[llvm-commits] Fix for PR1798 (ScalarEvolution)

[Wojciech Matyjewicz]

The attached patch should fix the aforementioned bug. It passes DejaGnu
testsuite. Nick also checked that it passes llvm-test and llvm-gcc
bootstrap (thanks!).

The patch:
1) changes SCEVSDivExpr into SCEVUDivExpr,
2) replaces PartialFact() function with BinomialCoefficient(); the
computations in BinomialCoefficient() are performed with the apprioprate
bitwidth necessary to avoid overflow.

The short explanation why the patch should be correct is contained in
the comments. The longer can be found in the bugzilla discussion:
http://llvm.org/bugs/show_bug.cgi?id=1798.

However, there is one problem. The fix needs support for integers of
arbitrary bitwitdth to work in every possible case. Here is a short
explanation why:
To evaluate a chrec of length K at a given iteration we need, in
general, to generate LLVM code performing accurate multiplication of K
numbers. Suppose, W is their bitwidth. Then, multiplication need to use
K*W bits, what can potentially be an arbitrary number.

I can see two ways what we can do now:
1) wait for the backend support,
2) make the patch unoptimal by using the more bits than needed to
perform the multiplication (the minimum power of 2 greater or equal to K*W)

What do you think?

-Wojtek
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