[Violet] Node tests

[LiarPrincess]

First batch of tests from Violet - Python VM written in Swift (connected to #98 Using tests from “Violet - Python VM written in Swift”).

Test failures

Binary operations

Let's use the following test as an example (I chose this one at random, there are other tests that are failing, maybe for different reasons):

self.xorTest(lhs: "-1", rhs: "18446744073709551615", expecting: "-18446744073709551616")

attaswift/BigInt says it equals to 0.

Other engines

• WolframAlpha - BitXor[-1, 18446744073709551615] -> -18446744073709551616 link
• Python 3.7.4

  Python 3.7.4 (default, Jul 20 2021, 13:20:24)
  [Clang 12.0.0 (clang-1200.0.32.2)] on darwin
  Type "help", "copyright", "credits" or "license" for more information.
  >>> -1 ^ 18446744073709551615
  -18446744073709551616

• Node - we generated our test with Node, soooo…

Why?

• -1 in two complement is represented as all 1 with the desired width.
• 18446744073709551615 is equal to 2^64 − 1 which is 1111111111111111111111111111111111111111111111111111111111111111 (basically 1 repeated 63 times)

So, obviously if both -1 and 18446744073709551615 are all 1 then xor will be 0, just like attaswift/BigInt returns.

Well… not exactly.

18446744073709551615 is positive, so its binary representation has to have 0 prefix in two complement (otherwise it would mean negative number).

With this:

lhs:    11111111111111111111111111111111111111111111111111111111111111111
rhs:    01111111111111111111111111111111111111111111111111111111111111111
result: 10000000000000000000000000000000000000000000000000000000000000000

Shift right

Let's use the following test as an example (I chose this one at random, there are other tests that are failing, maybe for different reasons):

self.shiftRightTest(value: "-1932735284", count: 5, expecting: "-60397978")

This is an interesting case (look at the last number: 7 vs 8):

Engine	Result
attaswift/BigInt	-60397977
Wolfram Alpha	-60397977
Node v17.5.0	-60397978
Python 3.7.4	-60397978
Swift 5.3.2*	-60397978
Violet	-60397978

(*) This is in Int range, so you can just -1932735284 >> 5 to test it.

Anyway… Wolfram and attaswift give -60397977, but Node, Python, Swift and Violet give -60397978.

Long story short, both answers are correct, it depends on how you round.

Doing this by hand:
1000 1100 1100 1100 1100 1100 1100 1100 >> 5 = 100 0110 0110 0110 0110 0110 0110 rem 0 1100

With sign extension to Int32: 1111_1100_0110_0110_0110_0110_0110_0110, which is (according to Swift repl):

 13> Int32(bitPattern: 0b1111_1100_0110_0110_0110_0110_0110_0110)
$R11: Int32 = -60397978

I think that attaswift uses sign + magnitude representation. If it was 2 complement then everything would be trivial, but it is not, so sometimes you need an adjustment: Swift uses what would be 'GMP_DIV_FLOOR' mode in 'GMP'. Which means that if we are negative and any of the removed bits is '1' then we have to round down.

Wolfram does not round down (which is “more” mathematically correct!).

[LiarPrincess]

Anyway… I will work on adding more tests later…

Btw. Take those explanations with a grain of salt. Obviously I wrote those tests (well Node generated them… but it is still my work), so subconsciously I will try to “make them correct” (maybe the better term would be “justify their shortcomings”).