impl Power for U256

[andrewvious]

Description

Closes #4449

Checklist

• I have linked to any relevant issues.
• I have commented my code, particularly in hard-to-understand areas.
• I have updated the documentation where relevant (API docs, the reference, and the Sway book).
• I have added tests that prove my fix is effective or that my feature works.
• I have added (or requested a maintainer to add) the necessary Breaking* or New Feature labels where relevant.
• I have done my best to ensure that my PR adheres to the Fuel Labs Code Review Standards.
• I have requested a review from the relevant team or maintainers.

[xunilrj]

How you tested this? I tried testing this on Wolfram and got this: https://www.wolframalpha.com/input?i=5%5E28+%3D%3D+2*18446744073709551615%2B359414837200037395 where 18446744073709551615 = u64::MAX.

Input
5^28 = 2×18446744073709551615 + 359414837200037395
Result
True
Left hand side
5^28 = 37252902984619140625
Right hand side
2 18446744073709551615 + 359414837200037395 = 37252902984619140625

So shouldn´t this line be?

assert_eq(five.pow(twenty_eight), U256::from((0, 0, 2, 359414837200037395)));

[eureka-cpu]

🤔 each slot in the U256 type is a u64 which at max is 18446744073709551615. The total number 5^28 can be represented by two u64::MAX and one with 359414837200037395. At least, that's my understanding from looking at the test. Would you mind explaining how U256 { 0, 0, 2, 359414837200037395 } is equal to 5^28?

[eureka-cpu]

Also odd that this test passes if that's true

[xunilrj]

I got from Wolfram: https://www.wolframalpha.com/input?i=5%5E28+%3D%3D+2*18446744073709551615%2B359414837200037395.

Another option is https://www.wolframalpha.com/input?i=convert+5%5E28+to+base+18446744073709551615%5D

input: convert 5^28 to base 18446744073709551615
Input interpretation
convert 37252902984619140625 to base18446744073709551615
Result
2:359414837200037395_18446744073709551615 (2 digits)

Where 359414837200037395 is the least significant digit; and 2 and the second least significant digit.

[xunilrj]

Another good indication is: https://www.wolframalpha.com/input?i=log_5%5B18446744073709551615%5D

Input
log(5, 18446744073709551615)
Result
log(18446744073709551615)/log(5)
Decimal approximation
27.563299716697155242853137766599266959746869658989720909693829506...

So u64::MAX is super close to 5^27.

[eureka-cpu]

Ah, I see now. You're using the maximum value of u64 as the base. Why is that?

[eureka-cpu]

So u64::MAX is super close to 5^27.

u64::MAX is 10996163476785723490 greater than 5^27 🤔

[xunilrj]

Ah, I see now. You're using the maximum value of u64 as the base. Why is that?

Isn´t this what U256 is doing with four u64? Each field is a u64 digit.

[eureka-cpu]

I suppose I misunderstood since their test cases seem to imply that every next u64 is catching the overflow of the previous. I'm mostly asking out of curiosity since this area isn't my forte @xunilrj , sorry to have started such a long thread on your PR @andrewvious 😅

This could imply a few different problems:

• assert_eq may be passing incorrectly (I think this is most likely, which could make the last problem true)
• the implementation of Power is somehow inaccurate
• the test case itself is inaccurate as @xunilrj stated

[andrewvious]

No worries @eureka-cpu, I appreciate both of you @xunilrj I see how it works now, where on overflow it just increments the next u64 over by one. For example, adding 1 to u64::MAX would read:

u256 {
     u64=a: 0,
     u64=b: 0,
     u64=c: 1,
     u64=d: 0
} 

[xunilrj]

Doing a quick test here I found that this test pass. So we may have another problem here.

#[test]
fn test_pow_u256() {
    let five = U256::from((0, 0, 0, 5));
    let two = U256::from((0, 0, 0, 2));
    assert_eq(five, two);
}

Maybe it is the same problem of #4868

[xunilrj]

I created an issue to understand what is happening with assert_eq here: #4989

[andrewvious]

@xunilrj I tried rewriting it using rust's logic of it (https://docs.rs/uint/latest/src/uint/uint.rs.html#991-1014) Do you see any apparent flaws in the way Sway's logic would see these changes? I've been having to use CI to test because theres some sort of compile issue happening on my local fork. I separated all the tests, first passes and other two fail

[xunilrj]

Hi @andrewvious, I am incorporating your PR into this one: #5195 and closing this one.