Update const_PI

Allow a patched best rounded value or the original value from the MS BASIC

src/basic/math_consts/aea8.const_PI.s

@@ -3,12 +3,23 @@
 ;; #LAYOUT# *   BASIC_0 #TAKE
 ;; #LAYOUT# *   *       #IGNORE
 
+; This file is under the MIT license, it contains code released by Microsoft Corporation.
+; See LICENSE for more information.
+
+; Math package - The floating point constant PI
+;
+; This is verified to be identical to the original Microsoft implementation where it was named PIVAL.
 ;
-; Math package - a constant, for documentation see:
 ; - https://www.c64-wiki.com/wiki/BASIC-ROM
 ; - Computes Mapping the Commodore 64, page 103
 ;
 
 const_PI:
 
+; The original BASIC didn't have the most accurate PI.
+
+!ifdef CONFIG_ORIGINAL_UNPATCHED_BASIC {
+    +PUT_CONST_PI_MS
+} else {
 	+PUT_CONST_PI
+}

tools/generate_constants.cc

@@ -52,6 +52,8 @@ std::vector<ConstEntry> GLOBAL_constants =
 
 	ConstEntry(   "HALF_PI", M_PI / 2.0           ),
 	ConstEntry(        "PI", M_PI                 ),
+	ConstEntry(     "PI_MS", 3.1415926529         ),      // This is the value of PI used in the Microsoft BASIC. It is only the third closest approximation
+
 	ConstEntry( "DOUBLE_PI", M_PI * 2.0           ),
 	ConstEntry(     "SQR_2", std::sqrt(2.0)       ),
 	ConstEntry( "INV_SQR_2", 1.0 / std::sqrt(2.0) ),

tools/similarity.c

@@ -20,9 +20,10 @@ int matches[MAX_SIZE];
 
 int phase_mask[MAX_SIZE+MAX_SIZE];
 
-#define NUM_CHUNKS 13
+#define NUM_CHUNKS 14
 // Pairs of start, end memory addresses of known exact similarity with the open source Microsoft BASIC
 unsigned short microsoft_basic_chunks[NUM_CHUNKS * 2] = {
+    0xAEA8, 0xAEAC,
     0xB248, 0xB24C,
     0xB391, 0xB39D,
     0xB3A2, 0xB3A5,