From 1286703bd7b932f3253b7e1b756b338637141a90 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Thu, 4 Oct 2018 21:14:39 +0200
Subject: [PATCH 01/13] Add Piet program for Euclidian Algorithm with the
 modulo operator

---
 .../code/piet/euclidian_algorithm_mod.png         | Bin 0 -> 136 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod.png

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod.png b/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod.png
new file mode 100644
index 0000000000000000000000000000000000000000..62459a1357e2fe1a3e6c758440c000eaac6da61f
GIT binary patch
literal 136
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gvEkKS{QiHL*UVAL{#N+sIM5UZPgg&ebxsLQ03Kp0bN~PV

literal 0
HcmV?d00001


From f8929ce44732f2ce565ef7671f7bd9e5a9e41c86 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Thu, 4 Oct 2018 21:36:00 +0200
Subject: [PATCH 02/13] Add larger version of the euclidian algorithm for human
 readers

---
 .../code/piet/euclidian_algorithm_mod_large.png   | Bin 0 -> 786 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod_large.png

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod_large.png b/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod_large.png
new file mode 100644
index 0000000000000000000000000000000000000000..026568aad1920cdc7e5c12fff6c2313bdada2eca
GIT binary patch
literal 786
zcmeAS@N?(olHy`uVBq!ia0y~yU{V9JPjD~+$>7?(r+^e^fk$L91B0G22s2hJwJ!sz
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literal 0
HcmV?d00001


From 9b4454e5ae0e096212253dd1c3dc0aac5c7dd604 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Fri, 5 Oct 2018 00:06:57 +0200
Subject: [PATCH 03/13] Add basic euclidian algorithm subtraction in Piet

---
 .../code/piet/euclidian_algorithm.piet        |  97 ++++++++++++++++++
 .../{ => mod}/euclidian_algorithm_mod.png     | Bin
 .../code/piet/mod/euclidian_algorithm_mod.ppm | Bin 0 -> 189 bytes
 .../euclidian_algorithm_mod_large.png         | Bin
 .../subtract/euclidian_algorithm_subtract.png | Bin 0 -> 327 bytes
 .../subtract/euclidian_algorithm_subtract.ppm | Bin 0 -> 2410 bytes
 6 files changed, 97 insertions(+)
 create mode 100644 contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
 rename contents/euclidean_algorithm/code/piet/{ => mod}/euclidian_algorithm_mod.png (100%)
 create mode 100644 contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm
 rename contents/euclidean_algorithm/code/piet/{ => mod}/euclidian_algorithm_mod_large.png (100%)
 create mode 100644 contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.png
 create mode 100644 contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
new file mode 100644
index 000000000..e400523e8
--- /dev/null
+++ b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
@@ -0,0 +1,97 @@
+function gcd(a, b)
+    while a ≠ b 
+        if a > b
+           a := a − b; 
+        else
+           b := b − a; 
+    return a;
+
+in(number)              A
+in(number)              BA
+
+// Start of loop
+duplicate               BBA
+push 3                  3BBA
+push 2                  23BBA
+roll                    ABB
+duplicate               AABB
+push 4                  4AABB
+push 1                  14AABB
+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
+
+    // Go down if a ≠ b
+    duplicate               BBA
+    push 3                  3BBA
+    push 2                  23BBA
+    roll                    ABB
+    duplicate               AABB
+    push 4                  4AABB
+    push 1                  14AABB
+    roll                    ABBA
+    push 2                  2ABBA
+    push 1                  12ABBA
+    roll                    BABA
+    greater                 0/1 BA          // A > B; 1 if true; 0 if false
+    pointer                 BA              // maybe a switch here instead?
+
+        // If A > B
+        duplicate               BBA
+        push 3                  3BBA
+        push 1                  13BBA
+        roll                    BAB
+        subtract                AB              // A = A - B
+        push 2                  2AB
+        push 1                  12AB
+        roll                    BA
+        // Go back to start of loop
+
+        // If B > A
+        // b = b - a
+        push 2                  2BA
+        push 1                  12BA
+        roll                    AB
+        duplicate               AAB
+        push 3                  3AAB
+        push 1                  13AAB
+        roll                    ABA
+        subtract                BA              // B = B - A
+        // Go back to start of loop
+
+// Go right if a = b (end of while loop)
+pop                     A
+out(number)             -
+
+---------------------------------------------------------------------------
+
+function gcd(a, b)
+    while b ≠ 0
+       t := b; 
+       b := a mod b; 
+       a := t; 
+    return a;
+
+in(number)              A
+in(number)              BA
+
+//  Start of loop
+duplicate               BBA
+not                     0/1 BA
+not                     1/0 BA
+pointer                 BA
+
+    // Go down if b ≠ 0
+    duplicate               TBA
+    push 3                  3TBA                  
+    push 1                  13TBA
+    roll                    BAT
+    mod                     BA          // b = a mod b; a = t
+    // Go back to the start of the loop
+
+// Go right if b = 0
+pop                     A
+out(number)             -
+
diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod.png b/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.png
similarity index 100%
rename from contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod.png
rename to contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.png
diff --git a/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm b/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm
new file mode 100644
index 0000000000000000000000000000000000000000..2292b07d3ecaea7daeff512c38ef85fd0fa2024e
GIT binary patch
literal 189
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zR50N(GBxG;&%kitz<-7VK*+!Vq!0Z6|DWOie-IBH8~_P`B!LL50H_xkfOLWZL;+9@
TkdLeeWC=(sQ1bzpN)QbIemy#O

