Re: [PATCH] x86/crc32: optimize tail handling for crc32c short inputs

[David Laight <david.laight.linux@gmail.com>]

On Wed, 5 Mar 2025 18:56:43 -0800
Eric Biggers <ebiggers@kernel.org> wrote:

> On Wed, Mar 05, 2025 at 10:07:39PM +0000, David Laight wrote:
> > On Wed, 5 Mar 2025 11:16:08 -0800
> > Eric Biggers <ebiggers@kernel.org> wrote:
> >   
> > > On Wed, Mar 05, 2025 at 02:26:53PM +0000, David Laight wrote:  
> > > > On Tue,  4 Mar 2025 13:32:16 -0800
> > > > Eric Biggers <ebiggers@kernel.org> wrote:
> > > >     
> > > > > From: Eric Biggers <ebiggers@google.com>
> > > > > 
> > > > > For handling the 0 <= len < sizeof(unsigned long) bytes left at the end,
> > > > > do a 4-2-1 step-down instead of a byte-at-a-time loop.  This allows
> > > > > taking advantage of wider CRC instructions.  Note that crc32c-3way.S
> > > > > already uses this same optimization too.    
> > > > 
> > > > An alternative is to add extra zero bytes at the start of the buffer.
> > > > They don't affect the crc and just need the first 8 bytes shifted left.
> > > > 
> > > > I think any non-zero 'crc-in' just needs to be xor'ed over the first
> > > > 4 actual data bytes.
> > > > (It's over 40 years since I did the maths of CRC.)  
> > ...  
> > > > 	David    
> > > 
> > > Sure, but that only works when len >= sizeof(unsigned long).  Also, the initial
> > > CRC sometimes has to be divided between two unsigned longs.  
> > 
> > Yes, I was thinking that might make it a bit more tricky.
> > I need to find some spare time :-)
> > 
> > I wasn't taught anything about using non-carry multiplies either.
> > And I can't remember the relevant 'number field' stuff either.
> > But (with no-carry maths) I think you have:
> > 	crc(n + 1) = (crc(n) + data(n)) * poly
> > If data(n+1) and data(n+2) are zero (handled elsewhere) you have:
> > 	crc(n + 3) = (((crc(n) + data(n)) * poly) * poly) * poly
> > I think that because it is a field this is the same as
> > 	crc(n + 3) = (crc(n) + data(n)) * (poly * poly * poly)
> > which is just a different crc polynomial.
> > If true your '3-way' cpu doesn't have to use big blocks.  
> 
> Well, to extend by some constant number of bits 'n', you can carryless-multiply
> by the polynomial x^n, pre-reduced by the CRC's generator polynomial.  That's
> basically how all the CRC implementations using carryless multiplication work.
> Take a look at the x86 and riscv optimized code, for example -- especially my
> new versions in the crc-next tree at
> https://web.git.kernel.org/pub/scm/linux/kernel/git/ebiggers/linux.git/log/?h=crc-next.
> 
> But x86 does not have a scalar carryless multiplication instruction, only vector
> (PCLMULQDQ).  It does have a scalar CRC instruction, for crc32c *specifically*,
> and that is what the code we're discussing is taking advantage of.  Given that
> there is overhead associated with using kernel-mode FPU (i.e. vector), it makes
> sense to do that, at least on short messages.
> 
> On longer messages a PCLMULQDQ-only implementation would work well, but so does
> interleaving the crc32c scalar instruction on multiple chunks, which is what is
> currently wired up in the kernel via crc32c-3way.S.  And yes, the chunks for
> that do not *have* to be long, but you still need to use pclmulqdq instructions
> to combine them

You should be able to use lookup tables to jump over the other chunks
(so processing a block of zero bytes).
Possibly 8 lookup tables of 16 entries each for each nibble (512 bytes).
Not nice for the d-cache though.

> (unless you do a really slow bit-at-a-time carryless
> multiplication), and you have to enter a kernel-mode FPU section to do that.

That pseudo-code is probably completely wrong.
I suspect that since it is 'just' doing 'data % poly' it relies on the fact that
	327 % 7 == 3 * (100 % 7) + 27
and reduces the length by one digit.
(Where a 'digit' could be 64 bits)
I need to look up pclmulqdq.
Trying to do anything with the simd instructions makes my head hurt.

	David