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Elliptic curve arithmetic: Difference between revisions
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a * 12345 = ( 10.7586 , 35.3875 )</lang>
=={{header|Java}}==
{{trans|D}}
<lang java>import static java.lang.Math.*;
import java.util.Locale;
public class Test {
public static void main(String[] args) {
Pt a = Pt.fromY(1);
Pt b = Pt.fromY(2);
System.out.printf("a = %s%n", a);
System.out.printf("b = %s%n", b);
Pt c = a.plus(b);
System.out.printf("c = a + b = %s%n", c);
Pt d = c.neg();
System.out.printf("d = -c = %s%n", d);
System.out.printf("c + d = %s%n", c.plus(d));
System.out.printf("a + b + d = %s%n", a.plus(b).plus(d));
System.out.printf("a * 12345 = %s%n", a.mult(12345));
}
}
class Pt {
final static int bCoeff = 7;
double x, y;
Pt(double x, double y) {
this.x = x;
this.y = y;
}
static Pt zero() {
return new Pt(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
}
boolean isZero() {
return this.x > 1e20 || this.x < -1e20;
}
static Pt fromY(double y) {
return new Pt(cbrt(pow(y, 2) - bCoeff), y);
}
Pt dbl() {
if (isZero())
return this;
double L = (3 * this.x * this.x) / (2 * this.y);
double x2 = pow(L, 2) - 2 * this.x;
return new Pt(x2, L * (this.x - x2) - this.y);
}
Pt neg() {
return new Pt(this.x, -this.y);
}
Pt plus(Pt q) {
if (this.x == q.x && this.y == q.y)
return dbl();
if (isZero())
return q;
if (q.isZero())
return this;
double L = (q.y - this.y) / (q.x - this.x);
double xx = pow(L, 2) - this.x - q.x;
return new Pt(xx, L * (this.x - xx) - this.y);
}
Pt mult(int n) {
Pt r = Pt.zero();
Pt p = this;
for (int i = 1; i <= n; i <<= 1) {
if ((i & n) != 0)
r = r.plus(p);
p = p.dbl();
}
return r;
}
@Override
public String toString() {
if (isZero())
return "Zero";
return String.format(Locale.US, "(%.3f,%.3f)", this.x, this.y);
}
}</lang>
<pre>a = (-1.817,1.000)
b = (-1.442,2.000)
c = a + b = (10.375,-33.525)
d = -c = (10.375,33.525)
c + d = Zero
a + b + d = Zero
a * 12345 = (10.759,35.387)</pre>
=={{header|PARI/GP}}==
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