Re: Executing code at compilation time

For a pretty complete list of closed forms for finite and infinite
sums that compiler writers can use for a reference page, see:


http://en.wikipedia.org/wiki/List_of_mathematical_series


Compilers can use these rules to lift a lot of mathematical operations
out of loops, eliminating the loop completely if that's all that the
loop was doing.


The OP in this thread was asking about a reduction that clearly
results from gcc using an application of a finite- sum rule.


Some folks think such tricks are "not right" in that they change the
"semantics" of the program by changing its algorithm. Others,
including myself, think that a program that gets the same results
faster and with fewer operations than its source code would lead you
to believe is a better program. If I can write an O(n^2) or even
O(2^n) algorithm and get O(1) runtime performance, I'm not going to
lodge a complaint.


Things get hazier in the event of O(infinity) or non-halting programs
- If you can use an infinite-sum rule to produce an executable that
comes to a halt with the result that the source-code operation "would
have" obtained if run to conclusion on some infinitely-fast computer,
is that an optimization or is that cheating?


                                                                Bear

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