diff --git a/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q.rs b/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q.rs
index 7882da55..3d2437d8 100644
--- a/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q.rs
+++ b/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q.rs
@@ -124,9 +124,9 @@ impl Euler1qFamily {
 /// normalized angle is numerically zero.
 ///
 /// `RZ(a + 2*pi*k) = (-1)^k * RZ(a)`, so every removed `2*pi` contributes a
-/// `pi` phase shift. Solving `angle = normalized + 2*pi*k` with
-/// `normalized in (-pi, pi]` in one step makes the compensation happen exactly
-/// once, including the `-pi -> +pi` boundary (`k = -1`).
+/// `pi` phase shift. The normalizer tracks `angle = normalized + 2*pi*k`
+/// through boundary corrections and applies the phase compensation once,
+/// including the `-pi -> +pi` boundary (`k = -1`).
 fn push_normalized_rz(
     angle: f64,
     gates: &mut SmallVec<[Euler1qGate; 5]>,
@@ -142,8 +142,18 @@ fn normalize_rotation_angle(angle: f64, phase: &mut f64) -> Result<f64, Compiler
             "euler 1q synthesis received a non-finite rotation angle: {angle}"
         )));
     }
-    let k = ((angle - PI) / TWO_PI).ceil();
-    let normalized = angle - TWO_PI * k;
+    let mut k = ((angle - PI) / TWO_PI).ceil();
+    let mut normalized = angle - TWO_PI * k;
+    // Rounding in the quotient or subtraction can cross a canonical boundary,
+    // e.g. the float just above -PI can normalize to the float just above PI.
+    // Keep the removed turn count in sync to preserve the scalar phase.
+    if normalized <= -PI {
+        normalized += TWO_PI;
+        k -= 1.0;
+    } else if normalized > PI {
+        normalized -= TWO_PI;
+        k += 1.0;
+    }
     *phase += k * PI;
     Ok(normalized)
 }
diff --git a/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q_test.rs b/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q_test.rs
index 416764a7..04b40157 100644
--- a/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q_test.rs
+++ b/crates/cqlib-core/src/compile/transform/decompose/unitary/euler_1q_test.rs
@@ -17,8 +17,8 @@ use ndarray::Array2;
 use num_complex::Complex64;
 
 use super::{
-    EULER_ANGLE_EPS, Euler1qCandidate, Euler1qFamily, Euler1qGate, push_normalized_rz,
-    synthesize_euler_1q_candidates,
+    EULER_ANGLE_EPS, Euler1qCandidate, Euler1qFamily, Euler1qGate, normalize_rotation_angle,
+    push_normalized_rz, synthesize_euler_1q_candidates,
 };
 use crate::circuit::StandardGate;
 use crate::circuit::test_utils::assert_matrix_approx_eq;
@@ -28,6 +28,41 @@ use crate::compile::transform::decompose::unitary::unitary_1q::{
 
 const MATRIX_EQ_EPS: f64 = 1e-12;
 
+fn pi_ulp_boundaries() -> [f64; 6] {
+    let below_pi = f64::from_bits(PI.to_bits() - 1);
+    let above_pi = f64::from_bits(PI.to_bits() + 1);
+    [below_pi, PI, above_pi, -below_pi, -PI, -above_pi]
+}
+
+#[test]
+fn normalize_rotation_angle_handles_pi_ulp_boundaries() {
+    for angle in pi_ulp_boundaries() {
+        let mut phase = 0.0;
+        let normalized = normalize_rotation_angle(angle, &mut phase).unwrap();
+        assert!(
+            normalized > -PI && normalized <= PI,
+            "input={angle:.17e}, normalized={normalized:.17e}, bits={:#018x}",
+            normalized.to_bits()
+        );
+    }
+}
+
+#[test]
+fn normalize_rotation_angle_preserves_phase_at_pi_ulp_boundaries() {
+    for angle in pi_ulp_boundaries() {
+        let initial_phase = 0.37;
+        let mut phase = initial_phase;
+        let normalized = normalize_rotation_angle(angle, &mut phase).unwrap();
+        for gate in [StandardGate::RX, StandardGate::RY, StandardGate::RZ] {
+            let expected = gate.matrix(&[angle]).unwrap().into_owned()
+                * Complex64::new(0.0, initial_phase).exp();
+            let actual =
+                gate.matrix(&[normalized]).unwrap().into_owned() * Complex64::new(0.0, phase).exp();
+            assert_matrix_approx_eq(&actual, &expected, MATRIX_EQ_EPS);
+        }
+    }
+}
+
 fn decomposition(theta: f64, phi: f64, lambda: f64) -> OneQubitUnitaryDecomposition {
     OneQubitUnitaryDecomposition {
         theta,
@@ -462,7 +497,11 @@ fn assert_xyx_synthesis(first: f64, middle: f64, last: f64, expected_ops: usize)
     assert_matrix_approx_eq(&candidate_matrix(candidate), &source, MATRIX_EQ_EPS);
     for gate in &candidate.gates {
         let angle = gate.param.unwrap();
-        assert!(angle > -PI && angle <= PI);
+        assert!(
+            angle > -PI && angle <= PI,
+            "XYX({first}, {middle}, {last}): gate={gate:?}, angle={angle:.17e}, bits={:#018x}",
+            angle.to_bits()
+        );
         assert!(angle.abs() > EULER_ANGLE_EPS);
     }
 }