On Tue, Dec 20, 2016 at 2:17 AM, Matt Turner <matts...@gmail.com> wrote: > On Mon, Dec 19, 2016 at 5:12 PM, Giuseppe Bilotta > <giuseppe.bilo...@gmail.com> wrote: >> Just one question though —not knowing much of the shader language, can >> I expect expm1 to be available? > > No, expm1 doesn't exist in GLSL.
This is extremely bothersome. Both the (exp(2x)-1)/(exp(2x)+1) and the 1-2/(exp(2x)+1) formulas give pretty good results when written in terms of expm1. On Tue, Dec 20, 2016 at 3:48 AM, Roland Scheidegger <srol...@vmware.com> wrote: > Not sure it really matters though one way or another. If you wanted good > accuracy around 0, you'd have to use a different formula plus a select > (seems like libm implementations actually use 3 cases depending on input > value magnitude - not so hot with vectors, but thankfully glsl doesn't > require 1 ULP accuracy). Brute-forcing over all floating points on CPU by switching between the two formulas above at appropriate thresholds gives a maximum relative error of the order of machine epsilon when using expm1, and the switch between the two formulas can be implemented with a select on two terms. However, this does require expm1. Nelson Beebe has a very detailed description of how to achieve very accurate results for tanh here https://www.math.utah.edu/~beebe/software/ieee/tanh.pdf and the results are a bit depressing, in that multiple thresholds are necessary. I'm not sure if these are the same used by libm, but in any case neither lends itself well to vectorization (in contrast to the switch between the two formulas above). An alternative approach could be to actually provide a software implementation of expm1 and use it to compute tanh. I wouldn't be surprised if this would turn out to not be slower than using exp itself, in fact. -- Giuseppe "Oblomov" Bilotta _______________________________________________ mesa-dev mailing list mesa-dev@lists.freedesktop.org https://lists.freedesktop.org/mailman/listinfo/mesa-dev
