mirror of
https://github.com/DanilaFe/abacus
synced 2024-11-17 16:09:32 -08:00
Phase out as many promoteTo calls as possible.
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parent
021e569491
commit
fd21014c39
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@ -11,6 +11,7 @@ import org.nwapw.abacus.tree.TokenType;
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import org.nwapw.abacus.tree.TreeNode;
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import java.util.ArrayList;
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import java.util.Date;
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import java.util.HashMap;
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import java.util.List;
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import java.util.function.BiFunction;
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@ -97,7 +98,7 @@ public class StandardPlugin extends Plugin {
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public static final Operator OP_DIVIDE = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1, new Function() {
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@Override
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protected boolean matchesParams(NumberInterface[] params) {
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return params.length == 2 && params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0;
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return params.length == 2 && params[1].compareTo(fromInt(params[0].getClass(), 0)) != 0;
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}
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@Override
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@ -113,7 +114,7 @@ public class StandardPlugin extends Plugin {
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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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&& params[0].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
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&& params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
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&& params[0].signum() >= 0;
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}
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@ -122,10 +123,11 @@ public class StandardPlugin extends Plugin {
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if (params[0].signum() == 0) {
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return fromInt(params[0].getClass(), 1);
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}
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NumberInterface one = fromInt(params[0].getClass(), 1);
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NumberInterface factorial = params[0];
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NumberInterface multiplier = params[0];
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//It is necessary to later prevent calls of factorial on anything but non-negative integers.
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while ((multiplier = multiplier.subtract(NaiveNumber.ONE.promoteTo(multiplier.getClass()))).signum() == 1) {
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while ((multiplier = multiplier.subtract(one)).signum() == 1) {
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factorial = factorial.multiply(multiplier);
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}
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return factorial;
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@ -192,7 +194,7 @@ public class StandardPlugin extends Plugin {
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
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return params[0].multiply(fromInt(params[0].getClass(), params[0].signum()));
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}
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};
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/**
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@ -201,31 +203,32 @@ public class StandardPlugin extends Plugin {
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public static final Function FUNCTION_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 && params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) > 0;
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return params.length == 1 && params[0].compareTo(fromInt(params[0].getClass(), 0)) > 0;
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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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NumberInterface one = fromInt(param.getClass(), 1);
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int powersOf2 = 0;
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while (FUNCTION_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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while (FUNCTION_ABS.apply(param.subtract(one)).compareTo(new NaiveNumber(0.1).promoteTo(param.getClass())) >= 0) {
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if (param.subtract(one).signum() == 1) {
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param = param.divide(fromInt(param.getClass(), 2));
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powersOf2++;
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if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
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if (param.subtract(one).signum() != 1) {
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break;
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//No infinite loop for you.
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}
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} else {
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param = param.multiply(fromInt(param.getClass(), 2));
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powersOf2--;
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if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != -1) {
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if (param.subtract(one).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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return getLog2(param).multiply(fromInt(param.getClass(), powersOf2)).add(getLogPartialSum(param));
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}
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/**
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@ -237,13 +240,13 @@ public class StandardPlugin extends Plugin {
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private NumberInterface getLogPartialSum(NumberInterface x) {
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NumberInterface maxError = x.getMaxError();
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x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
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x = x.subtract(fromInt(x.getClass(), 1)); //Terms used are for log(x+1).
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NumberInterface currentNumerator = x, currentTerm = x, sum = x;
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int n = 1;
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while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
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n++;
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currentNumerator = currentNumerator.multiply(x).negate();
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currentTerm = currentNumerator.divide(new NaiveNumber(n).promoteTo(x.getClass()));
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currentTerm = currentNumerator.divide(fromInt(x.getClass(), n));
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sum = sum.add(currentTerm);
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}
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return sum;
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@ -261,13 +264,14 @@ public class StandardPlugin extends Plugin {
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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 = fromInt(number.getClass(), 1), b = a, c = a;
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NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
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NumberInterface sum = fromInt(number.getClass(), 0);
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NumberInterface one = fromInt(number.getClass(), 1);
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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(fromInt(number.getClass(), 3));
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b = b.divide(fromInt(number.getClass(), 4));
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c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
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c = one.divide(fromInt(number.getClass(), n));
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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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@ -340,10 +344,10 @@ public class StandardPlugin extends Plugin {
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.negate();
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for (int i = 0; i < termsNeeded; i++) {
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M = M
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.multiply(new NaiveNumber(12 * i + 2).promoteTo(PreciseNumber.class))
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.multiply(new NaiveNumber(12 * i + 6).promoteTo(PreciseNumber.class))
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.multiply(new NaiveNumber(12 * i + 10).promoteTo(PreciseNumber.class))
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.divide(new NaiveNumber(Math.pow(i + 1, 3)).promoteTo(PreciseNumber.class));
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.multiply(new PreciseNumber((12 * i + 2) + ""))
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.multiply(new PreciseNumber((12 * i + 6) + ""))
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.multiply(new PreciseNumber((12 * i + 10) + ""))
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.divide(new PreciseNumber(Math.pow(i + 1, 3) + ""));
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L = L.add(lSummand);
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X = X.multiply(xMultiplier);
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sum = sum.add(M.multiply(L).divide(X));
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@ -371,7 +375,7 @@ public class StandardPlugin extends Plugin {
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} else {
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//We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
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//right and left refer to lhs and rhs in the above inequality.
