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author | Erik Faye-Lund <[email protected]> | 2014-09-26 18:11:19 +0200 |
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committer | Olivier Galibert <[email protected]> | 2014-10-10 20:44:27 +0200 |
commit | 326e303175ab700d59602f0e344e8d84e15f1aa8 (patch) | |
tree | 45c92344e8824cbc66021a1b1a244bc23d8deded /src/glsl/opt_if_simplification.cpp | |
parent | 070b2c2efc415f459e9c32415b401609acded565 (diff) |
glsl: improve accuracy of atan()
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 <[email protected]>
Reviewed-by: Ian Romanick <[email protected]>
Diffstat (limited to 'src/glsl/opt_if_simplification.cpp')
0 files changed, 0 insertions, 0 deletions