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Merge pull request #11728 from github/rdmarsh2/parameterize-range-analysis
C++: Parameterize the semantic range analysis
This commit is contained in:
Mathias Vorreiter Pedersen
@@ -0,0 +1,29 @@
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private import RangeAnalysisStage
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module FloatDelta implements DeltaSig {
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class Delta = float;
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bindingset[d]
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bindingset[result]
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float toFloat(Delta d) { result = d }
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bindingset[d]
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bindingset[result]
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int toInt(Delta d) { result = d }
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bindingset[n]
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bindingset[result]
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Delta fromInt(int n) { result = n }
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bindingset[f]
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Delta fromFloat(float f) {
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result =
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min(float diff, float res |
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diff = (res - f) and res = f.ceil()
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or
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diff = (f - res) and res = f.floor()
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|
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res order by diff
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)
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}
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}
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@@ -14,321 +14,328 @@ private import ModulusAnalysisSpecific::Private
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private import experimental.semmle.code.cpp.semantic.Semantic
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private import ConstantAnalysis
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private import RangeUtils
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private import RangeAnalysisStage
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/**
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* Holds if `e + delta` equals `v` at `pos`.
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*/
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private predicate valueFlowStepSsa(SemSsaVariable v, SemSsaReadPosition pos, SemExpr e, int delta) {
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semSsaUpdateStep(v, e, delta) and pos.hasReadOfVar(v)
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or
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exists(SemGuard guard, boolean testIsTrue |
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pos.hasReadOfVar(v) and
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guard = semEqFlowCond(v, e, delta, true, testIsTrue) and
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semGuardDirectlyControlsSsaRead(guard, pos, testIsTrue)
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)
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}
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/**
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* Holds if `add` is the addition of `larg` and `rarg`, neither of which are
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* `ConstantIntegerExpr`s.
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*/
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private predicate nonConstAddition(SemExpr add, SemExpr larg, SemExpr rarg) {
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exists(SemAddExpr a | a = add |
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larg = a.getLeftOperand() and
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rarg = a.getRightOperand()
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) and
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not larg instanceof SemConstantIntegerExpr and
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not rarg instanceof SemConstantIntegerExpr
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}
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/**
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* Holds if `sub` is the subtraction of `larg` and `rarg`, where `rarg` is not
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* a `ConstantIntegerExpr`.
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*/
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private predicate nonConstSubtraction(SemExpr sub, SemExpr larg, SemExpr rarg) {
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exists(SemSubExpr s | s = sub |
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larg = s.getLeftOperand() and
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rarg = s.getRightOperand()
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) and
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not rarg instanceof SemConstantIntegerExpr
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}
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/** Gets an expression that is the remainder modulo `mod` of `arg`. */
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private SemExpr modExpr(SemExpr arg, int mod) {
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exists(SemRemExpr rem |
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result = rem and
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arg = rem.getLeftOperand() and
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rem.getRightOperand().(SemConstantIntegerExpr).getIntValue() = mod and
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mod >= 2
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)
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or
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exists(SemConstantIntegerExpr c |
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mod = 2.pow([1 .. 30]) and
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c.getIntValue() = mod - 1 and
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result.(SemBitAndExpr).hasOperands(arg, c)
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)
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}
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/**
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* Gets a guard that tests whether `v` is congruent with `val` modulo `mod` on
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* its `testIsTrue` branch.
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*/
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private SemGuard moduloCheck(SemSsaVariable v, int val, int mod, boolean testIsTrue) {
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exists(SemExpr rem, SemConstantIntegerExpr c, int r, boolean polarity |
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result.isEquality(rem, c, polarity) and
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c.getIntValue() = r and
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rem = modExpr(v.getAUse(), mod) and
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(
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testIsTrue = polarity and val = r
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or
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testIsTrue = polarity.booleanNot() and
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mod = 2 and
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val = 1 - r and
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(r = 0 or r = 1)
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)
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)
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}
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/**
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* Holds if a guard ensures that `v` at `pos` is congruent with `val` modulo `mod`.
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*/
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private predicate moduloGuardedRead(SemSsaVariable v, SemSsaReadPosition pos, int val, int mod) {
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exists(SemGuard guard, boolean testIsTrue |
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pos.hasReadOfVar(v) and
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guard = moduloCheck(v, val, mod, testIsTrue) and
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semGuardControlsSsaRead(guard, pos, testIsTrue)
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)
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}
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/** Holds if `factor` is a power of 2 that divides `mask`. */
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bindingset[mask]
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private predicate andmaskFactor(int mask, int factor) {
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mask % factor = 0 and
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factor = 2.pow([1 .. 30])
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}
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/** Holds if `e` is evenly divisible by `factor`. */
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private predicate evenlyDivisibleExpr(SemExpr e, int factor) {
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exists(SemConstantIntegerExpr c, int k | k = c.getIntValue() |
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e.(SemMulExpr).getAnOperand() = c and factor = k.abs() and factor >= 2
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or
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e.(SemShiftLeftExpr).getRightOperand() = c and factor = 2.pow(k) and k > 0
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or
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e.(SemBitAndExpr).getAnOperand() = c and factor = max(int f | andmaskFactor(k, f))
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)
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}
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/**
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* Holds if `rix` is the number of input edges to `phi`.
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*/
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private predicate maxPhiInputRank(SemSsaPhiNode phi, int rix) {
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rix = max(int r | rankedPhiInput(phi, _, _, r))
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}
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/**
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* Gets the remainder of `val` modulo `mod`.
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*
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* For `mod = 0` the result equals `val` and for `mod > 1` the result is within
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* the range `[0 .. mod-1]`.
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*/
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bindingset[val, mod]
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private int remainder(int val, int mod) {
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mod = 0 and result = val
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or
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mod > 1 and result = ((val % mod) + mod) % mod
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}
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/**
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* Holds if `inp` is an input to `phi` and equals `phi` modulo `mod` along `edge`.
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*/
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private predicate phiSelfModulus(
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SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int mod
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) {
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exists(SemSsaBound phibound, int v, int m |
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edge.phiInput(phi, inp) and
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phibound.getAVariable() = phi and
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ssaModulus(inp, edge, phibound, v, m) and
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mod = m.gcd(v) and
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mod != 1
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)
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}
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/**
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* Holds if `b + val` modulo `mod` is a candidate congruence class for `phi`.
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*/
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private predicate phiModulusInit(SemSsaPhiNode phi, SemBound b, int val, int mod) {
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exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge |
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edge.phiInput(phi, inp) and
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ssaModulus(inp, edge, b, val, mod)
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)
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}
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/**
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* Holds if all inputs to `phi` numbered `1` to `rix` are equal to `b + val` modulo `mod`.
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*/
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pragma[nomagic]
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private predicate phiModulusRankStep(SemSsaPhiNode phi, SemBound b, int val, int mod, int rix) {
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/*
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* base case. If any phi input is equal to `b + val` modulo `mod`, that's a potential congruence
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* class for the phi node.
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module ModulusAnalysis<DeltaSig D, BoundSig<D> Bounds, UtilSig<D> U> {
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/**
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* Holds if `e + delta` equals `v` at `pos`.
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*/
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private predicate valueFlowStepSsa(SemSsaVariable v, SemSsaReadPosition pos, SemExpr e, int delta) {
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U::semSsaUpdateStep(v, e, D::fromInt(delta)) and pos.hasReadOfVar(v)
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or
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exists(SemGuard guard, boolean testIsTrue |
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pos.hasReadOfVar(v) and
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guard = U::semEqFlowCond(v, e, D::fromInt(delta), true, testIsTrue) and
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semGuardDirectlyControlsSsaRead(guard, pos, testIsTrue)
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)
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}
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rix = 0 and
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phiModulusInit(phi, b, val, mod)
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or
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exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int v1, int m1 |
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mod != 1 and
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val = remainder(v1, mod)
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|
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/**
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* Holds if `add` is the addition of `larg` and `rarg`, neither of which are
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* `ConstantIntegerExpr`s.
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*/
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private predicate nonConstAddition(SemExpr add, SemExpr larg, SemExpr rarg) {
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exists(SemAddExpr a | a = add |
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larg = a.getLeftOperand() and
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rarg = a.getRightOperand()
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) and
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not larg instanceof SemConstantIntegerExpr and
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not rarg instanceof SemConstantIntegerExpr
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}
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/**
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* Holds if `sub` is the subtraction of `larg` and `rarg`, where `rarg` is not
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* a `ConstantIntegerExpr`.
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*/
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private predicate nonConstSubtraction(SemExpr sub, SemExpr larg, SemExpr rarg) {
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exists(SemSubExpr s | s = sub |
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larg = s.getLeftOperand() and
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rarg = s.getRightOperand()
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) and
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not rarg instanceof SemConstantIntegerExpr
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}
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/** Gets an expression that is the remainder modulo `mod` of `arg`. */
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private SemExpr modExpr(SemExpr arg, int mod) {
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exists(SemRemExpr rem |
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result = rem and
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arg = rem.getLeftOperand() and
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rem.getRightOperand().(SemConstantIntegerExpr).getIntValue() = mod and
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mod >= 2
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)
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or
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exists(SemConstantIntegerExpr c |
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mod = 2.pow([1 .. 30]) and
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c.getIntValue() = mod - 1 and
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result.(SemBitAndExpr).hasOperands(arg, c)
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)
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}
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/**
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* Gets a guard that tests whether `v` is congruent with `val` modulo `mod` on
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* its `testIsTrue` branch.
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*/
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private SemGuard moduloCheck(SemSsaVariable v, int val, int mod, boolean testIsTrue) {
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exists(SemExpr rem, SemConstantIntegerExpr c, int r, boolean polarity |
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result.isEquality(rem, c, polarity) and
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c.getIntValue() = r and
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rem = modExpr(v.getAUse(), mod) and
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(
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testIsTrue = polarity and val = r
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or
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testIsTrue = polarity.booleanNot() and
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mod = 2 and
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val = 1 - r and
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(r = 0 or r = 1)
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)
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)
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}
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/**
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* Holds if a guard ensures that `v` at `pos` is congruent with `val` modulo `mod`.
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*/
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private predicate moduloGuardedRead(SemSsaVariable v, SemSsaReadPosition pos, int val, int mod) {
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exists(SemGuard guard, boolean testIsTrue |
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pos.hasReadOfVar(v) and
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guard = moduloCheck(v, val, mod, testIsTrue) and
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semGuardControlsSsaRead(guard, pos, testIsTrue)
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)
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}
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/** Holds if `factor` is a power of 2 that divides `mask`. */
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bindingset[mask]
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private predicate andmaskFactor(int mask, int factor) {
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mask % factor = 0 and
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factor = 2.pow([1 .. 30])
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}
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/** Holds if `e` is evenly divisible by `factor`. */
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private predicate evenlyDivisibleExpr(SemExpr e, int factor) {
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exists(SemConstantIntegerExpr c, int k | k = c.getIntValue() |
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e.(SemMulExpr).getAnOperand() = c and factor = k.abs() and factor >= 2
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or
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e.(SemShiftLeftExpr).getRightOperand() = c and factor = 2.pow(k) and k > 0
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or
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e.(SemBitAndExpr).getAnOperand() = c and factor = max(int f | andmaskFactor(k, f))
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)
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}
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/**
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* Holds if `rix` is the number of input edges to `phi`.
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*/
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private predicate maxPhiInputRank(SemSsaPhiNode phi, int rix) {
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rix = max(int r | rankedPhiInput(phi, _, _, r))
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}
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/**
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* Gets the remainder of `val` modulo `mod`.
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*
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* For `mod = 0` the result equals `val` and for `mod > 1` the result is within
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* the range `[0 .. mod-1]`.
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*/
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bindingset[val, mod]
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private int remainder(int val, int mod) {
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mod = 0 and result = val
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or
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mod > 1 and result = ((val % mod) + mod) % mod
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}
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/**
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* Holds if `inp` is an input to `phi` and equals `phi` modulo `mod` along `edge`.
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*/
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private predicate phiSelfModulus(
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SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int mod
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) {
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exists(Bounds::SemSsaBound phibound, int v, int m |
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edge.phiInput(phi, inp) and
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phibound.getAVariable() = phi and
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ssaModulus(inp, edge, phibound, v, m) and
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mod = m.gcd(v) and
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mod != 1
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)
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}
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/**
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* Holds if `b + val` modulo `mod` is a candidate congruence class for `phi`.
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*/
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private predicate phiModulusInit(SemSsaPhiNode phi, Bounds::SemBound b, int val, int mod) {
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exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge |
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edge.phiInput(phi, inp) and
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ssaModulus(inp, edge, b, val, mod)
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)
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}
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/**
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* Holds if all inputs to `phi` numbered `1` to `rix` are equal to `b + val` modulo `mod`.
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*/
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pragma[nomagic]
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private predicate phiModulusRankStep(
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SemSsaPhiNode phi, Bounds::SemBound b, int val, int mod, int rix
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) {
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/*
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* Recursive case. If `inp` = `b + v2` mod `m2`, we combine that with the preceding potential
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* congruence class `b + v1` mod `m1`. The result will be the congruence class of `v1` modulo
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* the greatest common denominator of `m1`, `m2`, and `v1 - v2`.
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* base case. If any phi input is equal to `b + val` modulo `mod`, that's a potential congruence
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* class for the phi node.
