diff --git a/docs/src/algorithm.rst b/docs/src/algorithm.rst
new file mode 100644
index 0000000..9b11857
--- /dev/null
+++ b/docs/src/algorithm.rst
@@ -0,0 +1,5 @@
+algorithm
+=============
+
+.. doxygenfile:: algorithm.hpp
+
diff --git a/docs/src/index.rst b/docs/src/index.rst
index 6aa449b..af5e99a 100644
--- a/docs/src/index.rst
+++ b/docs/src/index.rst
@@ -40,6 +40,7 @@ AARE
     :caption: C++ API
     :maxdepth: 1
     
+    algorithm
     NDArray
     NDView
     Frame
diff --git a/include/aare/algorithm.hpp b/include/aare/algorithm.hpp
index 88b8a4b..fc7d51f 100644
--- a/include/aare/algorithm.hpp
+++ b/include/aare/algorithm.hpp
@@ -7,13 +7,20 @@
 
 namespace aare {
 /**
- * @brief Find the index of the last element smaller than val
- * assume a sorted array
+ * @brief Index of the last element that is smaller than val.
+ * Requires a sorted array. Uses >= for ordering. If all elements
+ * are smaller it returns the last element and if all elements are
+ * larger it returns the first element.
+ * @param first iterator to the first element
+ * @param last iterator to the last element
+ * @param val value to compare
+ * @return index of the last element that is smaller than val
+ * 
  */
 template <typename T>
 size_t last_smaller(const T* first, const T* last, T val) {
     for (auto iter = first+1; iter != last; ++iter) {
-        if (*iter > val) {
+        if (*iter >= val) {
             return std::distance(first, iter-1);
         }
     }
@@ -25,6 +32,21 @@ size_t last_smaller(const NDArray<T, 1>& arr, T val) {
     return last_smaller(arr.begin(), arr.end(), val);
 }
 
+template <typename T>
+size_t last_smaller(const std::vector<T>& vec, T val) {
+    return last_smaller(vec.data(), vec.data()+vec.size(), val);
+}
+
+/**
+ * @brief Index of the first element that is larger than val.
+ * Requires a sorted array. Uses > for ordering. If all elements
+ * are larger it returns the first element and if all elements are
+ * smaller it returns the last element.
+ * @param first iterator to the first element
+ * @param last iterator to the last element
+ * @param val value to compare
+ * @return index of the first element that is larger than val
+ */
 template <typename T>
 size_t first_larger(const T* first, const T* last, T val) {
     for (auto iter = first; iter != last; ++iter) {
@@ -45,6 +67,14 @@ size_t first_larger(const std::vector<T>& vec, T val) {
     return first_larger(vec.data(), vec.data()+vec.size(), val);
 }
 
+/**
+ * @brief Index of the nearest element to val.
+ * Requires a sorted array. If there is no difference it takes the first element.
+ * @param first iterator to the first element
+ * @param last iterator to the last element
+ * @param val value to compare
+ * @return index of the nearest element
+ */
 template <typename T>
 size_t nearest_index(const T* first, const T* last, T val) {
     auto iter = std::min_element(first, last,
diff --git a/src/algorithm.test.cpp b/src/algorithm.test.cpp
index 5929131..e2ae8fa 100644
--- a/src/algorithm.test.cpp
+++ b/src/algorithm.test.cpp
@@ -49,6 +49,16 @@ TEST_CASE("nearest index works with std::array", "[algorithm]"){
     REQUIRE(aare::nearest_index(arr, -10.0) == 0);
 }
 
+TEST_CASE("nearest index when there is no different uses the first element", "[algorithm]"){
+    std::vector<int> vec = {5, 5, 5, 5, 5};
+    REQUIRE(aare::nearest_index(vec, 5) == 0);
+}
+
+TEST_CASE("nearest index when there is no different uses the first element also when all smaller", "[algorithm]"){
+    std::vector<int> vec = {5, 5, 5, 5, 5};
+    REQUIRE(aare::nearest_index(vec, 10) == 0);
+}
+
 
 TEST_CASE("last smaller", "[algorithm]"){
     aare::NDArray<double, 1> arr({5});
@@ -68,10 +78,59 @@ TEST_CASE("returns last bin strictly smaller", "[algorithm]"){
         arr[i] = i;
     }
     // arr 0, 1, 2, 3, 4
-    REQUIRE(aare::last_smaller(arr, 2.0) == 2);
+    REQUIRE(aare::last_smaller(arr, 2.0) == 1);
 
 }
 
+TEST_CASE("last_smaller with all elements smaller returns last element", "[algorithm]"){
+    aare::NDArray<double, 1> arr({5});
+    for (size_t i = 0; i < arr.size(); i++) {
+        arr[i] = i;
+    }
+    // arr 0, 1, 2, 3, 4
+    REQUIRE(aare::last_smaller(arr, 50.) == 4);
+}
+
+TEST_CASE("last_smaller with all elements bigger returns first element", "[algorithm]"){
+    aare::NDArray<double, 1> arr({5});
+    for (size_t i = 0; i < arr.size(); i++) {
+        arr[i] = i;
+    }
+    // arr 0, 1, 2, 3, 4
+    REQUIRE(aare::last_smaller(arr, -50.) == 0);
+}
+
+TEST_CASE("last smaller with all elements equal returns the first element", "[algorithm]"){
+    std::vector<int> vec = {5,5,5,5,5,5,5};
+    REQUIRE(aare::last_smaller(vec, 5) == 0);
+}
+
+
+TEST_CASE("first_lager with vector", "[algorithm]"){
+    std::vector<double> vec = {0, 1, 2, 3, 4};
+    REQUIRE(aare::first_larger(vec, 2.5) == 3);
+}
+
+TEST_CASE("first_lager with all elements smaller returns last element", "[algorithm]"){
+    std::vector<double> vec = {0, 1, 2, 3, 4};
+    REQUIRE(aare::first_larger(vec, 50.) == 4);
+}
+
+TEST_CASE("first_lager with all elements bigger returns first element", "[algorithm]"){
+    std::vector<double> vec = {0, 1, 2, 3, 4};
+    REQUIRE(aare::first_larger(vec, -50.) == 0);
+}
+
+TEST_CASE("first_lager with all elements the same as the check returns last", "[algorithm]"){
+    std::vector<int> vec = {14, 14, 14, 14, 14};
+    REQUIRE(aare::first_larger(vec, 14) == 4);
+}
+
+TEST_CASE("first larger with the same element", "[algorithm]"){
+    std::vector<int> vec = {7,8,9,10,11};
+    REQUIRE(aare::first_larger(vec, 9) == 3);
+}
+
 TEST_CASE("cumsum works", "[algorithm]"){
     std::vector<double> vec = {0, 1, 2, 3, 4};
     auto result = aare::cumsum(vec);
@@ -96,4 +155,5 @@ TEST_CASE("cumsum works with negative numbers", "[algorithm]"){
     REQUIRE(result[2] == -3);
     REQUIRE(result[3] == -6);
     REQUIRE(result[4] == -10);
-}
\ No newline at end of file
+}
+