random seed initialization added, tweaked sequence generation

STATUS.md

@@ -237,6 +237,7 @@ Floating point mathematical routines - not official, but well known and broadly
 | `$BFED`   | `exp_FAC1`             | NOT DONE |                                                    |
 | `$E043`   | `poly1_FAC1`           | NOT DONE |                                                    |
 | `$E059`   | `poly2_FAC1`           | NOT DONE |                                                    |
+| `$E09A`   | `rnd_A`                | DONE     |                                                    |
 | `$E0BE`   | `rnd_generate`         | DONE     |                                                    |
 | `$E264`   | `cos_FAC1`             | NOT DONE |                                                    |
 | `$E26B`   | `sin_FAC1`             | NOT DONE |                                                    |

c64/basic/board_x16/cx16_stubs.s

@@ -0,0 +1,8 @@
+// #LAYOUT# X16 BASIC_0 #TAKE
+// #LAYOUT# *   *       #IGNORE
+
+// Stubs for Commander X16 support
+
+
+rnd_seed_init:
+	jmp rnd_generate

c64/basic/math/e09a.interop

@@ -0,0 +1,5 @@
+This is an important floating point math routine, see:
+
+- https://www.atarimagazines.com/compute/issue72/random_numbers.php
+
+XXX - try to find real-life example

c64/basic/math/e09a.rnd_A.s

@@ -0,0 +1,26 @@
+// #LAYOUT# STD *       #TAKE
+// #LAYOUT# *   BASIC_0 #TAKE
+// #LAYOUT# *   *       #IGNORE
+
+//
+// Random number generator routine
+//
+// Input:
+// - .A (0 - reinitialize the seed with random value, $80 or above - create seed from FAC1)
+//
+// Output:
+// - FAC1
+//
+// See also:
+// - https://www.atarimagazines.com/compute/issue72/random_numbers.php
+//
+
+rnd_A:
+
+	cmp #$00
+	beq_16 rnd_seed_init
+
+	cmp #$80
+	bcc_16 rnd_generate
+
+	jmp rnd_seed_from_FAC1

c64/basic/math/e0be.rnd_generate.s

@@ -3,7 +3,7 @@
 // #LAYOUT# *   *       #IGNORE
 
 //
-// A fast random generator, idea from:
+// A fast pseudorandom generator, modified idea from:
 // - https://codebase64.org/doku.php?id=base:32bit_galois_lfsr
 //
 // Output:
@@ -15,8 +15,6 @@
 
 rnd_generate:
 
-	// Generate new 4-byte random number
-
 	asl RNDX+1
 	rol RNDX+2
 	rol RNDX+3
@@ -27,12 +25,15 @@ rnd_generate:
 	lda RNDX+1
 	eor #$B7
 	sta RNDX+1
+
 	lda RNDX+2
 	eor #$1D
 	sta RNDX+2
+
 	lda RNDX+3
 	eor #$C1
 	sta RNDX+3
+
 	lda RNDX+4
 	eor #$04
 	sta RNDX+4
@@ -41,23 +42,32 @@ rnd_generate:
 
 rnd_generate_copy:
 
-	// Copy the number to FAC1, order changed on purpose
+	// Copy the generated number to FAC1, mangle it a little
 
 	lda RNDX+3
+	eor #$62
 	sta FAC1_mantissa+0
+
 	lda RNDX+1
+	eor #$4E
 	sta FAC1_mantissa+1
-	lda RNDX+2
+
-	sta FAC1_mantissa+2
 	lda RNDX+4
+	eor #$97
+	sta FAC1_mantissa+2
+
+	lda RNDX+2
 	sta FAC1_mantissa+3
-	
+
+	// FALLTROUGH
+
+rnd_generate_finalize:
+
 	lda #$00
-	sta FACOV
 	sta FAC1_sign
 	
 	lda #$80
+	sta FACOV                          // just to prevent 0 after normalization
 	sta FAC1_exponent
-	sta RNDX+0                         // in case someone tries to use the float directly
 	
 	jmp normal_FAC1

c64/basic/math/rnd_seed_from_FAC1.s

@@ -0,0 +1,27 @@
+// #LAYOUT# STD *       #TAKE
+// #LAYOUT# *   BASIC_0 #TAKE
+// #LAYOUT# *   *       #IGNORE
+
+//
+// Initialize random seed using values from FAC1,
+// afterwards generate random number in FAC1
+//
+
+rnd_seed_from_FAC1:
+
+	lda FAC1_mantissa+0
+	sta RNDX+4
+
+	eor FAC1_mantissa+1
+	sta RNDX+3
+
+	eor FAC1_mantissa+2
+	sta RNDX+2
+
+	eor FAC1_mantissa+3
+	sta RNDX+1
+
+	eor FAC1_exponent
+	sta RNDX+0
+
+	jmp rnd_generate

c64/basic/math/rnd_seed_init.s

@@ -0,0 +1,33 @@
+// #LAYOUT# STD *       #TAKE
+// #LAYOUT# X16 *       #IGNORE
+// #LAYOUT# *   BASIC_0 #TAKE
+// #LAYOUT# *   *       #IGNORE
+
+//
+// Initialize random seed, afterwards generate random number in FAC1,
+// try to gather as much entropy from different sources as possible
+//
+
+rnd_seed_init:
+
+	eor CIA1_TIMALO                    // timer used for IRQ generation, use potential entropy from .A
+	sta RNDX+3
+
+	txa                                // .X might contain some entropy
+	eor VIC_RASTER                     // lowest 8 bits of current raster line
+	sta RNDX+1
+
+	tya                                // .Y might contain some entropy
+	eor CIA1_TIMAHI
+	sta RNDX+4
+
+	lda TIME+0                         // byte from jiffy counter might be useful too
+	eor SID_RANDOM                     // not sure if SID set correctly, but it will not hurt
+#if CONFIG_MB_MEGA_65
+	eor VIC_XPOS                       // not sure if VIC-IV visible, but it will not hurt
+#endif
+	sta RNDX+2
+
+	// RNDX+0 will be overwritten by generator
+
+	jmp rnd_generate