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*/
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exists(int v2, int m2 |
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rankedPhiInput(pragma[only_bind_out](phi), inp, edge, rix) and
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phiModulusRankStep(phi, b, v1, m1, rix - 1) and
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ssaModulus(inp, edge, b, v2, m2) and
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mod = m1.gcd(m2).gcd(v1 - v2)
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rix = 0 and
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phiModulusInit(phi, b, val, mod)
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or
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exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int v1, int m1 |
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mod != 1 and
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val = remainder(v1, mod)
|
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|
|
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/*
|
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* Recursive case. If `inp` = `b + v2` mod `m2`, we combine that with the preceding potential
|
||||
* congruence class `b + v1` mod `m1`. The result will be the congruence class of `v1` modulo
|
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* the greatest common denominator of `m1`, `m2`, and `v1 - v2`.
|
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*/
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exists(int v2, int m2 |
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rankedPhiInput(pragma[only_bind_out](phi), inp, edge, rix) and
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phiModulusRankStep(phi, b, v1, m1, rix - 1) and
|
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ssaModulus(inp, edge, b, v2, m2) and
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mod = m1.gcd(m2).gcd(v1 - v2)
|
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)
|
||||
or
|
||||
/*
|
||||
* Recursive case. If `inp` = `phi` mod `m2`, we combine that with the preceding potential
|
||||
* congruence class `b + v1` mod `m1`. The result will be a congruence class modulo the greatest
|
||||
* common denominator of `m1` and `m2`.
|
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*/
|
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|
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exists(int m2 |
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rankedPhiInput(phi, inp, edge, rix) and
|
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phiModulusRankStep(phi, b, v1, m1, rix - 1) and
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phiSelfModulus(phi, inp, edge, m2) and
|
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mod = m1.gcd(m2)
|
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)
|
||||
)
|
||||
or
|
||||
/*
|
||||
* Recursive case. If `inp` = `phi` mod `m2`, we combine that with the preceding potential
|
||||
* congruence class `b + v1` mod `m1`. The result will be a congruence class modulo the greatest
|
||||
* common denominator of `m1` and `m2`.
|
||||
*/
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||||
}
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exists(int m2 |
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rankedPhiInput(phi, inp, edge, rix) and
|
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phiModulusRankStep(phi, b, v1, m1, rix - 1) and
|
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phiSelfModulus(phi, inp, edge, m2) and
|
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mod = m1.gcd(m2)
|
||||
/**
|
||||
* Holds if `phi` is equal to `b + val` modulo `mod`.
|
||||
*/
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||||
private predicate phiModulus(SemSsaPhiNode phi, Bounds::SemBound b, int val, int mod) {
|
||||
exists(int r |
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maxPhiInputRank(phi, r) and
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phiModulusRankStep(phi, b, val, mod, r)
|
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)
|
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)
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `phi` is equal to `b + val` modulo `mod`.
|
||||
*/
|
||||
private predicate phiModulus(SemSsaPhiNode phi, SemBound b, int val, int mod) {
|
||||
exists(int r |
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maxPhiInputRank(phi, r) and
|
||||
phiModulusRankStep(phi, b, val, mod, r)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `v` at `pos` is equal to `b + val` modulo `mod`.
|
||||
*/
|
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private predicate ssaModulus(SemSsaVariable v, SemSsaReadPosition pos, SemBound b, int val, int mod) {
|
||||
phiModulus(v, b, val, mod) and pos.hasReadOfVar(v)
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||||
or
|
||||
b.(SemSsaBound).getAVariable() = v and pos.hasReadOfVar(v) and val = 0 and mod = 0
|
||||
or
|
||||
exists(SemExpr e, int val0, int delta |
|
||||
semExprModulus(e, b, val0, mod) and
|
||||
valueFlowStepSsa(v, pos, e, delta) and
|
||||
val = remainder(val0 + delta, mod)
|
||||
)
|
||||
or
|
||||
moduloGuardedRead(v, pos, val, mod) and b instanceof SemZeroBound
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e` is equal to `b + val` modulo `mod`.
|
||||
*
|
||||
* There are two cases for the modulus:
|
||||
* - `mod = 0`: The equality `e = b + val` is an ordinary equality.
|
||||
* - `mod > 1`: `val` lies within the range `[0 .. mod-1]`.
|
||||
*/
|
||||
cached
|
||||
predicate semExprModulus(SemExpr e, SemBound b, int val, int mod) {
|
||||
not ignoreExprModulus(e) and
|
||||
(
|
||||
e = b.getExpr(val) and mod = 0
|
||||
/**
|
||||
* Holds if `v` at `pos` is equal to `b + val` modulo `mod`.
|
||||
*/
|
||||
private predicate ssaModulus(
|
||||
SemSsaVariable v, SemSsaReadPosition pos, Bounds::SemBound b, int val, int mod
|
||||
) {
|
||||
phiModulus(v, b, val, mod) and pos.hasReadOfVar(v)
|
||||
or
|
||||
evenlyDivisibleExpr(e, mod) and
|
||||
val = 0 and
|
||||
b instanceof SemZeroBound
|
||||
b.(Bounds::SemSsaBound).getAVariable() = v and pos.hasReadOfVar(v) and val = 0 and mod = 0
|
||||
or
|
||||
exists(SemSsaVariable v, SemSsaReadPositionBlock bb |
|
||||
ssaModulus(v, bb, b, val, mod) and
|
||||
e = v.getAUse() and
|
||||
bb.getAnExpr() = e
|
||||
)
|
||||
or
|
||||
exists(SemExpr mid, int val0, int delta |
|
||||
semExprModulus(mid, b, val0, mod) and
|
||||
semValueFlowStep(e, mid, delta) and
|
||||
exists(SemExpr e, int val0, int delta |
|
||||
semExprModulus(e, b, val0, mod) and
|
||||
valueFlowStepSsa(v, pos, e, delta) and
|
||||
val = remainder(val0 + delta, mod)
|
||||
)
|
||||
or
|
||||
exists(SemConditionalExpr cond, int v1, int v2, int m1, int m2 |
|
||||
cond = e and
|
||||
condExprBranchModulus(cond, true, b, v1, m1) and
|
||||
condExprBranchModulus(cond, false, b, v2, m2) and
|
||||
mod = m1.gcd(m2).gcd(v1 - v2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1, mod)
|
||||
)
|
||||
or
|
||||
exists(SemBound b1, SemBound b2, int v1, int v2, int m1, int m2 |
|
||||
addModulus(e, true, b1, v1, m1) and
|
||||
addModulus(e, false, b2, v2, m2) and
|
||||
mod = m1.gcd(m2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1 + v2, mod)
|
||||
|
|
||||
b = b1 and b2 instanceof SemZeroBound
|
||||
moduloGuardedRead(v, pos, val, mod) and b instanceof Bounds::SemZeroBound
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e` is equal to `b + val` modulo `mod`.
|
||||
*
|
||||
* There are two cases for the modulus:
|
||||
* - `mod = 0`: The equality `e = b + val` is an ordinary equality.
|
||||
* - `mod > 1`: `val` lies within the range `[0 .. mod-1]`.
|
||||
*/
|
||||
cached
|
||||
predicate semExprModulus(SemExpr e, Bounds::SemBound b, int val, int mod) {
|
||||
not ignoreExprModulus(e) and
|
||||
(
|
||||
e = b.getExpr(D::fromInt(val)) and mod = 0
|
||||
or
|
||||
b = b2 and b1 instanceof SemZeroBound
|
||||
evenlyDivisibleExpr(e, mod) and
|
||||
val = 0 and
|
||||
b instanceof Bounds::SemZeroBound
|
||||
or
|
||||
exists(SemSsaVariable v, SemSsaReadPositionBlock bb |
|
||||
ssaModulus(v, bb, b, val, mod) and
|
||||
e = v.getAUse() and
|
||||
bb.getAnExpr() = e
|
||||
)
|
||||
or
|
||||
exists(SemExpr mid, int val0, int delta |
|
||||
semExprModulus(mid, b, val0, mod) and
|
||||
U::semValueFlowStep(e, mid, D::fromInt(delta)) and
|
||||
val = remainder(val0 + delta, mod)
|
||||
)
|
||||
or
|
||||
exists(SemConditionalExpr cond, int v1, int v2, int m1, int m2 |
|
||||
cond = e and
|
||||
condExprBranchModulus(cond, true, b, v1, m1) and
|
||||
condExprBranchModulus(cond, false, b, v2, m2) and
|
||||
mod = m1.gcd(m2).gcd(v1 - v2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1, mod)
|
||||
)
|
||||
or
|
||||
exists(Bounds::SemBound b1, Bounds::SemBound b2, int v1, int v2, int m1, int m2 |
|
||||
addModulus(e, true, b1, v1, m1) and
|
||||
addModulus(e, false, b2, v2, m2) and
|
||||
mod = m1.gcd(m2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1 + v2, mod)
|
||||
|
|
||||
b = b1 and b2 instanceof Bounds::SemZeroBound
|
||||
or
|
||||
b = b2 and b1 instanceof Bounds::SemZeroBound
|
||||
)
|
||||
or
|
||||
exists(int v1, int v2, int m1, int m2 |
|
||||
subModulus(e, true, b, v1, m1) and
|
||||
subModulus(e, false, any(Bounds::SemZeroBound zb), v2, m2) and
|
||||
mod = m1.gcd(m2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1 - v2, mod)
|
||||
)
|
||||
)
|
||||
or
|
||||
exists(int v1, int v2, int m1, int m2 |
|
||||
subModulus(e, true, b, v1, m1) and
|
||||
subModulus(e, false, any(SemZeroBound zb), v2, m2) and
|
||||
mod = m1.gcd(m2) and
|
||||
mod != 1 and
|
||||
val = remainder(v1 - v2, mod)
|
||||
}
|
||||
|
||||
private predicate condExprBranchModulus(
|
||||
SemConditionalExpr cond, boolean branch, Bounds::SemBound b, int val, int mod
|
||||
) {
|
||||
semExprModulus(cond.getBranchExpr(branch), b, val, mod)
|
||||
}
|
||||
|
||||
private predicate addModulus(SemExpr add, boolean isLeft, Bounds::SemBound b, int val, int mod) {
|
||||
exists(SemExpr larg, SemExpr rarg | nonConstAddition(add, larg, rarg) |
|
||||
semExprModulus(larg, b, val, mod) and isLeft = true
|
||||
or
|
||||
semExprModulus(rarg, b, val, mod) and isLeft = false
|
||||
)
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
private predicate condExprBranchModulus(
|
||||
SemConditionalExpr cond, boolean branch, SemBound b, int val, int mod
|
||||
) {
|
||||
semExprModulus(cond.getBranchExpr(branch), b, val, mod)
|
||||
}
|
||||
|
||||
private predicate addModulus(SemExpr add, boolean isLeft, SemBound b, int val, int mod) {
|
||||
exists(SemExpr larg, SemExpr rarg | nonConstAddition(add, larg, rarg) |
|
||||
semExprModulus(larg, b, val, mod) and isLeft = true
|
||||
or
|
||||
semExprModulus(rarg, b, val, mod) and isLeft = false
|
||||
)
|
||||
}
|
||||
|
||||
private predicate subModulus(SemExpr sub, boolean isLeft, SemBound b, int val, int mod) {
|
||||
exists(SemExpr larg, SemExpr rarg | nonConstSubtraction(sub, larg, rarg) |
|
||||
semExprModulus(larg, b, val, mod) and isLeft = true
|
||||
or
|
||||
semExprModulus(rarg, b, val, mod) and isLeft = false
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `inp` is an input to `phi` along `edge` and this input has index `r`
|
||||
* in an arbitrary 1-based numbering of the input edges to `phi`.
|
||||
*/
|
||||
private predicate rankedPhiInput(
|
||||
SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int r
|
||||
) {
|
||||
edge.phiInput(phi, inp) and
|
||||
edge =
|
||||
rank[r](SemSsaReadPositionPhiInputEdge e |
|
||||
e.phiInput(phi, _)
|
||||
|
|
||||
e order by e.getOrigBlock().getUniqueId()
|
||||
private predicate subModulus(SemExpr sub, boolean isLeft, Bounds::SemBound b, int val, int mod) {
|
||||
exists(SemExpr larg, SemExpr rarg | nonConstSubtraction(sub, larg, rarg) |
|
||||
semExprModulus(larg, b, val, mod) and isLeft = true
|
||||
or
|
||||
semExprModulus(rarg, b, val, mod) and isLeft = false
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `inp` is an input to `phi` along `edge` and this input has index `r`
|
||||
* in an arbitrary 1-based numbering of the input edges to `phi`.
|
||||
*/
|
||||
private predicate rankedPhiInput(
|
||||
SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, int r
|
||||
) {
|
||||
edge.phiInput(phi, inp) and
|
||||
edge =
|
||||
rank[r](SemSsaReadPositionPhiInputEdge e |
|
||||
e.phiInput(phi, _)
|
||||
|
|
||||
e order by e.getOrigBlock().getUniqueId()
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
@@ -1,830 +1,24 @@
|
||||
/**
|
||||
* Provides classes and predicates for range analysis.
|
||||
*
|
||||
* An inferred bound can either be a specific integer, the abstract value of an
|
||||
* SSA variable, or the abstract value of an interesting expression. The latter
|
||||
* category includes array lengths that are not SSA variables.
|
||||
*
|
||||
* If an inferred bound relies directly on a condition, then this condition is
|
||||
* reported as the reason for the bound.
|
||||
*/
|
||||
|
||||
/*
|
||||
* This library tackles range analysis as a flow problem. Consider e.g.:
|
||||
* ```
|
||||
* len = arr.length;
|
||||
* if (x < len) { ... y = x-1; ... y ... }
|
||||
* ```
|
||||
* In this case we would like to infer `y <= arr.length - 2`, and this is
|
||||
* accomplished by tracking the bound through a sequence of steps:
|
||||
* ```
|
||||
* arr.length --> len = .. --> x < len --> x-1 --> y = .. --> y
|
||||
* ```
|
||||
*
|
||||
* In its simplest form the step relation `E1 --> E2` relates two expressions
|
||||
* such that `E1 <= B` implies `E2 <= B` for any `B` (with a second separate
|
||||
* step relation handling lower bounds). Examples of such steps include
|
||||
* assignments `E2 = E1` and conditions `x <= E1` where `E2` is a use of `x`
|
||||
* guarded by the condition.
|
||||
*
|
||||
* In order to handle subtractions and additions with constants, and strict
|
||||
* comparisons, the step relation is augmented with an integer delta. With this
|
||||
* generalization `E1 --(delta)--> E2` relates two expressions and an integer
|
||||
* such that `E1 <= B` implies `E2 <= B + delta` for any `B`. This corresponds
|
||||
* to the predicate `boundFlowStep`.
|
||||
*
|
||||
* The complete range analysis is then implemented as the transitive closure of
|
||||
* the step relation summing the deltas along the way. If `E1` transitively
|
||||
* steps to `E2`, `delta` is the sum of deltas along the path, and `B` is an
|
||||
* interesting bound equal to the value of `E1` then `E2 <= B + delta`. This
|
||||
* corresponds to the predicate `bounded`.
|
||||
*
|
||||
* Phi nodes need a little bit of extra handling. Consider `x0 = phi(x1, x2)`.
|
||||
* There are essentially two cases:
|
||||
* - If `x1 <= B + d1` and `x2 <= B + d2` then `x0 <= B + max(d1,d2)`.
|
||||
* - If `x1 <= B + d1` and `x2 <= x0 + d2` with `d2 <= 0` then `x0 <= B + d1`.
|
||||
* The first case is for whenever a bound can be proven without taking looping
|
||||
* into account. The second case is relevant when `x2` comes from a back-edge
|
||||
* where we can prove that the variable has been non-increasing through the
|
||||
* loop-iteration as this means that any upper bound that holds prior to the
|
||||
* loop also holds for the variable during the loop.
|
||||
* This generalizes to a phi node with `n` inputs, so if
|
||||
* `x0 = phi(x1, ..., xn)` and `xi <= B + delta` for one of the inputs, then we
|
||||
* also have `x0 <= B + delta` if we can prove either:
|
||||
* - `xj <= B + d` with `d <= delta` or
|
||||
* - `xj <= x0 + d` with `d <= 0`
|
||||
* for each input `xj`.
|
||||
*
|
||||
* As all inferred bounds can be related directly to a path in the source code
|
||||
* the only source of non-termination is if successive redundant (and thereby
|
||||
* increasingly worse) bounds are calculated along a loop in the source code.
|
||||
* We prevent this by weakening the bound to a small finite set of bounds when
|
||||
* a path follows a second back-edge (we postpone weakening till the second
|
||||
* back-edge as a precise bound might require traversing a loop once).
|
||||
*/
|
||||
|
||||
private import RangeAnalysisSpecific as Specific
|
||||
private import RangeAnalysisStage
|
||||
private import RangeAnalysisSpecific
|
||||
private import experimental.semmle.code.cpp.semantic.analysis.FloatDelta
|
||||
private import RangeUtils
|
||||
private import SignAnalysisCommon
|
||||
private import ModulusAnalysis
|
||||
private import experimental.semmle.code.cpp.semantic.Semantic
|
||||
private import ConstantAnalysis
|
||||
private import experimental.semmle.code.cpp.semantic.SemanticBound as SemanticBound
|
||||
|
||||
cached
|
||||
private module RangeAnalysisCache {
|
||||
cached
|
||||
module RangeAnalysisPublic {
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `e`.
|
||||
* - `upper = true` : `e <= b + delta`
|
||||
* - `upper = false` : `e >= b + delta`
|
||||
*
|
||||
* The reason for the bound is given by `reason` and may be either a condition
|
||||
* or `NoReason` if the bound was proven directly without the use of a bounding
|
||||
* condition.
