DanilaFe/Abacus
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Code Issues Releases Wiki Activity

Phase out as many promoteTo calls as possible.

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This commit is contained in:
Danila Fedorin 2017-08-09 19:04:32 -07:00
parent 021e569491
commit fd21014c39
1 changed files with 40 additions and 34 deletions
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74
src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java
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@ -11,6 +11,7 @@ import org.nwapw.abacus.tree.TokenType;
import org.nwapw.abacus.tree.TreeNode;
import java.util.ArrayList;
import java.util.Date;
import java.util.HashMap;
import java.util.List;
import java.util.function.BiFunction;
@ -97,7 +98,7 @@ public class StandardPlugin extends Plugin {
public static final Operator OP_DIVIDE = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2 && params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0;
return params.length == 2 && params[1].compareTo(fromInt(params[0].getClass(), 0)) != 0;
}
@Override
@ -113,7 +114,7 @@ public class StandardPlugin extends Plugin {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1
&& params[0].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
&& params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
&& params[0].signum() >= 0;
}
@ -122,10 +123,11 @@ public class StandardPlugin extends Plugin {
if (params[0].signum() == 0) {
return fromInt(params[0].getClass(), 1);
}
NumberInterface one = fromInt(params[0].getClass(), 1);
NumberInterface factorial = params[0];
NumberInterface multiplier = params[0];
//It is necessary to later prevent calls of factorial on anything but non-negative integers.
while ((multiplier = multiplier.subtract(NaiveNumber.ONE.promoteTo(multiplier.getClass()))).signum() == 1) {
while ((multiplier = multiplier.subtract(one)).signum() == 1) {
factorial = factorial.multiply(multiplier);
}
return factorial;
@ -192,7 +194,7 @@ public class StandardPlugin extends Plugin {
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
return params[0].multiply(fromInt(params[0].getClass(), params[0].signum()));
}
};
/**
@ -201,31 +203,32 @@ public class StandardPlugin extends Plugin {
public static final Function FUNCTION_LN = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1 && params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) > 0;
return params.length == 1 && params[0].compareTo(fromInt(params[0].getClass(), 0)) > 0;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface param = params[0];
NumberInterface one = fromInt(param.getClass(), 1);
int powersOf2 = 0;
while (FUNCTION_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) {
while (FUNCTION_ABS.apply(param.subtract(one)).compareTo(new NaiveNumber(0.1).promoteTo(param.getClass())) >= 0) {
if (param.subtract(one).signum() == 1) {
param = param.divide(fromInt(param.getClass(), 2));
powersOf2++;
if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
if (param.subtract(one).signum() != 1) {
break;
//No infinite loop for you.
}
} else {
param = param.multiply(fromInt(param.getClass(), 2));
powersOf2--;
if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != -1) {
if (param.subtract(one).signum() != -1) {
break;
//No infinite loop for you.
}
}
}
return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
return getLog2(param).multiply(fromInt(param.getClass(), powersOf2)).add(getLogPartialSum(param));
}
/**
@ -237,13 +240,13 @@ public class StandardPlugin extends Plugin {
private NumberInterface getLogPartialSum(NumberInterface x) {
NumberInterface maxError = x.getMaxError();
x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
x = x.subtract(fromInt(x.getClass(), 1)); //Terms used are for log(x+1).
NumberInterface currentNumerator = x, currentTerm = x, sum = x;
int n = 1;
while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
n++;
currentNumerator = currentNumerator.multiply(x).negate();
currentTerm = currentNumerator.divide(new NaiveNumber(n).promoteTo(x.getClass()));
currentTerm = currentNumerator.divide(fromInt(x.getClass(), n));
sum = sum.add(currentTerm);
}
return sum;
@ -261,13 +264,14 @@ public class StandardPlugin extends Plugin {
//In the following, a=1/3^n, b=1/4^n, c = 1/n.
//a is also an error bound.
