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# goal of this assignment is to introduce Floating Point operations in MIPS

INSTRUCTIONS TO CANDIDATES

Goal

The goal of this assignment is to introduce Floating Point operations in MIPS.

Background

Newton devised a method to aproximate a root of an equation by repeatedly apply the formula until the error was sufficiently small. This formula, also known as the Newton–Raphson method, is defined as:

𝑥𝑛+1 = 𝑥𝑛 − (𝐹(𝑥𝑛)/𝐹′(𝑥𝑛))

Consider a continuous function F(x)=x3-4x2+1 with its derivative F’(x)=3x2-8x. Thus, by calculating successive values of x, the value of F(xn) will approach 0, and hence be a root of F.

The Assignment

Write a MIPS program which will find a value of xn such that F(xn)=0, to a tolerance of 10-6.

Prompt the user to enter an initial integer value for x, hence x1. Then calculate each new x value, using the formula above, until F(x) is sufficiently close to 0. Try the value of 2 as a test input value.

All calculations must be done as doubles. Your program should output x and the value of F(x) at each step and finally print the root (x) that you found. You should try other values for the initial value of x to test your program.

Note, your output will not be so clean since the default print of a double includes many decimal places and could be in scientific notation, don’t worry about aligning the output.

The output with an input of 2 should look like the following:

Please enter an integer: 2 x=2.0, F(x)=-7.0

x=0.25, F(x)=0.765625

x=0.6724137931034483, F(x)=-0.5045358563286728 x=0.5469975054591968, F(x)=-0.033160000071302154 x=0.5374642805088174, F(x)=-2.1525861187732254E-4 x=0.5374015797596746, F(x)=-9.386846855363729E-9 x=0.5374015797596746

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