diff --git a/common/types/compare.go b/common/types/compare.go
index e1968261..2e7c999b 100644
--- a/common/types/compare.go
+++ b/common/types/compare.go
@@ -20,28 +20,54 @@ import (
 	"github.com/google/cel-go/common/types/ref"
 )
 
+// compareDoubleInt orders a double against an int by their mathematical values.
+//
+// The int is split from the double rather than converted to one: ints above 2^53 have no exact
+// double representation, so converting rounds them to a neighbouring value. Callers screen NaN
+// before dispatching here.
 func compareDoubleInt(d Double, i Int) Int {
-	if d < math.MinInt64 {
+	f := float64(d)
+	if f < math.MinInt64 {
+		return IntNegOne
+	}
+	// MaxInt64 rounds up to 2^63 as a double, which is the first value above the int64 range.
+	if f >= math.MaxInt64 {
+		return IntOne
+	}
+	// The integral part is now within the int64 range, so it converts exactly.
+	whole := math.Trunc(f)
+	if Int(whole) < i {
 		return IntNegOne
 	}
-	if d > math.MaxInt64 {
+	if Int(whole) > i {
 		return IntOne
 	}
-	return compareDouble(d, Double(i))
+	// Equal whole parts, so the remaining fraction decides the order.
+	return compareDouble(Double(f-whole), 0)
 }
 
 func compareIntDouble(i Int, d Double) Int {
 	return -compareDoubleInt(d, i)
 }
 
+// compareDoubleUint orders a double against a uint by their mathematical values, splitting the
+// double instead of converting the uint for the reason given on compareDoubleInt.
 func compareDoubleUint(d Double, u Uint) Int {
-	if d < 0 {
+	f := float64(d)
+	if f < 0 {
+		return IntNegOne
+	}
+	if f >= doubleTwoTo64 {
+		return IntOne
+	}
+	whole := math.Trunc(f)
+	if Uint(whole) < u {
 		return IntNegOne
 	}
-	if d > math.MaxUint64 {
+	if Uint(whole) > u {
 		return IntOne
 	}
-	return compareDouble(d, Double(u))
+	return compareDouble(Double(f-whole), 0)
 }
 
 func compareUintDouble(u Uint, d Double) Int {
diff --git a/common/types/double_test.go b/common/types/double_test.go
index 47e875f2..984b24b4 100644
--- a/common/types/double_test.go
+++ b/common/types/double_test.go
@@ -116,6 +116,23 @@ func TestDoubleCompare(t *testing.T) {
 			b:   Int(204),
 			out: IntOne,
 		},
+		{
+			// 2^53+1 has no double representation, so it must not compare equal to 2^53.
+			a:   Double(1 << 53),
+			b:   Int(1<<53) + 1,
+			out: IntNegOne,
+		},
+		{
+			a:   Double(1 << 53),
+			b:   Uint(1<<53) + 1,
+			out: IntNegOne,
+		},
+		{
+			// MaxInt64 rounds up to 2^63 as a double, but remains below it as an int.
+			a:   Double(1 << 63),
+			b:   Int(math.MaxInt64),
+			out: IntOne,
+		},
 		{
 			a:   Double(1),
 			b:   String("1"),
@@ -407,6 +424,26 @@ func TestDoubleEqual(t *testing.T) {
 			b:   Int(10),
 			out: False,
 		},
+		{
+			a:   Double(1 << 53),
+			b:   Int(1<<53) + 1,
+			out: False,
+		},
+		{
+			a:   Double(1 << 53),
+			b:   Uint(1<<53) + 1,
+			out: False,
+		},
+		{
+			a:   Double(1 << 63),
+			b:   Int(math.MaxInt64),
+			out: False,
+		},
+		{
+			a:   Double(math.MaxUint64),
+			b:   Uint(math.MaxUint64),
+			out: False,
+		},
 	}
 	for _, tc := range tests {
 		got := tc.a.Equal(tc.b)
diff --git a/common/types/int_test.go b/common/types/int_test.go
index 560c3dfb..a8bc9b56 100644
--- a/common/types/int_test.go
+++ b/common/types/int_test.go
@@ -129,6 +129,17 @@ func TestIntCompare(t *testing.T) {
 			b:   Double(math.MinInt64) - 1025.0,
 			out: IntOne,
 		},
+		{
+			// 2^53+1 has no double representation, so it must not compare equal to 2^53.
+			a:   Int(1<<53) + 1,
+			b:   Double(1 << 53),
+			out: IntOne,
+		},
+		{
+			a:   Int(math.MaxInt64),
+			b:   Double(1 << 63),
+			out: IntNegOne,
+		},
 		{
 			a:   Int(1),
 			b:   String("1"),
@@ -429,6 +440,16 @@ func TestIntEqual(t *testing.T) {
 			b:   Double(math.NaN()),
 			out: False,
 		},
+		{
+			a:   Int(1<<53) + 1,
+			b:   Double(1 << 53),
+			out: False,
+		},
+		{
+			a:   Int(math.MaxInt64),
+			b:   Double(1 << 63),
+			out: False,
+		},
 		{
 			a:   Int(1),
 			b:   String("1"),
diff --git a/common/types/uint_test.go b/common/types/uint_test.go
index 2484fbf3..9a174350 100644
--- a/common/types/uint_test.go
+++ b/common/types/uint_test.go
@@ -117,6 +117,17 @@ func TestUintCompare(t *testing.T) {
 			b:   Double(-1.0),
 			out: IntOne,
 		},
+		{
+			// 2^53+1 has no double representation, so it must not compare equal to 2^53.
+			a:   Uint(1<<53) + 1,
+			b:   Double(1 << 53),
+			out: IntOne,
+		},
+		{
+			a:   Uint(math.MaxUint64),
+			b:   Double(math.MaxUint64),
+			out: IntNegOne,
+		},
 		{
 			a:   Uint(1),
 			b:   String("1"),
@@ -379,6 +390,16 @@ func TestUintEqual(t *testing.T) {
 			b:   Double(math.NaN()),
 			out: False,
 		},
+		{
+			a:   Uint(1<<53) + 1,
+			b:   Double(1 << 53),
+			out: False,
+		},
+		{
+			a:   Uint(math.MaxUint64),
+			b:   Double(math.MaxUint64),
+			out: False,
+		},
 	}
 	for _, tc := range tests {
 		got := tc.a.Equal(tc.b)