ModulusAnalysis shared between C# and Java

Author: tamasvajk

config/identical-files.json

@@ -66,6 +66,10 @@
     "java/ql/src/semmle/code/java/dataflow/Bound.qll",
     "csharp/ql/src/semmle/code/csharp/dataflow/Bound.qll"
   ],
+  "ModulusAnalysis Java/C#": [
+    "java/ql/src/semmle/code/java/dataflow/ModulusAnalysis.qll",
+    "csharp/ql/src/semmle/code/csharp/dataflow/ModulusAnalysis.qll"
+  ],
   "C++ SubBasicBlocks": [
     "cpp/ql/src/semmle/code/cpp/controlflow/SubBasicBlocks.qll",
     "cpp/ql/src/semmle/code/cpp/dataflow/internal/SubBasicBlocks.qll"

csharp/ql/src/semmle/code/csharp/dataflow/ModulusAnalysis.qll

@@ -0,0 +1,302 @@
+/**
+ * Provides inferences of the form: `e` equals `b + v` modulo `m` where `e` is
+ * an expression, `b` is a `Bound` (typically zero or the value of an SSA
+ * variable), and `v` is an integer in the range `[0 .. m-1]`.
+ */
+
+private import internal.rangeanalysis.ModulusAnalysisSpecific::Private
+private import Bound
+private import internal.rangeanalysis.SsaReadPositionCommon
+
+/**
+ * Holds if `e + delta` equals `v` at `pos`.
+ */
+private predicate valueFlowStepSsa(SsaVariable v, SsaReadPosition pos, Expr e, int delta) {
+  ssaUpdateStep(v, e, delta) and pos.hasReadOfVar(v)
+  or
+  exists(Guard guard, boolean testIsTrue |
+    pos.hasReadOfVar(v) and
+    guard = eqFlowCond(v, e, delta, true, testIsTrue) and
+    guardDirectlyControlsSsaRead(guard, pos, testIsTrue)
+  )
+}
+
+/**
+ * Holds if `add` is the addition of `larg` and `rarg`, neither of which are
+ * `ConstantIntegerExpr`s.
+ */
+private predicate nonConstAddition(Expr add, Expr larg, Expr rarg) {
+  exists(AddExpr a | a = add |
+    larg = a.getLhs() and
+    rarg = a.getRhs()
+  ) and
+  not larg instanceof ConstantIntegerExpr and
+  not rarg instanceof ConstantIntegerExpr
+}
+
+/**
+ * Holds if `sub` is the subtraction of `larg` and `rarg`, where `rarg` is not
+ * a `ConstantIntegerExpr`.
+ */
+private predicate nonConstSubtraction(Expr sub, Expr larg, Expr rarg) {
+  exists(SubExpr s | s = sub |
+    larg = s.getLhs() and
+    rarg = s.getRhs()
+  ) and
+  not rarg instanceof ConstantIntegerExpr
+}
+
+/** Gets an expression that is the remainder modulo `mod` of `arg`. */
+private Expr modExpr(Expr arg, int mod) {
+  exists(RemExpr rem |
+    result = rem and
+    arg = rem.getLeftOperand() and
+    rem.getRightOperand().(ConstantIntegerExpr).getIntValue() = mod and
+    mod >= 2
+  )
+  or
+  exists(ConstantIntegerExpr c |
+    mod = 2.pow([1 .. 30]) and
+    c.getIntValue() = mod - 1 and
+    result.(BitwiseAndExpr).hasOperands(arg, c)
+  )
+}
+
+/**
+ * Gets a guard that tests whether `v` is congruent with `val` modulo `mod` on
+ * its `testIsTrue` branch.
+ */
+private Guard moduloCheck(SsaVariable v, int val, int mod, boolean testIsTrue) {
+  exists(Expr rem, ConstantIntegerExpr c, int r, boolean polarity |
+    result.isEquality(rem, c, polarity) and
+    c.getIntValue() = r and
+    rem = modExpr(v.getAUse(), mod) and
+    (