|
||||
*/
|
||||
cached
|
||||
predicate semBounded(SemExpr e, SemBound b, int delta, boolean upper, SemReason reason) {
|
||||
bounded(e, b, delta, upper, _, _, reason) and
|
||||
bestBound(e, b, delta, upper)
|
||||
}
|
||||
module Bounds implements BoundSig<FloatDelta> {
|
||||
class SemBound instanceof SemanticBound::SemBound {
|
||||
string toString() { result = super.toString() }
|
||||
|
||||
SemExpr getExpr(float delta) { result = super.getExpr(delta) }
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `guard = boundFlowCond(_, _, _, _, _) or guard = eqFlowCond(_, _, _, _, _)`.
|
||||
*/
|
||||
cached
|
||||
predicate possibleReason(SemGuard guard) {
|
||||
guard = boundFlowCond(_, _, _, _, _) or guard = semEqFlowCond(_, _, _, _, _)
|
||||
class SemZeroBound extends SemBound instanceof SemanticBound::SemZeroBound { }
|
||||
|
||||
class SemSsaBound extends SemBound instanceof SemanticBound::SemSsaBound {
|
||||
SemSsaVariable getAVariable() { result = this.(SemanticBound::SemSsaBound).getAVariable() }
|
||||
}
|
||||
}
|
||||
|
||||
private import RangeAnalysisCache
|
||||
import RangeAnalysisPublic
|
||||
private module CppRangeAnalysis =
|
||||
RangeStage<FloatDelta, Bounds, CppLangImpl, RangeUtil<FloatDelta, CppLangImpl>>;
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `e` and this is the best such delta.
|
||||
* - `upper = true` : `e <= b + delta`
|
||||
* - `upper = false` : `e >= b + delta`
|
||||
*/
|
||||
private predicate bestBound(SemExpr e, SemBound b, int delta, boolean upper) {
|
||||
delta = min(int d | bounded(e, b, d, upper, _, _, _)) and upper = true
|
||||
or
|
||||
delta = max(int d | bounded(e, b, d, upper, _, _, _)) and upper = false
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `comp` corresponds to:
|
||||
* - `upper = true` : `v <= e + delta` or `v < e + delta`
|
||||
* - `upper = false` : `v >= e + delta` or `v > e + delta`
|
||||
*/
|
||||
private predicate boundCondition(
|
||||
SemRelationalExpr comp, SemSsaVariable v, SemExpr e, int delta, boolean upper
|
||||
) {
|
||||
comp.getLesserOperand() = semSsaRead(v, delta) and e = comp.getGreaterOperand() and upper = true
|
||||
or
|
||||
comp.getGreaterOperand() = semSsaRead(v, delta) and e = comp.getLesserOperand() and upper = false
|
||||
or
|
||||
exists(SemSubExpr sub, SemConstantIntegerExpr c, int d |
|
||||
// (v - d) - e < c
|
||||
comp.getLesserOperand() = sub and
|
||||
comp.getGreaterOperand() = c and
|
||||
sub.getLeftOperand() = semSsaRead(v, d) and
|
||||
sub.getRightOperand() = e and
|
||||
upper = true and
|
||||
delta = d + c.getIntValue()
|
||||
or
|
||||
// (v - d) - e > c
|
||||
comp.getGreaterOperand() = sub and
|
||||
comp.getLesserOperand() = c and
|
||||
sub.getLeftOperand() = semSsaRead(v, d) and
|
||||
sub.getRightOperand() = e and
|
||||
upper = false and
|
||||
delta = d + c.getIntValue()
|
||||
or
|
||||
// e - (v - d) < c
|
||||
comp.getLesserOperand() = sub and
|
||||
comp.getGreaterOperand() = c and
|
||||
sub.getLeftOperand() = e and
|
||||
sub.getRightOperand() = semSsaRead(v, d) and
|
||||
upper = false and
|
||||
delta = d - c.getIntValue()
|
||||
or
|
||||
// e - (v - d) > c
|
||||
comp.getGreaterOperand() = sub and
|
||||
comp.getLesserOperand() = c and
|
||||
sub.getLeftOperand() = e and
|
||||
sub.getRightOperand() = semSsaRead(v, d) and
|
||||
upper = true and
|
||||
delta = d - c.getIntValue()
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `comp` is a comparison between `x` and `y` for which `y - x` has a
|
||||
* fixed value modulo some `mod > 1`, such that the comparison can be
|
||||
* strengthened by `strengthen` when evaluating to `testIsTrue`.
|
||||
*/
|
||||
private predicate modulusComparison(SemRelationalExpr comp, boolean testIsTrue, int strengthen) {
|
||||
exists(
|
||||
SemBound b, int v1, int v2, int mod1, int mod2, int mod, boolean resultIsStrict, int d, int k
|
||||
|
|
||||
// If `x <= y` and `x =(mod) b + v1` and `y =(mod) b + v2` then
|
||||
// `0 <= y - x =(mod) v2 - v1`. By choosing `k =(mod) v2 - v1` with
|
||||
// `0 <= k < mod` we get `k <= y - x`. If the resulting comparison is
|
||||
// strict then the strengthening amount is instead `k - 1` modulo `mod`:
|
||||
// `x < y` means `0 <= y - x - 1 =(mod) k - 1` so `k - 1 <= y - x - 1` and
|
||||
// thus `k - 1 < y - x` with `0 <= k - 1 < mod`.
|
||||
semExprModulus(comp.getLesserOperand(), b, v1, mod1) and
|
||||
semExprModulus(comp.getGreaterOperand(), b, v2, mod2) and
|
||||
mod = mod1.gcd(mod2) and
|
||||
mod != 1 and
|
||||
(testIsTrue = true or testIsTrue = false) and
|
||||
(
|
||||
if comp.isStrict()
|
||||
then resultIsStrict = testIsTrue
|
||||
else resultIsStrict = testIsTrue.booleanNot()
|
||||
) and
|
||||
(
|
||||
resultIsStrict = true and d = 1
|
||||
or
|
||||
resultIsStrict = false and d = 0
|
||||
) and
|
||||
(
|
||||
testIsTrue = true and k = v2 - v1
|
||||
or
|
||||
testIsTrue = false and k = v1 - v2
|
||||
) and
|
||||
strengthen = (((k - d) % mod) + mod) % mod
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a condition that tests whether `v` is bounded by `e + delta`.
|
||||
*
|
||||
* If the condition evaluates to `testIsTrue`:
|
||||
* - `upper = true` : `v <= e + delta`
|
||||
* - `upper = false` : `v >= e + delta`
|
||||
*/
|
||||
private SemGuard boundFlowCond(
|
||||
SemSsaVariable v, SemExpr e, int delta, boolean upper, boolean testIsTrue
|
||||
) {
|
||||
exists(
|
||||
SemRelationalExpr comp, int d1, int d2, int d3, int strengthen, boolean compIsUpper,
|
||||
boolean resultIsStrict
|
||||
|
|
||||
comp = result.asExpr() and
|
||||
boundCondition(comp, v, e, d1, compIsUpper) and
|
||||
(testIsTrue = true or testIsTrue = false) and
|
||||
upper = compIsUpper.booleanXor(testIsTrue.booleanNot()) and
|
||||
(
|
||||
if comp.isStrict()
|
||||
then resultIsStrict = testIsTrue
|
||||
else resultIsStrict = testIsTrue.booleanNot()
|
||||
) and
|
||||
(
|
||||
if
|
||||
getTrackedTypeForSsaVariable(v) instanceof SemIntegerType or
|
||||
getTrackedTypeForSsaVariable(v) instanceof SemAddressType
|
||||
then
|
||||
upper = true and strengthen = -1
|
||||
or
|
||||
upper = false and strengthen = 1
|
||||
else strengthen = 0
|
||||
) and
|
||||
(
|
||||
exists(int k | modulusComparison(comp, testIsTrue, k) and d2 = strengthen * k)
|
||||
or
|
||||
not modulusComparison(comp, testIsTrue, _) and d2 = 0
|
||||
) and
|
||||
// A strict inequality `x < y` can be strengthened to `x <= y - 1`.
|
||||
(
|
||||
resultIsStrict = true and d3 = strengthen
|
||||
or
|
||||
resultIsStrict = false and d3 = 0
|
||||
) and
|
||||
delta = d1 + d2 + d3
|
||||
)
|
||||
or
|
||||
exists(boolean testIsTrue0 |
|
||||
semImplies_v2(result, testIsTrue, boundFlowCond(v, e, delta, upper, testIsTrue0), testIsTrue0)
|
||||
)
|
||||
or
|
||||
result = semEqFlowCond(v, e, delta, true, testIsTrue) and
|
||||
(upper = true or upper = false)
|
||||
or
|
||||
// guard that tests whether `v2` is bounded by `e + delta + d1 - d2` and
|
||||
// exists a guard `guardEq` such that `v = v2 - d1 + d2`.
|
||||
exists(SemSsaVariable v2, SemGuard guardEq, boolean eqIsTrue, int d1, int d2 |
|
||||
guardEq = semEqFlowCond(v, semSsaRead(v2, d1), d2, true, eqIsTrue) and
|
||||
result = boundFlowCond(v2, e, delta + d1 - d2, upper, testIsTrue) and
|
||||
// guardEq needs to control guard
|
||||
guardEq.directlyControls(result.getBasicBlock(), eqIsTrue)
|
||||
)
|
||||
}
|
||||
|
||||
private newtype TSemReason =
|
||||
TSemNoReason() or
|
||||
TSemCondReason(SemGuard guard) { possibleReason(guard) }
|
||||
|
||||
/**
|
||||
* A reason for an inferred bound. This can either be `CondReason` if the bound
|
||||
* is due to a specific condition, or `NoReason` if the bound is inferred
|
||||
* without going through a bounding condition.
|
||||
*/
|
||||
abstract class SemReason extends TSemReason {
|
||||
/** Gets a textual representation of this reason. */
|
||||
abstract string toString();
|
||||
}
|
||||
|
||||
/**
|
||||
* A reason for an inferred bound that indicates that the bound is inferred
|
||||
* without going through a bounding condition.
|
||||
*/
|
||||
class SemNoReason extends SemReason, TSemNoReason {
|
||||
override string toString() { result = "NoReason" }
|
||||
}
|
||||
|
||||
/** A reason for an inferred bound pointing to a condition. */
|
||||
class SemCondReason extends SemReason, TSemCondReason {
|
||||
/** Gets the condition that is the reason for the bound. */
|
||||
SemGuard getCond() { this = TSemCondReason(result) }
|
||||
|
||||
override string toString() { result = getCond().toString() }
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e + delta` is a valid bound for `v` at `pos`.
|
||||
* - `upper = true` : `v <= e + delta`
|
||||
* - `upper = false` : `v >= e + delta`
|
||||
*/
|
||||
private predicate boundFlowStepSsa(
|
||||
SemSsaVariable v, SemSsaReadPosition pos, SemExpr e, int delta, boolean upper, SemReason reason
|
||||
) {
|
||||
semSsaUpdateStep(v, e, delta) and
|
||||
pos.hasReadOfVar(v) and
|
||||
(upper = true or upper = false) and
|
||||
reason = TSemNoReason()
|
||||
or
|
||||
exists(SemGuard guard, boolean testIsTrue |
|
||||
pos.hasReadOfVar(v) and
|
||||
guard = boundFlowCond(v, e, delta, upper, testIsTrue) and
|
||||
semGuardDirectlyControlsSsaRead(guard, pos, testIsTrue) and
|
||||
reason = TSemCondReason(guard)
|
||||
)
|
||||
}
|
||||
|
||||
/** Holds if `v != e + delta` at `pos` and `v` is of integral type. */
|
||||
private predicate unequalFlowStepIntegralSsa(
|
||||
SemSsaVariable v, SemSsaReadPosition pos, SemExpr e, int delta, SemReason reason
|
||||
) {
|
||||
getTrackedTypeForSsaVariable(v) instanceof SemIntegerType and
|
||||
exists(SemGuard guard, boolean testIsTrue |
|
||||
pos.hasReadOfVar(v) and
|
||||
guard = semEqFlowCond(v, e, delta, false, testIsTrue) and
|
||||
semGuardDirectlyControlsSsaRead(guard, pos, testIsTrue) and
|
||||
reason = TSemCondReason(guard)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* An expression that does conversion, boxing, or unboxing
|
||||
*/
|
||||
private class ConvertOrBoxExpr extends SemUnaryExpr {
|
||||
ConvertOrBoxExpr() {
|
||||
this instanceof SemConvertExpr
|
||||
or
|
||||
this instanceof SemBoxExpr
|
||||
or
|
||||
this instanceof SemUnboxExpr
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* A cast that can be ignored for the purpose of range analysis.
|
||||
*/
|
||||
private class SafeCastExpr extends ConvertOrBoxExpr {
|
||||
SafeCastExpr() {
|
||||
conversionCannotOverflow(getTrackedType(pragma[only_bind_into](getOperand())),
|
||||
getTrackedType(this))
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `typ` is a small integral type with the given lower and upper bounds.
|
||||
*/
|
||||
private predicate typeBound(SemIntegerType typ, int lowerbound, int upperbound) {
|
||||
exists(int bitSize | bitSize = typ.getByteSize() * 8 |
|
||||
bitSize < 32 and
|
||||
(
|
||||
if typ.isSigned()
|
||||
then (
|
||||
upperbound = 1.bitShiftLeft(bitSize - 1) - 1 and
|
||||
lowerbound = -upperbound - 1
|
||||
) else (
|
||||
lowerbound = 0 and
|
||||
upperbound = 1.bitShiftLeft(bitSize) - 1
|
||||
)
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* A cast to a small integral type that may overflow or underflow.
|
||||
*/
|
||||
private class NarrowingCastExpr extends ConvertOrBoxExpr {
|
||||
NarrowingCastExpr() {
|
||||
not this instanceof SafeCastExpr and
|
||||
typeBound(getTrackedType(this), _, _)
|
||||
}
|
||||
|
||||
/** Gets the lower bound of the resulting type. */
|
||||
int getLowerBound() { typeBound(getTrackedType(this), result, _) }
|
||||
|
||||
/** Gets the upper bound of the resulting type. */
|
||||
int getUpperBound() { typeBound(getTrackedType(this), _, result) }
|
||||
}
|
||||
|
||||
/** Holds if `e >= 1` as determined by sign analysis. */
|
||||
private predicate strictlyPositiveIntegralExpr(SemExpr e) {
|
||||
semStrictlyPositive(e) and getTrackedType(e) instanceof SemIntegerType
|
||||
}
|
||||
|
||||
/** Holds if `e <= -1` as determined by sign analysis. */
|
||||
private predicate strictlyNegativeIntegralExpr(SemExpr e) {
|
||||
semStrictlyNegative(e) and getTrackedType(e) instanceof SemIntegerType
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e1 + delta` is a valid bound for `e2`.
