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 Ph:+61-2-8571-0847 .. Fx:+61-2-9692-9623 | unsolicited email not wanted here Views & opinions here are mine and not those of any past or present employer
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