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

[Paul Berry]

On 6 June 2012 10:31, Kenneth Graunke <kenneth at whitecape.org> wrote:

> On 06/06/2012 05:16 AM, Olivier Galibert wrote:
> > On Tue, Jun 05, 2012 at 04:51:54PM -0700, Paul Berry wrote:
> >> The best idea I've got so far would be a shader_runner test with a
> fragment
> >> shader that computes dFdx(asin(x)), compares it to the theoretical
> closed
> >> form derivative of asin(x) (which is 1/sqrt(1-x^2)), and draws red
> pixels
> >> if the result is outside a certain error tolerance.  We'd probably want
> to
> >> use a relative error (since the derivative of asin(x) can get quite
> large)
> >> and stop a bit shy of the endpoints where it goes to infinity.
> >
> > Can't you take the perfectly reasonable hypothesis that the system's
> > asin is precise, and upload something like a 256x256 R32FG32FB32FA32F
> > texture with reference values?  262144 testing points should be good
> > enough :-)
> >
> > And that's something that generalizes easily to all the functions you
> > may want to test on a segment.
> >
> >   OG.
>
> There's at least one problem with that: if the hardware only supports N
> active textures at once, and the application already asked to use all N
> of those...you don't have a texture available for this.  Which is maybe
> not a big deal if you just need one, say, for asin...but if you want one
> for asin, one for noise, one for ...
>
> I suppose you could combine them into one texture.  Still, it's kind of
> annoying to deal with.  Also, arithmetic instructions tend to be vastly
> cheaper than texture lookups, so you can probably get a fairly nice
> algebraic approximation in that amount of space.
>
>
There's some missing context here.  Ian was asking for suggestions on how
to *test* asin(), not how to implement it.  As a testing technique
Olivier's suggestion would be ok, although not ideal because it relies on
floating point textures--it would be nice if floating point texture support
weren't required to run our piglit tests for asin().

Also, it's not entirely clear to me from the original context, but I
thought Ian was looking for suggestions on how to test that dFdx(asin(x))
behaves well near x=0.  Testing asin(x) at 262144 points won't necessarily
validate that the derivative behaves well, because it's possible that a
small discontinuity near x=0 could result in a very badly behaved
derivative even if asin(x) is within tolerance for all x.
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