Re-write arctan(x)

src/taylor.py

@@ -61,21 +61,16 @@ def estimate(func_name, x, a, func_at_a, N):
 
 PI = 3.14159265358979323846264338327950288419716939937510582097494
 
+@cache
 def arctan(x):
     N = 10
     if x == 0:
         return 0, 0
     elif x == 1:
-        return pi/4, Decimal(10**-16)
-
-    a = 0
-    total_error = Decimal(0)
-    prev_value = 0
-    while a + 1 <= x:
-        prev_value = estimate('arctan', a + 1, a, prev_value, N)
-        total_error += max_error('arctan', a, a + 1, N)
-        a += 1
-    return estimate('arctan', x, floor(x), prev_value, N), total_error + max_error('arctan', floor(x), x, N)
+        return PI/4, 10**(-1)
+    total_error = max_error('arctan', floor(x), x, N)
+    prev_value, total_error = arctan(floor(float(x) - 0.0001))
+    return float(estimate('arctan', x, floor(x), prev_value, N)), total_error + float(max_error('arctan', floor(x), x, N))
 
 if __name__ == "__main__":
     for i in range(0, 4):