|
||||
* - `upper = true` : `e2 <= e1 + delta`
|
||||
* - `upper = false` : `e2 >= e1 + delta`
|
||||
*/
|
||||
private predicate boundFlowStep(SemExpr e2, SemExpr e1, int delta, boolean upper) {
|
||||
semValueFlowStep(e2, e1, delta) and
|
||||
(upper = true or upper = false)
|
||||
or
|
||||
e2.(SafeCastExpr).getOperand() = e1 and
|
||||
delta = 0 and
|
||||
(upper = true or upper = false)
|
||||
or
|
||||
exists(SemExpr x | e2.(SemAddExpr).hasOperands(e1, x) |
|
||||
// `x instanceof ConstantIntegerExpr` is covered by valueFlowStep
|
||||
not x instanceof SemConstantIntegerExpr and
|
||||
not e1 instanceof SemConstantIntegerExpr and
|
||||
if strictlyPositiveIntegralExpr(x)
|
||||
then upper = false and delta = 1
|
||||
else
|
||||
if semPositive(x)
|
||||
then upper = false and delta = 0
|
||||
else
|
||||
if strictlyNegativeIntegralExpr(x)
|
||||
then upper = true and delta = -1
|
||||
else
|
||||
if semNegative(x)
|
||||
then upper = true and delta = 0
|
||||
else none()
|
||||
)
|
||||
or
|
||||
exists(SemExpr x, SemSubExpr sub |
|
||||
e2 = sub and
|
||||
sub.getLeftOperand() = e1 and
|
||||
sub.getRightOperand() = x
|
||||
|
|
||||
// `x instanceof ConstantIntegerExpr` is covered by valueFlowStep
|
||||
not x instanceof SemConstantIntegerExpr and
|
||||
if strictlyPositiveIntegralExpr(x)
|
||||
then upper = true and delta = -1
|
||||
else
|
||||
if semPositive(x)
|
||||
then upper = true and delta = 0
|
||||
else
|
||||
if strictlyNegativeIntegralExpr(x)
|
||||
then upper = false and delta = 1
|
||||
else
|
||||
if semNegative(x)
|
||||
then upper = false and delta = 0
|
||||
else none()
|
||||
)
|
||||
or
|
||||
e2.(SemRemExpr).getRightOperand() = e1 and
|
||||
semPositive(e1) and
|
||||
delta = -1 and
|
||||
upper = true
|
||||
or
|
||||
e2.(SemRemExpr).getLeftOperand() = e1 and semPositive(e1) and delta = 0 and upper = true
|
||||
or
|
||||
e2.(SemBitAndExpr).getAnOperand() = e1 and
|
||||
semPositive(e1) and
|
||||
delta = 0 and
|
||||
upper = true
|
||||
or
|
||||
e2.(SemBitOrExpr).getAnOperand() = e1 and
|
||||
semPositive(e2) and
|
||||
delta = 0 and
|
||||
upper = false
|
||||
or
|
||||
Specific::hasBound(e2, e1, delta, upper)
|
||||
}
|
||||
|
||||
/** Holds if `e2 = e1 * factor` and `factor > 0`. */
|
||||
private predicate boundFlowStepMul(SemExpr e2, SemExpr e1, int factor) {
|
||||
exists(SemConstantIntegerExpr c, int k | k = c.getIntValue() and k > 0 |
|
||||
e2.(SemMulExpr).hasOperands(e1, c) and factor = k
|
||||
or
|
||||
exists(SemShiftLeftExpr e |
|
||||
e = e2 and e.getLeftOperand() = e1 and e.getRightOperand() = c and factor = 2.pow(k)
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e2 = e1 / factor` and `factor > 0`.
|
||||
*
|
||||
* This conflates division, right shift, and unsigned right shift and is
|
||||
* therefore only valid for non-negative numbers.
|
||||
*/
|
||||
private predicate boundFlowStepDiv(SemExpr e2, SemExpr e1, int factor) {
|
||||
exists(SemConstantIntegerExpr c, int k | k = c.getIntValue() and k > 0 |
|
||||
exists(SemDivExpr e |
|
||||
e = e2 and e.getLeftOperand() = e1 and e.getRightOperand() = c and factor = k
|
||||
)
|
||||
or
|
||||
exists(SemShiftRightExpr e |
|
||||
e = e2 and e.getLeftOperand() = e1 and e.getRightOperand() = c and factor = 2.pow(k)
|
||||
)
|
||||
or
|
||||
exists(SemShiftRightUnsignedExpr e |
|
||||
e = e2 and e.getLeftOperand() = e1 and e.getRightOperand() = c and factor = 2.pow(k)
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `v` at `pos`.
|
||||
* - `upper = true` : `v <= b + delta`
|
||||
* - `upper = false` : `v >= b + delta`
|
||||
*/
|
||||
private predicate boundedSsa(
|
||||
SemSsaVariable v, SemSsaReadPosition pos, SemBound b, int delta, boolean upper,
|
||||
boolean fromBackEdge, int origdelta, SemReason reason
|
||||
) {
|
||||
exists(SemExpr mid, int d1, int d2, SemReason r1, SemReason r2 |
|
||||
boundFlowStepSsa(v, pos, mid, d1, upper, r1) and
|
||||
bounded(mid, b, d2, upper, fromBackEdge, origdelta, r2) and
|
||||
// upper = true: v <= mid + d1 <= b + d1 + d2 = b + delta
|
||||
// upper = false: v >= mid + d1 >= b + d1 + d2 = b + delta
|
||||
delta = d1 + d2 and
|
||||
(if r1 instanceof SemNoReason then reason = r2 else reason = r1)
|
||||
)
|
||||
or
|
||||
exists(int d, SemReason r1, SemReason r2 |
|
||||
boundedSsa(v, pos, b, d, upper, fromBackEdge, origdelta, r2) or
|
||||
boundedPhi(v, b, d, upper, fromBackEdge, origdelta, r2)
|
||||
|
|
||||
unequalIntegralSsa(v, pos, b, d, r1) and
|
||||
(
|
||||
upper = true and delta = d - 1
|
||||
or
|
||||
upper = false and delta = d + 1
|
||||
) and
|
||||
(
|
||||
reason = r1
|
||||
or
|
||||
reason = r2 and not r2 instanceof SemNoReason
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `v != b + delta` at `pos` and `v` is of integral type.
|
||||
*/
|
||||
private predicate unequalIntegralSsa(
|
||||
SemSsaVariable v, SemSsaReadPosition pos, SemBound b, int delta, SemReason reason
|
||||
) {
|
||||
exists(SemExpr e, int d1, int d2 |
|
||||
unequalFlowStepIntegralSsa(v, pos, e, d1, reason) and
|
||||
boundedUpper(e, b, d1) and
|
||||
boundedLower(e, b, d2) and
|
||||
delta = d2 + d1
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is an upper bound for `e`.
|
||||
*
|
||||
* This predicate only exists to prevent a bad standard order in `unequalIntegralSsa`.
|
||||
*/
|
||||
pragma[nomagic]
|
||||
private predicate boundedUpper(SemExpr e, SemBound b, int delta) {
|
||||
bounded(e, b, delta, true, _, _, _)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a lower bound for `e`.
|
||||
*
|
||||
* This predicate only exists to prevent a bad standard order in `unequalIntegralSsa`.
|
||||
*/
|
||||
pragma[nomagic]
|
||||
private predicate boundedLower(SemExpr e, SemBound b, int delta) {
|
||||
bounded(e, b, delta, false, _, _, _)
|
||||
}
|
||||
|
||||
/** Weakens a delta to lie in the range `[-1..1]`. */
|
||||
bindingset[delta, upper]
|
||||
private int weakenDelta(boolean upper, int delta) {
|
||||
delta in [-1 .. 1] and result = delta
|
||||
or
|
||||
upper = true and result = -1 and delta < -1
|
||||
or
|
||||
upper = false and result = 1 and delta > 1
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `inp` when used as an input to
|
||||
* `phi` along `edge`.
|
||||
* - `upper = true` : `inp <= b + delta`
|
||||
* - `upper = false` : `inp >= b + delta`
|
||||
*/
|
||||
private predicate boundedPhiInp(
|
||||
SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, SemBound b, int delta,
|
||||
boolean upper, boolean fromBackEdge, int origdelta, SemReason reason
|
||||
) {
|
||||
edge.phiInput(phi, inp) and
|
||||
exists(int d, boolean fromBackEdge0 |
|
||||
boundedSsa(inp, edge, b, d, upper, fromBackEdge0, origdelta, reason)
|
||||
or
|
||||
boundedPhi(inp, b, d, upper, fromBackEdge0, origdelta, reason)
|
||||
or
|
||||
b.(SemSsaBound).getAVariable() = inp and
|
||||
d = 0 and
|
||||
(upper = true or upper = false) and
|
||||
fromBackEdge0 = false and
|
||||
origdelta = 0 and
|
||||
reason = TSemNoReason()
|
||||
|
|
||||
if semBackEdge(phi, inp, edge)
|
||||
then
|
||||
fromBackEdge = true and
|
||||
(
|
||||
fromBackEdge0 = true and delta = weakenDelta(upper, d - origdelta) + origdelta
|
||||
or
|
||||
fromBackEdge0 = false and delta = d
|
||||
)
|
||||
else (
|
||||
delta = d and fromBackEdge = fromBackEdge0
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `inp` when used as an input to
|
||||
* `phi` along `edge`.
|
||||
* - `upper = true` : `inp <= b + delta`
|
||||
* - `upper = false` : `inp >= b + delta`
|
||||
*
|
||||
* Equivalent to `boundedPhiInp(phi, inp, edge, b, delta, upper, _, _, _)`.
|
||||
*/
|
||||
pragma[noinline]
|
||||
private predicate boundedPhiInp1(
|
||||
SemSsaPhiNode phi, SemBound b, boolean upper, SemSsaVariable inp,
|
||||
SemSsaReadPositionPhiInputEdge edge, int delta
|
||||
) {
|
||||
boundedPhiInp(phi, inp, edge, b, delta, upper, _, _, _)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `phi` is a valid bound for `inp` when used as an input to `phi`
|
||||
* along `edge`.
|
||||
* - `upper = true` : `inp <= phi`
|
||||
* - `upper = false` : `inp >= phi`
|
||||
*/
|
||||
private predicate selfBoundedPhiInp(
|
||||
SemSsaPhiNode phi, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge, boolean upper
|
||||
) {
|
||||
exists(int d, SemSsaBound phibound |
|
||||
phibound.getAVariable() = phi and
|
||||
boundedPhiInp(phi, inp, edge, phibound, d, upper, _, _, _) and
|
||||
(
|
||||
upper = true and d <= 0
|
||||
or
|
||||
upper = false and d >= 0
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for some input, `inp`, to `phi`, and
|
||||
* thus a candidate bound for `phi`.
|
||||
* - `upper = true` : `inp <= b + delta`
|
||||
* - `upper = false` : `inp >= b + delta`
|
||||
*/
|
||||
pragma[noinline]
|
||||
private predicate boundedPhiCand(
|
||||
SemSsaPhiNode phi, boolean upper, SemBound b, int delta, boolean fromBackEdge, int origdelta,
|
||||
SemReason reason
|
||||
) {
|
||||
boundedPhiInp(phi, _, _, b, delta, upper, fromBackEdge, origdelta, reason)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if the candidate bound `b + delta` for `phi` is valid for the phi input
|
||||
* `inp` along `edge`.
|
||||
*/
|
||||
private predicate boundedPhiCandValidForEdge(
|
||||
SemSsaPhiNode phi, SemBound b, int delta, boolean upper, boolean fromBackEdge, int origdelta,
|
||||
SemReason reason, SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge
|
||||
) {
|
||||
boundedPhiCand(phi, upper, b, delta, fromBackEdge, origdelta, reason) and
|
||||
(
|
||||
exists(int d | boundedPhiInp1(phi, b, upper, inp, edge, d) | upper = true and d <= delta)
|
||||
or
|
||||
exists(int d | boundedPhiInp1(phi, b, upper, inp, edge, d) | upper = false and d >= delta)
|
||||
or
|
||||
selfBoundedPhiInp(phi, inp, edge, upper)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `phi`.
|
||||
* - `upper = true` : `phi <= b + delta`
|
||||
* - `upper = false` : `phi >= b + delta`
|
||||
*/
|
||||
private predicate boundedPhi(
|
||||
SemSsaPhiNode phi, SemBound b, int delta, boolean upper, boolean fromBackEdge, int origdelta,
|
||||
SemReason reason
|
||||
) {
|
||||
forex(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge | edge.phiInput(phi, inp) |
|
||||
boundedPhiCandValidForEdge(phi, b, delta, upper, fromBackEdge, origdelta, reason, inp, edge)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e` has an upper (for `upper = true`) or lower
|
||||
* (for `upper = false`) bound of `b`.
|
||||
*/
|
||||
private predicate baseBound(SemExpr e, int b, boolean upper) {
|
||||
Specific::hasConstantBound(e, b, upper)
|
||||
or
|
||||
upper = false and
|
||||
b = 0 and
|
||||
semPositive(e.(SemBitAndExpr).getAnOperand()) and
|
||||
// REVIEW: We let the language opt out here to preserve original results.
|
||||
not Specific::ignoreZeroLowerBound(e)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if the value being cast has an upper (for `upper = true`) or lower
|
||||
* (for `upper = false`) bound within the bounds of the resulting type.
|
||||
* For `upper = true` this means that the cast will not overflow and for
|
||||
* `upper = false` this means that the cast will not underflow.
|
||||
*/
|
||||
private predicate safeNarrowingCast(NarrowingCastExpr cast, boolean upper) {
|
||||
exists(int bound | bounded(cast.getOperand(), any(SemZeroBound zb), bound, upper, _, _, _) |
|
||||
upper = true and bound <= cast.getUpperBound()
|
||||
or
|
||||
upper = false and bound >= cast.getLowerBound()
|
||||
)
|
||||
}
|
||||
|
||||
pragma[noinline]
|
||||
private predicate boundedCastExpr(
|
||||
NarrowingCastExpr cast, SemBound b, int delta, boolean upper, boolean fromBackEdge, int origdelta,
|
||||
SemReason reason
|
||||
) {
|
||||
bounded(cast.getOperand(), b, delta, upper, fromBackEdge, origdelta, reason)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `b + delta` is a valid bound for `e`.
|
||||
* - `upper = true` : `e <= b + delta`
|
||||
* - `upper = false` : `e >= b + delta`
|
||||
*/
|
||||
private predicate bounded(
|
||||
SemExpr e, SemBound b, int delta, boolean upper, boolean fromBackEdge, int origdelta,
|
||||
SemReason reason
|
||||
) {
|
||||
not Specific::ignoreExprBound(e) and
|
||||
(
|
||||
e = b.getExpr(delta) and
|
||||
(upper = true or upper = false) and
|
||||
fromBackEdge = false and
|
||||
origdelta = delta and
|
||||
reason = TSemNoReason()
|
||||
or
|
||||
baseBound(e, delta, upper) and
|
||||
b instanceof SemZeroBound and
|
||||
fromBackEdge = false and
|
||||
origdelta = delta and
|
||||
reason = TSemNoReason()
|
||||
or
|
||||
exists(SemSsaVariable v, SemSsaReadPositionBlock bb |
|
||||
boundedSsa(v, bb, b, delta, upper, fromBackEdge, origdelta, reason) and
|
||||
e = v.getAUse() and
|
||||
bb.getBlock() = e.getBasicBlock()
|
||||
)
|
||||
or
|
||||
exists(SemExpr mid, int d1, int d2 |
|
||||
boundFlowStep(e, mid, d1, upper) and
|
||||
// Constants have easy, base-case bounds, so let's not infer any recursive bounds.
