为什么我的滚动adler32校验和不能正常运行？ （模算术）

Question

I am implementing, in go, a rolling version of the adler32 checksum.

This answer was helpful to double check my maths. However I am struggling at implementing it correctly in golang.

I wrote the following code:

func roll(adler, n, leave, enter uint32) uint32 {
    a := adler & 0xffff
    b := adler >> 16

    a = (a + enter - leave) % MOD
    b = (b - n*leave - 1 + a) % MOD
    return b<<16 | a
}

It tested it on various inputs and it worked fine, until I decided to run it on random data. Here is a sample where it does not work (I found several of them).

What is baffling me is that the same code in python works perfectly on those inputs:

def roll(adler, n, leave, enter):
    a = adler & 0xffff
    b = adler >> 16

    a = (a + enter - leave) % MOD
    b = (b - n*leave - 1 + a) % MOD
    return b<<16 | a

For good measure, I am including proof that this works in python. Note that the python checksum matches the non-rolling version of the go checksum (and that part is directly from the go core libraries).

I studied my results on all the other problematic samples, and found that I am never making a mistake on the least significant bits of the checksum (the "a" bits). Also, the error is consistently the same, equals to 0xe10000. I suspect a peculiarity of how go handles modulo operations on uint32 integers to be the cause of this.

What is happening and how do I fix my code?

Answer 1

The integers in Python are signed. You declared all the integers in the golang version to be unsigned. That's the difference.

When an unsigned number is subtracted from a smaller unsigned number, you get a huge unsigned number that gives a different remainder on division than the small negative difference would. When you wrap, you are effectively adding 2³². 2³² mod 65521 is 225, or 0xe1, which is why you're seeing that difference in b. It's much more likely to wrap on the b calculation, but it can happen for a as well, if a happens to be very small at that step.

Per the comment by @samgak, you also have to worry about the definition of the % operator in different languages for signed values. So the solution that works across different conventions would be to make the values positive by adding as many MODs as necessary, before doing the % MOD. For a, just add MOD. For b, add (1 + n * leave / MOD) * MOD.

Take care to make sure that the intermediate values don't overflow. The code in go can give erroneous results if n*leave is large enough to wrap the integer type being used.