Minkowski question-mark function: Difference between revisions
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Using an exact fraction for 4.04145188432738056 and bumping the iteration count from 52 up to 200 changes that difference to 1.43622e_12.
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.List;
public final class MinkowskiQuestionMarkFunction {
public static void main(String[] aArgs) {
System.out.println(String.format("%20.16f%20.16f", minkowski(0.5 * ( 1 + Math.sqrt(5) )), 5.0 / 3.0));
System.out.println(String.format("%20.16f%20.16f", minkowskiInverse(-5.0 / 9.0), ( Math.sqrt(13) - 7 ) / 6 ));
System.out.println(String.format("%20.16f%20.16f", minkowski(minkowskiInverse(0.718281828)), 0.718281828));
System.out.println(String.format("%20.16f%20.16f",
minkowski(minkowskiInverse(0.1213141516271819)), 0.1213141516171819));
}
private static double minkowski(double aX) {
if ( aX > 1 || aX < 0 ) {
return Math.floor(aX) + minkowski(aX - Math.floor(aX));
}
long p = (long) aX;
long q = 1;
long r = p + 1;
long s = 1;
double d = 1.0;
double y = (double) p;
while ( true ) {
d /= 2;
if ( d == 0.0 ) {
break;
}
long m = p + r;
if ( m < 0 || p < 0 ) {
break;
}
long n = q + s;
if ( n < 0 ) {
break;
}
if ( aX < (double) m / n ) {
r = m;
s = n;
} else {
y += d;
p = m;
q = n;
}
}
return y + d;
}
private static double minkowskiInverse(double aX) {
if ( aX > 1 || aX < 0 ) {
return Math.floor(aX) + minkowskiInverse(aX - Math.floor(aX));
}
if ( aX == 1 || aX == 0 ) {
return aX;
}
List<Integer> continuedFraction = new ArrayList<Integer>();
continuedFraction.add(0);
int current = 0;
int count = 1;
int i = 0;
while ( true ) {
aX *= 2;
if ( current == 0 ) {
if ( aX < 1 ) {
count += 1;
} else {
continuedFraction.add(0);
continuedFraction.set(i, count);
i += 1;
count = 1;
current = 1;
aX -= 1;
}
} else {
if ( aX > 1 ) {
count += 1;
aX -= 1;
} else {
continuedFraction.add(0);
continuedFraction.set(i, count);
i += 1;
count = 1;
current = 0;
}
}
if ( aX == Math.floor(aX) ) {
continuedFraction.set(i, count);
break;
}
if ( i == MAX_ITERATIONS ) {
break;
}
}
double reciprocal = 1.0 / continuedFraction.get(i);
for ( int j = i - 1; j >= 0; --j ) {
reciprocal = continuedFraction.get(j) + 1.0 / reciprocal;
}
return 1.0 / reciprocal;
}
private static final int MAX_ITERATIONS = 150;
}
</syntaxhighlight>
{{ out }}
<pre>
1.6666666666696983 1.6666666666666667
-0.5657414540893351 -0.5657414540893352
0.7182818280000092 0.7182818280000000
0.1213141516271825 0.1213141516171819
</pre>
=={{header|Julia}}==
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