Array data dependence analysis

[joscao]

Provides a array dependency analysis as* described by "Compilers: Principles, Techniques, and Tools".

Requires functionality of #179 and #178.

Implemented features:

• has_data_dependencyin analyse_array_data_dependency_detection.py allowing to determine if two array accesses in different loops exhibit a data dependency
• a notebook 06_array_data_dependency_detection.ipynb showing a full integration (from source code, manual selecting of arrays, to determining if there exists a dependency)
• a test test_analyse_array_data_dependency_detection.py testing 8 different test cases mostly taken from the Dragon book

Current Problems/Things I need help with: --> Expecting failure of tests due to missing ortools

• How do I integrate the requirement of ortools for the solving of the integer linear problem into loki?
• I have written an additional latex document, for exact formulation of linear algebra equations, since the Dragon is lacking them for this chapter, I will append it, how should it be preserved? array_data_dependency_description.pdf

Asterisk:
The following parts of the Dragon book are implemented:

• "11.6.1 Definition of Data Dependence of Array Accesses", i.e. the full linear algebra description of the problem (iteration space, array access function)
• "11.6.3 The GCD Test", i.e. a Gaussian Elimination algorithm specialized for Diophantine equations (i.e. pure integer matrix vector equation) and therefore the substitution of the result into the inequalities as described by equation (5) of the array_data_dependency_description mentioned above.
• Independent-Variables Test from "11.6.4 Heuristics for Solving Integer Linear Program"
• The Acyclic Test, Loop-Residue-Test, Memoization and the full Branch and bound solution to integer linear programming problems were not implemented, to ensure full usability a general integer linear program solver provided by ortools is used, therfore full usability is ensured, to the best of my abilities.

[reuterbal]

Again, just a quick response to your immediate questions:

To integrate ortools, I suggest to add them to pyproject.toml as an optional dependency for now, similar to the examples:

loki/pyproject.toml

Lines 62 to 65 in af8ec9f

	examples = [
	"jupyter",
	"ipyparams",
	]

Call the option dataflow_analysis or something similarly meaningful. The import of ortools should then be wrapped with a safeguard similar to open-fortran-parser and clean exception if it isn't available.

loki/loki/frontend/ofp.py

Lines 15 to 21 in af8ec9f

	try:
	import open_fortran_parser
	HAVE_OFP = True
	"""Indicate whether OpenFortranParser frontend is available."""
	except ImportError:
	HAVE_OFP = False

For the document, the best would probably be to convert this to a Sphinx document and integrate it into the documentation. But we can take care of that, so keeping the PDF like this is fine for now.

[joscao]

Since #178 and #179 are now stable, this branch has been rebased and most issues fixed.

Not functional (require help):

• ortools installation (cant seem to figure it out how to add it to install)
• test of notebook "06_..." complains about ungrouped-imports, but it is a notebook? that shouldnt matter there, at least to my understanding

Enhancements:

• convert function documentation to numpy style

[codecov]

Codecov Report

Merging #180 (e031348) into main (af8ec9f) will decrease coverage by 0.14%.
The diff coverage is 86.74%.

@@            Coverage Diff             @@
##             main     #180      +/-   ##
==========================================
- Coverage   92.14%   92.00%   -0.14%     
==========================================
  Files          90       93       +3     
  Lines       16690    16950     +260     
==========================================
+ Hits        15379    15595     +216     
- Misses       1311     1355      +44     

Flag	Coverage Δ
lint_rules	96.22% <ø> (ø)
loki	91.95% <86.74%> (-0.17%)	⬇️
transformations	91.40% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

Files	Coverage Δ
loki/analyse/util_linear_algebra.py	100.00% <100.00%> (ø)
loki/transform/transform_loop.py	96.12% <100.00%> (+0.03%)	⬆️
loki/analyse/util_polyhedron.py	92.68% <92.68%> (ø)
...analyse/analyse_array_data_dependency_detection.py	79.68% <79.68%> (ø)

[joscao]

• Missing if statement added if local column matrix is empty. 11103e4

Fixed: "Example 11.35 from Compilers: Principles, Techniques, and Tools" should return false due to indepdent variable test, that is not the case. Whats going on?