Update overview

docs/sources/overview.rst

@@ -35,7 +35,7 @@ A simple vector addition kernel can be expressed using the API as follows:
 
 
     @dpex.kernel
-    def sum(a, b, c):
+    def vecadd_kernel(a, b, c):
         i = dpex.get_global_id(0)
         c[i] = a[i] + b[i]
 
@@ -44,7 +44,7 @@ A simple vector addition kernel can be expressed using the API as follows:
     b = dpnp.ones(1024, device="gpu")
     c = dpnp.empty_like(a)
 
-    sum[dpex.Range(1024)](a, b, c)
+    vecadd_kernel[dpex.Range(1024)](a, b, c)
     print(c)
 
 In the above example, as the programmer allocated arrays on a ``gpu`` device
@@ -58,7 +58,7 @@ select a default device based on environment flag settings.
 
 `Dpnp`_ is a NumPy-replacement library being developed using SYCL and oneAPI.
 The library has an API similar to NumPy, but using SYCL and oneAPI is able to
-execute in parallel on different types of hardware.
+execute its functions in parallel on different types of hardware.
 
 Numba-dpex extends Numba's type system and compilation pipeline to compile dpnp
 functions and expressions in the same manner as Numba compiles NumPy. Unlike
@@ -69,6 +69,39 @@ option in ``numba.jit``. However, offloading by numba-dpex is not just
 restricted to CPUs and supports all devices that are presently supported by the
 kernel API.
 
+Numba-dpex provides a decorator ``dpjit`` that behaves identically to
+``numba.njit(parallel=True)`` and additionally supports dpnp compilation and
+offload. Note that ``dpjit`` is able to handle NumPy and dpnp expressions in the
+same function. All NumPy compilation and parallelization is done via the default
+Numba code-generation pipeline, whereas dpnp expressions are compiled using the
+numba-dpex pipeline.
+
+The vector addition example depicted using the kernel API can be easily
+expressed in several different ways using ``dpjit``.
+
+.. code-block:: python
+
+    import dpnp
+    import numba_dpex as dpex
+
+
+    @dpex.dpjit
+    def vecadd_v1(a, b):
+        return a + b
+
+
+    @dpex.dpjit
+    def vecadd_v2(a, b):
+        return dpnp.add(a, b)
+
+
+    @dpex.dpjit
+    def vecadd_v3(a, b):
+        c = dpnp.empty_like(a)
+        for i in prange(a.shape[0]):
+            c[i] = a[i] + b[i]
+        return c
+
 
 Contributing
 ------------