Alexandre Isoard a49643a387 [SCEV] Add URem support to SCEV
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
2017-09-01 14:59:59 +00:00
2017-08-31 15:51:23 +00:00
2017-09-01 14:59:59 +00:00
2017-09-01 14:59:59 +00:00
2017-09-01 14:59:59 +00:00
2014-03-02 13:08:46 +00:00
2017-08-24 15:40:33 +00:00
2016-01-26 21:29:08 +00:00
2017-07-01 03:24:06 +00:00
2017-01-12 18:02:42 +00:00
2017-08-18 02:39:28 +00:00

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