add Polynomial.calculate_horner

This allows to evaluate polynomials more efficiently.

Author: Deric-W

polynomial/core.py

@@ -291,6 +291,19 @@ def calculate(self, x):
 
         return sum(ak * (x ** k) for ak, k in self.terms)
 
+    def calculate_horner(self, x):
+        """Calculate the value of the polynomial at a given point
+        using Horner`s method.
+
+        This method is faster than calling calculate for almost all
+        polynomials except monomials but might produce slightly different
+        results when using floats.
+        """
+        result = 0
+        for coeff in self:
+            result = coeff + x * result
+        return result
+
     def __call__(self, x):
         """Calculate the value of the polynomial at a given point."""
         return self.calculate(x)

tests/test_polynomials_operations.py

@@ -1310,6 +1310,25 @@ def test_calculate_zero_polynomial(self):
         self.assertEqual(0, Constant(0).calculate(5))
         self.assertEqual(0, Monomial(0, 1).calculate(1.1))
 
+    def test_calculate_horner(self):
+        """Tests calculate_horner on a simple polynomial."""
+        a = Polynomial(1, 2, 3)
+
+        def eqn(x):
+            return x ** 2 + 2 * x + 3
+
+        for i in range(-100, 100):
+            i = i / 100
+            self.assertAlmostEqual(eqn(i), a.calculate_horner(i))
+
+    def test_calculate_horner_zero_polynomial(self):
+        """Test that calculations of zero polynomial values
+        using Horner`s method always give 0.
+        """
+        self.assertEqual(0, ZeroPolynomial().calculate_horner(1))
+        self.assertEqual(0, Constant(0).calculate_horner(5))
+        self.assertEqual(0, Monomial(0, 1).calculate_horner(1.1))
+
     def test_call(self):
         """Tests calculate on a simple polynomial."""
         a = Polynomial(1, 2, 3)