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NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
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NumberInterface sum = fromInt(params[0].getClass(), 0);
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NumberInterface nextNumerator = params[0];
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NumberInterface left = params[0].multiply(fromInt(params[0].getClass(), 3).intPow(params[0].ceiling().intValue())), right = maxError;
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do {
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@ -379,7 +383,7 @@ public class StandardPlugin extends Plugin {
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n++;
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nextNumerator = nextNumerator.multiply(params[0]);
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left = left.multiply(params[0]);
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NumberInterface nextN = (new NaiveNumber(n + 1)).promoteTo(params[0].getClass());
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NumberInterface nextN = fromInt(params[0].getClass(), n + 1);
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right = right.multiply(nextN);
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//System.out.println(left + ", " + right);
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}
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@ -395,18 +399,20 @@ public class StandardPlugin extends Plugin {
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public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
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@Override
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protected boolean matchesParams(NumberInterface[] params) {
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NumberInterface zero = fromInt(params[0].getClass(), 0);
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return params.length == 2
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&& !(params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
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&& params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) == 0)
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&& !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0);
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&& !(params[0].compareTo(zero) == 0
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&& params[1].compareTo(zero) == 0)
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&& !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(zero) != 0);
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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if (params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
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return NaiveNumber.ZERO.promoteTo(params[0].getClass());
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else if (params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
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return NaiveNumber.ONE.promoteTo(params[1].getClass());
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NumberInterface zero = fromInt(params[0].getClass(), 0);
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if (params[0].compareTo(zero) == 0)
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return zero;
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else if (params[1].compareTo(zero) == 0)
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return zero;
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//Detect integer bases:
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if(params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
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&& FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
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@ -481,7 +487,7 @@ public class StandardPlugin extends Plugin {
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionCos.apply(params[0]));
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return fromInt(params[0].getClass(), 1).divide(functionCos.apply(params[0]));
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}
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};
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/**
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@ -495,7 +501,7 @@ public class StandardPlugin extends Plugin {
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionSin.apply(params[0]));
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return fromInt(params[0].getClass(), 1).divide(functionSin.apply(params[0]));
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}
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};
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/**
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@ -526,7 +532,7 @@ public class StandardPlugin extends Plugin {
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* @return the value of the partial sum that has the same class as x.
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*/
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private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n) {
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NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
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NumberInterface sum = fromInt(x.getClass(), 0);
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for (int i = 0; i <= n; i++) {
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sum = sum.add(nthTermFunction.apply(i, x));
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}
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@ -544,13 +550,13 @@ public class StandardPlugin extends Plugin {
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public static NumberInterface factorial(Class<? extends NumberInterface> numberClass, int n) {
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if (!FACTORIAL_LISTS.containsKey(numberClass)) {
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FACTORIAL_LISTS.put(numberClass, new ArrayList<>());
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FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
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FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
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FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
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FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
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}
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ArrayList<NumberInterface> list = FACTORIAL_LISTS.get(numberClass);
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if (n >= list.size()) {
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while (list.size() < n + 16) {
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list.add(list.get(list.size() - 1).multiply(new NaiveNumber(list.size()).promoteTo(numberClass)));
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list.add(list.get(list.size() - 1).multiply(fromInt(numberClass, list.size())));
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}
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}
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return list.get(n);
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@ -582,7 +588,7 @@ public class StandardPlugin extends Plugin {
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* @return theta in [0, 2pi) that differs from phi by a multiple of 2pi.
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*/
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private static NumberInterface getSmallAngle(NumberInterface phi, NumberInterface pi) {
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NumberInterface twoPi = pi.multiply(new NaiveNumber("2").promoteTo(phi.getClass()));
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NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
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NumberInterface theta = FUNCTION_ABS.apply(phi).subtract(twoPi
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.multiply(FUNCTION_ABS.apply(phi).divide(twoPi).floor())); //Now theta is in [0, 2pi).
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if (phi.signum() < 0) {
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