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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)² = 55² = 3025.

The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 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
	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

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