diff --git a/src/qmckl_ao.org b/src/qmckl_ao.org
index 50bcfec..b0f9671 100644
--- a/src/qmckl_ao.org
+++ b/src/qmckl_ao.org
@@ -30,6 +30,7 @@ MunitResult test_qmckl_ao() {
     \[
     P_l(\mathbf{r},\mathbf{R}_i)  =   (x-X_i)^a (y-Y_i)^b (z-Z_i)^c 
     \]
+
     \begin{eqnarray*} 
     \frac{\partial }{\partial x} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
                    = & a (x-X_i)^{a-1} (y-Y_i)^b (z-Z_i)^c \\
@@ -38,6 +39,8 @@ MunitResult test_qmckl_ao() {
     \frac{\partial }{\partial z} P_l\left(\mathbf{r},\mathbf{R}_i \right) &
                    = & c (x-X_i)^a (y-Y_i)^b (z-Z_i)^{c-1} \\
     \end{eqnarray*} 
+
+    
     \begin{eqnarray*} 
     \left( \frac{\partial }{\partial x^2} + 
                \frac{\partial }{\partial y^2} + 
@@ -527,7 +530,7 @@ munit_assert_int(0, ==, test_qmckl_ao_polynomial_vgl(context));
      Computes the values, gradients and Laplacians at a given point of
      ~n~ Gaussian functions centered at the same point:
    
-     \[ v_i = exp(-a_i |X-R|^2) \]
+     \[ v_i = \exp(-a_i |X-R|^2) \]
      \[ \nabla_x v_i = -2 a_i (X_x -  R_x) v_i \]
      \[ \nabla_y v_i = -2 a_i (X_y -  R_y) v_i \]
      \[ \nabla_z v_i = -2 a_i (X_z -  R_z) v_i \]
@@ -740,7 +743,6 @@ munit_assert_int(0, ==, test_qmckl_ao_gaussian_vgl(context));
     return QMCKL_FAILURE;
   return MUNIT_OK;
 }
-
     #+END_SRC
   
 
diff --git a/src/qmckl_memory.org b/src/qmckl_memory.org
index e74913b..02a4cec 100644
--- a/src/qmckl_memory.org
+++ b/src/qmckl_memory.org
@@ -10,6 +10,7 @@
 *** Headers                                                        :noexport:
     #+BEGIN_SRC C :tangle qmckl_memory.c
 #include "qmckl.h"
+#include <assert.h>
     #+END_SRC
 
     #+BEGIN_SRC C :tangle test_qmckl_memory.c
@@ -22,6 +23,8 @@ MunitResult test_qmckl_memory() {
 
     Memory allocation function, letting the library choose how the
     memory will be allocated, and a pointer is returned to the user.
+    The context is passed to let the library store data related to the
+    allocation inside the context.
 
     #+BEGIN_SRC C :tangle qmckl.h
 void* qmckl_malloc(const qmckl_context ctx, const size_t size);
@@ -40,19 +43,20 @@ void* qmckl_malloc(const qmckl_context ctx, const size_t size);
 **** Source
      #+BEGIN_SRC C :tangle qmckl_memory.c
 void* qmckl_malloc(const qmckl_context ctx, const size_t size) {
-  if (ctx == (qmckl_context) 0) {
-    /* Avoids unused parameter error */
-    return malloc( (size_t) size );
-  }
-  return malloc( (size_t) size );
+  if (ctx == (qmckl_context) 0) {}; /* Avoid unused argument warning */
+  void * result = malloc( (size_t) size );
+  assert (result != NULL) ;
+  return result;
 }
 
      #+END_SRC
 
 **** Test                                                          :noexport:
      #+BEGIN_SRC C :tangle test_qmckl_memory.c
-int *a;
+int *a = NULL;
+munit_assert(a == NULL);
 a = (int*) qmckl_malloc( (qmckl_context) 1, 3*sizeof(int));
+munit_assert(a != NULL);
 a[0] = 1;
 a[1] = 2;
 a[2] = 3;
@@ -64,27 +68,33 @@ munit_assert_int(a[2], ==, 3);
 *** ~qmckl_free~
 
     #+BEGIN_SRC C :tangle qmckl.h
-void qmckl_free(void *ptr);
+void* qmckl_free(void *ptr);
     #+END_SRC
 
     #+BEGIN_SRC f90 :tangle qmckl_f.f90
   interface
-     subroutine qmckl_free (ptr) bind(C)
+     type (c_ptr) function qmckl_free (ptr) bind(C)
        use, intrinsic :: iso_c_binding
        type (c_ptr), intent(in), value :: ptr
-     end subroutine qmckl_free
+     end function qmckl_free
   end interface
     #+END_SRC
 **** Source
      #+BEGIN_SRC C :tangle qmckl_memory.c
-void qmckl_free(void *ptr) {
+void* qmckl_free(void *ptr) {
+  assert (ptr != NULL);
   free(ptr);
+  return NULL;
 }
+
      #+END_SRC
 
 **** Test                                                          :noexport:
      #+BEGIN_SRC C :tangle test_qmckl_memory.c
-qmckl_free(a);
+munit_assert(a != NULL);
+a = qmckl_free(a);
+munit_assert(a == NULL);
+
      #+END_SRC
 
 *** End of files                                                   :noexport: