[Mesa-dev] [PATCH] glsl: Fix pi/2 constant in acos built-in function

[Paul Berry]

On 4 June 2012 14:50, Ian Romanick <idr at freedesktop.org> wrote:

> On 06/04/2012 01:31 PM, Olivier Galibert wrote:
>
>> On Mon, Jun 04, 2012 at 01:11:13PM -0700, Ian Romanick wrote:
>>
>>> From: Ian Romanick<ian.d.romanick at intel.**com <ian.d.romanick at intel.com>
>>> >
>>>
>>> In single precision, 1.5707963 becomes 1.5707962513 which is too
>>> small.  However, 1.5707964 becomes 1.5707963705 which is just right.
>>> The value 1.5707964 is already used in asin.ir.
>>>
>>> NOTE: This is a candidate for stable release branches.
>>>
>>
>> If piglit stops bitching on that partical problem thanks to such a
>> small change, it's just beautiful.
>>
>
> It does fix the acos issue in piglit.  The closed-source test suite that
> we use still isn't happy, but I think that just means we need better
> approximations for acos and asin.
>
> asin(vec4(.2, .6, .8, 1.)) has an absolute error of (0.0000105351
> 0.0001987219 0.0001262426 0.0000003576).  The results for .6 and .8 are
> especially bad, but even the .2 result should be better.  The closed-source
> test suite wants an absolute error of 1e-5 for asin and acos.


Do we have any quantitative information about how much accuracy is really
needed for asin?  Of course, an error of 1.9e-4 would be embarrassingly bad
for scientific use, but are you sure that it isn't adequate for graphics
purposes?  I'd hate to spend a lot of effort implementing a more accurate
asin, only to find that the only user-visible effect is for shaders to run
slower because we're doing more accurate math.  As fun as it is to
numerically approximate trig functions (I'm not even kidding--I love this
stuff and I'm jealous that I don't have time to work on it right now) I'm
not convinced it's worth it yet.

Having said that, I *do* think it's worth making sure the asin function is
well-behaved enough near zero that derivatives won't do unexpected things.
If you do wind up working on this, I hope you'll keep the improvements I
made last july (d4c80f5f85c749df3fc091ff07b60ef4989fa6d9) where I made the
first two terms of the approximation pi/2 and pi/4-1.  If these terms
aren't exact, then asin behaves poorly near zero.


>
>
>  Do we need a better precision atan, or should piglit just be told to
>> shutup?  The shutup patch has been sent it ages ago, but I can't do
>> the "more precision" one if that's what's wanted.
>>
>
> I think we need a better atan.  The result that it produces is not very
> good.  I plan to look into that more tonight.
>

FYI, our formulas for atan and acos are exact trig identities in terms of
asin, so probably any improvement made to asin will carry over to the
others, at least until you reach the realm of rounding errors (which I'm
guessing you won't reach if your target is 1e-5).
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