Continued fraction/Arithmetic/G(matrix ng, continued fraction n): Difference between revisions
Continued fraction/Arithmetic/G(matrix ng, continued fraction n) (view source)
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This method is simple, and it memoizes terms. However, the memoization is in a linked list rather than a randomly accessible array.
The '''recurs''' routines do not execute recursions, but instead (thanks to '''$delay''') create what I will call "recursive thunks". Otherwise the stack would overflow.
The code leaks memory, so using a garbage collector may be a good idea.
<syntaxhighlight lang="ats">
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if (!terminated && m < needed)
{
if (
{
// Increase the space to twice what might be needed
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(+%)/plus1r2times1r2 0 1,999$2
0.853553</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.List;
public final class ContinuedFractionArithmeticG1 {
public static void main(String[] aArgs) {
List<CFData> cfData = List.of(
new CFData("[1; 5, 2] + 1 / 2 ", new int[] { 2, 1, 0, 2 }, (CFIterator) new R2cfIterator(13, 11) ),
new CFData("[3; 7] + 1 / 2 ", new int[] { 2, 1, 0, 2 }, (CFIterator) new R2cfIterator(22, 7) ),
new CFData("[3; 7] divided by 4 ", new int[] { 1, 0, 0, 4 }, (CFIterator) new R2cfIterator(22, 7) ),
new CFData("sqrt(2) ", new int[] { 0, 1, 1, 0 }, (CFIterator) new ReciprocalRoot2() ),
new CFData("1 / sqrt(2) ", new int[] { 0, 1, 1, 0 }, (CFIterator) new Root2() ),
new CFData("(1 + sqrt(2)) / 2 ", new int[] { 1, 1, 0, 2 }, (CFIterator) new Root2() ),
new CFData("(1 + 1 / sqrt(2)) / 2", new int[] { 1, 1, 0, 2 }, (CFIterator) new ReciprocalRoot2() ) );
for ( CFData data : cfData ) {
System.out.print(data.text + " -> ");
NG ng = new NG(data.arguments);
CFIterator iterator = data.iterator;
int nextTerm = 0;
for ( int i = 1; i <= 20 && iterator.hasNext(); i++ ) {
nextTerm = iterator.next();
if ( ! ng.needsTerm() ) {
System.out.print(ng.egress() + " ");
}
ng.ingress(nextTerm);
}
while ( ! ng.done() ) {
System.out.print(ng.egressDone() + " ");
}
System.out.println();
}
}
private static class NG {
public NG(int[] aArgs) {
a1 = aArgs[0]; a = aArgs[1]; b1 = aArgs[2]; b = aArgs[3];
}
public void ingress(int aN) {
int temp = a; a = a1; a1 = temp + a1 * aN;
temp = b; b = b1; b1 = temp + b1 * aN;
}
public int egress() {
final int n = a / b;
int temp = a; a = b; b = temp - b * n;
temp = a1; a1 = b1; b1 = temp - b1 * n;
return n;
}
public boolean needsTerm() {
return ( b == 0 || b1 == 0 ) || ( a * b1 != a1 * b );
}
public int egressDone() {
if ( needsTerm() ) {
a = a1;
b = b1;
}
return egress();
}
public boolean done() {
return ( b == 0 || b1 == 0 );
}
private int a1, a, b1, b;
}
private static abstract class CFIterator {
public abstract boolean hasNext();
public abstract int next();
}
private static class R2cfIterator extends CFIterator {
public R2cfIterator(int aNumerator, int aDenominator) {
numerator = aNumerator; denominator = aDenominator;
}
public boolean hasNext() {
return denominator != 0;
}
public int next() {
int div = numerator / denominator;
int rem = numerator % denominator;
numerator = denominator;
denominator = rem;
return div;
}
private int numerator, denominator;
}
private static class Root2 extends CFIterator {
public Root2() {
firstReturn = true;
}
public boolean hasNext() {
return true;
}
public int next() {
if ( firstReturn ) {
firstReturn = false;
return 1;
}
return 2;
}
private boolean firstReturn;
}
private static class ReciprocalRoot2 extends CFIterator {
public ReciprocalRoot2() {
firstReturn = true;
secondReturn = true;
}
public boolean hasNext() {
return true;
}
public int next() {
if ( firstReturn ) {
firstReturn = false;
return 0;
}
if ( secondReturn ) {
secondReturn = false;
return 1;
}
return 2;
}
private boolean firstReturn, secondReturn;
}
private static record CFData(String text, int[] arguments, CFIterator iterator) {}
}
</syntaxhighlight>
{{ out }}
<pre>
[1; 5, 2] + 1 / 2 -> 1 1 2 7
[3; 7] + 1 / 2 -> 3 1 1 1 4
[3; 7] divided by 4 -> 0 1 3 1 2
sqrt(2) -> 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
1 / sqrt(2) -> 0 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
(1 + sqrt(2)) / 2 -> 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 4
(1 + 1 / sqrt(2)) / 2 -> 0 1 5 1 4 1 4 1 4 1 4 1 4 1 4 1 4 1 5
</pre>
=={{header|Julia}}==
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{{trans|Kotlin}}
{{libheader|Wren-dynamic}}
<syntaxhighlight lang="
var CFData = Tuple.create("Tuple", ["str", "ng", "r", "gen"])
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