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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.
git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@312329 91177308-0d34-0410-b5e6-96231b3b80d8
Analysis Opportunities:
//===---------------------------------------------------------------------===//
In test/Transforms/LoopStrengthReduce/quadradic-exit-value.ll, the
ScalarEvolution expression for %r is this:
{1,+,3,+,2}<loop>
Outside the loop, this could be evaluated simply as (%n * %n), however
ScalarEvolution currently evaluates it as
(-2 + (2 * (trunc i65 (((zext i64 (-2 + %n) to i65) * (zext i64 (-1 + %n) to i65)) /u 2) to i64)) + (3 * %n))
In addition to being much more complicated, it involves i65 arithmetic,
which is very inefficient when expanded into code.
//===---------------------------------------------------------------------===//
In formatValue in test/CodeGen/X86/lsr-delayed-fold.ll,
ScalarEvolution is forming this expression:
((trunc i64 (-1 * %arg5) to i32) + (trunc i64 %arg5 to i32) + (-1 * (trunc i64 undef to i32)))
This could be folded to
(-1 * (trunc i64 undef to i32))
//===---------------------------------------------------------------------===//