1 files changed, 100 insertions, 0 deletions
diff --git a/2018/21_notes.txt b/2018/21_notes.txt
new file mode 100644
index 0000000..905f861
--- /dev/null
+++ b/2018/21_notes.txt
@@ -0,0 +1,100 @@
+L0: // r4 <- 123
+    // r4 <- 72
+    // r4 <- 1
+    jmp L1
+    // jmp L0
+L1: r4 <- 0
+L2: r3 <- r4 | 65536
+    r4 <- 3730679
+L3: // r5 <- r3 & 255
+    // r4 <- r4 + (r3 & 255)
+    // r4 <- (r4 + (r3 & 255)) & 16777215
+    // r4 <- ((r4 + (r3 & 255)) & 16777215) * 65899
+    r4 <- (((r4 + (r3 & 255)) & 16777215) * 65899) & 16777215
+    // r5 <- 256 > r3
+    if (r3 >= 256)
+        then jmp L4
+        else jmp L8
+L4: r5 <- 0
+L5: r2 <- r5 + 1
+    r2 <- r2 * 256
+    // r2 <- r2 > r3
+    if (r2 <= r3)
+        then jmp L6
+        else jmp L7
+L6: r5 <- r5 + 1
+    jmp L5
+L7: r3 <- r5
+    jmp L3
+L8: // r5 <- r4 == r0
+    if (r4 != r0)
+        then jmp L2
+        [else exit]
+
+
+            ↓‾‾‾‾‾‾‾‾‾‾‾|
+0 → 1 → 2 → 3 → 4 → 5 → 7
+        ↑   ↓       ↕
+        └── 8       6
+            ↓
+            *
+
+L5:
+loop {
+    r2 = (r5 + 1) * 256;
+    if r2 > r3 { jmp L7; }
+    r5 += 1;
+}
+
+L5:
+Let x = ceil((r3 + 1) / 256).
+Set r5 = x - 1; r2 = x * 256.
+Jump to L7.
+This takes (x+1)*5+2*x = 7*x+5 instructions.
+
+
+// --------------------------
+
+
+L0: jmp L1 [4 instrs]
+L1: r4 <- 0
+L2: r3 <- r4 | 65536
+    r4 <- 3730679
+L3: r4 <- (((r4 + (r3 & 0xff)) & 0xffffff) * 65899) & 0xffffff [6 instrs]
+    if (r3 >= 256)
+        then jmp L4
+        else jmp L8
+L4: Set r3 = ceil((r3 + 1) / 256) - 1. [7*ceil((r3+1)/256)+6 instrs]
+    jmp L3
+L8: // r5 <- r4 == r0
+    if (r4 != r0)
+        then jmp L2
+        [else exit]
+
+
+            ↓‾‾‾|
+0 → 1 → 2 → 3 → 4
+        ↑   ↓
+        └── 8
+            ↓
+            *
+
+
+// --------------------------
+
+
+Earliest exit is if r0 is equal to the value in r4 on the first arrival at L8.
+
+
+L3:
+loop {
+    r4 = (((r4 + (r3 & 0xff)) & 0xffffff) * 65899) & 0xffffff  [6 instrs]
+    if r3 < 256 { jmp L8 }
+    r3 = ceil((r3 + 1) / 256) - 1  [7*ceil((r3+1)/256)+6 instrs]
+}
+
+exit at 8
+-> r4 == r0 at end of 3, jmp to 8
+-> r4 == r0 and r3 < 256 at end of 3
+-> r3 < 256 and r0 == (((r4 + (r3 & 255)) & 16777215) * 65899) & 16777215 at start of 3
+-> r3 < 256 and r0 == (r4 + r3) * 65899 (mod 2^24) at start of 3