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Fix floating point comparisons involving infinity/NaN for cross-type numeric comparisons #1150

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copybara-service merged 1 commit into from
Jul 28, 2026
Merged

Fix floating point comparisons involving infinity/NaN for cross-type numeric comparisons #1150

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48 changes: 48 additions & 0 deletions verifier/src/main/java/dev/cel/verifier/axioms/AxiomHelpers.java
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Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,9 @@

import com.microsoft.z3.BoolExpr;
import com.microsoft.z3.Context;
import com.microsoft.z3.FPExpr;
import com.microsoft.z3.IntExpr;
import com.microsoft.z3.RealExpr;

/** Helper methods for Z3 axioms operations. */
final class AxiomHelpers {
Expand Down Expand Up @@ -47,5 +49,51 @@ static IntExpr mkTruncatedMod(Context ctx, IntExpr a, IntExpr b) {
return (IntExpr) ctx.mkSub(a, ctx.mkMul(mkTruncatedDiv(ctx, a, b), b));
}

/**
* Safe comparison between a Z3 Real (from int/uint) and a Z3 FloatingPoint (double) for {@code
* <}.
*/
static BoolExpr mkRealLtFp(Context ctx, RealExpr real, FPExpr fp) {
return mkSafeFpComparison(ctx, fp, isPosInf(ctx, fp), ctx.mkLt(real, ctx.mkFPToReal(fp)));
}

/**
* Safe comparison between a Z3 FloatingPoint (double) and a Z3 Real (from int/uint) for {@code
* <}.
*/
static BoolExpr mkFpLtReal(Context ctx, FPExpr fp, RealExpr real) {
return mkSafeFpComparison(ctx, fp, isNegInf(ctx, fp), ctx.mkLt(ctx.mkFPToReal(fp), real));
}

/**
* Safe comparison between a Z3 Real (from int/uint) and a Z3 FloatingPoint (double) for {@code
* <=}.
*/
static BoolExpr mkRealLeFp(Context ctx, RealExpr real, FPExpr fp) {
return mkSafeFpComparison(ctx, fp, isPosInf(ctx, fp), ctx.mkLe(real, ctx.mkFPToReal(fp)));
}

/**
* Safe comparison between a Z3 FloatingPoint (double) and a Z3 Real (from int/uint) for {@code
* <=}.
*/
static BoolExpr mkFpLeReal(Context ctx, FPExpr fp, RealExpr real) {
return mkSafeFpComparison(ctx, fp, isNegInf(ctx, fp), ctx.mkLe(ctx.mkFPToReal(fp), real));
}

private static BoolExpr isPosInf(Context ctx, FPExpr fp) {
return ctx.mkAnd(ctx.mkFPIsInfinite(fp), ctx.mkFPIsPositive(fp));
}

private static BoolExpr isNegInf(Context ctx, FPExpr fp) {
return ctx.mkAnd(ctx.mkFPIsInfinite(fp), ctx.mkFPIsNegative(fp));
}

private static BoolExpr mkSafeFpComparison(
Context ctx, FPExpr fp, BoolExpr infCondition, BoolExpr finiteComparison) {
BoolExpr isFinite = ctx.mkNot(ctx.mkOr(ctx.mkFPIsNaN(fp), ctx.mkFPIsInfinite(fp)));
return ctx.mkOr(infCondition, ctx.mkAnd(isFinite, finiteComparison));
}

private AxiomHelpers() {}
}
28 changes: 16 additions & 12 deletions verifier/src/main/java/dev/cel/verifier/axioms/GreaterAxiom.java
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Expand Up @@ -88,33 +88,37 @@ final class GreaterAxiom {
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGt(
ctx.mkInt2Real(typeSystem.getInt(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
AxiomHelpers.mkFpLtReal(
ctx,
(FPExpr) typeSystem.getDouble(rhs),
ctx.mkInt2Real(typeSystem.getInt(lhs))))))
.addBinaryOverloadTranslator(
Comparison.GREATER_UINT64_DOUBLE.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGt(
ctx.mkInt2Real(typeSystem.getUint(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
AxiomHelpers.mkFpLtReal(
ctx,
(FPExpr) typeSystem.getDouble(rhs),
ctx.mkInt2Real(typeSystem.getUint(lhs))))))
.addBinaryOverloadTranslator(
Comparison.GREATER_DOUBLE_INT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGt(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
ctx.mkInt2Real(typeSystem.getInt(rhs))))))
AxiomHelpers.mkRealLtFp(
ctx,
ctx.mkInt2Real(typeSystem.getInt(rhs)),
(FPExpr) typeSystem.getDouble(lhs)))))
.addBinaryOverloadTranslator(
Comparison.GREATER_DOUBLE_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGt(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
ctx.mkInt2Real(typeSystem.getUint(rhs))))))
AxiomHelpers.mkRealLtFp(
ctx,
ctx.mkInt2Real(typeSystem.getUint(rhs)),
(FPExpr) typeSystem.getDouble(lhs)))))
.addBinaryOverloadTranslator(
Comparison.GREATER_INT64_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Expand Down
28 changes: 16 additions & 12 deletions verifier/src/main/java/dev/cel/verifier/axioms/GreaterEqualsAxiom.java
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Original file line number Diff line number Diff line change
Expand Up @@ -88,33 +88,37 @@ final class GreaterEqualsAxiom {
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGe(
ctx.mkInt2Real(typeSystem.getInt(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
AxiomHelpers.mkFpLeReal(
ctx,
(FPExpr) typeSystem.getDouble(rhs),
ctx.mkInt2Real(typeSystem.getInt(lhs))))))
.addBinaryOverloadTranslator(
Comparison.GREATER_EQUALS_UINT64_DOUBLE.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGe(
ctx.mkInt2Real(typeSystem.getUint(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
AxiomHelpers.mkFpLeReal(
ctx,
(FPExpr) typeSystem.getDouble(rhs),
ctx.mkInt2Real(typeSystem.getUint(lhs))))))
.addBinaryOverloadTranslator(
Comparison.GREATER_EQUALS_DOUBLE_INT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGe(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
ctx.mkInt2Real(typeSystem.getInt(rhs))))))
AxiomHelpers.mkRealLeFp(
ctx,
ctx.mkInt2Real(typeSystem.getInt(rhs)),
(FPExpr) typeSystem.getDouble(lhs)))))
.addBinaryOverloadTranslator(
Comparison.GREATER_EQUALS_DOUBLE_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkGe(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
ctx.mkInt2Real(typeSystem.getUint(rhs))))))
AxiomHelpers.mkRealLeFp(
ctx,
ctx.mkInt2Real(typeSystem.getUint(rhs)),
(FPExpr) typeSystem.getDouble(lhs)))))
.addBinaryOverloadTranslator(
Comparison.GREATER_EQUALS_INT64_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Expand Down
20 changes: 12 additions & 8 deletions verifier/src/main/java/dev/cel/verifier/axioms/LessAxiom.java
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Expand Up @@ -88,32 +88,36 @@ final class LessAxiom {
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLt(
AxiomHelpers.mkRealLtFp(
ctx,