literal 0
HcmV?d00001

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod_large.png b/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod_large.png
similarity index 100%
rename from contents/euclidean_algorithm/code/piet/euclidian_algorithm_mod_large.png
rename to contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod_large.png
diff --git a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.png b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.png
new file mode 100644
index 0000000000000000000000000000000000000000..684df44549810de5a77f0abb2b3aab5a7553d3fe
GIT binary patch
literal 327
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literal 0
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diff --git a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
new file mode 100644
index 0000000000000000000000000000000000000000..1f2476f59c13ad5db4f23221b3fcd79157fe9680
GIT binary patch
literal 2410
zcmeH{O=`n15QVk&DFj_7w1$N2yC_|x_zEpGArR7%{y=XxH&fs9*g=dGY>{MBIuT-K
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literal 0
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From d4b17ab51836228cefcb73d2b8155e156280e734 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Fri, 5 Oct 2018 23:10:13 +0200
Subject: [PATCH 04/13] Refactor euclidian algorithm subtract in Piet

---
 .../subtract/euclidian_algorithm_subtract.ppm | Bin 2410 -> 8189 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
index 1f2476f59c13ad5db4f23221b3fcd79157fe9680..b8e6cf4316d965e53caa1c60e670d91b16384ede 100644
GIT binary patch
literal 8189
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z+olgcyKkva>*ez{tv7Ekn|_s^Kb~Hff0q5f$Nu%@ZL{3|T|K^k{N8T*r|tLkdetrN
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literal 2410
zcmeH{O=`n15QVk&DFj_7w1$N2yC_|x_zEpGArR7%{y=XxH&fs9*g=dGY>{MBIuT-K
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S9s^}i`w&fFPE;6|8DYPfUXp77


From 4d2cc2bb0ae972f31d979deb8b8893d9b3c886f5 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sat, 6 Oct 2018 00:13:27 +0200
Subject: [PATCH 05/13] Add absolute value commands to text code

---
 .../code/piet/euclidian_algorithm.piet        | 29 +++++++++++++++++++
 1 file changed, 29 insertions(+)

