Improve handling of JumpBound truncation constraints #403
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RyanGlScott
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Jul 23, 2024
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Given some symbolic value, @x@, we'd like to compute its possible upper and lower bounds after it is truncated to @w@ bits. To do this, we first find the bound of x by (recursively) calling `exprRangePred`. This bound is a statement of the following form (see `RangePred` for more info): "r bits of x are bounded between @low@ and @high@". Then, we check the following: - If x has a bound (r, l, w) AND - If r is less than or equal to w => Pass-through the bound (r, l, w) Otherwise, we deem x "unbounded" Declaring x unbounded in the second case seems to throw away useful information that causes many jump tables to remain unclassified. We attempt to improve on that in this commit. Consider an example where x is bounded by (64, 0, 10) (that is, the 64 bits of x are constrained to be between 0 and 10) and we want to find the bound of truncating x to 8 bits. With the current logic, since 64 > 8, we'd declare x unbounded. However, the bound (8, 0, 10) should also be valid: if 64 bits of x are bounded to [0, 10], then surely 8 bits of x also lie between 0 and 10. If the upper bound is instead larger than the largest 8-bit value, we can truncate it to the largest value. For example, (64, 0, 10000) becomes (8, 0, 255). Instead of losing the bound completely, we're able to tighten it!
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Background
Given some symbolic value,
x, we'd like to compute its possible upper and lower bounds after it is truncated towbits.To do this, we first find the bound of x by (recursively) calling
exprRangePred. This bound is a statement of the following form (seeRangePredfor more info): "rbits ofxare bounded betweenlowandhigh".Then, we check the following:
xhas a bound(r, l, h)ANDris less than or equal tow=> Pass-through the bound(r, l, h)Otherwise, we deem
x"unbounded"Proposal
Declaring
xunbounded in the second case seems to throw away useful information that causes many jump tables to remain unclassified. We attempt to improve on that in this commit.Consider an example where
xis bounded by(64, 0, 10)(that is, the 64 bits ofxare constrained to be between 0 and 10) and we want to find the bound of truncatingxto 8 bits.With the current logic, since 64 > 8, we'd declare x unbounded. However, the bound
(8, 0, 10)should also be valid: if 64 bits ofxare bounded to [0, 10], then surely 8 bits ofxalso lie between 0 and 10.If the upper bound is instead larger than the largest 8-bit value, we can truncate it to the largest value.
For example,
(64, 0, 10000)becomes(8, 0, 255).Instead of losing the bound completely, we're able to tighten it!
Evaluation
Using Reopt's ground truth evaluation, we found that this change significantly improved jump table classification in coreutil binaries compiled with
GCC_O1. Out of 912 total jump tables in the dataset, macaw (launched through Reopt) currently reaches + classifies 109 jump tables. After this change, macaw correctly classifies 857/912 jump tables.