Re: [patch 5/6] [RFD] timekeeping: Provide optional 128bit math

Peter Zijlstra
2016-12-09T05:41:55Z

On Fri, Dec 09, 2016 at 06:22:03AM +0100, Ingo Molnar wrote:
>
> * Peter Zijlstra <peterz@infradead.org> wrote:
>
> > On Fri, Dec 09, 2016 at 05:08:26AM +0100, Ingo Molnar wrote:
> > > > +#if defined(CONFIG_ARCH_SUPPORTS_INT128) && defined(__SIZEOF_INT128__)
> > > > +static inline u64 timekeeping_delta_to_ns(struct tk_read_base *tkr, u64 delta)
> > > > +{
> > > > + unsigned __int128 nsec;
> > > > +
> > > > + nsec = ((unsigned __int128)delta * tkr->mult) + tkr->xtime_nsec;
> > > > + return (u64) (nsec >> tkr->shift);
> > > > +}
> > >
> > > Actually, 128-bit multiplication shouldn't be too horrible - at least on 64-bit
> > > architectures. (128-bit division is another matter, but there's no division here.)
> >
> > IIRC there are 64bit architectures that do not have a 64x64->128 mult,
> > only a 64x64->64 mult instruction. Its not immediately apparent using
> > __int128 will generate optimal code for those, nor is it a given GCC
> > will not require libgcc functions for those.
>
> Well, if the overflow case is rare (which it is in this case) then it should still
> be relatively straightforward, something like:
>
> X and Y are 64-bit:
>
> X = Xh*2^32 + Xl
> Y = Yh*2^32 + Yl
>
> X*Y = (Xh*2^32 + Xl)*(Yh*2^32 + Yl)
>
> = Xh*2^32*(Yh*2^32 + Yl)
> + Xl*(Yh*2^32 + Yl)
>
> = Xh*Yh*2^64
> + Xh*Yl*2^32
> + Xl*Yh*2^32
> + XL*Yl
>
> Which is four 32x32->64 multiplications in the worst case.

Yeah, that's the full 64x64->128 mult on 3bit. Luckily we only need
64x32->96, which reduces to 2 32x32->64 mults.

But my point was that unconditionally using __int128 might not be the
right thing.

> Where a valid overflow threshold is relatively easy to determine in a hot path
> compatible fashion:
>
> if (Xh != 0 || Yh != 0)
> slow_path();
>
> And this simple and fast overflow check should still cover the overwhelming
> majority of 'sane' systems. (A more involved 'could it overflow' check of counting
> the high bits with 8 bit granularity by looking at the high bytes not at the words
> could be done in the slow path - to still avoid the 4 multiplications in most
> cases.)
>
> Am I missing something?

Yeah, the fact that we only need the 2 mults and that the fallback
already does the second multiply conditionally :-) But then look at the
email where I said that that condition actually makes the thing vastly
more expensive on some archs (like tilegx).