|
||||
not e instanceof SemConstantIntegerExpr and
|
||||
bounded(mid, b, d2, upper, fromBackEdge, origdelta, reason) and
|
||||
// upper = true: e <= mid + d1 <= b + d1 + d2 = b + delta
|
||||
// upper = false: e >= mid + d1 >= b + d1 + d2 = b + delta
|
||||
delta = d1 + d2
|
||||
)
|
||||
or
|
||||
exists(SemSsaPhiNode phi |
|
||||
boundedPhi(phi, b, delta, upper, fromBackEdge, origdelta, reason) and
|
||||
e = phi.getAUse()
|
||||
)
|
||||
or
|
||||
exists(SemExpr mid, int factor, int d |
|
||||
boundFlowStepMul(e, mid, factor) and
|
||||
not e instanceof SemConstantIntegerExpr and
|
||||
bounded(mid, b, d, upper, fromBackEdge, origdelta, reason) and
|
||||
b instanceof SemZeroBound and
|
||||
delta = d * factor
|
||||
)
|
||||
or
|
||||
exists(SemExpr mid, int factor, int d |
|
||||
boundFlowStepDiv(e, mid, factor) and
|
||||
not e instanceof SemConstantIntegerExpr and
|
||||
bounded(mid, b, d, upper, fromBackEdge, origdelta, reason) and
|
||||
b instanceof SemZeroBound and
|
||||
d >= 0 and
|
||||
delta = d / factor
|
||||
)
|
||||
or
|
||||
exists(NarrowingCastExpr cast |
|
||||
cast = e and
|
||||
safeNarrowingCast(cast, upper.booleanNot()) and
|
||||
boundedCastExpr(cast, b, delta, upper, fromBackEdge, origdelta, reason)
|
||||
)
|
||||
or
|
||||
exists(
|
||||
SemConditionalExpr cond, int d1, int d2, boolean fbe1, boolean fbe2, int od1, int od2,
|
||||
SemReason r1, SemReason r2
|
||||
|
|
||||
cond = e and
|
||||
boundedConditionalExpr(cond, b, upper, true, d1, fbe1, od1, r1) and
|
||||
boundedConditionalExpr(cond, b, upper, false, d2, fbe2, od2, r2) and
|
||||
(
|
||||
delta = d1 and fromBackEdge = fbe1 and origdelta = od1 and reason = r1
|
||||
or
|
||||
delta = d2 and fromBackEdge = fbe2 and origdelta = od2 and reason = r2
|
||||
)
|
||||
|
|
||||
upper = true and delta = d1.maximum(d2)
|
||||
or
|
||||
upper = false and delta = d1.minimum(d2)
|
||||
)
|
||||
)
|
||||
}
|
||||
|
||||
private predicate boundedConditionalExpr(
|
||||
SemConditionalExpr cond, SemBound b, boolean upper, boolean branch, int delta,
|
||||
boolean fromBackEdge, int origdelta, SemReason reason
|
||||
) {
|
||||
bounded(cond.getBranchExpr(branch), b, delta, upper, fromBackEdge, origdelta, reason)
|
||||
}
|
||||
import CppRangeAnalysis
|
||||
|
||||
@@ -3,86 +3,90 @@
|
||||
*/
|
||||
|
||||
private import experimental.semmle.code.cpp.semantic.Semantic
|
||||
private import RangeAnalysisStage
|
||||
private import experimental.semmle.code.cpp.semantic.analysis.FloatDelta
|
||||
|
||||
/**
|
||||
* Holds if the specified expression should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadCopy(SemExpr e) { none() }
|
||||
module CppLangImpl implements LangSig<FloatDelta> {
|
||||
/**
|
||||
* Holds if the specified expression should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadCopy(SemExpr e) { none() }
|
||||
|
||||
/**
|
||||
* Ignore the bound on this expression.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreExprBound(SemExpr e) { none() }
|
||||
/**
|
||||
* Ignore the bound on this expression.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreExprBound(SemExpr e) { none() }
|
||||
|
||||
/**
|
||||
* Ignore any inferred zero lower bound on this expression.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreZeroLowerBound(SemExpr e) { none() }
|
||||
/**
|
||||
* Ignore any inferred zero lower bound on this expression.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreZeroLowerBound(SemExpr e) { none() }
|
||||
|
||||
/**
|
||||
* Holds if the specified expression should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadArithmeticExpr(SemExpr e) { none() }
|
||||
/**
|
||||
* Holds if the specified expression should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadArithmeticExpr(SemExpr e) { none() }
|
||||
|
||||
/**
|
||||
* Holds if the specified variable should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadAssignment(SemSsaVariable v) { none() }
|
||||
/**
|
||||
* Holds if the specified variable should be excluded from the result of `ssaRead()`.
|
||||
*
|
||||
* This predicate is to keep the results identical to the original Java implementation. It should be
|
||||
* removed once we have the new implementation matching the old results exactly.
|
||||
*/
|
||||
predicate ignoreSsaReadAssignment(SemSsaVariable v) { none() }
|
||||
|
||||
/**
|
||||
* Adds additional results to `ssaRead()` that are specific to Java.
|
||||
*
|
||||
* This predicate handles propagation of offsets for post-increment and post-decrement expressions
|
||||
* in exactly the same way as the old Java implementation. Once the new implementation matches the
|
||||
* old one, we should remove this predicate and propagate deltas for all similar patterns, whether
|
||||
* or not they come from a post-increment/decrement expression.
|
||||
*/
|
||||
SemExpr specificSsaRead(SemSsaVariable v, int delta) { none() }
|
||||
/**
|
||||
* Adds additional results to `ssaRead()` that are specific to Java.
|
||||
*
|
||||
* This predicate handles propagation of offsets for post-increment and post-decrement expressions
|
||||
* in exactly the same way as the old Java implementation. Once the new implementation matches the
|
||||
* old one, we should remove this predicate and propagate deltas for all similar patterns, whether
|
||||
* or not they come from a post-increment/decrement expression.
|
||||
*/
|
||||
SemExpr specificSsaRead(SemSsaVariable v, float delta) { none() }
|
||||
|
||||
/**
|
||||
* Holds if `e >= bound` (if `upper = false`) or `e <= bound` (if `upper = true`).
|
||||
*/
|
||||
predicate hasConstantBound(SemExpr e, int bound, boolean upper) { none() }
|
||||
/**
|
||||
* Holds if `e >= bound` (if `upper = false`) or `e <= bound` (if `upper = true`).
|
||||
*/
|
||||
predicate hasConstantBound(SemExpr e, float bound, boolean upper) { none() }
|
||||
|
||||
/**
|
||||
* Holds if `e >= bound + delta` (if `upper = false`) or `e <= bound + delta` (if `upper = true`).
|
||||
*/
|
||||
predicate hasBound(SemExpr e, SemExpr bound, int delta, boolean upper) { none() }
|
||||
/**
|
||||
* Holds if `e >= bound + delta` (if `upper = false`) or `e <= bound + delta` (if `upper = true`).
|
||||
*/
|
||||
predicate hasBound(SemExpr e, SemExpr bound, float delta, boolean upper) { none() }
|
||||
|
||||
/**
|
||||
* Holds if the value of `dest` is known to be `src + delta`.
|
||||
*/
|
||||
predicate additionalValueFlowStep(SemExpr dest, SemExpr src, int delta) { none() }
|
||||
/**
|
||||
* Holds if the value of `dest` is known to be `src + delta`.
|
||||
*/
|
||||
predicate additionalValueFlowStep(SemExpr dest, SemExpr src, float delta) { none() }
|
||||
|
||||
/**
|
||||
* Gets the type that range analysis should use to track the result of the specified expression,
|
||||
* if a type other than the original type of the expression is to be used.
|
||||
*
|
||||
* This predicate is commonly used in languages that support immutable "boxed" types that are
|
||||
* actually references but whose values can be tracked as the type contained in the box.
|
||||
*/
|
||||
SemType getAlternateType(SemExpr e) { none() }
|
||||
/**
|
||||
* Gets the type that range analysis should use to track the result of the specified expression,
|
||||
* if a type other than the original type of the expression is to be used.
|
||||
*
|
||||
* This predicate is commonly used in languages that support immutable "boxed" types that are
|
||||
* actually references but whose values can be tracked as the type contained in the box.
|
||||
*/
|
||||
SemType getAlternateType(SemExpr e) { none() }
|
||||
|
||||
/**
|
||||
* Gets the type that range analysis should use to track the result of the specified source
|
||||
* variable, if a type other than the original type of the expression is to be used.
|
||||
*
|
||||
* This predicate is commonly used in languages that support immutable "boxed" types that are
|
||||
* actually references but whose values can be tracked as the type contained in the box.
|
||||
*/
|
||||
SemType getAlternateTypeForSsaVariable(SemSsaVariable var) { none() }
|
||||
/**
|
||||
* Gets the type that range analysis should use to track the result of the specified source
|
||||
* variable, if a type other than the original type of the expression is to be used.
|
||||
*
|
||||
* This predicate is commonly used in languages that support immutable "boxed" types that are
|
||||
* actually references but whose values can be tracked as the type contained in the box.
|
||||
*/
|
||||
SemType getAlternateTypeForSsaVariable(SemSsaVariable var) { none() }
|
||||
}
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -3,133 +3,138 @@
|
||||
*/
|
||||
|
||||
private import experimental.semmle.code.cpp.semantic.Semantic
|
||||
private import RangeAnalysisSpecific as Specific
|
||||
private import RangeAnalysisSpecific
|
||||
private import RangeAnalysisStage as Range
|
||||
private import ConstantAnalysis
|
||||
|
||||
/**
|
||||
* Gets an expression that equals `v - d`.
|
||||
*/
|
||||
SemExpr semSsaRead(SemSsaVariable v, int delta) {
|
||||
// There are various language-specific extension points that can be removed once we no longer
|
||||
// expect to match the original Java implementation's results exactly.
|
||||
result = v.getAUse() and delta = 0
|
||||
or
|
||||
exists(int d1, SemConstantIntegerExpr c |
|
||||
result.(SemAddExpr).hasOperands(semSsaRead(v, d1), c) and
|
||||
delta = d1 - c.getIntValue() and
|
||||
not Specific::ignoreSsaReadArithmeticExpr(result)
|
||||
)
|
||||
or
|
||||
exists(SemSubExpr sub, int d1, SemConstantIntegerExpr c |
|
||||
result = sub and
|
||||
sub.getLeftOperand() = semSsaRead(v, d1) and
|
||||
sub.getRightOperand() = c and
|
||||
delta = d1 + c.getIntValue() and
|
||||
not Specific::ignoreSsaReadArithmeticExpr(result)
|
||||
)
|
||||
or
|
||||
result = v.(SemSsaExplicitUpdate).getSourceExpr() and
|
||||
delta = 0 and
|
||||
not Specific::ignoreSsaReadAssignment(v)
|
||||
or
|
||||
result = Specific::specificSsaRead(v, delta)
|
||||
or
|
||||
result.(SemCopyValueExpr).getOperand() = semSsaRead(v, delta) and
|
||||
not Specific::ignoreSsaReadCopy(result)
|
||||
or
|
||||
result.(SemStoreExpr).getOperand() = semSsaRead(v, delta)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a condition that tests whether `v` equals `e + delta`.
|
||||
*
|
||||
* If the condition evaluates to `testIsTrue`:
|
||||
* - `isEq = true` : `v == e + delta`
|
||||
* - `isEq = false` : `v != e + delta`
|
||||
*/
|
||||
SemGuard semEqFlowCond(SemSsaVariable v, SemExpr e, int delta, boolean isEq, boolean testIsTrue) {
|
||||
exists(boolean eqpolarity |
|
||||
result.isEquality(semSsaRead(v, delta), e, eqpolarity) and
|
||||
(testIsTrue = true or testIsTrue = false) and
|
||||
eqpolarity.booleanXor(testIsTrue).booleanNot() = isEq
|
||||
)
|
||||
or
|
||||
exists(boolean testIsTrue0 |
|
||||
semImplies_v2(result, testIsTrue, semEqFlowCond(v, e, delta, isEq, testIsTrue0), testIsTrue0)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `v` is an `SsaExplicitUpdate` that equals `e + delta`.
|
||||
*/
|
||||
predicate semSsaUpdateStep(SemSsaExplicitUpdate v, SemExpr e, int delta) {
|
||||
exists(SemExpr defExpr | defExpr = v.getSourceExpr() |
|
||||
defExpr.(SemCopyValueExpr).getOperand() = e and delta = 0
|
||||
module RangeUtil<Range::DeltaSig D, Range::LangSig<D> Lang> implements Range::UtilSig<D> {
|
||||
/**
|
||||
* Gets an expression that equals `v - d`.
|
||||
*/
|
||||
SemExpr semSsaRead(SemSsaVariable v, D::Delta delta) {
|
||||
// There are various language-specific extension points that can be removed once we no longer
|
||||
// expect to match the original Java implementation's results exactly.
|
||||
result = v.getAUse() and delta = D::fromInt(0)
|
||||
or
|
||||
defExpr.(SemStoreExpr).getOperand() = e and delta = 0
|
||||
exists(D::Delta d1, SemConstantIntegerExpr c |
|
||||
result.(SemAddExpr).hasOperands(semSsaRead(v, d1), c) and
|
||||
delta = D::fromFloat(D::toFloat(d1) - c.getIntValue()) and
|
||||
not Lang::ignoreSsaReadArithmeticExpr(result)
|
||||
)
|
||||
or
|
||||
defExpr.(SemAddOneExpr).getOperand() = e and delta = 1
|
||||
exists(SemSubExpr sub, D::Delta d1, SemConstantIntegerExpr c |
|
||||
result = sub and
|
||||
sub.getLeftOperand() = semSsaRead(v, d1) and
|
||||
sub.getRightOperand() = c and
|
||||
delta = D::fromFloat(D::toFloat(d1) + c.getIntValue()) and
|
||||
not Lang::ignoreSsaReadArithmeticExpr(result)
|
||||
)
|
||||
or
|
||||
defExpr.(SemSubOneExpr).getOperand() = e and delta = -1
|
||||
result = v.(SemSsaExplicitUpdate).getSourceExpr() and
|
||||
delta = D::fromFloat(0) and
|
||||
not Lang::ignoreSsaReadAssignment(v)
|
||||
or
|
||||
e = defExpr and
|
||||
not (
|
||||
defExpr instanceof SemCopyValueExpr or
|
||||
defExpr instanceof SemStoreExpr or
|
||||
defExpr instanceof SemAddOneExpr or
|
||||
defExpr instanceof SemSubOneExpr
|
||||
) and
|
||||
delta = 0
|
||||
)
|
||||
}
|
||||
result = Lang::specificSsaRead(v, delta)
|
||||
or
|
||||
result.(SemCopyValueExpr).getOperand() = semSsaRead(v, delta) and
|
||||
not Lang::ignoreSsaReadCopy(result)
|
||||
or
|
||||
result.(SemStoreExpr).getOperand() = semSsaRead(v, delta)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `e1 + delta` equals `e2`.
|
||||
*/
|
||||
predicate semValueFlowStep(SemExpr e2, SemExpr e1, int delta) {
|
||||
e2.(SemCopyValueExpr).getOperand() = e1 and delta = 0
|
||||
or
|
||||
e2.(SemStoreExpr).getOperand() = e1 and delta = 0
|
||||
or
|
||||
e2.(SemAddOneExpr).getOperand() = e1 and delta = 1
|
||||
or
|
||||
e2.(SemSubOneExpr).getOperand() = e1 and delta = -1
|
||||
or
|
||||
Specific::additionalValueFlowStep(e2, e1, delta)
|
||||
or
|
||||
exists(SemExpr x | e2.(SemAddExpr).hasOperands(e1, x) |
|
||||
x.(SemConstantIntegerExpr).getIntValue() = delta
|
||||
)
|
||||
or
|
||||
exists(SemExpr x, SemSubExpr sub |
|
||||
e2 = sub and
|
||||
sub.getLeftOperand() = e1 and
|
||||
sub.getRightOperand() = x
|
||||
|
|
||||
x.(SemConstantIntegerExpr).getIntValue() = -delta
|
||||
)
|
||||
}
|
||||
/**
|
||||
* Gets a condition that tests whether `v` equals `e + delta`.
