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https://github.com/DanilaFe/abacus
synced 2024-12-23 16:00:09 -08:00
Add natural log function. May not be terribly efficient currently, but it works and is usable.
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@ -126,6 +126,81 @@ public class StandardPlugin extends Plugin {
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return sum;
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return sum;
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}
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}
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});
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});
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registerFunction("ln", new Function() {
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@Override
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protected boolean matchesParams(NumberInterface[] params) {
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return params.length == 1;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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NumberInterface param = params[0];
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int powersOf2 = 0;
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while(StandardPlugin.this.getFunction("abs").apply(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass()))).compareTo((new NaiveNumber(0.1)).promoteTo(param.getClass())) >= 0){
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if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() == 1) {
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param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
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powersOf2++;
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if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
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break;
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//No infinite loop for you.
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}
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}
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else {
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param = param.multiply(new NaiveNumber(2).promoteTo(param.getClass()));
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powersOf2--;
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if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
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break;
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//No infinite loop for you.
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}
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}
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}
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return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
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}
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/**
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* Returns the partial sum of the Taylor series for logx (around x=1).
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* Automatically determines the number of terms needed based on the precision of x.
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* @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
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* @return the partial sum.
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*/
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private NumberInterface getLogPartialSum(NumberInterface x){
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NumberInterface maxError = StandardPlugin.this.getMaxError(x);
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x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
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NumberInterface currentTerm = x, sum = x;
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int n = 1;
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while(StandardPlugin.this.getFunction("abs").apply(currentTerm).compareTo(maxError) > 0){
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n++;
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currentTerm = currentTerm.multiply(x).multiply((new NaiveNumber(n-1)).promoteTo(x.getClass())).divide((new NaiveNumber(n)).promoteTo(x.getClass())).negate();
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sum = sum.add(currentTerm);
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}
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return sum;
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}
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/**
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* Returns natural log of 2 to the required precision of the class of number.
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* @param number a number of the same type as the return type. (Used for precision.)
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* @return the value of log(2) with the appropriate precision.
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*/
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private NumberInterface getLog2(NumberInterface number){
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NumberInterface maxError = StandardPlugin.this.getMaxError(number);
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//NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
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//We'll use the series \sigma_{n >= 1) ((1/3^n + 1/4^n) * 1/n)
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//In the following, a=1/3^n, b=1/4^n, c = 1/n.
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//a is also an error bound.
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NumberInterface a = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
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NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
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int n = 0;
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while(a.compareTo(maxError) >= 1){
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n++;
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a = a.divide((new NaiveNumber(3)).promoteTo(number.getClass()));
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b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
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c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
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sum = sum.add(a.add(b).multiply(c));
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}
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return sum;
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}
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});
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}
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}
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/**
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/**
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