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Message-ID: <20120501183356.GL16237@port70.net>
Date: Tue, 1 May 2012 20:33:56 +0200
From: Szabolcs Nagy <nsz@...t70.net>
To: musl@...ts.openwall.com
Subject: Re: math todo
* Rich Felker <dalias@...ifal.cx> [2012-05-01 10:44:38 -0400]:
> On Tue, May 01, 2012 at 11:14:58AM +0200, Szabolcs Nagy wrote:
> > yes, actually
> > fesetround(FE_UPWARD);
> > exp(-inf) = 0x1p-1074; // smallest subnormal
> > instead of 0, which is 1ulp depending on your definition of ulp :)
>
> This is incorrect (because the result is exact, the error is ==1ulp,
> and IEEE requires <1ulp). But for the large finite negative arguments,
> 0x1p-1074 is the correctly rounded answer in rounds-upward mode.
>
ok
> > > BTW under asm, we may also want to switch to the faster acos
> > > implementation.
> > ok i'll add it
> > (for double it is known to work, but i havent tested it for
> > the long double case)
>
> Even if we can't switch ld we could still switch it for the
> float/double versions and keep our original asm for ld80.
>
ok
> All of the nextafter stuff looks overly complicated. Shouldn't these
> functions all just be (essentially):
>
> if (x>y) rep_x--;
> else if (x<y) rep_x++;
>
> modulo a little handling for sign and ±0?
>
yes
and that's what is done, but under/overflow flags are
also handled and for double two uint32_t is used instead
of one uint64_t ++
(and comparision is done using int instead of float compare)
it can be a bit simpler
> > 99 ulp want: 0 got: 8000000000000000 round: m acos arg0: 0x1p+0 arg1: 0x0p+0 want: 0x0p+0 got: -0x0p+0
> > 99 ulp want: 8000000000000000 got: 8000000000000001 round: p atan arg0: -0x1p-1074 arg1: 0x0p+0 want: -0x0p+0 got: -0x1p-1074
> > 99 ulp want: 0 got: 1 round: m atan arg0: 0x1p-1074 arg1: 0x0p+0 want: 0x0p+0 got: 0x1p-1074
> > 99 ulp want: 0 got: 1 round: z atan arg0: 0x1p-1074 arg1: 0x0p+0 want: 0x0p+0 got: 0x1p-1074
> > 99 ulp want: 8000000000000000 got: 8000000000000001 round: z atan arg0: -0x1p-1074 arg1: 0x0p+0 want: -0x0p+0 got: -0x1p-1074
>
> IMO this is 1ulp not >99ulp. For denormals ulp is not x * 0x1p-52 but
> the actual last place of significance.
>
yes it is 1ulp, but it's a huge relative error, same for sign differences
> > all: 69734 fail: 12787 failbad: 107 failepic: 72
>
> Like your choice of naming. :-)
:)
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