Add some comments to piet pseudocode file

Author: ThijsRay

contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet

@@ -1,3 +1,14 @@
+This file describes the path that the Piet program takes in a more human readable form. 
+Two functions are implemented:
+- GCD with subtraction
+- GCD with the modulo operator
+
+-------------------
+SUBTRACTION
+-------------------
+
+Pseudo code:
+
 function gcd(a, b)
     while a ≠ b 
         if a > b
@@ -6,9 +17,12 @@ function gcd(a, b)
            b := b − a; 
     return a;
 
-in(number)              A
-// absolute of A
-duplicate               AA
+
+Piet code:
+
+COMMAND                 STATE OF STACK
+in(number)              A           // Take A as an input
+duplicate               AA          // Start to take the absolute value of A
 push 1                  1AA
 duplicate               11AA
 subtract                0AA
@@ -20,11 +34,10 @@ subtract                -2 1/0 A
 multiply                -2/0 A
 push 1                  1 -2/0 A
 add                     -1/1 A
-multiply                A
+multiply                A           // A should now be an absolute value
 
-in(number)              BA
-// absolute of B
-duplicate               BBA
+in(number)              BA          // Take B as an input
+duplicate               BBA         // Start to take the absolute value of B
 push 1                  1BBA
 duplicate               11BBA
 subtract                0BBA
@@ -36,9 +49,9 @@ subtract                -2 1/0 BA
 multiply                -2/0 BA
 push 1                  1 -2/0 BA
 add                     -1/1 BA
-multiply                BA
+multiply                BA          // B should now be an absolute value
 
-// Start of loop
+// Start of the main loop while a ≠ b 
 duplicate               BBA
 push 3                  3BBA
 push 2                  23BBA
@@ -50,9 +63,9 @@ roll                    ABBA
 subtract                0/x BA
 not                     1/0 BA      // 1 if a = b and 0 if a ≠ b
 not                     0/1 BA      // 1 if a ≠ b and 0 if a = b
-pointer                 BA
+pointer                 BA          // If a ≠ b, the DP should change one clockwise, otherwise, go straight ahead.
 
-    // Go left if a ≠ b
+    // Go left if a ≠ b (DP changed one clockwise)
     duplicate               BBA
     push 3                  3BBA
     push 2                  23BBA
@@ -65,9 +78,9 @@ pointer                 BA
     push 1                  12ABBA
     roll                    BABA
     greater                 0/1 BA          // A > B; 1 if true; 0 if false
-    pointer                 BA              // maybe a switch here instead?
+    pointer                 BA              // If A > B, DP goes one clockwise, otherwise, DP stays the same. 
 
-        // If A > B
+        // If A > B (DP has changed 1 clockwise)
         duplicate               BBA
         push 3                  3BBA
         push 1                  13BBA
@@ -78,8 +91,7 @@ pointer                 BA
         roll                    BA
         // Go back to start of loop
 
-        // If B > A
-        // b = b - a
+        // If B > A (DP stayed the same)
         push 2                  2BA
         push 1                  12BA
         roll                    AB
@@ -92,17 +104,26 @@ pointer                 BA
 
 // Go down if a = b (end of while loop)
 pop                     A
-out(number)             -
+out(number)             -               // Print out A when done.
 
 ---------------------------------------------------------------------------
 
+-------------------
+MODULO
+-------------------
+
+Pseudo code:
+
 function gcd(a, b)
     while b ≠ 0
        t := b; 
        b := a mod b; 
        a := t; 
     return a;
 
+Piet code:
+
+COMMAND                 STATE OF STACK
 in(number)              A
 in(number)              BA
 
@@ -122,5 +143,4 @@ pointer                 BA
 
 // Go right if b = 0
 pop                     A
-out(number)             -
-
+out(number)             -               // Print out A when done.