Comment all the things

hal_test.go

@@ -140,44 +140,49 @@ func TestNewton2(t *testing.T) {
 	input := []string{
 		"01 START",
 		"02 LOADNUM 1",
-		"03 STORE 10",
-
-		"10 MUL 10",
-		"11 STORE 11",
-		"12 MUL 10",
-		"13 MUL 10",
-		"14 MUL 10",
-		"15 STORE 20",
-		"16 MUL 10",
-		"17 MULNUM 8",
-		"18 STORE 12",
-		"19 LOAD 11",
-		"20 MULNUM 3",
-		"21 ADD 12",
-		"22 SUBNUM 3",
-		"23 STORE 15",
-
-		"24 SUB 50",
-		"25 JUMPNULL 45",
-		"26 LOAD 15",
+		"03 STORE 10", // Every x is saved to reg 10
+
+		// f(x)
+		"10 MUL 10",   // x²
+		"11 STORE 11", // Save x² to reg 11 for later use since we need that in the second part of the function
+		"12 MUL 10",   // x³
+		"13 MUL 10",   // x⁴
+		"14 MUL 10",   // x⁵
+		"15 STORE 20", // This is x⁵ which we save here to save a few instructions
+		"16 MUL 10",   // x⁶
+		"17 MULNUM 8", // x⁶ * 8
+		"18 STORE 12", // Reg 12 now contains the result of the first part of f(x)
+		"19 LOAD 11",  // Put x² from earlier back in the accumulator
+		"20 MULNUM 3", // x² * 3
+		"21 ADD 12",   // Add the first and second part of the function together, basically 8x⁶ + 3x²
+		"22 SUBNUM 3", // (8x⁶ + 3x²) - 3
+		"23 STORE 15", // Result in reg 15
+
+		// This is our exit condition:
+		// We compare the current result with the last calculated result, if both are equal, we exit
+		"24 SUB 50",      // 50 contains the last result
+		"25 JUMPNULL 45", // If both are equal, we exit
+		"26 LOAD 15",     // Otherwise load reg 15 again, store it as the current last result and continue
 		"27 STORE 50",
 
-		"30 LOAD 20",
-		"31 MULNUM 48",
-		"32 STORE 21",
-		"33 LOAD 10",
-		"34 MULNUM 6",
-		"35 ADD 21",
-		"36 STORE 25",
-
-		"40 LOAD 15",
-		"41 DIV 25",
-		"42 MULNUM -1",
-		"43 ADD 10",
-		"44 JUMP 03",
-
-		"45 LOAD 10",
-		"46 OUT 1",
+		// f'(x)
+		"30 LOAD 20",   // x⁵ which we saved earlier while calculating x⁶
+		"31 MULNUM 48", // x⁵ * 48
+		"32 STORE 21",  // Store the result in 21
+		"33 LOAD 10",   // Load our x
+		"34 MULNUM 6",  // x * 6
+		"35 ADD 21",    // (x * 6) + 48x⁵
+		"36 STORE 25",  // Store the result, which is the total result of f'(x) in reg 25
+
+		// x - f(x) / f'(x)
+		"40 LOAD 15",   // load f(x)
+		"41 DIV 25",    // f(x) / f'(x)
+		"42 MULNUM -1", // Invert the result
+		"43 ADD 10",    // Add x: Because we inverted the result before, we can do this instead of SUB - lets us reuse the content of the accumulator
+		"44 JUMP 03",   // Go to the beginning
+
+		"45 LOAD 10", // Load the result
+		"46 OUT 1",   // Print t
 		"47 STOP",
 	}