Implement branch-free single-division lowering of affine division/remainder
This implements the lowering of `floordiv`, `ceildiv` and `mod` operators from
affine expressions to the arithmetic primitive operations. Integer division
rules in affine expressions explicitly require rounding towards either negative
or positive infinity unlike machine implementations that round towards zero.
In the general case, implementing `floordiv` and `ceildiv` using machine signed
division requires computing both the quotient and the remainder. When the
divisor is positive, this can be simplified by adjusting the dividend and the
quotient by one and switching signs.
In the current use cases, we are unlikely to encounter affine expressions with
negative divisors (affine divisions appear in loop transformations such as
tiling that guarantee that divisors are positive by construction). Therefore,
it is reasonable to use branch-free single-division implementation. In case of
affine maps, divisors can only be literals so we can check the sign and
implement the case for negative divisors when the need arises.
The affine lowering pass can still fail when applied to semi-affine maps
(division or modulo by a symbol).
PiperOrigin-RevId: 228668181
3 files changed
tree: eec4006c7384e615df275bfa311a6f6dd977e82c
- mlir/
