Question

A third degree polynomial equation (a cubic equation) is of the form p(x) = c₃x ³ + c₂x ² + c₁x + c₀, where x and the four coefficients are integers for this exercise. Suppose the values of the coefficients c₀, c₁, c₂, and c₃have been loaded into registers $t0, $t1, $t2, and $t3, respectively. Suppose the value of x is in $t7.

Write the MIPS32 instructions that would evaluate this polynomial, placing the result in $t9.

Answer 1

# A third degree polynomial equation is p(x) = c3x 3 + c2x 2 + c1x + c0,

       .text
        .globl main

main:
        lw   $t0,c0          # get c0 -- Load word of c0 to the register of t0
        lw   $t1,c1          # get c1 -- Load word of c1 to the register of t1
        lw   $t2,c2          # get c2 -- Load word of c2 to the register of t2
        lw   $t3,c3          # get c3 -- Load word of c3 to the register of t3
       lw   $t7,x          # get x -- Load word of x to the register of t7

        mult $t7,$t7        # x2 -- Multiply x => x*x=x2
        mflo $t4             # $t4 = x2 -- move x2 to $t4
        nop                   # No operation performed
      
       mult $t4,$t7       # x3 -- Multiply x => x2*x=x3
        mflo $t5            # $t5 = x3 -- move x3 to $t5
        nop
      
       mult $t1,$t7        # c1x -- Multiply c1 by x => c1*x=c1x
        mflo $t6             # $t6 = c1x -- move c1x to $t6
        nop

       mult $t2,$t4        # c2x2 -- Multiply c2 by x2 => c2*x2=c2x2
        mflo $t8             # $t8 = c2x2 -- move c2x2 to $t8
        nop

       mult $t3,$t5        # c3x3 -- Multiply c3 by x3 => c3*x3=c3x3
        mflo $t9             # $t9 = c3x3
        nop
     
        addu $t9,$t9,$t8    # $t9 = c3x3 + c2x2 -- add c3x3 and c2x2. Hence c3x3+c2x2 and load it to $t9 register
        addu $t9,$t9,$t6    # $t9 = c3x3 + c2x2 + c1x
       addu $t9,$t9,$t0    # $t9 = c3x3 + c2x2 + c1x + c0
      
        sw   $t9,value      # p(x) = c3x3 + c2x2 + c1x + c0 -- polynomial