NumberInterface a = fromInt(number.getClass(), 1), b = a, c = a;
NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
NumberInterface sum = fromInt(number.getClass(), 0);
NumberInterface one = fromInt(number.getClass(), 1);
int n = 0;
while (a.compareTo(maxError) >= 1) {
n++;
a = a.divide(fromInt(number.getClass(), 3));
b = b.divide(fromInt(number.getClass(), 4));
c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
c = one.divide(fromInt(number.getClass(), n));
sum = sum.add(a.add(b).multiply(c));
}
return sum;
@ -340,10 +344,10 @@ public class StandardPlugin extends Plugin {
.negate();
for (int i = 0; i < termsNeeded; i++) {
M = M
.multiply(new NaiveNumber(12 * i + 2).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12 * i + 6).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12 * i + 10).promoteTo(PreciseNumber.class))
.divide(new NaiveNumber(Math.pow(i + 1, 3)).promoteTo(PreciseNumber.class));
.multiply(new PreciseNumber((12 * i + 2) + ""))
.multiply(new PreciseNumber((12 * i + 6) + ""))
.multiply(new PreciseNumber((12 * i + 10) + ""))
.divide(new PreciseNumber(Math.pow(i + 1, 3) + ""));
L = L.add(lSummand);
X = X.multiply(xMultiplier);
sum = sum.add(M.multiply(L).divide(X));
@ -371,7 +375,7 @@ public class StandardPlugin extends Plugin {
} else {
//We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
//right and left refer to lhs and rhs in the above inequality.
NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
NumberInterface sum = fromInt(params[0].getClass(), 0);
NumberInterface nextNumerator = params[0];
NumberInterface left = params[0].multiply(fromInt(params[0].getClass(), 3).intPow(params[0].ceiling().intValue())), right = maxError;
do {
@ -379,7 +383,7 @@ public class StandardPlugin extends Plugin {
n++;
nextNumerator = nextNumerator.multiply(params[0]);
left = left.multiply(params[0]);
NumberInterface nextN = (new NaiveNumber(n + 1)).promoteTo(params[0].getClass());
NumberInterface nextN = fromInt(params[0].getClass(), n + 1);
right = right.multiply(nextN);
//System.out.println(left + ", " + right);
}
@ -395,18 +399,20 @@ public class StandardPlugin extends Plugin {
public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
NumberInterface zero = fromInt(params[0].getClass(), 0);
return params.length == 2
&& !(params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
&& params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) == 0)
&& !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0);
&& !(params[0].compareTo(zero) == 0
&& params[1].compareTo(zero) == 0)
&& !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(zero) != 0);
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
if (params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
return NaiveNumber.ZERO.promoteTo(params[0].getClass());
else if (params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
return NaiveNumber.ONE.promoteTo(params[1].getClass());
NumberInterface zero = fromInt(params[0].getClass(), 0);
if (params[0].compareTo(zero) == 0)
return zero;
else if (params[1].compareTo(zero) == 0)
return zero;
//Detect integer bases:
if(params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
&& FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
@ -481,7 +487,7 @@ public class StandardPlugin extends Plugin {
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionCos.apply(params[0]));
return fromInt(params[0].getClass(), 1).divide(functionCos.apply(params[0]));
}
};
/**
@ -495,7 +501,7 @@ public class StandardPlugin extends Plugin {
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionSin.apply(params[0]));
return fromInt(params[0].getClass(), 1).divide(functionSin.apply(params[0]));
}
};
/**
@ -526,7 +532,7 @@ public class StandardPlugin extends Plugin {
* @return the value of the partial sum that has the same class as x.
*/
private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n) {
NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
NumberInterface sum = fromInt(x.getClass(), 0);
for (int i = 0; i <= n; i++) {
sum = sum.add(nthTermFunction.apply(i, x));
}
@ -544,13 +550,13 @@ public class StandardPlugin extends Plugin {
public static NumberInterface factorial(Class<? extends NumberInterface> numberClass, int n) {
if (!FACTORIAL_LISTS.containsKey(numberClass)) {
FACTORIAL_LISTS.put(numberClass, new ArrayList<>());
FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
}
ArrayList<NumberInterface> list = FACTORIAL_LISTS.get(numberClass);
if (n >= list.size()) {
while (list.size() < n + 16) {
list.add(list.get(list.size() - 1).multiply(new NaiveNumber(list.size()).promoteTo(numberClass)));
list.add(list.get(list.size() - 1).multiply(fromInt(numberClass, list.size())));
}
}
return list.get(n);
@ -582,7 +588,7 @@ public class StandardPlugin extends Plugin {
* @return theta in [0, 2pi) that differs from phi by a multiple of 2pi.
*/
private static NumberInterface getSmallAngle(NumberInterface phi, NumberInterface pi) {
NumberInterface twoPi = pi.multiply(new NaiveNumber("2").promoteTo(phi.getClass()));
NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
NumberInterface theta = FUNCTION_ABS.apply(phi).subtract(twoPi
.multiply(FUNCTION_ABS.apply(phi).divide(twoPi).floor())); //Now theta is in [0, 2pi).
if (phi.signum() < 0) {