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Ingy döt Net 2023-09-01 09:35:06 -07:00
parent 61b93a2cd1
commit 5af6d93694
858 changed files with 20572 additions and 2082 deletions
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118
Task/Minkowski-question-mark-function/C++/minkowski-question-mark-function.cpp Normal file
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#include <cmath>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <vector>
constexpr int32_t MAX_ITERATIONS = 151;
double minkowski(const double& x) {
if ( x < 0 || x > 1 ) {
return floor(x) + minkowski(x - floor(x));
}
int64_t p = (int64_t) x;
int64_t q = 1;
int64_t r = p + 1;
int64_t s = 1;
double d = 1.0;
double y = (double) p;
while ( true ) {
d /= 2;
if ( d == 0.0 ) {
break;
}
int64_t m = p + r;
if ( m < 0 || p < 0 ) {
break;
}
int64_t n = q + s;
if ( n < 0 ) {
break;
}
if ( x < (double) m / n ) {
r = m;
s = n;
} else {
y += d;
p = m;
q = n;
}
}
return y + d;
}
double minkowski_inverse(double x) {
if ( x < 0 || x > 1 ) {
return floor(x) + minkowski_inverse(x - floor(x));
}
if ( x == 0 || x == 1 ) {
return x;
}
std::vector<int32_t> continued_fraction(1, 0);
int32_t current = 0;
int32_t count = 1;
int32_t i = 0;
while ( true ) {
x *= 2;
if ( current == 0 ) {
if ( x < 1 ) {
count += 1;
} else {
continued_fraction.emplace_back(0);
continued_fraction[i] = count;
i += 1;
count = 1;
current = 1;
x -= 1;
}
} else {
if ( x > 1 ) {
count += 1;
x -= 1;
} else {
continued_fraction.emplace_back(0);
continued_fraction[i] = count;
i += 1;
count = 1;
current = 0;
}
}
if ( x == floor(x) ) {
continued_fraction[i] = count;
break;
}
if ( i == MAX_ITERATIONS ) {
break;
}
}
double reciprocal = 1.0 / continued_fraction[i];
for ( int32_t j = i - 1; j >= 0; --j ) {
reciprocal = continued_fraction[j] + 1.0 / reciprocal;
}
return 1.0 / reciprocal;
}
int main() {
std::cout << std::setw(20) << std::fixed << std::setprecision(16) << minkowski(0.5 * ( 1 + sqrt(5) ))
<< std::setw(20) << 5.0 / 3.0 << std::endl;
std::cout << std::setw(20) << minkowski_inverse(-5.0 / 9.0)
<< std::setw(20) << ( sqrt(13) - 7 ) / 6 << std::endl;
std::cout << std::setw(20) << minkowski(minkowski_inverse(0.718281828182818))
<< std::setw(20) << 0.718281828182818 << std::endl;
std::cout << std::setw(20) << minkowski_inverse(minkowski(0.1213141516271819))
<< std::setw(20) << 0.1213141516171819 << std::endl;
}

117
Task/Minkowski-question-mark-function/Java/minkowski-question-mark-function.java Normal file
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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",
minkowskiInverse(minkowski(0.1213141516271819)), 0.1213141516171819));
}
private static double minkowski(double aX) {
if ( aX < 0 || aX > 1 ) {
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 < 0 || aX > 1 ) {
return Math.floor(aX) + minkowskiInverse(aX - Math.floor(aX));
}
if ( aX == 0 || aX == 1 ) {
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;
}