#Copyright 2021 by John Bowman
#Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), 
#to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, 
#and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
#The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
#THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 
#FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, 
#WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

#This program looks for the smallest distance between two sets of coordinates
#using the distance formula: d = sqrt((xj-xi)^2 + (yj-yi)^2 + (zj-zi)^2)
#and outputs the smallest distance along with the coordinates 
#that produce the smallest distance

#Developed using MARS 4.5 MIPS Assembler and Runtime Simulator

.data
  message: .asciiz "The pairs of coordinates that are closest to each other are "
  message2: .asciiz "\nThe square root of these coordinates is: "
  space: .asciiz " "
  openPar: .asciiz "("
  closePar: .asciiz ")"
  comma: .asciiz ","
  precision: .float 0.005
  numbers: .float #Float array. Every two rows represents a set of data. i.e. x1,y1,z1 - x2,y2,z2
  -86.197052961689, -11.611577927042, 61.992590409186,
  13.27904907337, 19.916714939069, -20.722319227382,
  -4.2258863849783, 45.297465287969, -90.569809463764,
  -95.944184921756, 47.662103394222, 64.51404880929,
  -21.807443326017, -24.698308698634, 75.762861069285,
  -36.6654951049497, 43.494575924847, 86.447702712523,
  47.778522103541, -65.538547015254, 59.179507921132,
  54.530144848978, -67.933306319424, -36.693280039158,
  84.306270676353, 21.53150037385, 44.934044045448,
  73.659364837401, 81.085378856605, -73.1797878870
  
.text
  lwc1 $f8, precision #Load precision into $f8
 
  #Initialize counter variables
  li $t0, 0 
  li $t1, 5
  
  #Initialize register $f10, the register selected for storing the smallest square root
  #Assign very large number because we need the first square root generated to be smaller than this number
  #Otherwise, branching will fail
  la $a0, 40000000
  mtc1 $a0, $f10
  cvt.s.w $f10, $f10
  
  startLoop:
    beq $t0,$t1,exitLoop #Terminate after five iterations
    nop
    
    la $a0, numbers
   
    mul $t3, $t0, 12
    add $a0, $a0, $t3
    
    l.s $f0, 0($a0) #xi
    l.s $f1, 4($a0) #yi
    l.s $f2, 8($a0) #zi
    
    la $a0, numbers
    mul $t3, $t0, 12
    add $a0, $a0, $t3
    
    l.s $f3, 0($a0) #xj
    l.s $f4, 4($a0) #yj
    l.s $f5, 8($a0) #zj
    
    mov.s $f18, $f0
    mov.s $f19, $f1
    mov.s $f20, $f2
    mov.s $f21, $f3
    mov.s $f22, $f4
    mov.s $f23, $f5
    
    sub.s $f3, $f3, $f0 #xj - xi
    sub.s $f4, $f4, $f1 #yj - yi
    sub.s $f5, $f5, $f2 #zj - zi
    
    mul.s $f3, $f3, $f3 #square value of xj-xi
    mul.s $f4, $f4, $f4 #square value of yj-yi
    mul.s $f5, $f5, $f5 #square value of zj-zi
    
    #Add results together
    add.s $f3, $f3, $f4
    add.s $f3, $f3, $f5
    
    mov.s $f0, $f3
     
    #Compute square root with Newton-Raphson approximation
    dowhile:
      mul.s $f6, $f3, $f3
      sub.s $f6, $f6, $f0
      add.s $f7, $f3, $f3
      div.s $f6, $f6, $f7
      sub.s $f3, $f3, $f6
      
      c.lt.s $f6, $f8
    bc1f dowhile
    nop
   
    addi $t0,$t0,1 #Increment looping value
  
    #If a smaller square root is found, store it and its coordinates by branching to continue label
    c.lt.s $f3, $f10
    bc1t continue
    nop
      
    j startLoop #Unconditionally jump to beginning of loop
    nop
    
  #When a smaller square root is found, store it and the coordinates that generated it
  #Return to beginning of startLoop
  continue:
      mov.s $f10, $f3
      mov.s $f11, $f18 #x1
      mov.s $f13, $f19 #y1
      mov.s $f14, $f20 #z1
      mov.s $f15, $f21 #x2
      mov.s $f16, $f22 #y2
      mov.s $f17, $f23 #z2
      j startLoop #Uncontionally jump to beginning of startLoop
      nop
    
  #Print results  
  exitLoop:
    #print pairs header
    la $a0, message
    li $v0, 4
    syscall
  
    la $a0, openPar
    li $v0, 4
    syscall
    
    mov.s $f12, $f11
    li $v0, 2
    syscall
  
    la  $a0, comma
    li $v0, 4
    syscall
    
    mov.s $f12, $f15
    li $v0, 2
    syscall
    
    la $a0, closePar
    li $v0, 4
    syscall
  
    la  $a0, space
    li $v0, 4
    syscall
    
    la $a0, openPar
    li $v0, 4
    syscall
    
    mov.s $f12, $f13
    li $v0, 2
    syscall
  
    la  $a0, comma
    li $v0, 4
    syscall
    
    mov.s $f12, $f16
    li $v0, 2
    syscall
    
    la $a0, closePar
    li $v0, 4
    syscall
  
    la  $a0, space
    li $v0, 4
    syscall
    
    la $a0, openPar
    li $v0, 4
    syscall
    
    mov.s $f12, $f14
    li $v0, 2
    syscall
  
    la  $a0, comma
    li $v0, 4
    syscall
    
    mov.s $f12, $f17
    li $v0, 2
    syscall
    
    la $a0, closePar
    li $v0, 4
    syscall
    
    
    #Print message for smallest square root
    la $a0, message2
    li $v0, 4
    syscall
    
    #Print value of smallest square root
    mov.s $f12, $f10
    li $v0, 2
    syscall

    #Terminate program
    li $v0, 10
    syscall