Fast equal-area mapping of the (hemi)sphere using SIMD

We present a fast vectorized implementation of a transform that maps
points in the unit square to the surface of the sphere, while preserving fractional
area. The mapping uses the octahedral map combined with an equal-area param-
eterization and has many desirable features such as low distortion, straightforward
interpolation, and fast inverse and forward transforms. Our SIMD implementation
completely avoids branching and uses polynomial approximations for the trigono-
metric operations, along with other tricks. This results in up to 9 times speed-up
over a traditional scalar implementation. Source code is available online