diff --git a/.gas-snapshot b/.gas-snapshot
index 461ebb55..518bed2e 100644
--- a/.gas-snapshot
+++ b/.gas-snapshot
@@ -103,9 +103,10 @@ LibDecimalFloatGtTest:testGtXNotY(int256,int256,int256,int256) (runs: 5101, μ:
 LibDecimalFloatGtTest:testGtXPositiveYNegative(int256,int256,int256,int256) (runs: 5101, μ: 11846, ~: 11803)
 LibDecimalFloatGtTest:testGtXPositiveYZero(int256,int256,int256) (runs: 5101, μ: 8970, ~: 8743)
 LibDecimalFloatGtTest:testGtZero(int256,int256) (runs: 5101, μ: 3437, ~: 3437)
-LibDecimalFloatImplementationNormalizeTest:testExamples() (gas: 158985)
-LibDecimalFloatImplementationNormalizeTest:testIsNormalizedReference(int256,int256) (runs: 5101, μ: 3516, ~: 3522)
-LibDecimalFloatImplementationNormalizeTest:testNormalized(int256,int256) (runs: 5101, μ: 8977, ~: 8940)
+LibDecimalFloatImplementationNormalizeTest:testExamples() (gas: 157225)
+LibDecimalFloatImplementationNormalizeTest:testIdempotent(int256,int256) (runs: 5101, μ: 9458, ~: 9419)
+LibDecimalFloatImplementationNormalizeTest:testIsNormalizedReference(int256,int256) (runs: 5101, μ: 3549, ~: 3555)
+LibDecimalFloatImplementationNormalizeTest:testNormalized(int256,int256) (runs: 5101, μ: 8934, ~: 8895)
 LibDecimalFloatImplementationWithTargetExponentTest:testWithTargetExponentExamples() (gas: 12292)
 LibDecimalFloatImplementationWithTargetExponentTest:testWithTargetExponentLargerExponentOverflowRescaleRevert(int256,int256,int256) (runs: 5098, μ: 12560, ~: 12463)
 LibDecimalFloatImplementationWithTargetExponentTest:testWithTargetExponentLargerExponentVeryLargeDiffRevert(int256,int256,int256) (runs: 5101, μ: 11365, ~: 11301)
diff --git a/test/src/lib/implementation/LibDecimalFloatImplementation.normalize.t.sol b/test/src/lib/implementation/LibDecimalFloatImplementation.normalize.t.sol
index c7ac754d..2981dbfe 100644
--- a/test/src/lib/implementation/LibDecimalFloatImplementation.normalize.t.sol
+++ b/test/src/lib/implementation/LibDecimalFloatImplementation.normalize.t.sol
@@ -43,9 +43,22 @@ contract LibDecimalFloatImplementationNormalizeTest is Test {
         checkNormalized(1e37, 0, 1e37, 0);
         checkNormalized(type(int256).max, 0, 5.7896044618658097711785492504343953926e37, 39);
         checkNormalized(type(int256).min, 0, -5.7896044618658097711785492504343953926e37, 39);
+        checkNormalized(42, 0, 42e36, -36);
+        checkNormalized(42e36, -36, 42e36, -36);
 
         for (int256 i = 76; i >= 0; i--) {
             checkNormalized(int256(10 ** uint256(i)), 0, 1e37, i - 37);
         }
     }
+
+    /// Normalization should be idempotent.
+    function testIdempotent(int256 signedCoefficient, int256 exponent) external pure {
+        exponent = bound(exponent, EXPONENT_MIN, EXPONENT_MAX);
+        (int256 normalizedSignedCoefficient, int256 normalizedExponent) =
+            LibDecimalFloatImplementation.normalize(signedCoefficient, exponent);
+        (int256 actualSignedCoefficient, int256 actualExponent) =
+            LibDecimalFloatImplementation.normalize(normalizedSignedCoefficient, normalizedExponent);
+        assertEq(actualSignedCoefficient, normalizedSignedCoefficient);
+        assertEq(actualExponent, normalizedExponent);
+    }
 }