Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

Control Flow Driven Splitting of Loop Nests 219
optimization problems. They have been successfully utilized in the domains
of code generation for irregular architectures [13, 16] or VLSI CAD [4].
3. ANALYSIS AND OPTIMIZATION ALGORITHM
This section presents the techniques required for loop nest splitting. The
optimization consists of four sequentially executed tasks. In the beginning, all
conditions in a loop nest are analyzed separately without considering any
interdependencies in-between. First, it is detected if conditions have any influence
on the control flow of a loop nest. If not, such redundant conditions are
removed from the code. For every single remaining condition, an optimized
geometric model is created in the second step. Third, these geometric models
are combined to a global search space representing all conditions in all ifstatements
of the loop nest simultaneously. To obtain an optimized result for
a loop nest, this global search space is explored in a fourth step. Before going
into details (cf. also [5, 6]), some preliminaries are required.
Definition 1:
1.
2.
Let be a loop nest of depth N, where denotes a single
loop.
Let and be the index variable, lower bound and upper bound of
loop with
The optimization goal for loop nest splitting is to determine values
for every loop with
and
all loop-variant if-statements in are satisfied for all values of the index
variables with
loop nest splitting by all values and leads to the minimization of
if-statement execution.
The values and are used for generating the splitting if-statement.
The techniques described in the following require that some preconditions are
met:
1.
2.
3.
All loop bounds and are constants.
If-statements have the format if
with loop-invariant
conditions that are combined with logical operators
Loop-variant conditions are affine expressions of and can thus have
the format
and
Assumption 2 is due to the current state of implementation of our tools.
By applying de Morgan’s rule on
and inverting the comparators