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Date: Thu, 7 Dec 2017 12:09:23 +1100 (AEDT)
From: Damian McGuckin <damianm@....com.au>
To: musl@...ts.openwall.com
Subject: Re: remquo - underlying logic
On Wed, 6 Dec 2017, Szabolcs Nagy wrote:
> it's not clear to me how you use fma (x-(int)(x/y)*y ?), but efficient
> fma instruction is not available on all targets and the software
> implementation can be very slow. and i suspect such approach would break
> fenv correctness.
Quite likely. Besides, my testing was flawed and FMA is NOT the answer I
thought it was.
> (musl is compiled with -std=c99 so x*y+z is not contracted to fma(x,y,z)
> automatically when the instruction is available, you have to add
> -ffp-contract=fast if that's what you want, but it might break some code
> in musl that relies on exact arithmetics, most math code should work
> either way though.)
For a lot of reasons, FMA is not the answer.
That said, over that range, I am experimenting using a simplistic form of
double-double arithmetic for that calculation.
Would you agree that when
(int) (x / y) < 2^52
the computation (int) (x / y) is accurate to within epsilon, i.e. if it
should be at most be incorrect by +/- 1.?
If so, and using the same sort of logic that log.c uses to split the
calculation of
k * log(2.0)
into a high and low component, or maybe into 4 components, would you agree
that it is possible to come up with an accurate computation of
x - y * (int) (x / y)
It should be much quicker than long division.
Regards - Damian
Pacific Engineering Systems International, 277-279 Broadway, Glebe NSW 2037
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