Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4635383 | Applied Mathematics and Computation | 2007 | 15 Pages |
Abstract
In essence, we want to test the hypothesis that two computing operations are the same (in some statistical sense). To test this hypothesis, we would construct a function of the computing times required for each called revised differences di's defined as [(Xi âYi)/{(Xi + Yi)/2}] and then construct a t-statistic based on the sample mean and sample mean square of these di's. If the data are approximately normal, then the t-statistic will have an approximate Student's-t distribution. We next propose some alternative tests as robustness against the normality assumption. To combat idiosyncrasies of computer clocks, the operations are kept inside a nested loop and observed for input size sufficiently large for reliable run time measurements. The formula we provide here is however more effective for comparing “compound operations” (that is, a group of operations taken as a whole) and we caution the reader against the dangerous practice of trying to isolate individual operations from a compound one while using this formula. As the formula helps us in deciding whether a group of operations is likely to be efficient or inefficient if implemented in a larger code, we propose to use it in conjunction with the philosophy of measurement and tuning which is a practical method of improving the efficiency of actual running programs.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Soubhik Chakraborty, Kiran Kumar Sundararajan,