[ARITH] Refactor to use explicit div/mod functions instead of operators.

[tqchen]

This PR is part of #3977

Summary of changes:

• Removed the operator overload for % and / and explicitly ask developers to use the specific division functions
• Introduce indexdiv and indexmod, a special division function can be redirected to either floordiv/truncdiv. The requirement to use this function is that we know the operands are non-negative, we might introduce additional constraints attachment if necessary as in https://discuss.tvm.ai/t/discuss-embed-more-bound-information-into-var-or-expr/4079
• Refactor the existing code to make use of the division functions
• For now we maintain the old behavior of the code, and we can switch the implementation of indexdiv/mod in a separate PR.

[tqchen]

cc @yzhliu @icemelon9 @wweic @xqdan @sgrechanik-h @derisavi @umangyadav @icemelon9 @kazum

[ajtulloch]

This looks really great @tqchen.

[tqchen]

Additional notes on division modes:

• floordiv is relatively easier for simplification as it does not require to know the sign of operand a
  • we can do floordiv(a+ 17, 16) -> floordiv(a + 1, 16), regardless of the sign of a
  • However, we need to prove the sign of the operands eventually when lower to the low level code, as we can only lower floordiv(a, b)->truncdiv(a, b) if a>=0 and b>=0
• truncdiv is easier to for codegen, as it directly corresponds to low level instructions, but it is harder for simplification:
  • truncdiv(a+ 17, 16) -> truncdiv(a + 1, 16) only if a+1>=0.

So we have to make the choice of division mode for index calculations. indexdiv/mod tries to isolate that choice into a single place. It also brings additional information to the function that a and b are non-negative at the moment we call the function.

• Currently, we lower indexdiv-> truncdiv, we plan to move to floordiv
• We can plugin additional hints: indexdiv(a, b)->floordiv(a, nonneg_hint(b) if b is Var else b)

[icemelon]

lgtm