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I respectfully disagree. This will be part of an optimizing compiler. If the meteor decides to hit us after all then someone will have a nearly impossible to diagnose bug.
There are also large classes of expressions for which Eriks heuristic method does not work at all regardless of how many iterations it uses or require such a large number of iterations that it becomes impractical.
For example: (uint64)x / 3 and ((uint64)x * 0x5555556) >> 32 are the same for x in the interval 0..0x7FFFFFFF but not outside it. That gives a 0.5^k error probability where k is the number of iterations - which is fairly good, but if you combine a couple of those you can make the error probability arbitrarily high.
And I'm not even "cheating" with comparisons here - a single comparison against a constant can make the error probability arbitrarily high. They could be special-cased of course, but can the expressions above be special cased?
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David, if these expressions are analytic expressions (defined and differentiable for all values of input), then a simple proof by induction will ALWAYS verify their equivalence. So you only have to try for a few values.
BHM
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Maybe so, but that's not what we have here, they are expressions with types such as int32 (see original post) and the class of expressions is not limited to something simple.
For example, 1/x and 2/x differ only for x=1 and x=2 (edit: and -1 and -2), but there are 2^32 possibilities for x if it is an int32 and even more if it is an int64 - the chance that either 1 or 2 is tested isn't that big.
modified on Sunday, April 3, 2011 8:58 AM
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Can you define or characterize this "good portion"?
For example, if you want to detect equivalence between bounded-degree polynomials (two computer programs or expressions such that their result is eventually a polynomial in the input), and you know the degree bound, it can be easily done by checking a small and finite number of inputs.
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A good portion is hard to define 
It should find "significantly" more equivalences than merely comparing whether two expressions are equal.
The class of expressions is not constrained in any way. I suppose I could first detect whether two expressions are both polynomials and then use a special comparison, but there are plenty of other types of expression so in order to find a "good portion" of equivalences I'd need something for them too.
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Well, I suppose that you know that for polynomials of degree n, you need to check for equality at (n+1) points. If all are equal, the polynomials are the same.
Anyway, detecting polynomials is NOT easy. They can be computed in many ways, with for loops, while loops and other kinds of computations. It's not always visible by analyzing an expression that it is a polynomial.
Alex.
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I could detect Some polynomials and match them that way I suppose.
That may be more effort than it's worth.. well I guess I'll try it and see how much it helps.
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This is an excellent question - the bad news is, the answer is rather complicated. You would need to implement a unification algorithm[^] to do it correctly.
Things would not be as bad if you considered Prolog[^] as the language for your implementation, but something tells me that that would be out of the question 
On the other hand, you can always embed Prolog to get unification for free.
But no matter how you look at it, the learning curve is going to be steep.
Good luck!
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That page only seems to discuss logic formula's (unless I'm missing something?), does it also work for other formula's?
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Absolutely. Formally, you can represent A+B as add(A,B), and define an additional rule that add(A,B) :== add(B,A). In fact, since you are interested only in a yes/no answer (as opposed to variable assignments produced by unification), you don't even need to implement a complete unification: a simpler recursive matching algorithm would do. The only challenge in its implementation is matching ((A+B)+C) trees to (A+(B+C)). You can deal with it by flattening the list of operands, and trying all possible orderings on one of the sides. Don't forget to memoize[^] your matches, both positive and negative. Otherwise, your search will be too slow.
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java or C# , which better?
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I would personally prefer C#.
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As far as algorithms go, they are equal.
"You get that on the big jobs."
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Actually, I wouldn't say that.
What is the algorithm for 64bit unsigned division in Java?
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For a Java-programmer, Java is better. For a C# programmer, C# is better. Try to find where they differ, as that decides which of the two is best for the given circumstance.
I are Troll 
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COBOL 
Regards
David R
---------------------------------------------------------------
"Every program eventually becomes rococo, and then rubble." - Alan Perlis
The only valid measurement of code quality: WTFs/minute.
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Even better - I once spent 6 months doing MUMPS. DOn't think I've recovered. 
Regards
David R
---------------------------------------------------------------
"Every program eventually becomes rococo, and then rubble." - Alan Perlis
The only valid measurement of code quality: WTFs/minute.
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Strange, I had Mumps when I was a boy and recovered after a couple of weeks.
I must get a clever new signature for 2011.
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Look at the IDE which is available for the language. As both with Java and C# you can create nice programs, the IDE is important. And I prefer Visual Studio.
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Neither: they are just different. Some problems may be solved easier in one language, but that does not make it better than the other. Every language has its fans, detractors and bigots. I would just use the language that you feel most comfortable with, whatever it may be.
I must get a clever new signature for 2011.
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None of them, and both of them. A better question would be: which language is better for doing -whatever-?
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C# is better, in my biased opinion. It started out as what looked like a Microsoft attempt to copy Java, but it's evolved into much more than that.
The later versions of C# have eliminated a lot of the bloat of previous languages, allowing succinct expression of programming ideas in code. This leads to greater clarity, which makes code more reliable and maintainable.
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without context, without goals, this is a stupid question.
Luc Pattyn [Forum Guidelines] [My Articles] Nil Volentibus Arduum
Please use <PRE> tags for code snippets, they preserve indentation, improve readability, and make me actually look at the code.
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After reading the book Pro C # and. Net 4
I discovered the enormous benefits offered by C # compared with Java 
There are many differences: LINQ , WPF , WCF
Today, I like C# 
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