ZoneAlgorithms's computePHI relies on being provided with consistent a
schedule to compute the statement prodecessors of a statement containing
PHINodes. Otherwise unexpected results such as PHI nodes with multiple
predecessors can occur which would result in problems in the
algorithms expecting consistent data.
In the added test case, statement instances are scrubbed from the
SCoP their execution would result in undefined behavior (Due to a nsw
overflow). As already being undefined behavior in LLVM-IR, neither
AssumedContext nor InvalidContext are updated, giving computePHI no
means to avoid these cases.
Intoduce a new SCoP property, the DefinedBehaviorContext, that among
the runtime-checked conditions, also tracks the assumptions not needing
a runtime check, in particular those affecting the assumed control flow.
This replaces the manual combination of the 3 other contexts that was
already done in computePHI and setNewAccessRelation. Currently, the only
additional assumption is that loop induction variables will nsw flag for
not wrap, but potentially more can be added. Use in
hasFeasibleRuntimeContext, isl::ast_build and gisting are other
potential uses.
To limit computational complexity, the DefinedBehaviorContext is not
availabe if it grows too large (atm hardcoded to 8 disjuncts).
Possible other fixes include bailing out in computePHI when
inconsistencies are detected, choose an arbitrary value for inconsistent
cases (since it is undefined behavior anyways), or make the code
receiving the result from ComputePHI handle inconsistent data. All of
them reduce the quality of implementation having to bail out more often
and disabling the ability to assert on actually wrong results.
This fixes llvm.org/PR48783.
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
Michael Kruse