|
||||
*
|
||||
* If the condition evaluates to `testIsTrue`:
|
||||
* - `isEq = true` : `v == e + delta`
|
||||
* - `isEq = false` : `v != e + delta`
|
||||
*/
|
||||
SemGuard semEqFlowCond(
|
||||
SemSsaVariable v, SemExpr e, D::Delta delta, boolean isEq, boolean testIsTrue
|
||||
) {
|
||||
exists(boolean eqpolarity |
|
||||
result.isEquality(semSsaRead(v, delta), e, eqpolarity) and
|
||||
(testIsTrue = true or testIsTrue = false) and
|
||||
eqpolarity.booleanXor(testIsTrue).booleanNot() = isEq
|
||||
)
|
||||
or
|
||||
exists(boolean testIsTrue0 |
|
||||
semImplies_v2(result, testIsTrue, semEqFlowCond(v, e, delta, isEq, testIsTrue0), testIsTrue0)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets the type used to track the specified expression's range information.
|
||||
*
|
||||
* Usually, this just `e.getSemType()`, but the language can override this to track immutable boxed
|
||||
* primitive types as the underlying primitive type.
|
||||
*/
|
||||
SemType getTrackedType(SemExpr e) {
|
||||
result = Specific::getAlternateType(e)
|
||||
or
|
||||
not exists(Specific::getAlternateType(e)) and result = e.getSemType()
|
||||
}
|
||||
/**
|
||||
* Holds if `v` is an `SsaExplicitUpdate` that equals `e + delta`.
|
||||
*/
|
||||
predicate semSsaUpdateStep(SemSsaExplicitUpdate v, SemExpr e, D::Delta delta) {
|
||||
exists(SemExpr defExpr | defExpr = v.getSourceExpr() |
|
||||
defExpr.(SemCopyValueExpr).getOperand() = e and delta = D::fromFloat(0)
|
||||
or
|
||||
defExpr.(SemStoreExpr).getOperand() = e and delta = D::fromFloat(0)
|
||||
or
|
||||
defExpr.(SemAddOneExpr).getOperand() = e and delta = D::fromFloat(1)
|
||||
or
|
||||
defExpr.(SemSubOneExpr).getOperand() = e and delta = D::fromFloat(-1)
|
||||
or
|
||||
e = defExpr and
|
||||
not (
|
||||
defExpr instanceof SemCopyValueExpr or
|
||||
defExpr instanceof SemStoreExpr or
|
||||
defExpr instanceof SemAddOneExpr or
|
||||
defExpr instanceof SemSubOneExpr
|
||||
) and
|
||||
delta = D::fromFloat(0)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets the type used to track the specified source variable's range information.
|
||||
*
|
||||
* Usually, this just `e.getType()`, but the language can override this to track immutable boxed
|
||||
* primitive types as the underlying primitive type.
|
||||
*/
|
||||
SemType getTrackedTypeForSsaVariable(SemSsaVariable var) {
|
||||
result = Specific::getAlternateTypeForSsaVariable(var)
|
||||
or
|
||||
not exists(Specific::getAlternateTypeForSsaVariable(var)) and result = var.getType()
|
||||
/**
|
||||
* Holds if `e1 + delta` equals `e2`.
|
||||
*/
|
||||
predicate semValueFlowStep(SemExpr e2, SemExpr e1, D::Delta delta) {
|
||||
e2.(SemCopyValueExpr).getOperand() = e1 and delta = D::fromFloat(0)
|
||||
or
|
||||
e2.(SemStoreExpr).getOperand() = e1 and delta = D::fromFloat(0)
|
||||
or
|
||||
e2.(SemAddOneExpr).getOperand() = e1 and delta = D::fromFloat(1)
|
||||
or
|
||||
e2.(SemSubOneExpr).getOperand() = e1 and delta = D::fromFloat(-1)
|
||||
or
|
||||
Lang::additionalValueFlowStep(e2, e1, delta)
|
||||
or
|
||||
exists(SemExpr x | e2.(SemAddExpr).hasOperands(e1, x) |
|
||||
D::fromInt(x.(SemConstantIntegerExpr).getIntValue()) = delta
|
||||
)
|
||||
or
|
||||
exists(SemExpr x, SemSubExpr sub |
|
||||
e2 = sub and
|
||||
sub.getLeftOperand() = e1 and
|
||||
sub.getRightOperand() = x
|
||||
|
|
||||
D::fromInt(-x.(SemConstantIntegerExpr).getIntValue()) = delta
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets the type used to track the specified expression's range information.
|
||||
*
|
||||
* Usually, this just `e.getSemType()`, but the language can override this to track immutable boxed
|
||||
* primitive types as the underlying primitive type.
|
||||
*/
|
||||
SemType getTrackedType(SemExpr e) {
|
||||
result = Lang::getAlternateType(e)
|
||||
or
|
||||
not exists(Lang::getAlternateType(e)) and result = e.getSemType()
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets the type used to track the specified source variable's range information.
|
||||
*
|
||||
* Usually, this just `e.getType()`, but the language can override this to track immutable boxed
|
||||
* primitive types as the underlying primitive type.
|
||||
*/
|
||||
SemType getTrackedTypeForSsaVariable(SemSsaVariable var) {
|
||||
result = Lang::getAlternateTypeForSsaVariable(var)
|
||||
or
|
||||
not exists(Lang::getAlternateTypeForSsaVariable(var)) and result = var.getType()
|
||||
}
|
||||
}
|
||||
|
||||
@@ -6,488 +6,494 @@
|
||||
* three-valued domain `{negative, zero, positive}`.
|
||||
*/
|
||||
|
||||
private import RangeAnalysisStage
|
||||
private import SignAnalysisSpecific as Specific
|
||||
private import experimental.semmle.code.cpp.semantic.Semantic
|
||||
private import ConstantAnalysis
|
||||
private import RangeUtils
|
||||
private import Sign
|
||||
|
||||
/**
|
||||
* An SSA definition for which the analysis can compute the sign.
|
||||
*
|
||||
* The actual computation of the sign is done in an override of the `getSign()` predicate. The
|
||||
* charpred of any subclass must _not_ invoke `getSign()`, directly or indirectly. This ensures
|
||||
* that the charpred does not introduce negative recursion. The `getSign()` predicate may be
|
||||
* recursive.
|
||||
*/
|
||||
abstract private class SignDef instanceof SemSsaVariable {
|
||||
final string toString() { result = super.toString() }
|
||||
module SignAnalysis<DeltaSig D, UtilSig<D> Utils> {
|
||||
/**
|
||||
* An SSA definition for which the analysis can compute the sign.
|
||||
*
|
||||
* The actual computation of the sign is done in an override of the `getSign()` predicate. The
|
||||
* charpred of any subclass must _not_ invoke `getSign()`, directly or indirectly. This ensures
|
||||
* that the charpred does not introduce negative recursion. The `getSign()` predicate may be
|
||||
* recursive.
|
||||
*/
|
||||
abstract private class SignDef instanceof SemSsaVariable {
|
||||
final string toString() { result = super.toString() }
|
||||
|
||||
/** Gets the possible signs of this SSA definition. */
|
||||
abstract Sign getSign();
|
||||
}
|
||||
|
||||
/** An SSA definition whose sign is computed based on standard flow. */
|
||||
abstract private class FlowSignDef extends SignDef {
|
||||
abstract override Sign getSign();
|
||||
}
|
||||
|
||||
/** An SSA definition whose sign is determined by the sign of that definitions source expression. */
|
||||
private class ExplicitSignDef extends FlowSignDef instanceof SemSsaExplicitUpdate {
|
||||
final override Sign getSign() { result = semExprSign(super.getSourceExpr()) }
|
||||
}
|
||||
|
||||
/** An SSA Phi definition, whose sign is the union of the signs of its inputs. */
|
||||
private class PhiSignDef extends FlowSignDef instanceof SemSsaPhiNode {
|
||||
final override Sign getSign() {
|
||||
exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge |
|
||||
edge.phiInput(this, inp) and
|
||||
result = semSsaSign(inp, edge)
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
/** An SSA definition whose sign is computed by a language-specific implementation. */
|
||||
abstract class CustomSignDef extends SignDef {
|
||||
abstract override Sign getSign();
|
||||
}
|
||||
|
||||
/**
|
||||
* An expression for which the analysis can compute the sign.
|
||||
*
|
||||
* The actual computation of the sign is done in an override of the `getSign()` predicate. The
|
||||
* charpred of any subclass must _not_ invoke `getSign()`, directly or indirectly. This ensures
|
||||
* that the charpred does not introduce negative recursion. The `getSign()` predicate may be
|
||||
* recursive.
|
||||
*
|
||||
* Concrete implementations extend one of the following subclasses:
|
||||
* - `ConstantSignExpr`, for expressions with a compile-time constant value.
|
||||
* - `FlowSignExpr`, for expressions whose sign can be computed from the signs of their operands.
|
||||
* - `CustomsignExpr`, for expressions whose sign can be computed by a language-specific
|
||||
* implementation.
|
||||
*
|
||||
* If the same expression matches more than one of the above subclasses, the sign is computed as
|
||||
* follows:
|
||||
* - The sign of a `ConstantSignExpr` is computed solely from `ConstantSignExpr.getSign()`,
|
||||
* regardless of any other subclasses.
|
||||
* - If a non-`ConstantSignExpr` expression matches exactly one of `FlowSignExpr` or
|
||||
* `CustomSignExpr`, the sign is computed by that class' `getSign()` predicate.
|
||||
* - If a non-`ConstantSignExpr` expression matches both `FlowSignExpr` and `CustomSignExpr`, the
|
||||
* sign is the _intersection_ of the signs of those two classes' `getSign()` predicates. Thus,
|
||||
* both classes have the opportunity to _restrict_ the set of possible signs, not to generate new
|
||||
* possible signs.
|
||||
* - If an expression does not match any of the three subclasses, then it can have any sign.
|
||||
*
|
||||
* Note that the `getSign()` predicate is introduced only in subclasses of `SignExpr`.
|
||||
*/
|
||||
abstract class SignExpr instanceof SemExpr {
|
||||
SignExpr() { not Specific::ignoreExprSign(this) }
|
||||
|
||||
final string toString() { result = super.toString() }
|
||||
|
||||
abstract Sign getSign();
|
||||
}
|
||||
|
||||
/** An expression whose sign is determined by its constant numeric value. */
|
||||
private class ConstantSignExpr extends SignExpr {
|
||||
ConstantSignExpr() {
|
||||
this instanceof SemConstantIntegerExpr or
|
||||
exists(this.(SemNumericLiteralExpr).getApproximateFloatValue())
|
||||
/** Gets the possible signs of this SSA definition. */
|
||||
abstract Sign getSign();
|
||||
}
|
||||
|
||||
final override Sign getSign() {
|
||||
exists(int i | this.(SemConstantIntegerExpr).getIntValue() = i |
|
||||
i < 0 and result = TNeg()
|
||||
/** An SSA definition whose sign is computed based on standard flow. */
|
||||
abstract private class FlowSignDef extends SignDef {
|
||||
abstract override Sign getSign();
|
||||
}
|
||||
|
||||
/** An SSA definition whose sign is determined by the sign of that definitions source expression. */
|
||||
private class ExplicitSignDef extends FlowSignDef instanceof SemSsaExplicitUpdate {
|
||||
final override Sign getSign() { result = semExprSign(super.getSourceExpr()) }
|
||||
}
|
||||
|
||||
/** An SSA Phi definition, whose sign is the union of the signs of its inputs. */
|
||||
private class PhiSignDef extends FlowSignDef instanceof SemSsaPhiNode {
|
||||
final override Sign getSign() {
|
||||
exists(SemSsaVariable inp, SemSsaReadPositionPhiInputEdge edge |
|
||||
edge.phiInput(this, inp) and
|
||||
result = semSsaSign(inp, edge)
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
/** An SSA definition whose sign is computed by a language-specific implementation. */
|
||||
abstract class CustomSignDef extends SignDef {
|
||||
abstract override Sign getSign();
|
||||
}
|
||||
|
||||
/**
|
||||
* An expression for which the analysis can compute the sign.
|
||||
*
|
||||
* The actual computation of the sign is done in an override of the `getSign()` predicate. The
|
||||
* charpred of any subclass must _not_ invoke `getSign()`, directly or indirectly. This ensures
|
||||
* that the charpred does not introduce negative recursion. The `getSign()` predicate may be
|
||||
* recursive.
|
||||
*
|
||||
* Concrete implementations extend one of the following subclasses:
|
||||
* - `ConstantSignExpr`, for expressions with a compile-time constant value.
|
||||
* - `FlowSignExpr`, for expressions whose sign can be computed from the signs of their operands.
|
||||
* - `CustomsignExpr`, for expressions whose sign can be computed by a language-specific
|
||||
* implementation.
|
||||
*
|
||||
* If the same expression matches more than one of the above subclasses, the sign is computed as
|
||||
* follows:
|
||||
* - The sign of a `ConstantSignExpr` is computed solely from `ConstantSignExpr.getSign()`,
|
||||
* regardless of any other subclasses.
|
||||
* - If a non-`ConstantSignExpr` expression matches exactly one of `FlowSignExpr` or
|
||||
* `CustomSignExpr`, the sign is computed by that class' `getSign()` predicate.
|
||||
* - If a non-`ConstantSignExpr` expression matches both `FlowSignExpr` and `CustomSignExpr`, the
|
||||
* sign is the _intersection_ of the signs of those two classes' `getSign()` predicates. Thus,
|
||||
* both classes have the opportunity to _restrict_ the set of possible signs, not to generate new
|
||||
* possible signs.
|
||||
* - If an expression does not match any of the three subclasses, then it can have any sign.
|
||||
*
|
||||
* Note that the `getSign()` predicate is introduced only in subclasses of `SignExpr`.
|
||||
*/
|
||||
abstract class SignExpr instanceof SemExpr {
|
||||
SignExpr() { not Specific::ignoreExprSign(this) }
|
||||
|
||||
final string toString() { result = super.toString() }
|
||||
|
||||
abstract Sign getSign();
|
||||
}
|
||||
|
||||
/** An expression whose sign is determined by its constant numeric value. */
|
||||
private class ConstantSignExpr extends SignExpr {
|
||||
ConstantSignExpr() {
|
||||
this instanceof SemConstantIntegerExpr or
|
||||
exists(this.(SemNumericLiteralExpr).getApproximateFloatValue())
|
||||
}
|
||||
|
||||
final override Sign getSign() {
|
||||
exists(int i | this.(SemConstantIntegerExpr).getIntValue() = i |
|
||||
i < 0 and result = TNeg()
|
||||
or
|
||||
i = 0 and result = TZero()
|
||||
or
|
||||
i > 0 and result = TPos()
|
||||
)
|
||||
or
|
||||
i = 0 and result = TZero()
|
||||
or
|
||||
i > 0 and result = TPos()
|
||||
)
|
||||
or
|
||||
not exists(this.(SemConstantIntegerExpr).getIntValue()) and
|
||||
exists(float f | f = this.(SemNumericLiteralExpr).getApproximateFloatValue() |
|
||||
f < 0 and result = TNeg()
|
||||
or
|
||||
f = 0 and result = TZero()
|
||||
or
|
||||
f > 0 and result = TPos()
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
abstract private class NonConstantSignExpr extends SignExpr {
|
||||
NonConstantSignExpr() { not this instanceof ConstantSignExpr }
|
||||
|
||||
final override Sign getSign() {
|
||||
// The result is the _intersection_ of the signs computed from flow and by the language.
