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Date: Mon, 17 Oct 2011 23:39:58 +0200
From: Ingo Molnar <mingo@elte.hu>
To: "H. Peter Anvin" <hpa@zytor.com>
Cc: Thomas Gleixner <tglx@linutronix.de>,
        Linus Torvalds <torvalds@linux-foundation.org>,
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Subject: Re: Linux 3.1-rc9
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* H. Peter Anvin <hpa@zytor.com> wrote:

> On 10/17/2011 02:19 PM, Ingo Molnar wrote:
> > 
> > it's 64/32 division - it's the /1000000000 /1000000 /1000 divisions 
> > in the large majority of cases, to convert between 
> > seconds/milliseconds/microseconds and scalar nanoseconds.
> > 
> > the kernel-internal ktime_t in the 32-bit optimized case is:
> > 
> > union ktime {
> >         s32     sec, nsec;
> > };
> > 
> > which is the same as timespec and arithmetically close to timeval, 
> > which many ABIs use. So conversion is easy in that case - but 
> > arithmetics gets a bit harder.
> > 
> > If we used a scalar 64-bit form for all kernel internal time 
> > representations:
> > 
> > 	s64	nsecs;
> > 
> > then conversions back to timespec/timeval would involve dividing this 
> > 64-bit value with 1000000000 or 1000000.
> > 
> > Is there no faster approximation for those than bit by bit?
> > 
> > In particular we could try something like:
> > 
> > 	(high*2^32 + low)/1e9 ~==  ( high * (2^64/1e9) ) / 2^32
> > 
> > ... which reduces it all to a 64-bit multiplication (or two 32-bit 
> > multiplications) with a known constant, at the cost of 1 nsec 
> > imprecision of the result - but that's an OK approximation in my 
> > opinion.
> > 
> 
> We can do much better than that with reciprocal multiplication.  

Yes, 2^64/1e9 is the reciprocal.

Thanks,

	Ingo