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
index e400523e8..96d437b8e 100644
--- a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
+++ b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
@@ -7,7 +7,36 @@ function gcd(a, b)
     return a;
 
 in(number)              A
+// absolute of A
+duplicate               AA
+push 1                  1AA
+duplicate               11AA
+subtract                0AA
+greater                 0/1A        // 1 if A > 0, 0 if A <= 0
+not                     1/0A        // 0 if A > 0, 1 if A <= 0
+push 1                  1 1/0 A
+push 3                  31 1/0 A
+subtract                -2 1/0 A
+multiply                -2/0 A
+push 1                  1 -2/0 A
+add                     -1/1 A
+multiply                A
+
 in(number)              BA
+// absolute of B
+duplicate               BBA
+push 1                  1BBA
+duplicate               11BBA
+subtract                0BBA
+greater                 0/1BA        // 1 if B > 0, 0 if B <= 0
+not                     1/0BA        // 0 if B > 0, 1 if B <= 0
+push 1                  1 1/0 BA
+push 3                  31 1/0 BA
+subtract                -2 1/0 BA
+multiply                -2/0 BA
+push 1                  1 -2/0 BA
+add                     -1/1 BA
+multiply                BA
 
 // Start of loop
 duplicate               BBA

From 2ced02770ec21a6dceee6d897be0c474fe9672eb Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sat, 6 Oct 2018 00:39:50 +0200
Subject: [PATCH 06/13] Add working Piet program with absolute operator in it

---
 .../code/piet/euclidian_algorithm.piet        |   4 +-
 .../subtract/euclidian_algorithm_subtract.ppm | 169 ++++++++++++------
 2 files changed, 112 insertions(+), 61 deletions(-)

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
index 96d437b8e..57122f5bd 100644
--- a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
+++ b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
@@ -52,7 +52,7 @@ 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
 
-    // Go down if a ≠ b
+    // Go left if a ≠ b
     duplicate               BBA
     push 3                  3BBA
     push 2                  23BBA
@@ -90,7 +90,7 @@ pointer                 BA
         subtract                BA              // B = B - A
         // Go back to start of loop
 
-// Go right if a = b (end of while loop)
+// Go down if a = b (end of while loop)
 pop                     A
 out(number)             -
 
diff --git a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
index b8e6cf431..0a4614c4d 100644
--- a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
+++ b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
@@ -1,95 +1,146 @@
 P3
 # a piet program euclidian_algorithm_subtract.ppm
-25 25
+31 30
 255
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-255 192 192  255   0   0    0   0 192    0 192   0    0 192   0  192 255 192 
-  0 255   0  192   0   0  255 255 192    0 192 192  255   0 255    0 192   0 
-  0 255   0    0 255   0    0   0   0  192 192   0    0   0   0  255 255 255 
-255 255 255  255 255 255  255 255 255    0   0   0  192   0   0    0   0   0 
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-  0   0   0  255 255 255  255 255 255  255 255 255  255 255 255    0 192   0 
-255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255  192   0   0    0   0   0  255 255 255    0   0   0  192 192   0 
-  0   0   0  255 255 255  255 255 255  255 255 255  255 255 255    0   0   0 
-255 255 255    0   0   0  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 192  192   0 192    0 192 192  192 255 255  255 255 192    0 255   0 
+255   0 255  255 255 192  255 255   0  255 255   0  192 192   0  192 255 192 
+  0 192 192  192 255 255  192 192 255  192   0 192    0 255 255  255 255   0 
+192 192   0  192   0 192  255 192 192  192 255 255  192   0 192  255 192 255 
+255 192 255  255   0 255  192   0   0  255 255   0  192 192   0    0 192   0 
+  0 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255   0  255 255 255    0   0   0 
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+255 192 255    0   0   0    0   0   0    0   0   0    0   0   0    0   0   0 
+  0   0   0    0 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
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 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255  255 255 255  255 255 255  255 192 192    0   0   0  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255    0   0   0  255 255 255    0   0   0  255 255 255  255 255 255 
+  0 255 255  255 255   0  255 255   0  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255  255 255 255  255 255 255  255 255 255  255   0   0    0   0   0 
+255 255 255    0   0   0  255 255 255    0   0   0  255 255 255    0   0   0 
+  0   0   0    0   0   0    0   0   0    0   0   0    0   0   0    0   0   0 
+  0   0   0    0   0   0    0   0   0    0   0   0    0   0   0    0   0   0 
+  0   0   0    0   0   0    0   0   0  255 255   0  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255    0   0   0  255 255 255    0   0   0  255 255 255 
-255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255  255 255 255  255 255 255  255 255 255  255 255 255    0   0 192 
   0   0   0  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  192 192   0  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255    0   0   0  255 255 255    0   0   0 
+255 255 255    0   0   0  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
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+255 255 255  255 255 255    0   0   0  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
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+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
+255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
@@ -106,4 +157,4 @@ P3
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
 255 255 255  255 255 255  255 255 255  255 255 255  255 255 255  255 255 255 
-255 255 255  
+