|
||||
(result = this.(FlowSignExpr).getSignRestriction() or not this instanceof FlowSignExpr) and
|
||||
(result = this.(CustomSignExpr).getSignRestriction() or not this instanceof CustomSignExpr)
|
||||
}
|
||||
}
|
||||
|
||||
/** An expression whose sign is computed from the signs of its operands. */
|
||||
abstract private class FlowSignExpr extends NonConstantSignExpr {
|
||||
abstract Sign getSignRestriction();
|
||||
}
|
||||
|
||||
/** An expression whose sign is computed by a language-specific implementation. */
|
||||
abstract class CustomSignExpr extends NonConstantSignExpr {
|
||||
abstract Sign getSignRestriction();
|
||||
}
|
||||
|
||||
/** An expression whose sign is unknown. */
|
||||
private class UnknownSignExpr extends SignExpr {
|
||||
UnknownSignExpr() {
|
||||
not this instanceof FlowSignExpr and
|
||||
not this instanceof CustomSignExpr and
|
||||
not this instanceof ConstantSignExpr and
|
||||
(
|
||||
// Only track numeric types.
|
||||
getTrackedType(this) instanceof SemNumericType
|
||||
or
|
||||
// Unless the language says to track this expression anyway.
|
||||
Specific::trackUnknownNonNumericExpr(this)
|
||||
)
|
||||
not exists(this.(SemConstantIntegerExpr).getIntValue()) and
|
||||
exists(float f | f = this.(SemNumericLiteralExpr).getApproximateFloatValue() |
|
||||
f < 0 and result = TNeg()
|
||||
or
|
||||
f = 0 and result = TZero()
|
||||
or
|
||||
f > 0 and result = TPos()
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
final override Sign getSign() { semAnySign(result) }
|
||||
}
|
||||
abstract private class NonConstantSignExpr extends SignExpr {
|
||||
NonConstantSignExpr() { not this instanceof ConstantSignExpr }
|
||||
|
||||
/**
|
||||
* A `Load` expression whose sign is computed from the sign of its SSA definition, restricted by
|
||||
* inference from any intervening guards.
|
||||
*/
|
||||
class UseSignExpr extends FlowSignExpr {
|
||||
SemSsaVariable v;
|
||||
|
||||
UseSignExpr() { v.getAUse() = this }
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
// Propagate via SSA
|
||||
// Propagate the sign from the def of `v`, incorporating any inference from guards.
|
||||
result = semSsaSign(v, any(SemSsaReadPositionBlock bb | bb.getAnExpr() = this))
|
||||
or
|
||||
// No block for this read. Just use the sign of the def.
|
||||
// REVIEW: How can this happen?
|
||||
not exists(SemSsaReadPositionBlock bb | bb.getAnExpr() = this) and
|
||||
result = semSsaDefSign(v)
|
||||
final override Sign getSign() {
|
||||
// The result is the _intersection_ of the signs computed from flow and by the language.
|
||||
(result = this.(FlowSignExpr).getSignRestriction() or not this instanceof FlowSignExpr) and
|
||||
(result = this.(CustomSignExpr).getSignRestriction() or not this instanceof CustomSignExpr)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/** A binary expression whose sign is computed from the signs of its operands. */
|
||||
private class BinarySignExpr extends FlowSignExpr {
|
||||
SemBinaryExpr binary;
|
||||
/** An expression whose sign is computed from the signs of its operands. */
|
||||
abstract private class FlowSignExpr extends NonConstantSignExpr {
|
||||
abstract Sign getSignRestriction();
|
||||
}
|
||||
|
||||
BinarySignExpr() { binary = this }
|
||||
/** An expression whose sign is computed by a language-specific implementation. */
|
||||
abstract class CustomSignExpr extends NonConstantSignExpr {
|
||||
abstract Sign getSignRestriction();
|
||||
}
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
exists(SemExpr left, SemExpr right |
|
||||
binaryExprOperands(binary, left, right) and
|
||||
/** An expression whose sign is unknown. */
|
||||
private class UnknownSignExpr extends SignExpr {
|
||||
UnknownSignExpr() {
|
||||
not this instanceof FlowSignExpr and
|
||||
not this instanceof CustomSignExpr and
|
||||
not this instanceof ConstantSignExpr and
|
||||
(
|
||||
// Only track numeric types.
|
||||
Utils::getTrackedType(this) instanceof SemNumericType
|
||||
or
|
||||
// Unless the language says to track this expression anyway.
|
||||
Specific::trackUnknownNonNumericExpr(this)
|
||||
)
|
||||
}
|
||||
|
||||
final override Sign getSign() { semAnySign(result) }
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Load` expression whose sign is computed from the sign of its SSA definition, restricted by
|
||||
* inference from any intervening guards.
|
||||
*/
|
||||
class UseSignExpr extends FlowSignExpr {
|
||||
SemSsaVariable v;
|
||||
|
||||
UseSignExpr() { v.getAUse() = this }
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
// Propagate via SSA
|
||||
// Propagate the sign from the def of `v`, incorporating any inference from guards.
|
||||
result = semSsaSign(v, any(SemSsaReadPositionBlock bb | bb.getAnExpr() = this))
|
||||
or
|
||||
// No block for this read. Just use the sign of the def.
|
||||
// REVIEW: How can this happen?
|
||||
not exists(SemSsaReadPositionBlock bb | bb.getAnExpr() = this) and
|
||||
result = semSsaDefSign(v)
|
||||
}
|
||||
}
|
||||
|
||||
/** A binary expression whose sign is computed from the signs of its operands. */
|
||||
private class BinarySignExpr extends FlowSignExpr {
|
||||
SemBinaryExpr binary;
|
||||
|
||||
BinarySignExpr() { binary = this }
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
exists(SemExpr left, SemExpr right |
|
||||
binaryExprOperands(binary, left, right) and
|
||||
result =
|
||||
semExprSign(pragma[only_bind_out](left))
|
||||
.applyBinaryOp(semExprSign(pragma[only_bind_out](right)), binary.getOpcode())
|
||||
)
|
||||
or
|
||||
exists(SemDivExpr div | div = binary |
|
||||
result = semExprSign(div.getLeftOperand()) and
|
||||
result != TZero() and
|
||||
div.getRightOperand().(SemFloatingPointLiteralExpr).getFloatValue() = 0
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
pragma[nomagic]
|
||||
private predicate binaryExprOperands(SemBinaryExpr binary, SemExpr left, SemExpr right) {
|
||||
binary.getLeftOperand() = left and binary.getRightOperand() = right
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert`, `Box`, or `Unbox` expression.
|
||||
*/
|
||||
private class SemCastExpr instanceof SemUnaryExpr {
|
||||
string toString() { result = super.toString() }
|
||||
|
||||
SemCastExpr() {
|
||||
this instanceof SemConvertExpr
|
||||
or
|
||||
this instanceof SemBoxExpr
|
||||
or
|
||||
this instanceof SemUnboxExpr
|
||||
}
|
||||
}
|
||||
|
||||
/** A unary expression whose sign is computed from the sign of its operand. */
|
||||
private class UnarySignExpr extends FlowSignExpr {
|
||||
SemUnaryExpr unary;
|
||||
|
||||
UnarySignExpr() { unary = this and not this instanceof SemCastExpr }
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
result =
|
||||
semExprSign(pragma[only_bind_out](left))
|
||||
.applyBinaryOp(semExprSign(pragma[only_bind_out](right)), binary.getOpcode())
|
||||
)
|
||||
or
|
||||
exists(SemDivExpr div | div = binary |
|
||||
result = semExprSign(div.getLeftOperand()) and
|
||||
result != TZero() and
|
||||
div.getRightOperand().(SemFloatingPointLiteralExpr).getFloatValue() = 0
|
||||
semExprSign(pragma[only_bind_out](unary.getOperand())).applyUnaryOp(unary.getOpcode())
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert`, `Box`, or `Unbox` expression, whose sign is computed based on
|
||||
* the sign of its operand and the source and destination types.
|
||||
*/
|
||||
abstract private class CastSignExpr extends FlowSignExpr {
|
||||
SemUnaryExpr cast;
|
||||
|
||||
CastSignExpr() { cast = this and cast instanceof SemCastExpr }
|
||||
|
||||
override Sign getSignRestriction() { result = semExprSign(cast.getOperand()) }
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert` expression.
|
||||
*/
|
||||
private class ConvertSignExpr extends CastSignExpr {
|
||||
override SemConvertExpr cast;
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Box` expression.
|
||||
*/
|
||||
private class BoxSignExpr extends CastSignExpr {
|
||||
override SemBoxExpr cast;
|
||||
}
|
||||
|
||||
/**
|
||||
* An `Unbox` expression.
|
||||
*/
|
||||
private class UnboxSignExpr extends CastSignExpr {
|
||||
override SemUnboxExpr cast;
|
||||
|
||||
UnboxSignExpr() {
|
||||
exists(SemType fromType | fromType = Utils::getTrackedType(cast.getOperand()) |
|
||||
// Only numeric source types are handled here.
|
||||
fromType instanceof SemNumericType
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
private predicate unknownSign(SemExpr e) { e instanceof UnknownSignExpr }
|
||||
|
||||
/**
|
||||
* Holds if `lowerbound` is a lower bound for `v` at `pos`. This is restricted
|
||||
* to only include bounds for which we might determine a sign.
|
||||
*/
|
||||
private predicate lowerBound(
|
||||
SemExpr lowerbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isStrict
|
||||
) {
|
||||
exists(boolean testIsTrue, SemRelationalExpr comp |
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(semGetComparisonGuard(comp), pos, testIsTrue) and
|
||||
not unknownSign(lowerbound)
|
||||
|
|
||||
testIsTrue = true and
|
||||
comp.getLesserOperand() = lowerbound and
|
||||
comp.getGreaterOperand() = Utils::semSsaRead(v, D::fromInt(0)) and
|
||||
(if comp.isStrict() then isStrict = true else isStrict = false)
|
||||
or
|
||||
testIsTrue = false and
|
||||
comp.getGreaterOperand() = lowerbound and
|
||||
comp.getLesserOperand() = Utils::semSsaRead(v, D::fromInt(0)) and
|
||||
(if comp.isStrict() then isStrict = false else isStrict = true)
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
pragma[nomagic]
|
||||
private predicate binaryExprOperands(SemBinaryExpr binary, SemExpr left, SemExpr right) {
|
||||
binary.getLeftOperand() = left and binary.getRightOperand() = right
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert`, `Box`, or `Unbox` expression.
|
||||
*/
|
||||
private class SemCastExpr extends SemUnaryExpr {
|
||||
SemCastExpr() {
|
||||
this instanceof SemConvertExpr
|
||||
or
|
||||
this instanceof SemBoxExpr
|
||||
or
|
||||
this instanceof SemUnboxExpr
|
||||
}
|
||||
}
|
||||
|
||||
/** A unary expression whose sign is computed from the sign of its operand. */
|
||||
private class UnarySignExpr extends FlowSignExpr {
|
||||
SemUnaryExpr unary;
|
||||
|
||||
UnarySignExpr() { unary = this and not this instanceof SemCastExpr }
|
||||
|
||||
override Sign getSignRestriction() {
|
||||
result = semExprSign(pragma[only_bind_out](unary.getOperand())).applyUnaryOp(unary.getOpcode())
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert`, `Box`, or `Unbox` expression, whose sign is computed based on
|
||||
* the sign of its operand and the source and destination types.
|
||||
*/
|
||||
abstract private class CastSignExpr extends FlowSignExpr {
|
||||
SemUnaryExpr cast;
|
||||
|
||||
CastSignExpr() { cast = this and cast instanceof SemCastExpr }
|
||||
|
||||
override Sign getSignRestriction() { result = semExprSign(cast.getOperand()) }
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Convert` expression.
|
||||
*/
|
||||
private class ConvertSignExpr extends CastSignExpr {
|
||||
override SemConvertExpr cast;
|
||||
}
|
||||
|
||||
/**
|
||||
* A `Box` expression.
|
||||
*/
|
||||
private class BoxSignExpr extends CastSignExpr {
|
||||
override SemBoxExpr cast;
|
||||
}
|
||||
|
||||
/**
|
||||
* An `Unbox` expression.
|
||||
*/
|
||||
private class UnboxSignExpr extends CastSignExpr {
|
||||
override SemUnboxExpr cast;
|
||||
|
||||
UnboxSignExpr() {
|
||||
exists(SemType fromType | fromType = getTrackedType(cast.getOperand()) |
|
||||
// Only numeric source types are handled here.
|
||||
fromType instanceof SemNumericType
|
||||
/**
|
||||
* Holds if `upperbound` is an upper bound for `v` at `pos`. This is restricted
|
||||
* to only include bounds for which we might determine a sign.
|
||||
*/
|
||||
private predicate upperBound(
|
||||
SemExpr upperbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isStrict
|
||||
) {
|
||||
exists(boolean testIsTrue, SemRelationalExpr comp |
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(semGetComparisonGuard(comp), pos, testIsTrue) and
|
||||
not unknownSign(upperbound)
|
||||
|
|
||||
testIsTrue = true and
|
||||
comp.getGreaterOperand() = upperbound and
|
||||
comp.getLesserOperand() = Utils::semSsaRead(v, D::fromInt(0)) and
|
||||
(if comp.isStrict() then isStrict = true else isStrict = false)
|
||||
or
|
||||
testIsTrue = false and
|
||||
comp.getLesserOperand() = upperbound and
|
||||
comp.getGreaterOperand() = Utils::semSsaRead(v, D::fromInt(0)) and
|
||||
(if comp.isStrict() then isStrict = false else isStrict = true)
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
private predicate unknownSign(SemExpr e) { e instanceof UnknownSignExpr }
|
||||
/**
|
||||
* Holds if `eqbound` is an equality/inequality for `v` at `pos`. This is
|
||||
* restricted to only include bounds for which we might determine a sign. The
|
||||
* boolean `isEq` gives the polarity:
|
||||
* - `isEq = true` : `v = eqbound`
|
||||
* - `isEq = false` : `v != eqbound`
|
||||
*/
|
||||
private predicate eqBound(SemExpr eqbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isEq) {
|
||||
exists(SemGuard guard, boolean testIsTrue, boolean polarity |
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(guard, pos, testIsTrue) and
|
||||
guard.isEquality(eqbound, Utils::semSsaRead(v, D::fromInt(0)), polarity) and
|
||||
isEq = polarity.booleanXor(testIsTrue).booleanNot() and
|
||||
not unknownSign(eqbound)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `lowerbound` is a lower bound for `v` at `pos`. This is restricted
|
||||
* to only include bounds for which we might determine a sign.
|
||||
*/
|
||||
private predicate lowerBound(
|
||||
SemExpr lowerbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isStrict
|
||||
) {
|
||||
exists(boolean testIsTrue, SemRelationalExpr comp |
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(semGetComparisonGuard(comp), pos, testIsTrue) and
|
||||
not unknownSign(lowerbound)
|
||||
|
|
||||
testIsTrue = true and
|
||||
comp.getLesserOperand() = lowerbound and
|
||||
comp.getGreaterOperand() = semSsaRead(v, 0) and
|
||||
(if comp.isStrict() then isStrict = true else isStrict = false)
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that needs to be positive in
|
||||
* order for `v` to be positive.
|
||||
*/
|
||||
private predicate posBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
upperBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, true)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that needs to be negative in
|
||||
* order for `v` to be negative.
