On Fri, Sep 26, 2014 at 6:11 PM, Erik Faye-Lund <kusmab...@gmail.com> wrote: > Our current atan()-approximation is pretty inaccurate at 1.0, so > let's try to improve the situation by doing a direct approximation > without going through atan. > > This new implementation uses an 11th degree polynomial to approximate > atan in the [-1..1] range, and the following identitiy to reduce the > entire range to [-1..1]: > > atan(x) = 0.5 * pi * sign(x) - atan(1.0 / x) > > This range-reduction idea is taken from the paper "Fast computation > of Arctangent Functions for Embedded Applications: A Comparative > Analysis" (Ukil et al. 2011). > > The polynomial that approximates atan(x) is: > > x * 0.9999793128310355 - x^3 * 0.3326756418091246 + > x^5 * 0.1938924977115610 - x^7 * 0.1173503194786851 + > x^9 * 0.0536813784310406 - x^11 * 0.0121323213173444 > > This polynomial was found with the following GNU Octave script: > > x = linspace(0, 1); > y = atan(x); > n = [1, 3, 5, 7, 9, 11]; > format long; > polyfitc(x, y, n) > > The polyfitc function is not built-in, but too long to include here. > It can be downloaded from the following URL: > > http://www.mathworks.com/matlabcentral/fileexchange/47851-constraint-polynomial-fit/content/polyfitc.m > > This fixes the following piglit test: > shaders/glsl-const-folding-01 > > Signed-off-by: Erik Faye-Lund <kusmab...@gmail.com> > Reviewed-by: Ian Romanick <ian.d.roman...@intel.com>
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