From ca31a494225d8adf88e6ab482824f01c226cbdd7 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sat, 6 Oct 2018 00:49:29 +0200
Subject: [PATCH 07/13] Add some comments to piet pseudocode file

---
 .../code/piet/euclidian_algorithm.piet        | 56 +++++++++++++------
 1 file changed, 38 insertions(+), 18 deletions(-)

diff --git a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet b/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
index 57122f5bd..d91499ae5 100644
--- a/contents/euclidean_algorithm/code/piet/euclidian_algorithm.piet
+++ b/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
@@ -92,10 +104,16 @@ 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; 
@@ -103,6 +121,9 @@ function gcd(a, 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.

From 6f35490f08359c434d2f891f926413e7928947ab Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sat, 6 Oct 2018 01:23:52 +0200
Subject: [PATCH 08/13] Add some art to fill up the empty space in the
 euclidian subtraction Piet program

---
 .../subtract/euclidian_algorithm_subtract.ppm | Bin 12154 -> 2011 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm b/contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
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From 3758037ec8ea5f16454fba562e54f9f1c5676ba8 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sat, 6 Oct 2018 01:31:01 +0200
Subject: [PATCH 09/13] Add larger .png file for subtract method

---
 .../code/piet/mod/euclidian_algorithm_mod.ppm   | Bin 189 -> 0 bytes
 .../subtract/euclidian_algorithm_subtract.png   | Bin 327 -> 500 bytes
 .../subtract/euclidian_algorithm_subtract.ppm   | Bin 2011 -> 0 bytes
 .../euclidian_algorithm_subtract_large.png      | Bin 0 -> 2473 bytes
 4 files changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm
 delete mode 100644 contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract.ppm
 create mode 100644 contents/euclidean_algorithm/code/piet/subtract/euclidian_algorithm_subtract_large.png

diff --git a/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm b/contents/euclidean_algorithm/code/piet/mod/euclidian_algorithm_mod.ppm
deleted file mode 100644
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From 516331237d78bb3c9be7dbd92e60600d9898ee6e Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sun, 7 Oct 2018 16:08:26 +0200
Subject: [PATCH 10/13] Add the images to the euclidian algorithm page

---
 contents/euclidean_algorithm/euclidean_algorithm.md | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/contents/euclidean_algorithm/euclidean_algorithm.md b/contents/euclidean_algorithm/euclidean_algorithm.md
index ff05c7af9..ad84587ff 100644
--- a/contents/euclidean_algorithm/euclidean_algorithm.md
+++ b/contents/euclidean_algorithm/euclidean_algorithm.md
@@ -63,6 +63,8 @@ The algorithm is a simple way to find the *greatest common divisor* (GCD) of two
 [import:25-40, lang="LOLCODE"](code/lolcode/euclid.lol)
 {% sample lang="bash" %}
 [import:24-38, lang="bash"](code/bash/euclid.bash)
+{% sample lang="piet" %}
+> ![](code/piet/subtract/euclidian_algorithm_subtract_large.png) ![](code/piet/subtract/euclidian_algorithm_subtract.png)
 {% endmethod %}
 
