xqdan commented on pull request #5772:
URL: https://github.com/apache/incubator-tvm/pull/5772#issuecomment-654589703
> @xqdan sorry for the delayed reply. I take a closer look, and
unfortunately the new rules may not be correct.
>
> ```
> TVM_TRY_REWRITE_IF(
> truncdiv(x + c1, c3) - truncdiv(x, c3), truncdiv(truncmod(x, c3) +
c1, c3),
> CanProveGreaterEqual(x.Eval(), 0) && c1.Eval()->value >= 0 &&
c3.Eval()->value > 0);
> ```
>
> In particular, the new rule is closely related to the above rule(which is
on top of the current rule. Pay attention to the special case of `truncmod(x,
c3)` in the above term.
>
> In particular, let us say `c3=3, c1=1, x = 11`, then
>
> ```
> truncdiv(11 + 1, 3) - truncdiv(11, 3) = 4 - 3 = 1 = truncdiv(truncmod(11,
3)+1, 3)
> ```
>
> Let `x =y * c4 + c5` and replace `y` by x, we can derive a counter-example
for the listed rule. To re-use the above rule a bit, a likely generalization
should be.
>
> It is not too hard to prove the above rule(by decomposing x into z * c3 +
r).
>
> To get to a similar rule that applies to your case, we could replace x by
x + c4, then get to
>
> ```
> TVM_TRY_REWRITE_IF(
> truncdiv(x + c4 + c1, c3) - truncdiv(x + c4, c3),
truncdiv(truncmod(x + c4, c3) + c1, c3),
> CanProveGreaterEqual((x + c4).Eval(), 0) && c1.Eval()->value >= 0
&& c3.Eval()->value > 0);
> ```
>
> =>
>
> ```
> TVM_TRY_REWRITE_IF(
> truncdiv(x + c5, c3) - truncdiv(x + c4, c3), truncdiv(truncmod(x +
c4, c3) + (c5-c4), c3),
> CanProveGreaterEqual((x + c4).Eval(), 0) && (c5 -
c4).Eval()->value >= 0 && c3.Eval()->value > 0);
> ```
@tqchen thanks for reply.
I get your point, but what we seek is to eliminate 'x' here,
The new rule 2 above (not in the code) can exclude the case you post, since
(11+1 - 11) %3 == 0 is not satisfied.
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