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# hyphenrf's solution

## to Difference Of Squares in the MIPS Assembly Track

Published at Jul 30 2020 · 0 comments
Instructions
Test suite
Solution

Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.

The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)Â² = 55Â² = 3025.

The sum of the squares of the first ten natural numbers is 1Â² + 2Â² + ... + 10Â² = 385.

Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.

## Source

Problem 6 at Project Euler http://projecteuler.net/problem=6

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### runner.mips

``````#
# Test difference_of_squares with some examples
#
# s0 - num of tests left to run
# s1 - address of input word
# s2 - address of expected output word
# s3 - input word
# s4 - output word
#
# difference_of_squares must:
# - be named difference_of_squares and declared as global
# - read input integer from a0
# - follow the convention of using the t0-9 registers for temporary storage
# - (if it wants to use s0-7 then it is responsible for pushing existing values to the stack then popping them back off before returning)
# - write integer result to v0

.data

n: .word 4                             # number of test cases
ins:  .word    0,   5,   10,      100  # input numbers
outs: .word    0, 170, 2640, 25164150  # expected result

failmsg: .asciiz "failed for test input: "
expectedmsg: .asciiz ". expected "
tobemsg: .asciiz " to be "
okmsg: .asciiz "all tests passed"

.text

runner:
lw      \$s0, n
la      \$s1, ins
la      \$s2, outs

run_test:
lw      \$s3, 0(\$s1)             # read input from memory
move    \$a0, \$s3                # move it to a0
jal     difference_of_squares   # call subroutine under test
move    \$v1, \$v0                # move return value in v0 to v1 because we need v0 for syscall

lw      \$s4, 0(\$s2)             # read expected output from memory
bne     \$v1, \$s4, exit_fail     # if expected doesn't match actual, jump to fail

addi    \$s1, \$s1, 4             # move to next word in input
addi    \$s2, \$s2, 4             # move to next word in output
sub     \$s0, \$s0, 1             # decrement num of tests left to run
bgt     \$s0, \$zero, run_test    # if more than zero tests to run, jump to run_test

exit_ok:
la      \$a0, okmsg              # put address of okmsg into a0
li      \$v0, 4                  # 4 is print string
syscall

li      \$v0, 10                 # 10 is exit with zero status (clean exit)
syscall

exit_fail:
la      \$a0, failmsg            # put address of failmsg into a0
li      \$v0, 4                  # 4 is print string
syscall

move    \$a0, \$s3                # set arg of syscall to input that failed the test
li      \$v0, 1                  # 1 is print int
syscall

la      \$a0, expectedmsg
li      \$v0, 4
syscall

move    \$a0, \$v1                # print actual that failed on
li      \$v0, 1
syscall

la      \$a0, tobemsg
li      \$v0, 4
syscall

move    \$a0, \$s4                # print expected value that failed on
li      \$v0, 1
syscall

li      \$a0, 1                  # set exit code to 1
li      \$v0, 17                 # terminate with the exit code in \$a0
syscall

# # Include your implementation here if you wish to run this from the MARS GUI.
# .include "impl.mips"``````
``````.globl difference_of_squares

# \$t0 - square of sums
# \$t1 - sum of squares
# \$t2 - a square
# registers that are referenced before assignment need to be cleared
.text
difference_of_squares:
move  \$t0, \$zero
move  \$t1, \$zero
LOOP:
beqz  \$a0, STOP

mul   \$t2, \$a0, \$a0

subi  \$a0, \$a0, 1
j     LOOP
STOP:
mul   \$t0, \$t0, \$t0
sub   \$v0, \$t0, \$t1
jr    \$ra``````