Abstract

In compiler theory, the Banerjee test is a dependence test. The Banerjee test assumes that all loop indices are independent, however in reality, this is often not true. The Bannerjee test is a conservative test. That is, it will not break a dependence that does not exist.This means that the only thing the test can guarantee is the absence of dependence.This paper proposes an innovative algorithm which allows precise determination of information about dependences and can act in situation where certain cycling limits are known.

Highlights

  • In previous researches we presented Banerjee test for the analysis of data dependencies

  • Psarris et al [Psarris91] demonstrated a sufficient condition for Banerjee test accuracy, which we will present in Theorem 2.2

  • Based on the analysis of [Psarris91] we prove a sufficient condition of Banerjee test accuracy, which condition is less restrictive than the above

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Summary

INTRODUCTION

In previous researches we presented Banerjee test for the analysis of data dependencies. The empirical results provided in [Shen90] shows that the number of iterations is relatively high for a cycle instead of dependence equations resulting coefficients are usually low, often even denominations These empirical results combined with the results of Theorem 2.3 formally prove that the Banerjee test proves accurate in practice, that it causes the whole of the limits of cycling solutions and not just real solutions. An xn x and i N, 1 ≤ i ≤ n, Li ≤ xi ≤ Ui This assumption combined with lemma 3.3 and Banerjee formulas (3.4,3.6) of calculus of limits for an amount shows that for any x from the interval exist integers n 1 w ai xi şi xn , so that i 1 x = w + anxn ; L ≤ w ≤ U; we have the relation: Ln ≤ xn ≤ Un ;.

The implementation of algorithm
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