implement Mersenne; include "sys.m";	sys : Sys;include "draw.m";include "keyring.m";	keyring: Keyring;	IPint: import keyring; # Test primality of Mersenne numbers Mersenne: module{	init: fn(nil: ref Draw->Context, argv: list of string);}; init(nil: ref Draw->Context, argv: list of string){	sys = load Sys Sys->PATH;	keyring = load Keyring Keyring->PATH;	p := 3;	if(tl argv != nil)		p = int hd tl argv;	if(isprime(p) && (p == 2 || lucas(p)))		s := "";	else		s = "not ";	sys->print("2^%d-1 is %sprime\n", p, s);} # s such that s^2 <= nsqrt(n: int): int{	v := n;	r := 0;	for(t := 1<<30; t; t >>= 2){		if(t+r <= v){			v -= t+r;			r = (r>>1)|t;		}		else			r = r>>1;	}	return r;} isprime(n: int): int{	if(n < 2)		return 0;	if(n == 2)		return 1;	if((n&1) == 0)		return 0;	s := sqrt(n);	for(i := 3; i <= s; i += 2)		if(n%i == 0)			return 0;	return 1;} pow(b : ref IPint, n : int): ref IPint{	zero := IPint.inttoip(0);	one := IPint.inttoip(1);	if((b.cmp(zero) == 0 && n != 0) || b.cmp(one) == 0 || n == 1)		return b;	if(n == 0)		return one;	c := b;	b = one;	while(n){		while(!(n & 1)){			n >>= 1;			c = c.mul(c);		}		n--;		b = c.mul(b);	}	return b;} lucas(p: int): int{	zero := IPint.inttoip(0);	one := IPint.inttoip(1);	two := IPint.inttoip(2);	bigp := pow(two, p).sub(one);	u := IPint.inttoip(4);	for(i := 2; i < p; i++){		u = u.mul(u);		if(u.cmp(two) <= 0)			u = two.sub(u);		else			u = u.sub(two).expmod(one, bigp);	}	return u.cmp(zero) == 0;}