Faster Asin() Was Hiding in Plain Sight

3 days ago

The author reflects on the importance of research before acting to save time, using their experience with PSRayTracing as an example.
A faster approximation for the arcsine function was sought to improve the performance of PSRayTracing, leading to the exploration of Taylor series and Padé approximants.
Initial attempts with Taylor series showed speed improvements but had significant errors outside the range [-0.8, 0.8], requiring fallback to std::asin().
Padé approximants were then explored, offering better accuracy with less error, especially when combined with half-angle transformations for edge cases.
A significant breakthrough came from discovering a fast arcsine approximation from Nvidia's Cg Toolkit, which was both elegant and significantly faster across various hardware.
Benchmarking showed the Cg approximation was consistently faster than std::asin(), with speedups ranging from 1.02x to 1.89x depending on the hardware.
The author learned the value of checking existing solutions before diving into complex optimizations, highlighting the importance of community knowledge and historical resources.

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