#include <cstring>
#include <cmath>
#include <cassert>
#include "numalgo.h"
#include "primes.h"

using namespace std;

vector<int> smallprimes;
bool smallprimes_inited=false;

void fillsmallprimes(){
	smallprimes_inited=true;
	//TODO: reserve expected amount of space in smallprimes
	smallprimes.push_back(2);
	const int highbound=65000;
	bool composite[highbound/2]; //entries for 3, 5, 7, 9, etc.
	memset(composite,0,highbound/2*sizeof(bool));
	int roothighbound=sqrt(highbound);
	for(int i=3;i<=highbound;i+=2){
		if(composite[i/2-1])continue;
		smallprimes.push_back(i);
		if(i>roothighbound)continue;
		for(int j=i*i;j<=highbound;j+=2*i){
			composite[j/2-1]=true;
		}
	}
	//for(int p : smallprimes)cerr<<p<<' ';
	//cerr<<endl;
}

pair<Bigint,Bigint> genprimepair(int nbits){
	// for x = nbits/2:
	// (2^x)^2 = 2^(2x)
	// (2^x + 2^(x-2))^2 = 2^(2x) + 2^(2x-1) + 2^(2x-4)
	// ergo: (2^x + lambda*2^(x-2))^2 \in [2^(2x), 2^(2x+1)), for lambda \in [0,1]
	// To make sure the primes "differ in length by a few digits" [RSA78], we use x1=x-2 in the first
	// prime and x2-x+2 in the second
	int x1=nbits/2-2,x2=(nbits+1)/2+2;
	assert(x1+x2==nbits);
	return make_pair(
		randprime(Bigint::one<<x1,(Bigint::one<<x1)+(Bigint::one<<(x1-2))),
		randprime(Bigint::one<<x2,(Bigint::one<<x2)+(Bigint::one<<(x2-2))));
}

Bigint randprime(const Bigint &biglow,const Bigint &bighigh){
	if(!smallprimes_inited)fillsmallprimes();

	assert(bighigh>biglow);
	static const int maxrangesize=100001;
	Bigint diff(bighigh-biglow);
	Bigint low,high; //inclusive
	if(diff<=maxrangesize){
		low=biglow;
		high=bighigh;
	} else {
		high=low=cryptrandom_big(diff-maxrangesize);
		high+=maxrangesize;
	}
	if(low.even())low+=1;
	if(high.even())high-=1;
	Bigint sizeb(high-low+1);
	assert(sizeb>=0&&sizeb<=maxrangesize);
	int nnums=(sizeb.lowdigits()+1)/2;

	bool composite[nnums]; //low, low+2, low+4, ..., high (all odd numbers)
	memset(composite,0,nnums*sizeof(bool));
	int nsmallprimes=smallprimes.size();
	for(int i=1;i<nsmallprimes;i++){
		int pr=smallprimes[i];
		int lowoffset=low.divmod(Bigint(pr)).second.lowdigits();
		int startat;
		if(lowoffset==0)startat=0;
		else if((pr-lowoffset)%2==0)startat=(pr-lowoffset)/2;
		else startat=pr-lowoffset;
		for(int i=startat;i<nnums;i+=pr){ //skips ahead `2*pr` each time (so `pr` array elements)
			composite[i]=true;
		}
	}
}

bool bailliePSW(const Bigint&);