ctx.mkInt2Real(typeSystem.getInt(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
(FPExpr) typeSystem.getDouble(rhs)))))
.addBinaryOverloadTranslator(
Comparison.LESS_UINT64_DOUBLE.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLt(
AxiomHelpers.mkRealLtFp(
ctx,
ctx.mkInt2Real(typeSystem.getUint(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
(FPExpr) typeSystem.getDouble(rhs)))))
.addBinaryOverloadTranslator(
Comparison.LESS_DOUBLE_INT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLt(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
AxiomHelpers.mkFpLtReal(
ctx,
(FPExpr) typeSystem.getDouble(lhs),
ctx.mkInt2Real(typeSystem.getInt(rhs))))))
.addBinaryOverloadTranslator(
Comparison.LESS_DOUBLE_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLt(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
AxiomHelpers.mkFpLtReal(
ctx,
(FPExpr) typeSystem.getDouble(lhs),
ctx.mkInt2Real(typeSystem.getUint(rhs))))))
.addBinaryOverloadTranslator(
Comparison.LESS_INT64_UINT64.celOverloadDecl(),
Expand Down
20 changes: 12 additions & 8 deletions verifier/src/main/java/dev/cel/verifier/axioms/LessEqualsAxiom.java
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Original file line number Diff line number Diff line change
Expand Up @@ -88,32 +88,36 @@ final class LessEqualsAxiom {
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLe(
AxiomHelpers.mkRealLeFp(
ctx,
ctx.mkInt2Real(typeSystem.getInt(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
(FPExpr) typeSystem.getDouble(rhs)))))
.addBinaryOverloadTranslator(
Comparison.LESS_EQUALS_UINT64_DOUBLE.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLe(
AxiomHelpers.mkRealLeFp(
ctx,
ctx.mkInt2Real(typeSystem.getUint(lhs)),
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(rhs))))))
(FPExpr) typeSystem.getDouble(rhs)))))
.addBinaryOverloadTranslator(
Comparison.LESS_EQUALS_DOUBLE_INT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLe(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
AxiomHelpers.mkFpLeReal(
ctx,
(FPExpr) typeSystem.getDouble(lhs),
ctx.mkInt2Real(typeSystem.getInt(rhs))))))
.addBinaryOverloadTranslator(
Comparison.LESS_EQUALS_DOUBLE_UINT64.celOverloadDecl(),
(ctx, typeSystem, constraintSink, lhs, rhs) ->
Optional.of(
typeSystem.wrapBool(
ctx.mkLe(
ctx.mkFPToReal((FPExpr) typeSystem.getDouble(lhs)),
AxiomHelpers.mkFpLeReal(
ctx,
(FPExpr) typeSystem.getDouble(lhs),
ctx.mkInt2Real(typeSystem.getUint(rhs))))))
.addBinaryOverloadTranslator(
Comparison.LESS_EQUALS_INT64_UINT64.celOverloadDecl(),
Expand Down
50 changes: 50 additions & 0 deletions verifier/src/test/java/dev/cel/verifier/CelVerifierZ3ImplTest.java
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Expand Up @@ -498,6 +498,34 @@ private enum IsAlwaysTrueTestCase {
IEEE_754_NEG_ZERO_IN_LIST("-0.0 in [0.0]"),
IEEE_754_POS_ZERO_IN_LIST("0.0 in [-0.0]"),
IEEE_754_NAN_IN_LIST_FALSE("!((0.0/0.0) in [1.0, (0.0/0.0)])"),
CROSS_TYPE_NUMERIC_LESS_NAN_INT_FALSE("!(x < (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_INT_NAN_FALSE("!((0.0 / 0.0) < x)"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_NAN_INT_FALSE("!(x <= (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_NAN_INT_FALSE("!(x > (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_NAN_INT_FALSE("!(x >= (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_NAN_UINT_FALSE("!(u < (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_UINT_NAN_FALSE("!((0.0 / 0.0) < u)"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_NAN_UINT_FALSE("!(u <= (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_NAN_UINT_FALSE("!(u > (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_NAN_UINT_FALSE("!(u >= (0.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_POS_INF_INT("x < (1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_POS_INF_INT("x <= (1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_GREATER_POS_INF_INT_FALSE("!(x > (1.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_POS_INF_INT_FALSE("!(x >= (1.0 / 0.0))"),
