Polynomial Evaluation /96 Evaluating the polynomial: x13+x7+x4+x2+X Without considering the redundancies this polynomial evaluation requires 22 multiplications. Examining the exponents and considering their binary representations: 1=0001,2=0010,4=0100,7=0111,13=1101. x7 can be considered as x4 X x2 Xx.Applying sub-expression sharing to the exponents the polynomial can be evaluated as follows: x8×(x4×x)+x2×(x4×X)+x4+X2+X The terms x2,x4 and x8 each require one multiplication as shown below: X2=X×X,X4=X2×X2,8=x4×X4 Thus,we require 6 instead of 22 multiplications. 2021年2月 通信抗干扰技术国家重点实验室 102021年2月 通信抗干扰技术国家重点实验室 10 Polynomial Evaluation  Evaluating the polynomial: x 13 + x7 + x4 + x2 + x  Without considering the redundancies this polynomial evaluation requires 22 multiplications.  Examining the exponents and considering their binary representations: 1 = 0001, 2 = 0010, 4 = 0100, 7 = 0111, 13 = 1101.  x7 can be considered as x4 × x 2 × x. Applying sub-expression sharing to the exponents the polynomial can be evaluated as follows: x 8 × (x4 × x) + x2 × (x4 × x) + x4 + x2 + x  The terms x2, x4 and x8 each require one multiplication as shown below: x 2 = x × x, x4 = x2 × x 2 , x8 = x4 × x 4  Thus, we require 6 instead of 22 multiplications