Write a MIPS program that finds a fixed-point of the function f(x) = x*x - 2*x +

Question

Write a MIPS program that finds a fixed-point of the

function f(x) = x*x - 2*x + 1. There are two fixed-points for this function, but I want you to

find the one that is between 0 and 1. The fixed-point can be found iteratively by starting with a

value of x between 0 and 1, computing f(x) and taking the average between x and f(x). Then

repeat the calculation with this average as the new value for x. In other words, let g(x) compute

the next estimate for the fixed-point as g(x) = (x + f(x)/2 = (x*x – x + 1)/2. Then compute the

assignment statement x = g(x) many times. Write a MIPS program that does this computation

using double precision numbers. It will be sufficient for this assignment to execute the

assignment statement x = g(x) exactly 10 times and store the double precision value of x in

double precision register $f0. Start with 1.0 as the initial value of x.

*Must be in MIPS assembly language to recieve credit

Explanation / Answer

.text

.globl main

main:

li.d $f0, 1.0

li.d $f2, 1.0

li.d $f4, 0.5

loop:

bge $t0, 10, end

mov.d $f6, $f0

mul.d $f6, $f6, $f6

sub.d $f6, $f6, $f0

add.d $f6, $f6, $f2

mul.d $f6, $f6, $f4

mov.d $f0, $f6

addi $t0, $t0, 1

j loop

end:

li $v0, 3

mov.d $f12, $f0

syscall

li $v0, 10

syscall

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