CROSS_TYPE_NUMERIC_GREATER_POS_INF_DOUBLE_INT("(1.0 / 0.0) > x"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_POS_INF_DOUBLE_INT("(1.0 / 0.0) >= x"),
CROSS_TYPE_NUMERIC_LESS_POS_INF_DOUBLE_INT_FALSE("!((1.0 / 0.0) < x)"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_POS_INF_DOUBLE_INT_FALSE("!((1.0 / 0.0) <= x)"),
CROSS_TYPE_NUMERIC_GREATER_NEG_INF_INT("x > (-1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_NEG_INF_INT("x >= (-1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_LESS_NEG_INF_INT_FALSE("!(x < (-1.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_NEG_INF_INT_FALSE("!(x <= (-1.0 / 0.0))"),
CROSS_TYPE_NUMERIC_LESS_NEG_INF_DOUBLE_INT("(-1.0 / 0.0) < x"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_NEG_INF_DOUBLE_INT("(-1.0 / 0.0) <= x"),
CROSS_TYPE_NUMERIC_LESS_POS_INF_UINT("u < (1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_LESS_EQUALS_POS_INF_UINT("u <= (1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_GREATER_NEG_INF_UINT("u > (-1.0 / 0.0)"),
CROSS_TYPE_NUMERIC_GREATER_EQUALS_NEG_INF_UINT("u >= (-1.0 / 0.0)"),
STRING_IN_LIST("'b' in ['a', 'b', 'c']"),
INT_IN_MAP("1 in {1: 2}"),
MAP_MISSING_KEY("!(3 in {1: 'a', 2: 'b'})"),
Expand Down Expand Up @@ -1426,6 +1454,14 @@ private enum EquivalenceTestCase {
CROSS_TYPE_NUMERIC_EQUALITY_INT_DOUBLE("request == 1.0", "request == 1"),
CROSS_TYPE_NUMERIC_EQUALITY_UINT_DOUBLE("request == 1u", "request == 1.0"),
CROSS_TYPE_NUMERIC_EQUALITY_INT_UINT("request == 1", "request == 1u"),
CROSS_TYPE_NUMERIC_NAN_LESS_INT("x < (0.0 / 0.0)", "false"),
CROSS_TYPE_NUMERIC_NAN_LESS_UINT("u < (0.0 / 0.0)", "false"),
CROSS_TYPE_NUMERIC_NAN_GREATER_INT("x > (0.0 / 0.0)", "false"),
CROSS_TYPE_NUMERIC_NAN_GREATER_UINT("u > (0.0 / 0.0)", "false"),
CROSS_TYPE_NUMERIC_POS_INF_GREATER_INT("(1.0 / 0.0) > x", "true"),
CROSS_TYPE_NUMERIC_POS_INF_LESS_INT("x < (1.0 / 0.0)", "true"),
CROSS_TYPE_NUMERIC_NEG_INF_GREATER_INT("x > (-1.0 / 0.0)", "true"),
CROSS_TYPE_NUMERIC_NEG_INF_LESS_INT("(-1.0 / 0.0) < x", "true"),
STATIC_DOUBLE_EQUALITY("d + 1.0 == d + 1.0", "d == d"),
MAP_FIELD_SELECT("string_int_map.my_field > 0", "string_int_map['my_field'] > 0"),
HETEROGENEOUS_LIST_SIZES_SAFE_FALSE("!([1, 2] == [1, 2, 3])", "true"),
Expand Down Expand Up @@ -2715,4 +2751,18 @@ public void verifyImplication_loopExceedsLimit_returnsTruncatedInconclusive() th
assertThat(result.message())
.contains("implication holds within the current loop unroll limit");
}

@Test
public void verifyImplication_symbolicNan_crossNumericComparisonReturnsFalse() throws Exception {
// Assumption: d is NaN (d != d)
CelAbstractSyntaxTree assumeAst = CEL.compile("d != d").getAst();
// Assertion: x < d is false when d is NaN
CelAbstractSyntaxTree assertAst = CEL.compile("!(x < d)").getAst();

CelVerifier verifier = CelVerifierFactory.newVerifier().build();
CelVerificationResult result =
((CelVerifierZ3Impl) verifier)
.verifyImplication(assumeAst, assertAst, ImmutableMap.of(), "Implication");
assertThat(result.status()).isEqualTo(VerificationStatus.VERIFIED);
}
}
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