 Here, we simply line the two numbers up every step and subtract the lower value from the higher one every timestep. Once the two values are equal, we call that value the greatest common divisor. A graph of `a` and `b` as they change every step would look something like this:
@@ -132,6 +134,8 @@ Modern implementations, though, often use the modulus operator (%) like so
 [import:9-23, lang="LOLCODE"](code/lolcode/euclid.lol)
 {% sample lang="bash" %}
 [import:10-22, lang="bash"](code/bash/euclid.bash)
+{% sample lang="piet" %}
+> ![](code/piet/mod/euclidian_algorithm_mod_large.png) ![](code/piet/mod/euclidian_algorithm_mod.png)
 {% endmethod %}
 
 Here, we set `b` to be the remainder of `a%b` and `a` to be whatever `b` was last timestep. Because of how the modulus operator works, this will provide the same information as the subtraction-based implementation, but when we show `a` and `b` as they change with time, we can see that it might take many fewer steps:
@@ -209,6 +213,10 @@ and modulo method:
 [import, lang="LOLCODE"](code/lolcode/euclid.lol)
 {% sample lang="bash" %}
 [import, lang="bash"](code/bash/euclid.bash)
+{% sample lang="piet" %}
+> ![](code/piet/subtract/euclidian_algorithm_subtract_large.png) ![](code/piet/subtract/euclidian_algorithm_subtract.png)
+
+> ![](code/piet/mod/euclidian_algorithm_mod_large.png) ![](code/piet/mod/euclidian_algorithm_mod.png)
 {% endmethod %}
 
 <script>

From 55c5624c7a96be6bc2d595251f2f6d6d0e0c7126 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sun, 7 Oct 2018 16:13:05 +0200
Subject: [PATCH 11/13] Add Piet as a language

---
 book.json | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/book.json b/book.json
index 7fae5c319..9e872d1da 100644
--- a/book.json
+++ b/book.json
@@ -167,6 +167,10 @@
         {
           "lang": "lolcode",
           "name": "LOLCODE"
+        },
+        {
+          "lang": "piet",
+          "name": "Piet"
         }
       ]
     }

From 16ee02dc7be9f7d22ac5799cce66677b7f131d9a Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sun, 7 Oct 2018 16:14:13 +0200
Subject: [PATCH 12/13] Add name to contributers list

---
 CONTRIBUTORS.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
index e840617b6..c942f3bc2 100644
--- a/CONTRIBUTORS.md
+++ b/CONTRIBUTORS.md
@@ -37,4 +37,5 @@
 - Ken Power
 - PaddyKe
 - nic-hartley
+- Thijs Raymakers
 - crafter312

From 539cd5869d75cd93b3b60b1c37d2c7fe6de24536 Mon Sep 17 00:00:00 2001
From: Thijs Raymakers <thijs@raymakers.nl>
Date: Sun, 7 Oct 2018 16:28:05 +0200
Subject: [PATCH 13/13] Add text version of the program to the 'Example code'
 section

---
 contents/euclidean_algorithm/euclidean_algorithm.md | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/contents/euclidean_algorithm/euclidean_algorithm.md b/contents/euclidean_algorithm/euclidean_algorithm.md
index ad84587ff..8e336f174 100644
--- a/contents/euclidean_algorithm/euclidean_algorithm.md
+++ b/contents/euclidean_algorithm/euclidean_algorithm.md
@@ -214,9 +214,16 @@ and modulo method:
 {% sample lang="bash" %}
 [import, lang="bash"](code/bash/euclid.bash)
 {% sample lang="piet" %}
+A text version of the program is provided for both versions.
+#### Subtraction
 > ![](code/piet/subtract/euclidian_algorithm_subtract_large.png) ![](code/piet/subtract/euclidian_algorithm_subtract.png)
 
+[import:23-107](code/piet/euclidian_algorithm.piet)
+
+#### Modulo
 > ![](code/piet/mod/euclidian_algorithm_mod_large.png) ![](code/piet/mod/euclidian_algorithm_mod.png)
+
+[import:126-146](code/piet/euclidian_algorithm.piet)
 {% endmethod %}
 
 <script>