import java.util.Stack;
/*** * @author ljs 2011-5-19* * solve extended gcd using Binary Method**/
public class ExtGCD_Binary {/*** caculate x,y to satisfy Bezout Identity: u.x + v.y = gcd(u,v)* @param u* @param v* @return {d,x,y} for: d = u.x + v.y;*/public static int[] extGCDBinary(int u,int v){u=(u<0)?-u:u;v=(v<0)?-v:v;if(u==0)return new int[]{v,0,1};if(v==0)return new int[]{u,1,0};int k=0;while((u & 0x01)==0 && (v & 0x01) == 0){u>>=1; //divide by 2v>>=1;k++;}//with respect to d=gcd(u,v)=u.s+v.t/* the operation type is defined as:1: c, u / 2^c (push two numbers to stack: first push c, then push the op number 1)2: c, v / 2^c  (push two numbers to stack: first push c, then push the op number 2)3: gcd(u-v, v) (only push the op number 3 to stack)4: gcd(u, u-v) (only push the op number 4 to stack)  */Stack<Integer> ops= new Stack<Integer>();//at this time, there is at least one number is odd between m and nint t=-v; //set it negative for later comparison of (t>0)if((v & 0x01)==1){//if v is oddt = u;}//process t as a possible even numberboolean firstNoOp = true;while(t != 0){if(firstNoOp) {firstNoOp = false;}else{if(t>0)ops.push(3);elseops.push(4);}int c=0;while((t & 0x01)==0){//do until t is not even t>>=1;c++;}if(t>0) {//u > v (the max is replaced by |t|)u=t; if(c>0) {ops.push(c);  ops.push(1);      }}else{ //u<v (the max is replaced by |t|)v=-t;if(c>0){ops.push(c);   ops.push(2);}}//now u and v are all odd, then u-v is event = u-v; }int d = u;//the following steps are to caculate x,y in d=u.x + v.yint x=1,y=0;//special processing for the last operationif(!ops.isEmpty()){//e.g. for input u=3,v=3, then ops is empty, d=3int op = ops.pop();int c = ops.pop();//op number 3 and 4 can not be the last step since: u-v = v, then v is even; or u=u-v, then u=0; //both are not possible     int tmp = 1<<c;if(op == 1){                x = 1;y = 1- tmp;u = v;for(int i=0;i<c;i++)u <<= 1;             }else if(op == 2){x = 1- tmp;y = -1;v = -u;for(int i=0;i<c;i++)v <<= 1;   }}while(!ops.isEmpty()){    int op = ops.pop();switch(op){case 1:{int c = ops.pop();for(int i=0;i<c;i++){if((x & 0x01)==0){//if x is even x >>= 1;}else{y += u;int tmp = x - v;while(y ==0 || tmp ==0){y += (u<<1); //*2tmp -= (v<<1); //*2};x = tmp >>1;}u <<= 1;}break;}case 2:{                 int c = ops.pop();for(int i=0;i<c;i++){if((y & 0x01)==0){//if y is even                                y >>= 1;}else{x += v;int tmp = y-u;while(x ==0 || tmp ==0){x += (v<<1);  //*2tmp -= (u<<1);  //*2};y = tmp >>1;}v <<= 1;                     }y = -y;v = -v;break;}case 3:y -= x;u += v;break;case 4:x += y;                  v = u - v;y = -y;break;}}//e.g. gcd(1,4)y = (v<0)?-y:y;for(int i=0;i<k;i++)d <<=1;return new int[]{d,x,y};}public static void print(int m,int n,int[] extGCDResult){m = (m<0)?-m:m;n = (n<0)?-n:n;System.out.format("extended gcd of %d and %d is: %d = %d.{%d} + %d.{%d}%5s%n",m,n,extGCDResult[0],m,extGCDResult[1],n,extGCDResult[2],(m*extGCDResult[1] + n * extGCDResult[2] == extGCDResult[0])?"OK":"WRONG!!!");        }public static void main(String[] args) {int m = -18;int n= 12;print(m,n,extGCDBinary(m,n));//co-primem = 15;n= 28;print(m,n,extGCDBinary(m,n));m = 6;n= 3;print(m,n,extGCDBinary(m,n));m = 6;n= 3;print(m,n,extGCDBinary(m,n));m = 6;n= 0;print(m,n,extGCDBinary(m,n));m = 0;n= 6;print(m,n,extGCDBinary(m,n));m = 0;n= 0;print(m,n,extGCDBinary(m,n));m = 1;n= 1;print(m,n,extGCDBinary(m,n));m = 3;n= 3;print(m,n,extGCDBinary(m,n));m = 2;n= 2;print(m,n,extGCDBinary(m,n));m = 1;n= 4;print(m,n,extGCDBinary(m,n));m = 4;n= 1;print(m,n,extGCDBinary(m,n));m = 10;n= 14;print(m,n,extGCDBinary(m,n));m = 14;n= 10;print(m,n,extGCDBinary(m,n));m = 10;n= 4;print(m,n,extGCDBinary(m,n));m = 273;n= 24;print(m,n,extGCDBinary(m,n));m = 120;n= 23;print(m,n,extGCDBinary(m,n));}
}