From 40b23f19d6906994ed1f6392f46d927123568699 Mon Sep 17 00:00:00 2001
From: Jiri Pittner <jiri@pittnerovi.com>
Date: Thu, 28 Dec 2023 23:57:02 +0100
Subject: [PATCH] improved simple factorization

---
 numbers.cc | 8 ++++----
 numbers.h  | 2 +-
 2 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/numbers.cc b/numbers.cc
index ac8c217..4a829ad 100644
--- a/numbers.cc
+++ b/numbers.cc
@@ -22,12 +22,12 @@
 namespace LA {
 
 template<typename N>
-N primefactor(const N &x)
+N primefactor(const N &x, const N &last)
 {
 N i,t;
    if ( x <= 2 ) return x;
    if ( !(x & 1) ) return 2;
-   i = 3;
+   i = last >3 ? last : 3;
    for (;;) { 
       t = x / i; 
     if ( t < i ) break;
@@ -47,7 +47,7 @@ N y=x;
 N last=0;
 while(y>1)
 	{
-	N z=primefactor(y);
+	N z=primefactor(y,last);
 	if(z!=last)
 		{	
 		std::pair<N,N> p;
@@ -121,7 +121,7 @@ return y;
 //force instantization
 
 #define INSTANTIZE(N) \
-template N primefactor(const N &x); \
+template N primefactor(const N &x, const N &last); \
 template FACTORIZATION<N>  factorization(const N &x); \
 template N nextprime(N x); \
 template std::ostream & operator<<(std::ostream &s, const FACTORIZATION<N>  &x); \
diff --git a/numbers.h b/numbers.h
index da3a9d7..bc70856 100644
--- a/numbers.h
+++ b/numbers.h
@@ -31,7 +31,7 @@
 namespace LA {
 
 template<typename N>
-N primefactor(const N &x);
+N primefactor(const N &x, const N &last=0);
 
 template<typename N>
 bool isprime(const N &x) {return x>1 && x==primefactor(x);}