+      testIsTrue = polarity and val = r
+      or
+      testIsTrue = polarity.booleanNot() and
+      mod = 2 and
+      val = 1 - r and
+      (r = 0 or r = 1)
+    )
+  )
+}
+
+/**
+ * Holds if a guard ensures that `v` at `pos` is congruent with `val` modulo `mod`.
+ */
+private predicate moduloGuardedRead(SsaVariable v, SsaReadPosition pos, int val, int mod) {
+  exists(Guard guard, boolean testIsTrue |
+    pos.hasReadOfVar(v) and
+    guard = moduloCheck(v, val, mod, testIsTrue) and
+    guardControlsSsaRead(guard, pos, testIsTrue)
+  )
+}
+
+/** Holds if `factor` is a power of 2 that divides `mask`. */
+bindingset[mask]
+private predicate andmaskFactor(int mask, int factor) {
+  mask % factor = 0 and
+  factor = 2.pow([1 .. 30])
+}
+
+/** Holds if `e` is evenly divisible by `factor`. */
+private predicate evenlyDivisibleExpr(Expr e, int factor) {
+  exists(ConstantIntegerExpr c, int k | k = c.getIntValue() |
+    e.(MulExpr).getAnOperand() = c and factor = k.abs() and factor >= 2
+    or
+    e.(LShiftExpr).getRhs() = c and factor = 2.pow(k) and k > 0
+    or
+    e.(BitwiseAndExpr).getAnOperand() = c and factor = max(int f | andmaskFactor(k, f))
+  )
+}
+
+/**
+ * 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(
+  SsaPhiNode phi, SsaVariable inp, SsaReadPositionPhiInputEdge edge, int r
+) {
+  edge.phiInput(phi, inp) and
+  edge =
+    rank[r](SsaReadPositionPhiInputEdge e | e.phiInput(phi, _) | e order by getId(e.getOrigBlock()))
+}
+
+/**
+ * Holds if `rix` is the number of input edges to `phi`.
+ */
+private predicate maxPhiInputRank(SsaPhiNode phi, int rix) {
+  rix = max(int r | rankedPhiInput(phi, _, _, r))
+}
+
+/**
+ * Gets the remainder of `val` modulo `mod`.
+ *
+ * For `mod = 0` the result equals `val` and for `mod > 1` the result is within
+ * the range `[0 .. mod-1]`.
+ */
+bindingset[val, mod]
+private int remainder(int val, int mod) {
+  mod = 0 and result = val
+  or
+  mod > 1 and result = ((val % mod) + mod) % mod
+}
+
+/**
+ * Holds if `inp` is an input to `phi` and equals `phi` modulo `mod` along `edge`.
+ */
+private predicate phiSelfModulus(
+  SsaPhiNode phi, SsaVariable inp, SsaReadPositionPhiInputEdge edge, int mod
+) {
+  exists(SsaBound phibound, int v, int m |
+    edge.phiInput(phi, inp) and
+    phibound.getSsa() = phi and
+    ssaModulus(inp, edge, phibound, v, m) and
+    mod = m.gcd(v) and
+    mod != 1
+  )
+}
+
+/**
+ * Holds if `b + val` modulo `mod` is a candidate congruence class for `phi`.
+ */
+private predicate phiModulusInit(SsaPhiNode phi, Bound b, int val, int mod) {
+  exists(SsaVariable inp, SsaReadPositionPhiInputEdge edge |
+    edge.phiInput(phi, inp) and
+    ssaModulus(inp, edge, b, val, mod)
+  )
+}
+
+/**
+ * Holds if all inputs to `phi` numbered `1` to `rix` are equal to `b + val` modulo `mod`.
+ */
+private predicate phiModulusRankStep(SsaPhiNode phi, Bound b, int val, int mod, int rix) {
+  rix = 0 and
+  phiModulusInit(phi, b, val, mod)
+  or
+  exists(SsaVariable inp, SsaReadPositionPhiInputEdge edge, int v1, int m1 |
