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

Ingo Molnar
2016-12-09T05:22:09Z

* 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.

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?

Thanks,

Ingo