@@ -1 +1 @@
-0.8.5
+0.8.7
@@ -111,6 +111,7 @@
     'colvec',
     'unitvec',
     'norm',
+    'normsq',
     'isunitvec',
     'iszerovec',
     'isunittwist',
@@ -120,6 +121,7 @@
     'unittwist2',
     'angdiff',
     'removesmall',
+    'cross',
 # spatialmath.base.animate
     'Animate',
     'Animate2',
 
@@ -76,12 +76,32 @@ def test_isunitvec(self):
     def test_norm(self):
         self.assertAlmostEqual(norm([0, 0, 0]), 0)
         self.assertAlmostEqual(norm([1, 2, 3]), math.sqrt(14))
-
+        self.assertAlmostEqual(norm(np.r_[1, 2, 3]), math.sqrt(14))
+        
         x, y = sym.symbol('x y')
         v = [x, y]
         self.assertEqual(norm(v), sym.sqrt(x**2 + y**2))
         self.assertEqual(norm(np.r_[v]), sym.sqrt(x**2 + y**2))
 
+    def test_norm(self):
+        self.assertAlmostEqual(norm([0, 0, 0]), 0)
+        self.assertAlmostEqual(normsq([1, 2, 3]), 14)
+        self.assertAlmostEqual(normsq(np.r_[1, 2, 3]), 14)
+
+        x, y = sym.symbol('x y')
+        v = [x, y]
+        self.assertEqual(normsq(v), x**2 + y**2)
+        self.assertEqual(normsq(np.r_[v]), x**2 + y**2)
+
+    def test_cross(self):
+
+        A = np.eye(3)
+
+        for i in range(0, 3):
+            j = (i + 1) % 3
+            k = (i + 2) % 3
+            self.assertTrue(all(cross(A[:,i], A[:,j]) == A[:,k]))
+
     def test_isunittwist(self):
         # 3D
         # unit rotational twist
 
@@ -17,7 +17,7 @@
 
 try:  # pragma: no cover
     # print('Using SymPy')
-    from sympy import Matrix
+    import sympy
 
     _symbolics = True
 
@@ -122,16 +122,82 @@ def norm(v):
         >>> from spatialmath.base import *
         >>> norm([3, 4])
 
+    .. note:: This function does not use NumPy, it is ~2x faster than 
+        `numpy.linalg.norm()` for a 3-vector
+
     :seealso: :func:`~spatialmath.base.unit`
 
     :SymPy: supported
     """
-    v = getvector(v)
-    if v.dtype.kind == 'O':
-        return Matrix(v).norm()
+    sum = 0
+    for x in v:
+        sum += x * x
+
+    if isinstance(sum, sympy.Expr):
+        return sympy.sqrt(sum)
     else:
-        return np.linalg.norm(v)
+        return math.sqrt(sum)
+
+def normsq(v):
+    """
+    Squared norm of vector
+
+    :param v: any vector
+    :type v: array_like(n)
+    :return: norm of vector
+    :rtype: float
 
+    ``norm(sq)`` is the sum of squared elements of the vector ``v`` 
+    or :math:`|v|^2`.
+
+    .. runblock:: pycon
+
+        >>> from spatialmath.base import *
+        >>> normsq([2, 3])
+
+    .. note:: This function does not use NumPy, it is ~2x faster than 
+        `numpy.linalg.norm() ** 2` for a 3-vector
+
+    :seealso: :func:`~spatialmath.base.unit`
+
+    :SymPy: supported
+    """
+    sum = 0
+    for x in v:
+        sum += x * x
+
+    return sum
+
+def cross(u, v):
+    """
+    Cross product of vectors
+
+    :param u: any vector
+    :type u: array_like(3)
+    :param v: any vector
+    :type v: array_like(3)
+    :return: cross product
+    :rtype: nd.array(3)
+
+    ``cross(u, v)`` is the cross product of the vectors ``u`` and ``v``.
+
+    .. runblock:: pycon
+
+        >>> from spatialmath.base import *
+        >>> cross([1, 0, 0], [0, 1, 0])
+
+    .. note:: This function does not use NumPy, it is ~1.5x faster than 
+        `numpy.cross()`
+
+    :seealso: :func:`~spatialmath.base.unit`
+
+    :SymPy: supported
+    """
+    return np.r_[
+        u[1] * v[2] - u[2] * v[1],
+        u[2] * v[0] - u[0] * v[2],
+        u[0] * v[1] - u[1] * v[0]
+                ]
 
 def isunitvec(v, tol=10):
     """
@@ -277,9 +343,9 @@ def unittwist(S, tol=10):
     Returns None if the twist has zero magnitude
     """
 
-    s = getvector(S, 6)
+    S = getvector(S, 6)
 
-    if iszerovec(s, tol=tol):
+    if iszerovec(S, tol=tol):
         return None
 
     v = S[0:3]
@@ -322,9 +388,9 @@ def unittwist_norm(S, tol=10):
     .. note:: Returns (None,None) if the twist has zero magnitude
     """
 
-    s = getvector(S, 6)
+    S = getvector(S, 6)
 
-    if iszerovec(s, tol=tol):
+    if iszerovec(S, tol=tol):
         return (None, None)
 
     v = S[0:3]
@@ -460,4 +526,4 @@ def removesmall(v, tol=100):
 if __name__ == '__main__':  # pragma: no cover
     import pathlib
 
-    exec(open(pathlib.Path(__file__).parent.absolute() / "test_vectors.py").read())  # pylint: disable=exec-used
+    exec(open(pathlib.Path(__file__).parent.absolute() / "test" / "test_vectors.py").read())  # pylint: disable=exec-used
@@ -216,15 +216,27 @@ def result(op, t):
 misc_setup = '''
 from spatialmath import base
 import numpy as np
-s = np.r_[1,2,3,4,5,6]
+s = np.r_[1.0,2,3,4,5,6]
+a = np.r_[1.0, 2.0, 3.0]
+b = np.r_[-5.0, 4.0, 3.0]
+
 '''
 table.rule()
 
+t = timeit.timeit(stmt='c = np.cross(a,b)', setup=misc_setup, number=N)
+result("np.cross()", t)
+
+t = timeit.timeit(stmt='c = base.cross(a,b)', setup=misc_setup, number=N)
+result("cross()", t)
+
 t = timeit.timeit(stmt='a = np.inner(s,s).sum()', setup=misc_setup, number=N)
 result("inner()", t)
 
 t = timeit.timeit(stmt='a = np.linalg.norm(s) ** 2', setup=misc_setup, number=N)
-result("norm**2", t)
+result("np.norm**2", t)
+
+t = timeit.timeit(stmt='a = base.normsq(s)', setup=misc_setup, number=N)
+result("base.normsq", t)
 
 t = timeit.timeit(stmt='a = (s ** 2).sum()', setup=misc_setup, number=N)
 result("s**2.sum()", t)