+    mod != 1 and
+    val = remainder(v1, mod)
+  |
+    exists(int v2, int m2 |
+      rankedPhiInput(phi, inp, edge, rix) and
+      phiModulusRankStep(phi, b, v1, m1, rix - 1) and
+      ssaModulus(inp, edge, b, v2, m2) and
+      mod = m1.gcd(m2).gcd(v1 - v2)
+    )
+    or
+    exists(int m2 |
+      rankedPhiInput(phi, inp, edge, rix) and
+      phiModulusRankStep(phi, b, v1, m1, rix - 1) and
+      phiSelfModulus(phi, inp, edge, m2) and
+      mod = m1.gcd(m2)
+    )
+  )
+}
+
+/**
+ * Holds if `phi` is equal to `b + val` modulo `mod`.
+ */
+private predicate phiModulus(SsaPhiNode phi, Bound b, int val, int mod) {
+  exists(int r |
+    maxPhiInputRank(phi, r) and
+    phiModulusRankStep(phi, b, val, mod, r)
+  )
+}
+
+/**
+ * Holds if `v` at `pos` is equal to `b + val` modulo `mod`.
+ */
+private predicate ssaModulus(SsaVariable v, SsaReadPosition pos, Bound b, int val, int mod) {
+  phiModulus(v, b, val, mod) and pos.hasReadOfVar(v)
+  or
+  b.(SsaBound).getSsa() = v and pos.hasReadOfVar(v) and val = 0 and mod = 0
+  or
+  exists(Expr e, int val0, int delta |
+    exprModulus(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 ZeroBound
+}
+
+/**
+ * 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 exprModulus(Expr e, Bound b, int val, int mod) {
+  e = b.getExpr(val) and mod = 0
+  or
+  evenlyDivisibleExpr(e, mod) and val = 0 and b instanceof ZeroBound
+  or
+  exists(SsaVariable v, SsaReadPositionBlock bb |
+    ssaModulus(v, bb, b, val, mod) and
+    e = v.getAUse() and
+    getABasicBlockExpr(bb.getBlock()) = e
+  )
+  or
+  exists(Expr mid, int val0, int delta |
+    exprModulus(mid, b, val0, mod) and
+    valueFlowStep(e, mid, delta) and
+    val = remainder(val0 + delta, mod)
+  )
+  or
+  exists(ConditionalExpr 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(Bound b1, Bound 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 ZeroBound
+    or
+    b = b2 and b1 instanceof ZeroBound
+  )
+  or
+  exists(int v1, int v2, int m1, int m2 |
+    subModulus(e, true, b, v1, m1) and
+    subModulus(e, false, any(ZeroBound zb), v2, m2) and
+    mod = m1.gcd(m2) and
+    mod != 1 and
+    val = remainder(v1 - v2, mod)
+  )
+}
+
+private predicate condExprBranchModulus(
+  ConditionalExpr cond, boolean branch, Bound b, int val, int mod
+) {
+  exprModulus(cond.getTrueExpr(), b, val, mod) and branch = true
+  or
+  exprModulus(cond.getFalseExpr(), b, val, mod) and branch = false
+}
+
+private predicate addModulus(Expr add, boolean isLeft, Bound b, int val, int mod) {
+  exists(Expr larg, Expr rarg | nonConstAddition(add, larg, rarg) |
+    exprModulus(larg, b, val, mod) and isLeft = true
+    or
+    exprModulus(rarg, b, val, mod) and isLeft = false
+  )
+}
+
+private predicate subModulus(Expr sub, boolean isLeft, Bound b, int val, int mod) {
+  exists(Expr larg, Expr rarg | nonConstSubtraction(sub, larg, rarg) |
+    exprModulus(larg, b, val, mod) and isLeft = true
+    or
+    exprModulus(rarg, b, val, mod) and isLeft = false
+  )
+}