Convert decimal number to rational: Difference between revisions
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Line 662:
3.14159265358979 → 104348 / 33215
2.71828182845905 → 49171 / 18089</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <cmath>
#include <cstdint>
#include <iostream>
#include <limits>
#include <numeric>
#include <vector>
class Rational {
public:
Rational(const int64_t& numer, const uint64_t& denom) : numerator(numer), denominator(denom) { }
Rational negate() {
return Rational(-numerator, denominator);
}
std::string to_string() {
return std::to_string(numerator) + " / " + std::to_string(denominator);
}
private:
int64_t numerator;
uint64_t denominator;
};
/**
* Return a Rational such that its numerator / denominator = 'decimal', correct to dp decimal places,
* where dp is minimum of 'decimal_places' and the number of decimal places in 'decimal'.
*/
Rational decimal_to_rational(double decimal, const uint32_t& decimal_places) {
const double epsilon = 1.0 / std::pow(10, decimal_places);
const bool negative = ( decimal < 0.0 );
if ( negative ) {
decimal = -decimal;
}
if ( decimal < std::numeric_limits<double>::min() ) {
return Rational(0, 1);
}
if ( std::abs( decimal - std::round(decimal) ) < epsilon ) {
return Rational(std::round(decimal), 1);
}
uint64_t a = 0;
uint64_t b = 1;
uint64_t c = static_cast<uint64_t>(std::ceil(decimal));
uint64_t d = 1;
const uint64_t auxiliary_1 = std::numeric_limits<uint64_t>::max() / 2;
while ( c < auxiliary_1 && d < auxiliary_1 ) {
const double auxiliary_2 = static_cast<double>( a + c ) / ( b + d );
if ( std::abs(decimal - auxiliary_2) < epsilon ) {
break;
}
if ( decimal > auxiliary_2 ) {
a = a + c;
b = b + d;
} else {
c = a + c;
d = b + d;
}
}
const uint64_t divisor = std::gcd(( a + c ), ( b + d ));
Rational result(( a + c ) / divisor, ( b + d ) / divisor);
return ( negative ) ? result.negate() : result;
}
int main() {
for ( const double& decimal : { 3.1415926535, 0.518518, -0.75, 0.518518518518, -0.9054054054054, -0.0, 2.0 } ) {
std::cout << decimal_to_rational(decimal, 9).to_string() << std::endl;
}
}
</syntaxhighlight>
{{ out }}
<pre>
104348 / 33215
36975 / 71309
-3 / 4
14 / 27
-67 / 74
0 / 1
2 / 1
</pre>
=={{header|Clojure}}==
Line 1,177 ⟶ 1,266:
print n & ":", parserational(n)
loop</syntaxhighlight>
=={{header|Frink}}==
<syntaxhighlight lang="frink">println[toRational[0.9054054]]
println[toRational[0.518518]]
println[toRational[0.75]]</syntaxhighlight>
{{out}}
<pre>
4527027/5000000 (exactly 0.9054054)
259259/500000 (exactly 0.518518)
3/4 (exactly 0.75)
</pre>
=={{header|Fōrmulæ}}==
Line 1,227 ⟶ 1,328:
Even when rationalization expressions are intrinsic in Fōrmulæ, we can write explicit functions:
[[File:Fōrmulæ - Convert decimal number to rational
[[File:Fōrmulæ - Convert decimal number to rational 14.png]]
Line 1,234 ⟶ 1,335:
[[File:Fōrmulæ - Convert decimal number to rational
[[File:Fōrmulæ - Convert decimal number to rational 17.png]]
Line 3,049 ⟶ 3,150:
const proc: main is func
begin
writeln(bigRational parse "0.9(054)");
writeln(bigRational parse "0.(518)");
writeln(bigRational parse "0.75");
writeln(bigRational parse "3.(142857)");
writeln(bigRational parse "0.(8867924528301)");
writeln(bigRational parse "0.(846153)");
writeln(bigRational parse "0.9054054");
writeln(bigRational parse "0.518518");
writeln(bigRational parse "0.14285714285714");
writeln(bigRational parse "3.14159265358979");
writeln(bigRational parse "2.718281828");
writeln(bigRational parse "31.415926536");
writeln(bigRational parse "0.000000000");
writeln;
writeln(fraction(bigRational("0.9(054)")));
writeln(fraction(bigRational("0.(518)")));
Line 3,064 ⟶ 3,181:
end func;</syntaxhighlight>
{{out}}
<pre>
0.9(054)
0.(518)
0.75
3.(142857)
0.(8867924528301)
0.(846153)
0.9054054
0.518518
0.14285714285714
3.14159265358979
2.718281828
31.415926536
0.0
67/74
14/27
3/4
Line 3,076 ⟶ 3,208:
679570457/250000000
3926990817/125000000
0/1
</pre>
=={{header|Sidef}}==
Line 3,400 ⟶ 3,533:
{{libheader|Wren-rat}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var tests = [0.9054054, 0.518518, 0.75]
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