Editing Linear-feedback shift register (section)

== Xorshift LFSRs ==
{{Main | Xorshift}}
As shown by [[George Marsaglia]]<ref name="marsaglia">{{cite journal
| first=George | last=Marsaglia | author-link=George Marsaglia
| title=Xorshift RNGs
| journal=[[Journal of Statistical Software]]
| volume=8 | issue=14
| date=July 2003
| url=https://www.jstatsoft.org/v08/i14/paper | doi=10.18637/jss.v008.i14| doi-access=free}}</ref> and further analysed by [[Richard P. Brent]],<ref name="brent">{{cite journal
| first=Richard P. | last=Brent | author-link=Richard P. Brent
| title=Note on Marsaglia's Xorshift Random Number Generators
| journal=[[Journal of Statistical Software]]
| volume=11 | issue=5
| date=August 2004
| url=https://www.jstatsoft.org/v11/i05/paper | doi=10.18637/jss.v011.i05| doi-access=free| hdl=1885/34049| hdl-access=free}}</ref> linear feedback shift registers can be implemented using XOR and Shift operations. This approach lends itself to fast execution in software because these operations typically map efficiently into modern processor instructions.

Below is a [[C (programming language)|C]] code example for a 16-bit maximal-period Xorshift LFSR using the 7,9,13 triplet from John Metcalf:<ref>{{cite web |last1=Metcalf |first1=John |title=16-Bit Xorshift Pseudorandom Numbers in Z80 Assembly |url=http://www.retroprogramming.com/2017/07/xorshift-pseudorandom-numbers-in-z80.html |website=Retro Programming |access-date=5 January 2022|date=22 July 2017}}</ref>
<syntaxhighlight lang="c">
#include <stdint.h>
unsigned lfsr_xorshift(void)
{
    uint16_t start_state = 0xACE1u;  /* Any nonzero start state will work. */
    uint16_t lfsr = start_state;
    unsigned period = 0;

    do
    {   // 7,9,13 triplet from http://www.retroprogramming.com/2017/07/xorshift-pseudorandom-numbers-in-z80.html
        lfsr ^= lfsr >> 7;
        lfsr ^= lfsr << 9;
        lfsr ^= lfsr >> 13;
        ++period;
    }
    while (lfsr != start_state);

    return period;
}
</syntaxhighlight>