Status
UInt128 tests from gist	🟢 Works
UInt256 tests from gist	🟢 Works

I also tested DoubleWidth in some of my projects (including the decimal thingie), and it seems to be working. Note that I only use unsigned types (UInt128/UInt256), and I do not test edge cases (UInt128.max = all bits 1 etc.), so some paths are still not tested. In terms of performance DoubleWidth seems to be 25-35% slower than direct implementation.

Anyway, I confirm that this PR fully solves #272.

EDIT: CI says that if failed on Linux, but I tested it on both mac and Ubuntu, so this may be something related to CI, not to this PR. IDK.

[xwu]

Great, cleaned up the commit history; this is ready to go. Will update main apple/swift repo soon.

[xwu]

@swift-ci test

[stephentyrone]

@swift-ci test

[stephentyrone]

Linux test failure is a misconfiguration of CI, which I've notified Mishal of. We'll merge this as-is.