rand() use XOR to break up unwanted pair correlation (#1107)

* rand() use XOR to break up unwanted pair correlation

This form of rand() cannot return the same value twice in a row.
Two additonal EOR instructions produce a more even distribution of successive pairs.
see comments on #951

* rand.s document purpose of XOR

* suggested srand() optimization: zero fill unnecessary

* test to validate implementation of rand()

* srand() improving behaviour and adding startup test

* srand() with a tail call to rand() for better initial shuffle

* srand() can fall through to rand() instead of tail call

libsrc/common/rand.s

@@ -15,14 +15,14 @@
 ;  Multiplier must be 1 (mod 4)
 ;  Added value must be 1 (mod 2)
 ;  This guarantees max. period (2**32)
-;  The lowest bits have poor entropy and
-;  exhibit easily detectable patterns, so
-;  only the upper bits 16-22 and 24-31 of the
-;  4-byte state are returned.
+;  The quality of entropy in the bits of the seed are poorest in the lowest
+;  bits, and best in the highest bits.
 ;
-;  The best 8 bits, 24-31 are returned in the
-;  low byte A to provide the best entropy in the
-;  most commonly used part of the return value.
+;  The high 8 bits are used for the low byte A to provide the best entropy in
+;  the most commonly used part of the return value.
+;
+;  Finally XOR with the lower 2 bytes is used on the output, which breaks up
+;  some minor deficient sequential patterns. (#951)
 ;
 ;  Uses the following LCG values for ax + c (mod m)
 ;  a = $01010101
@@ -42,10 +42,15 @@
 
 ; The seed. When srand() is not called, the C standard says that that rand()
 ; should behave as if srand() was called with an argument of 1 before.
-rand:   .dword   1
+rand:   .dword $B5B5B4B4
 
 .code
 
+_srand: sta     rand+0          ; Store the seed
+        stx     rand+1
+        sta     rand+2          ; argument << 16 is convenient fill for MSW
+        stx     rand+3
+        ; fall through to rand() to sufficiently "shuffle" first rand() result
 _rand:  clc
         lda     rand+0
         adc     #$B3
@@ -54,18 +59,11 @@ _rand:  clc
         sta     rand+1
         adc     rand+2
         sta     rand+2
+        eor     rand+0
         and     #$7f            ; Suppress sign bit (make it positive)
         tax
         lda     rand+2
         adc     rand+3
         sta     rand+3
+        eor     rand+1
         rts                     ; return bit (16-22,24-31) in (X,A)
-
-_srand: sta     rand+0          ; Store the seed
-        stx     rand+1
-        lda     #0
-        sta     rand+2          ; Set MSW to zero
-        sta     rand+3
-        rts
-
-