
April 17th, 2013, 03:11 AM
#1
Lehmer gcd algorithm
Hey guys!
I have a problem with programming a Lehmer's gcd algorithm. It works fine but the problem is that it's slower than the basic euclidean algorithm. Can anyone tell me where is the problem.
This is my code in java:
private static BigInteger LEHMER(BigInteger A0, BigInteger A1) {
BigInteger compareNum = new BigInteger("4294967296"); //4294967296 = math.pow(2,32)
while( A1.compareTo(compareNum) >= 0) {
int h = A0.bitCount()+1  32;
BigInteger a0 = A0.shiftRight(h);
BigInteger a1 = A1.shiftRight(h);
BigInteger u0 = new BigInteger("1");
BigInteger u1 = new BigInteger("0");
BigInteger v0 = new BigInteger("0");
BigInteger v1 = new BigInteger("1");
while( !a1.add(u1).equals(BigInteger.ZERO) &&
!a1.add(v1).equals(BigInteger.ZERO)) {
BigInteger q0 = a0.add(u0).divide(a1.add(u1));
if (!q0.equals(a0.add(v0).divide(a1.add(v1))))
break;
BigInteger r = a0.subtract(q0.multiply(a1)); a0 = a1; a1 = r;
r = u0.subtract(q0.multiply(u1)); u0 = u1; u1 = r;
r = v0.subtract(q0.multiply(v1)); v0 = v1; v1 = r;
}
if (v0.equals(BigInteger.ZERO)) {
BigInteger R = A0.remainder(A1); A0 = A1; A1 = R;
}
else {
BigInteger R = u0.multiply(A0).add(v0.multiply(A1));
BigInteger T = u1.multiply(A0).add(v1.multiply(A1));
A0 = R; A1 = T;
}
}
while (A1.compareTo(BigInteger.ZERO) > 0) {
BigInteger R = A0.remainder(A1); A0 = A1; A1 = R;
}
return A0;
}
The basic Euclidean algorithm:
private static BigInteger EA(BigInteger a, BigInteger b) {
while ( !b.equals(BigInteger.ZERO) ) {
BigInteger q = a.divide(b);
BigInteger r = a.subtract(q.multiply(b)); a = b; b = r;
}
return a;
}
Thank you for your help!

July 19th, 2021, 08:37 AM
#2
Re: Lehmer gcd algorithm
Hi,
Looks good.
Seems, for u0, u1, v0, v1 you do not need to use BigInteger type, just use primitive int (unsigned?) or long (you may extract 63 bits in this case).

July 19th, 2021, 12:45 PM
#3
Re: Lehmer gcd algorithm
Well, good reply on the question asked more than eight years back!
Victor Nijegorodov
Posting Permissions
 You may not post new threads
 You may not post replies
 You may not post attachments
 You may not edit your posts

Forum Rules

Click Here to Expand Forum to Full Width
