diff --git a/ecc_rs.pyi b/ecc_rs.pyi
index b8bd9c2..a516e4d 100644
--- a/ecc_rs.pyi
+++ b/ecc_rs.pyi
@@ -2,5 +2,50 @@
 
 point = tuple[int, int]
 
-def add(p1: point, p2: point) -> point: ...
-def multiply(point: point, n: int) -> point: ...
+def add(p1: point, p2: point) -> point:
+    """
+    Adds two points on the SM2 elliptic curve.
+
+    Performs point addition on the SM2 curve defined by `sm2p256v1()`.
+
+    Args:
+        p1 (point): A tuple representing the x and y coordinates of the first point.
+        p2 (point): A tuple representing the x and y coordinates of the second point.
+
+    Raises:
+        Panic: If the x or y coordinates of either point are not valid on the curve.
+
+    Returns:
+        point: A tuple representing the x and y coordinates of the resulting point after addition.
+
+    Example:
+        >>> p1 = (x1, y1)
+        >>> p2 = (x2, y2)
+        >>> result = add(p1, p2)
+    """
+    ...
+
+def multiply(point: point, n: int) -> point:
+    """
+    multiply(point, n)
+
+    Performs scalar multiplication of a point on the SM2 curve.
+
+    performs the multiplication operation on the SM2 curve defined by `sm2p256v1()`.
+
+    Args:
+        point (point): representing the x and y coordinates of the point.
+        n (int): representing the scalar to multiply the point by.
+
+    Raises:
+        Panic: If the x or y coordinates of the point are not less than the curve parameter `p`.
+
+    Returns:
+        point: representing the x and y coordinates of the result point.
+
+    Example:
+        >>> point = (g, g)
+        >>> n = 10
+        >>> result = multiply(point, n)
+    """
+    ...
diff --git a/readme.md b/readme.md
new file mode 100644
index 0000000..3871c33
--- /dev/null
+++ b/readme.md
@@ -0,0 +1,4 @@
+# ecc_rs
+
+a simple rust implementation of SM2 binding for python.  
+powered by pyo3.
diff --git a/src/lib.rs b/src/lib.rs
index 06688d0..f799ce0 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -325,12 +325,12 @@ fn add(p1: (BigUint, BigUint), p2: (BigUint, BigUint)) -> (BigUint, BigUint) {
     let x2 = p2.0;
     let y2 = p2.1;
 
-    // 检查 x 和 y 是否小于曲线参数 p
-    if x1 >= curve.p || y1 >= curve.p {
-        panic!("Point p1 coordinates are out of range");
-    }
-    if x2 >= curve.p || y2 >= curve.p {
-        panic!("Point p2 coordinates are out of range");
+    // Check if x and y are less than the curve parameter p
+    match (x1 >= curve.p, y1 >= curve.p, x2 >= curve.p, y2 >= curve.p) {
+        (true, _, _, _) | (_, true, _, _) | (_, _, true, _) | (_, _, _, true) => {
+            panic!("Point coordinates are out of range");
+        }
+        _ => (),
     }
 
     let point1 = Point {
@@ -351,8 +351,18 @@ fn add(p1: (BigUint, BigUint), p2: (BigUint, BigUint)) -> (BigUint, BigUint) {
 
 /// SM2 multiply
 #[pyfunction]
-fn multiply(point: (BigUint, BigUint), n: BigUint) -> (BigUint, BigUint) {
+fn multiply(point: (BigUint, BigUint), mut n: BigUint) -> (BigUint, BigUint) {
     let curve = sm2p256v1();
+
+    if n >= curve.n {
+        n %= &curve.n;
+    }
+
+    match (point.0 < curve.p, point.1 < curve.p) {
+        (false, _) | (_, false) => panic!("Point coordinates are out of range"),
+        _ => {}
+    }
+
     // Construct the point with BigUint values
     let point = Point {
         x: point.0,