if x < 10 or y < 10 return xy d = ⌊ max(length(p), length(q)) / 2 ⌋ x_high, x_low = split x as a string at d y_high, y_low = split y as a string at d a = karatsuba(x_high, y_high) b = karatsuba(x_high + x_low, y_high + y_low) c = karatsuba(x_low, y_low) result = c*10^2d + (b-c-a)*10^d + a return result