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4ae192a3d9
The polynomial used for asin_expr() was suboptimal (and its source was
not documented).
A better approximation is found in the _Handbook_of_Mathematical_Functions_
by Abramowitz and Stegun, which is used in Nvidia's Cg toolkit. However,
while this approximation gives a good absolute error bound, its relative
error exceeds the 4096 ulp allowed by the Vulkan spec. Taking a page
from the spirv implementation of asin(), we implement a piecewise
approximation where a Taylor series is used for small values of |x|.
This patch also harmonizes the GLSL and Vulkan implementations by moving
the implementation to common code (nir_builder).
Running tests on asin() with a grid of 64000 samples between 0.0 and +1.0,
the original asin() at 32 bits has:
```
glsl spirv
RMSE: 1.756451e-04 1.609091e-04
worst abs error: 3.904104e-04 at 0.937001 3.904104e-04 at 0.937001
worst ulp error: 11800 at 6.2499e-05 3826 at 0.841331
```
whereas the new implementation has for both:
```
RMSE: 2.528056e-05
worst abs error: 4.962087e-05 at 0.451149
worst ulp error: 2379 at 0.215106
```
Reviewed-by: Marek Olšák <marek.olsak@amd.com>
Reviewed-by: Alyssa Rosenzweig <alyssa.rosenzweig@intel.com>
Acked-by: Mel Henning <mhenning@darkrefraction.com>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/40862>
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