i965/vec4_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.
In
b2c6ba0c4b21391dc35018e1c8c4f7f7d8952bea, we made this same change in
the FS backend to great effect. Might as well keep it consistent and make
the same change for vec4. Also, this took the time to run the test:
ES31-CTS.arrays_of_arrays.InteractionFunctionCalls1
from 6:49.62 to 3:31.40 on Timothy Arceri's machine.
Reviewed-by: Matt Turner <mattst88@gmail.com>