|
||||
*/
|
||||
private predicate negBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, true)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that can restrict whether `v`
|
||||
* can be zero.
|
||||
*/
|
||||
private predicate zeroBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) or
|
||||
upperBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, _)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be positive at `pos`. */
|
||||
private predicate posBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
posBound(bound, v, pos) and TPos() = semExprSign(bound)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be negative at `pos`. */
|
||||
private predicate negBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
negBound(bound, v, pos) and TNeg() = semExprSign(bound)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be zero at `pos`. */
|
||||
private predicate zeroBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) and TNeg() = semExprSign(bound)
|
||||
or
|
||||
testIsTrue = false and
|
||||
comp.getGreaterOperand() = lowerbound and
|
||||
comp.getLesserOperand() = semSsaRead(v, 0) and
|
||||
(if comp.isStrict() then isStrict = false else isStrict = true)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `upperbound` is an upper bound for `v` at `pos`. This is restricted
|
||||
* to only include bounds for which we might determine a sign.
|
||||
*/
|
||||
private predicate upperBound(
|
||||
SemExpr upperbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isStrict
|
||||
) {
|
||||
exists(boolean testIsTrue, SemRelationalExpr comp |
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(semGetComparisonGuard(comp), pos, testIsTrue) and
|
||||
not unknownSign(upperbound)
|
||||
|
|
||||
testIsTrue = true and
|
||||
comp.getGreaterOperand() = upperbound and
|
||||
comp.getLesserOperand() = semSsaRead(v, 0) and
|
||||
(if comp.isStrict() then isStrict = true else isStrict = false)
|
||||
lowerBound(bound, v, pos, false) and TZero() = semExprSign(bound)
|
||||
or
|
||||
testIsTrue = false and
|
||||
comp.getLesserOperand() = upperbound and
|
||||
comp.getGreaterOperand() = semSsaRead(v, 0) and
|
||||
(if comp.isStrict() then isStrict = false else isStrict = true)
|
||||
)
|
||||
}
|
||||
upperBound(bound, v, pos, _) and TPos() = semExprSign(bound)
|
||||
or
|
||||
upperBound(bound, v, pos, false) and TZero() = semExprSign(bound)
|
||||
or
|
||||
eqBound(bound, v, pos, true) and TZero() = semExprSign(bound)
|
||||
or
|
||||
eqBound(bound, v, pos, false) and TZero() != semExprSign(bound)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `eqbound` is an equality/inequality for `v` at `pos`. This is
|
||||
* restricted to only include bounds for which we might determine a sign. The
|
||||
* boolean `isEq` gives the polarity:
|
||||
* - `isEq = true` : `v = eqbound`
|
||||
* - `isEq = false` : `v != eqbound`
|
||||
*/
|
||||
private predicate eqBound(SemExpr eqbound, SemSsaVariable v, SemSsaReadPosition pos, boolean isEq) {
|
||||
exists(SemGuard guard, boolean testIsTrue, boolean polarity |
|
||||
/**
|
||||
* Holds if there is a bound that might restrict whether `v` has the sign `s`
|
||||
* at `pos`.
|
||||
*/
|
||||
private predicate hasGuard(SemSsaVariable v, SemSsaReadPosition pos, Sign s) {
|
||||
s = TPos() and posBound(_, v, pos)
|
||||
or
|
||||
s = TNeg() and negBound(_, v, pos)
|
||||
or
|
||||
s = TZero() and zeroBound(_, v, pos)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at `pos` based on its definition, where the sign
|
||||
* might be ruled out by a guard.
|
||||
*/
|
||||
pragma[noinline]
|
||||
private Sign guardedSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = semSsaDefSign(v) and
|
||||
pos.hasReadOfVar(v) and
|
||||
semGuardControlsSsaRead(guard, pos, testIsTrue) and
|
||||
guard.isEquality(eqbound, semSsaRead(v, 0), polarity) and
|
||||
isEq = polarity.booleanXor(testIsTrue).booleanNot() and
|
||||
not unknownSign(eqbound)
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that needs to be positive in
|
||||
* order for `v` to be positive.
|
||||
*/
|
||||
private predicate posBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
upperBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, true)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that needs to be negative in
|
||||
* order for `v` to be negative.
|
||||
*/
|
||||
private predicate negBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, true)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if `bound` is a bound for `v` at `pos` that can restrict whether `v`
|
||||
* can be zero.
|
||||
*/
|
||||
private predicate zeroBound(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) or
|
||||
upperBound(bound, v, pos, _) or
|
||||
eqBound(bound, v, pos, _)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be positive at `pos`. */
|
||||
private predicate posBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
posBound(bound, v, pos) and TPos() = semExprSign(bound)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be negative at `pos`. */
|
||||
private predicate negBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
negBound(bound, v, pos) and TNeg() = semExprSign(bound)
|
||||
}
|
||||
|
||||
/** Holds if `bound` allows `v` to be zero at `pos`. */
|
||||
private predicate zeroBoundOk(SemExpr bound, SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
lowerBound(bound, v, pos, _) and TNeg() = semExprSign(bound)
|
||||
or
|
||||
lowerBound(bound, v, pos, false) and TZero() = semExprSign(bound)
|
||||
or
|
||||
upperBound(bound, v, pos, _) and TPos() = semExprSign(bound)
|
||||
or
|
||||
upperBound(bound, v, pos, false) and TZero() = semExprSign(bound)
|
||||
or
|
||||
eqBound(bound, v, pos, true) and TZero() = semExprSign(bound)
|
||||
or
|
||||
eqBound(bound, v, pos, false) and TZero() != semExprSign(bound)
|
||||
}
|
||||
|
||||
/**
|
||||
* Holds if there is a bound that might restrict whether `v` has the sign `s`
|
||||
* at `pos`.
|
||||
*/
|
||||
private predicate hasGuard(SemSsaVariable v, SemSsaReadPosition pos, Sign s) {
|
||||
s = TPos() and posBound(_, v, pos)
|
||||
or
|
||||
s = TNeg() and negBound(_, v, pos)
|
||||
or
|
||||
s = TZero() and zeroBound(_, v, pos)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at `pos` based on its definition, where the sign
|
||||
* might be ruled out by a guard.
|
||||
*/
|
||||
pragma[noinline]
|
||||
private Sign guardedSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = semSsaDefSign(v) and
|
||||
pos.hasReadOfVar(v) and
|
||||
hasGuard(v, pos, result)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at `pos` based on its definition, where no guard
|
||||
* can rule it out.
|
||||
*/
|
||||
pragma[noinline]
|
||||
private Sign unguardedSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = semSsaDefSign(v) and
|
||||
pos.hasReadOfVar(v) and
|
||||
not hasGuard(v, pos, result)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at read position `pos`, where a guard could have
|
||||
* ruled out the sign but does not.
|
||||
* This does not check that the definition of `v` also allows the sign.
|
||||
*/
|
||||
private Sign guardedSsaSignOk(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = TPos() and
|
||||
forex(SemExpr bound | posBound(bound, v, pos) | posBoundOk(bound, v, pos))
|
||||
or
|
||||
result = TNeg() and
|
||||
forex(SemExpr bound | negBound(bound, v, pos) | negBoundOk(bound, v, pos))
|
||||
or
|
||||
result = TZero() and
|
||||
forex(SemExpr bound | zeroBound(bound, v, pos) | zeroBoundOk(bound, v, pos))
|
||||
}
|
||||
|
||||
/** Gets a possible sign for `v` at `pos`. */
|
||||
private Sign semSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = unguardedSsaSign(v, pos)
|
||||
or
|
||||
result = guardedSsaSign(v, pos) and
|
||||
result = guardedSsaSignOk(v, pos)
|
||||
}
|
||||
|
||||
/** Gets a possible sign for `v`. */
|
||||
pragma[nomagic]
|
||||
Sign semSsaDefSign(SemSsaVariable v) { result = v.(SignDef).getSign() }
|
||||
|
||||
/** Gets a possible sign for `e`. */
|
||||
cached
|
||||
Sign semExprSign(SemExpr e) {
|
||||
exists(Sign s | s = e.(SignExpr).getSign() |
|
||||
if
|
||||
getTrackedType(e) instanceof SemUnsignedIntegerType and
|
||||
s = TNeg() and
|
||||
not Specific::ignoreTypeRestrictions(e)
|
||||
then result = TPos()
|
||||
else result = s
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Dummy predicate that holds for any sign. This is added to improve readability
|
||||
* of cases where the sign is unrestricted.
|
||||
*/
|
||||
predicate semAnySign(Sign s) { any() }
|
||||
|
||||
/** Holds if `e` can be positive and cannot be negative. */
|
||||
predicate semPositive(SemExpr e) {
|
||||
semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TNeg()
|
||||
}
|
||||
|
||||
/** Holds if `e` can be negative and cannot be positive. */
|
||||
predicate semNegative(SemExpr e) {
|
||||
semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TPos()
|
||||
}
|
||||
|
||||
/** Holds if `e` is strictly positive. */
|
||||
predicate semStrictlyPositive(SemExpr e) {
|
||||
semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TZero()
|
||||
}
|
||||
|
||||
/** Holds if `e` is strictly negative. */
|
||||
predicate semStrictlyNegative(SemExpr e) {
|
||||
semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TZero()
|
||||
hasGuard(v, pos, result)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at `pos` based on its definition, where no guard
|
||||
* can rule it out.
|
||||
*/
|
||||
pragma[noinline]
|
||||
private Sign unguardedSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = semSsaDefSign(v) and
|
||||
pos.hasReadOfVar(v) and
|
||||
not hasGuard(v, pos, result)
|
||||
}
|
||||
|
||||
/**
|
||||
* Gets a possible sign of `v` at read position `pos`, where a guard could have
|
||||
* ruled out the sign but does not.
|
||||
* This does not check that the definition of `v` also allows the sign.
|
||||
*/
|
||||
private Sign guardedSsaSignOk(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = TPos() and
|
||||
forex(SemExpr bound | posBound(bound, v, pos) | posBoundOk(bound, v, pos))
|
||||
or
|
||||
result = TNeg() and
|
||||
forex(SemExpr bound | negBound(bound, v, pos) | negBoundOk(bound, v, pos))
|
||||
or
|
||||
result = TZero() and
|
||||
forex(SemExpr bound | zeroBound(bound, v, pos) | zeroBoundOk(bound, v, pos))
|
||||
}
|
||||
|
||||
/** Gets a possible sign for `v` at `pos`. */
|
||||
private Sign semSsaSign(SemSsaVariable v, SemSsaReadPosition pos) {
|
||||
result = unguardedSsaSign(v, pos)
|
||||
or
|
||||
result = guardedSsaSign(v, pos) and
|
||||
result = guardedSsaSignOk(v, pos)
|
||||
}
|
||||
|
||||
/** Gets a possible sign for `v`. */
|
||||
pragma[nomagic]
|
||||
Sign semSsaDefSign(SemSsaVariable v) { result = v.(SignDef).getSign() }
|
||||
|
||||
/** Gets a possible sign for `e`. */
|
||||
cached
|
||||
Sign semExprSign(SemExpr e) {
|
||||
exists(Sign s | s = e.(SignExpr).getSign() |
|
||||
if
|
||||
Utils::getTrackedType(e) instanceof SemUnsignedIntegerType and
|
||||
s = TNeg() and
|
||||
not Specific::ignoreTypeRestrictions(e)
|
||||
then result = TPos()
|
||||
else result = s
|
||||
)
|
||||
}
|
||||
|
||||
/**
|
||||
* Dummy predicate that holds for any sign. This is added to improve readability
|
||||
* of cases where the sign is unrestricted.
|
||||
*/
|
||||
predicate semAnySign(Sign s) { any() }
|
||||
|
||||
/** Holds if `e` can be positive and cannot be negative. */
|
||||
predicate semPositive(SemExpr e) {
|
||||
semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TNeg()
|
||||
}
|
||||
|
||||
/** Holds if `e` can be negative and cannot be positive. */
|
||||
predicate semNegative(SemExpr e) {
|
||||
semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TPos()
|
||||
}
|
||||
|
||||
/** Holds if `e` is strictly positive. */
|
||||
predicate semStrictlyPositive(SemExpr e) {
|
||||
semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TZero()
|
||||
}
|
||||
|
||||
/** Holds if `e` is strictly negative. */
|
||||
predicate semStrictlyNegative(SemExpr e) {
|
||||
semExprSign(e) = TNeg() and
|
||||
not semExprSign(e) = TPos() and
|
||||
not semExprSign(e) = TZero()
|
||||
}
|
||||
}
|
||||
|
||||
@@ -1,9 +1,16 @@
|
||||
import cpp
|
||||
import experimental.semmle.code.cpp.semantic.analysis.ModulusAnalysis
|
||||
import experimental.semmle.code.cpp.semantic.Semantic
|
||||
import experimental.semmle.code.cpp.semantic.analysis.RangeUtils
|
||||
import experimental.semmle.code.cpp.semantic.analysis.FloatDelta
|
||||
import experimental.semmle.code.cpp.semantic.analysis.RangeAnalysisSpecific
|
||||
import experimental.semmle.code.cpp.semantic.analysis.RangeAnalysis
|
||||
import semmle.code.cpp.ir.IR as IR
|
||||
import TestUtilities.InlineExpectationsTest
|
||||
|
||||
module ModulusAnalysisInstantiated =
|
||||
ModulusAnalysis<FloatDelta, Bounds, RangeUtil<FloatDelta, CppLangImpl>>;
|
||||
|
||||
class ModulusAnalysisTest extends InlineExpectationsTest {
|
||||
ModulusAnalysisTest() { this = "ModulusAnalysisTest" }
|
||||
|
||||
@@ -23,7 +30,7 @@ class ModulusAnalysisTest extends InlineExpectationsTest {
|
||||
|
||||
private string getAModString(SemExpr e) {
|
||||
exists(SemBound b, int delta, int mod |
|
||||
semExprModulus(e, b, delta, mod) and
|
||||
ModulusAnalysisInstantiated::semExprModulus(e, b, delta, mod) and
|
||||
result = b.toString() + "," + delta.toString() + "," + mod.toString() and
|
||||
not (delta = 0 and mod = 0)
|
||||
)
|
||||
|
||||
@@ -1,9 +1,14 @@
|
||||
import cpp
|
||||
import experimental.semmle.code.cpp.semantic.analysis.SignAnalysisCommon
|
||||
import experimental.semmle.code.cpp.semantic.Semantic
|
||||
import experimental.semmle.code.cpp.semantic.analysis.RangeUtils
|
||||
import experimental.semmle.code.cpp.semantic.analysis.FloatDelta
|
||||
import experimental.semmle.code.cpp.semantic.analysis.RangeAnalysisSpecific
|
||||
import semmle.code.cpp.ir.IR as IR
|
||||
import TestUtilities.InlineExpectationsTest
|
||||
|
||||
module SignAnalysisInstantiated = SignAnalysis<FloatDelta, RangeUtil<FloatDelta, CppLangImpl>>;
|
||||
|
||||
class SignAnalysisTest extends InlineExpectationsTest {
|
||||
SignAnalysisTest() { this = "SignAnalysisTest" }
|
||||
|
||||
@@ -21,4 +26,6 @@ class SignAnalysisTest extends InlineExpectationsTest {
|
||||
}
|
||||
}
|
||||
|
||||
private string getASignString(SemExpr e) { result = strictconcat(semExprSign(e).toString(), "") }
|
||||
private string getASignString(SemExpr e) {
|
||||
result = strictconcat(SignAnalysisInstantiated::semExprSign(e).toString(), "")
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user