A zero-extended value can be interpreted as a piecewise defined signed
value. If the value was non-negative it stays the same, otherwise it
is the sum of the original value and 2^n where n is the bit-width of
the original (or operand) type. Examples:
zext i8 127 to i32 -> { [127] }
zext i8 -1 to i32 -> { [256 + (-1)] } = { [255] }
zext i8 %v to i32 -> [v] -> { [v] | v >= 0; [256 + v] | v < 0 }
However, LLVM/Scalar Evolution uses zero-extend (potentially lead by a
truncate) to represent some forms of modulo computation. The left-hand side
of the condition in the code below would result in the SCEV
"zext i1 <false, +, true>for.body" which is just another description
of the C expression "i & 1 != 0" or, equivalently, "i % 2 != 0".
for (i = 0; i < N; i++)
if (i & 1 != 0 /* == i % 2 */)
/* do something */
If we do not make the modulo explicit but only use the mechanism described
above we will get the very restrictive assumption "N < 3", because for all
values of N >= 3 the SCEVAddRecExpr operand of the zero-extend would wrap.
Alternatively, we can make the modulo in the operand explicit in the
resulting piecewise function and thereby avoid the assumption on N. For the
example this would result in the following piecewise affine function:
{ [i0] -> [(1)] : 2*floor((-1 + i0)/2) = -1 + i0;
[i0] -> [(0)] : 2*floor((i0)/2) = i0 }
To this end we can first determine if the (immediate) operand of the
zero-extend can wrap and, in case it might, we will use explicit modulo
semantic to compute the result instead of emitting non-wrapping assumptions.
Note that operands with large bit-widths are less likely to be negative
because it would result in a very large access offset or loop bound after the
zero-extend. To this end one can optimistically assume the operand to be
positive and avoid the piecewise definition if the bit-width is bigger than
some threshold (here MaxZextSmallBitWidth).
We choose to go with a hybrid solution of all modeling techniques described
above. For small bit-widths (up to MaxZextSmallBitWidth) we will model the
wrapping explicitly and use a piecewise defined function. However, if the
bit-width is bigger than MaxZextSmallBitWidth we will employ overflow
assumptions and assume the "former negative" piece will not exist.
llvm-svn: 267408
These flags are now always passed to all tests and need to be disabled if
not needed. Disabling these flags, rather than passing them to almost all
tests, significantly simplfies our RUN: lines.
llvm-svn: 249422
This will allow to generate non-wrap assumptions for integer expressions
that are part of the SCoP. We compare the common isl representation of
the expression with one computed with modulo semantic. For all parameter
combinations they are not equal we can have integer overflows.
The nsw flags are respected when the modulo representation is computed,
nuw and nw flags are ignored for now.
In order to not increase compile time to much, the non-wrap assumptions
are collected in a separate boundary context instead of the assumed
context. This helps compile time as the boundary context can become
complex and it is therefor not advised to use it in other operations
except runtime check generation. However, the assumed context is e.g.,
used to tighten dependences. While the boundary context might help to
tighten the assumed context it is doubtful that it will help in practice
(it does not effect lnt much) as the boundary (or no-wrap assumptions)
only restrict the very end of the possible value range of parameters.
PET uses a different approach to compute the no-wrap context, though lnt runs
have shown that this version performs slightly better for us.
llvm-svn: 247732
Johannes Doerfert