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Published at Jul 30 2020
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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.

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

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

```
#
# 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
add $t1, $t1, $t2
add $t0, $t0, $a0
subi $a0, $a0, 1
j LOOP
STOP:
mul $t0, $t0, $t0
sub $v0, $t0, $t1
jr $ra
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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