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Relative Census Analysis Supports the Census Method of WCET Analysis


Niklas Holsti

Research group:

Publication Type:

Report - MRTC


Mälardalen Real-Time Research Centre, Mälardalen University




In the "census method" of WCET analysis, the number of executions of a program loop is bounded from above by the "census", defined as the total number of possible combined values of the variables that influence loop termination. Considering only integer-valued variables, an upper bound on the census is typically found by counting the number of integer points in the volume of states generated by a relational value-analysis, such as a polyhedral analysis. Any non-linear computation of variables significant to loop termination can then introduce huge over-estimation in the census bound, since the result of the non-linear computation is unbounded in the polyhedral model. For example, a single unbounded 32-bit variable causes an over-estimation by the factor 2^32. We aim to counteract such over-estimation by computing the number of values that the unbounded variable(s) can take, for each value-combination of the other variables. This typically smaller number – the relative census – replaces the huge number of all representable values as a factor in the census bound. This report formally defines the relative census (RC) concept and studies its mathematical properties. The report also develops formulas for bounding the evolution of the RC along program execution flow, as required for static analysis tools. The report concludes with a discussion of possible forms of static analysis of RC, in particular for supporting census-based WCET analysis.


author = {Niklas Holsti},
title = {Relative Census Analysis Supports the Census Method of WCET Analysis},
month = {November},
year = {2014},
publisher = {M{\"a}lardalen Real-Time Research Centre, M{\"a}lardalen University},
url = {}