i965/fs_live_variables: Do liveness analysis bottom-to-top
From Muchnick's Advanced Compiler Design and Implementation:
"To determine which variables are live at each point in a flowgraph, we
perform a backward data-flow analysis"
Previously, we were walking the blocks forwards and updating the livein and
then the liveout. However, the livein calculation depends on the liveout
and the liveout depends on the successor blocks. The net result is that it
takes one full iteration to go from liveout to livein and then another
full iteration to propagate to the predecessors. This works out to an
O(n^2) computation where n is the number of blocks. If we run things in
the other order, it's O(nl) where l is the maximum loop depth which is
practically bounded by 3.
On my HSW desktop, one particular shadertoy test gets a 20% improvement in
compile times:
N Min Max Median Avg Stddev
x 10 15.965 16.884 16.026 16.1822 0.
34736846
+ 10 12.813 13.052 12.876 12.8891 0.
06913666
Difference at 95.0% confidence
-3.2931 +/- 0.235316
-20.3501% +/- 1.45417%
(Student's t, pooled s = 0.250444)
Reviewed-by: Matt Turner <mattst88@gmail.com>