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Merge branch 'master' of github.com:DanilaFe/abacus

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This commit is contained in:
Danila Fedorin 2017-07-27 14:08:31 -07:00
commit b84ca8a121
2 changed files with 134 additions and 7 deletions
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2
src/org/nwapw/abacus/number/NaiveNumber.java
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@ -29,7 +29,7 @@ public class NaiveNumber implements NumberInterface {
@Override
public int precision() {
return 15;
return 18;
}
@Override

139
src/org/nwapw/abacus/plugin/StandardPlugin.java
View File

@ -4,6 +4,9 @@ import org.nwapw.abacus.function.Function;
import org.nwapw.abacus.number.NaiveNumber;
import org.nwapw.abacus.number.NumberInterface;
import javax.print.attribute.standard.MediaSize;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.function.BiFunction;
/**
@ -75,6 +78,7 @@ public class StandardPlugin extends Plugin {
});
registerFunction("!", new Function() {
//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
@ -92,6 +96,23 @@ public class StandardPlugin extends Plugin {
factorial = factorial.multiply(multiplier);
}
return factorial;
/*if(!storedList.containsKey(params[0].getClass())){
storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
}*/
}
});
registerFunction("abs", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
}
});
@ -103,7 +124,112 @@ public class StandardPlugin extends Plugin {
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
boolean takeReciprocal = params[0].signum() == -1;
params[0] = StandardPlugin.this.getFunction("abs").apply(params[0]);
NumberInterface sum = sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
if(takeReciprocal){
sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
}
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;
}
});
registerFunction("pow", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return StandardPlugin.this.getFunction("exp").apply(StandardPlugin.this.getFunction("ln").apply(params[0]).multiply(params[1]));
}
});
registerFunction("sqrt", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return StandardPlugin.this.getFunction("pow").apply(params[0], (new NaiveNumber(0.5)));
}
});
}
@ -125,15 +251,16 @@ public class StandardPlugin extends Plugin {
* @param x where the function is evaluated.
* @return
*/
private int getNTermsExp(NumberInterface maxError, NumberInterface x){
//We need n such that x^(n+2) <= (n+1)! * maxError
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;
NumberInterface LHS = x.intPow(2), RHS = maxError;
while(LHS.compareTo(RHS) > 0){
x = this.getFunction("abs").apply(x);
NumberInterface LHS = x, RHS = maxError;
while (LHS.compareTo(RHS) > 0) {
n++;
LHS = LHS.multiply(x);
RHS = RHS.multiply(new NaiveNumber(n).promoteTo(RHS.getClass()));
RHS = RHS.multiply(new NaiveNumber(n + 1).promoteTo(RHS.getClass()));
}
return n;
}