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In LLVM IR the following code: %r = urem <ty> %t, %b is equivalent to %q = udiv <ty> %t, %b %s = mul <ty> nuw %q, %b %r = sub <ty> nuw %t, %q ; (t / b) * b + (t % b) = t As UDiv, Mul and Sub are already supported by SCEV, URem can be implemented with minimal effort using that relation: %r --> (-%b * (%t /u %b)) + %t We implement two special cases: - if %b is 1, the result is always 0 - if %b is a power-of-two, we produce a zext/trunc based expression instead That is, the following code: %r = urem i32 %t, 65536 Produces: %r --> (zext i16 (trunc i32 %a to i16) to i32) Note that while this helps get a tighter bound on the range analysis and the known-bits analysis, this exposes some normalization shortcoming of SCEVs: %div = udim i32 %a, 65536 %mul = mul i32 %div, 65536 %rem = urem i32 %a, 65536 %add = add i32 %mul, %rem Will usually not be reduced. llvm-svn: 312329
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