Tonelli-Shanks algorithm: Difference between revisions
Added Java
(Added solution for D) |
(Added Java) |
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Line 910:
41660815127637347468140745042827704103445750172002x tosh (10^50x)+577
32102985369940620849741983987300038903725266634508 67897014630059379150258016012699961096274733366069</lang>
=={{header|Java}}==
{{trans|Kotlin}}
{{works with|Java|9}}
<lang Java>import java.math.BigInteger;
import java.util.List;
import java.util.Map;
import java.util.function.BiFunction;
import java.util.function.Function;
public class TonelliShanks {
private static final BigInteger ZERO = BigInteger.ZERO;
private static final BigInteger ONE = BigInteger.ONE;
private static final BigInteger TEN = BigInteger.TEN;
private static final BigInteger TWO = BigInteger.valueOf(2);
private static final BigInteger FOUR = BigInteger.valueOf(4);
private static class Solution {
private BigInteger root1;
private BigInteger root2;
private boolean exists;
Solution(BigInteger root1, BigInteger root2, boolean exists) {
this.root1 = root1;
this.root2 = root2;
this.exists = exists;
}
}
private static Solution ts(Long n, Long p) {
return ts(BigInteger.valueOf(n), BigInteger.valueOf(p));
}
private static Solution ts(BigInteger n, BigInteger p) {
BiFunction<BigInteger, BigInteger, BigInteger> powModP = (BigInteger a, BigInteger e) -> a.modPow(e, p);
Function<BigInteger, BigInteger> ls = (BigInteger a) -> powModP.apply(a, p.subtract(ONE).divide(TWO));
if (!ls.apply(n).equals(ONE)) return new Solution(ZERO, ZERO, false);
BigInteger q = p.subtract(ONE);
BigInteger ss = ZERO;
while (q.and(ONE).equals(ZERO)) {
ss = ss.add(ONE);
q = q.shiftRight(1);
}
if (ss.equals(ONE)) {
BigInteger r1 = powModP.apply(n, p.add(ONE).divide(FOUR));
return new Solution(r1, p.subtract(r1), true);
}
BigInteger z = TWO;
while (!ls.apply(z).equals(p.subtract(ONE))) z = z.add(ONE);
BigInteger c = powModP.apply(z, q);
BigInteger r = powModP.apply(n, q.add(ONE).divide(TWO));
BigInteger t = powModP.apply(n, q);
BigInteger m = ss;
while (true) {
if (t.equals(ONE)) return new Solution(r, p.subtract(r), true);
BigInteger i = ZERO;
BigInteger zz = t;
while (!zz.equals(BigInteger.ONE) && i.compareTo(m.subtract(ONE)) < 0) {
zz = zz.multiply(zz).mod(p);
i = i.add(ONE);
}
BigInteger b = c;
BigInteger e = m.subtract(i).subtract(ONE);
while (e.compareTo(ZERO) > 0) {
b = b.multiply(b).mod(p);
e = e.subtract(ONE);
}
r = r.multiply(b).mod(p);
c = b.multiply(b).mod(p);
t = t.multiply(c).mod(p);
m = i;
}
}
public static void main(String[] args) {
List<Map.Entry<Long, Long>> pairs = List.of(
Map.entry(10L, 13L),
Map.entry(56L, 101L),
Map.entry(1030L, 10009L),
Map.entry(1032L, 10009L),
Map.entry(44402L, 100049L),
Map.entry(665820697L, 1000000009L),
Map.entry(881398088036L, 1000000000039L)
);
for (Map.Entry<Long, Long> pair : pairs) {
Solution sol = ts(pair.getKey(), pair.getValue());
System.out.printf("n = %s\n", pair.getKey());
System.out.printf("p = %s\n", pair.getValue());
if (sol.exists) {
System.out.printf("root1 = %s\n", sol.root1);
System.out.printf("root2 = %s\n", sol.root2);
} else {
System.out.println("No solution exists");
}
System.out.println();
}
BigInteger bn = new BigInteger("41660815127637347468140745042827704103445750172002");
BigInteger bp = TEN.pow(50).add(BigInteger.valueOf(577));
Solution sol = ts(bn, bp);
System.out.printf("n = %s\n", bn);
System.out.printf("p = %s\n", bp);
if (sol.exists) {
System.out.printf("root1 = %s\n", sol.root1);
System.out.printf("root2 = %s\n", sol.root2);
} else {
System.out.println("No solution exists");
}
}
}</lang>
{{out}}
<pre>n = 10
p = 13
root1 = 7
root2 = 6
n = 56
p = 101
root1 = 37
root2 = 64
n = 1030
p = 10009
root1 = 1632
root2 = 8377
n = 1032
p = 10009
No solution exists
n = 44402
p = 100049
root1 = 30468
root2 = 69581
n = 665820697
p = 1000000009
root1 = 378633312
root2 = 621366697
n = 881398088036
p = 1000000000039
root1 = 791399408049
root2 = 208600591990
n = 41660815127637347468140745042827704103445750172002
p = 100000000000000000000000000000000000000000000000577
root1 = 32102985369940620849741983987300038903725266634508
root2 = 67897014630059379150258016012699961096274733366069</pre>
=={{header|Kotlin}}==
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