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Add natural log function. May not be terribly efficient currently, but it works and is usable.

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This commit is contained in:
Arthur Drobot 2017-07-27 13:04:41 -07:00
parent c15b737738
commit 18a5a99887
1 changed files with 78 additions and 3 deletions
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81
src/org/nwapw/abacus/plugin/StandardPlugin.java
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@ -126,6 +126,81 @@ public class StandardPlugin extends Plugin {
return sum;
}
});
registerFunction("ln", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface param = params[0];
int powersOf2 = 0;
while(StandardPlugin.this.getFunction("abs").apply(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass()))).compareTo((new NaiveNumber(0.1)).promoteTo(param.getClass())) >= 0){
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() == 1) {
param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2++;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
else {
param = param.multiply(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2--;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
}
return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
}
/**
* Returns the partial sum of the Taylor series for logx (around x=1).
* Automatically determines the number of terms needed based on the precision of x.
* @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
* @return the partial sum.
*/
private NumberInterface getLogPartialSum(NumberInterface x){
NumberInterface maxError = StandardPlugin.this.getMaxError(x);
x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
NumberInterface currentTerm = x, sum = x;
int n = 1;
while(StandardPlugin.this.getFunction("abs").apply(currentTerm).compareTo(maxError) > 0){
n++;
currentTerm = currentTerm.multiply(x).multiply((new NaiveNumber(n-1)).promoteTo(x.getClass())).divide((new NaiveNumber(n)).promoteTo(x.getClass())).negate();
sum = sum.add(currentTerm);
}
return sum;
}
/**
* Returns natural log of 2 to the required precision of the class of number.
* @param number a number of the same type as the return type. (Used for precision.)
* @return the value of log(2) with the appropriate precision.
*/
private NumberInterface getLog2(NumberInterface number){
NumberInterface maxError = StandardPlugin.this.getMaxError(number);
//NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
//We'll use the series \sigma_{n >= 1) ((1/3^n + 1/4^n) * 1/n)
//In the following, a=1/3^n, b=1/4^n, c = 1/n.
//a is also an error bound.
NumberInterface a = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
int n = 0;
while(a.compareTo(maxError) >= 1){
n++;
a = a.divide((new NaiveNumber(3)).promoteTo(number.getClass()));
b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
sum = sum.add(a.add(b).multiply(c));
}
return sum;
}
});
}
/**
@ -145,16 +220,16 @@ public class StandardPlugin extends Plugin {
* @param x where the function is evaluated.
* @return
*/
private int getNTermsExp(NumberInterface maxError, NumberInterface x){
private int getNTermsExp(NumberInterface maxError, NumberInterface x) {
//We need n such that |x^(n+1)| <= (n+1)! * maxError
//The variables LHS and RHS refer to the above inequality.
int n = 0;
x = this.getFunction("abs").apply(x);
NumberInterface LHS = x, RHS = maxError;
while(LHS.compareTo(RHS) > 0){
while (LHS.compareTo(RHS) > 0) {
n++;
LHS = LHS.multiply(x);
RHS = RHS.multiply(new NaiveNumber(n+1).promoteTo(RHS.getClass()));
RHS = RHS.multiply(new NaiveNumber(n + 1).promoteTo(RHS.getClass()));
}
return n;
}