====== 16-bit "798" Xorshift ======

  * original idea: [[https://www.jstatsoft.org/article/view/v008i14|George Marsaglia]]
  * idea for fast 8-bit implementation: [[http://www.retroprogramming.com/2017/07/xorshift-pseudorandom-numbers-in-z80.html|John Metcalf]]
  * ported by: Veikko Sariola

Xorshift is a fast pseudorandom generator algorithm originally developed by [[https://www.jstatsoft.org/article/view/v008i14|George Marsaglia]]. [[http://www.retroprogramming.com/2017/07/xorshift-pseudorandom-numbers-in-z80.html|John Metcalf]] found a 16-bit version of the algorithm that is fast on 8-bit platforms with only single bit shifts available. It has a period of 65535 and passes reasonable tests for randomness. His pseudocode is reprinted here:

<code c>
/* 16-bit xorshift PRNG */

unsigned x = 1;

unsigned xorshift( )
{
    x ^= x << 7;
    x ^= x >> 9;
    x ^= x << 8;
    return x;
}
</code>

Here is an implementation for the C64. 30 cycles without the RTS.

<code asm>
rng_zp_low = $02
rng_zp_high = $03
        ; seeding
        LDA #1 ; seed, can be anything except 0
        STA rng_zp_low
        LDA #0
        STA rng_zp_high
        ...
        ; the RNG. You can get 8-bit random numbers in A or 16-bit numbers
        ; from the zero page addresses. Leaves X/Y unchanged.
random  LDA rng_zp_high
        LSR
        LDA rng_zp_low
        ROR
        EOR rng_zp_high
        STA rng_zp_high ; high part of x ^= x << 7 done
        ROR             ; A has now x >> 9 and high bit comes from low byte
        EOR rng_zp_low
        STA rng_zp_low  ; x ^= x >> 9 and the low part of x ^= x << 7 done
        EOR rng_zp_high 
        STA rng_zp_high ; x ^= x << 8 done
        RTS
</code>

Results:

{{:base:xorshift_798_results.png?400|}}