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Minkowski question-mark function: Difference between revisions

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Minkowski question-mark function (view source)

Revision as of 11:44, 12 February 2024

5,815 bytes added ,  3 months ago
Add C# implementation
m (Formatting code.)
(Add C# implementation)
 
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Line 126:
-0.5657414540893350 -0.5657414540893351
0.7182818280000091 0.1213141516171819
</pre>
 
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
 
class Program
{
const int MAXITER = 151;
 
static double Minkowski(double x)
{
if (x > 1 || x < 0)
{
return Math.Floor(x) + Minkowski(x - Math.Floor(x));
}
ulong p = (ulong)x;
ulong q = 1;
ulong r = p + 1;
ulong s = 1;
double d = 1.0;
double y = (double)p;
while (true)
{
d = d / 2;
if (y + d == y)
{
break;
}
ulong m = p + r;
if (m < 0 || p < 0)
{
break;
}
ulong n = q + s;
if (n < 0)
{
break;
}
if (x < (double)m / (double)n)
{
r = m;
s = n;
}
else
{
y = y + d;
p = m;
q = n;
}
}
return y + d;
}
 
static double MinkowskiInv(double x)
{
if (x > 1 || x < 0)
{
return Math.Floor(x) + MinkowskiInv(x - Math.Floor(x));
}
if (x == 1 || x == 0)
{
return x;
}
uint[] contFrac = new uint[] { 0 };
uint curr = 0;
uint count = 1;
int i = 0;
while (true)
{
x *= 2;
if (curr == 0)
{
if (x < 1)
{
count++;
}
else
{
i++;
Array.Resize(ref contFrac, i + 1);
contFrac[i - 1] = count;
count = 1;
curr = 1;
x--;
}
}
else
{
if (x > 1)
{
count++;
x--;
}
else
{
i++;
Array.Resize(ref contFrac, i + 1);
contFrac[i - 1] = count;
count = 1;
curr = 0;
}
}
if (x == Math.Floor(x))
{
contFrac[i] = count;
break;
}
if (i == MAXITER)
{
break;
}
}
double ret = 1.0 / contFrac[i];
for (int j = i - 1; j >= 0; j--)
{
ret = contFrac[j] + 1.0 / ret;
}
return 1.0 / ret;
}
 
static void Main(string[] args)
{
Console.WriteLine("{0,19:0.0000000000000000} {1,19:0.0000000000000000}", Minkowski(0.5 * (1 + Math.Sqrt(5))), 5.0 / 3.0);
Console.WriteLine("{0,19:0.0000000000000000} {1,19:0.0000000000000000}", MinkowskiInv(-5.0 / 9.0), (Math.Sqrt(13) - 7) / 6);
Console.WriteLine("{0,19:0.0000000000000000} {1,19:0.0000000000000000}", Minkowski(MinkowskiInv(0.718281828)),
MinkowskiInv(Minkowski(0.1213141516171819)));
}
}
</syntaxhighlight>
{{out}}
<pre>
1.6666666666697000 1.6666666666666700
-0.5657414540893350 -0.5657414540893350
0.7182818280000090 0.1213141516171820
 
</pre>
 
=={{header|C++}}==
<syntaxhighlight lang="c++">
#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;
}
</syntaxhighlight>
{{ out }}
<pre>
1.6666666666696983 1.6666666666666667
-0.5657414540893351 -0.5657414540893352
0.7182818281828269 0.7182818281828180
0.1213141516171819 0.1213141516171819
</pre>
 
Line 552 ⟶ 818:
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(minkowski(0.1213141516271819)), 0.1213141516171819));
}
private static double minkowski(double aX) {
if ( aX >< 10 || aX <> 01 ) {
return Math.floor(aX) + minkowski(aX - Math.floor(aX));
}
Line 596 ⟶ 862:
private static double minkowskiInverse(double aX) {
if ( aX >< 10 || aX <> 01 ) {
return Math.floor(aX) + minkowskiInverse(aX - Math.floor(aX));
}
if ( aX == 10 || aX == 01 ) {
return aX;
}
Line 609 ⟶ 875:
int count = 1;
int i = 0;
 
while ( true ) {
aX *= 2;
Line 649 ⟶ 915:
 
double reciprocal = 1.0 / continuedFraction.get(i);
for ( int j = i - 1; j >= 0; j--j ) {
reciprocal = continuedFraction.get(j) + 1.0 / reciprocal;
}
Line 662 ⟶ 928:
{{ out }}
<pre>
1.6666666666696983 1.6666666666666667
-0.5657414540893351 -0.5657414540893352
0.7182818280000092 0.7182818280000000
Line 1,220 ⟶ 1,486:
{{trans|FreeBASIC}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./fmt" for Fmt
 
var MAXITER = 151
Aspen138
337

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