mirror of
https://github.com/DanilaFe/abacus
synced 2024-12-23 16:00:09 -08:00
Move all functions to a static context, stopping unnecessary lookups.
This commit is contained in:
parent
6b8d8497e2
commit
03eb669eb3
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@ -16,6 +16,213 @@ import java.util.function.BiFunction;
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*/
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public class StandardPlugin extends Plugin {
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public static final Operator OP_ADD = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, 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 sum = params[0];
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for(int i = 1; i < params.length; i++){
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sum = sum.add(params[i]);
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}
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return sum;
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}
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});
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public static final Operator OP_SUBTRACT = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
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@Override
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protected boolean matchesParams(NumberInterface[] params) {
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return params.length == 2;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return params[0].subtract(params[1]);
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}
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});
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public static final Operator OP_MULTIPLY = 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 >= 1;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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NumberInterface product = params[0];
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for(int i = 1; i < params.length; i++){
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product = product.multiply(params[i]);
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}
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return product;
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}
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});
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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 >= 1;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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NumberInterface product = params[0];
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for(int i = 1; i < params.length; i++){
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product = product.multiply(params[i]);
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}
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return product;
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}
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});
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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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return params.length == 2;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return FUNCTION_EXP.apply(FUNCTION_LN.apply(params[0]).multiply(params[1]));
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}
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});
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public static final Operator OP_FACTORIAL = new Operator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0, new Function() {
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//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
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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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if(params[0].signum() == 0){
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return (new NaiveNumber(1)).promoteTo(params[0].getClass());
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}
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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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factorial = factorial.multiply(multiplier);
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}
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return factorial;
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/*if(!storedList.containsKey(params[0].getClass())){
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storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
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storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
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storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
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}*/
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}
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});
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public static final Function FUNCTION_ABS = 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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return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
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}
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};
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public static final Function FUNCTION_EXP = 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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boolean takeReciprocal = params[0].signum() == -1;
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params[0] = FUNCTION_ABS.apply(params[0]);
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NumberInterface sum = sumSeries(params[0], StandardPlugin::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
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if(takeReciprocal){
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sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
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}
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return sum;
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}
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};
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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;
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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(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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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 = 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(FUNCTION_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 = 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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public static final Function FUNCTION_SQRT = 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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return OP_CARET.getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
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}
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};
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public StandardPlugin(PluginManager manager) {
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super(manager);
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}
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@ -25,217 +232,17 @@ public class StandardPlugin extends Plugin {
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registerNumber("naive", NaiveNumber.class);
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registerNumber("precise", PreciseNumber.class);
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registerOperator("+", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, 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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registerOperator("+", OP_ADD);
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registerOperator("-", OP_SUBTRACT);
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registerOperator("*", OP_MULTIPLY);
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registerOperator("/", OP_DIVIDE);
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registerOperator("^", OP_CARET);
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registerOperator("!", OP_FACTORIAL);
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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NumberInterface sum = params[0];
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for(int i = 1; i < params.length; i++){
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sum = sum.add(params[i]);
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}
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return sum;
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}
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}));
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registerOperator("-", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
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@Override
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protected boolean matchesParams(NumberInterface[] params) {
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return params.length == 2;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return params[0].subtract(params[1]);
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}
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}));
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registerOperator("*", 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 >= 1;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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NumberInterface product = params[0];
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for(int i = 1; i < params.length; i++){
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product = product.multiply(params[i]);
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}
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return product;
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}
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}));
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registerOperator("/", 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;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return params[0].divide(params[1]);
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}
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}));
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registerOperator("^", 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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return params.length == 2;
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}
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@Override
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protected NumberInterface applyInternal(NumberInterface[] params) {
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return StandardPlugin.this.getFunction("exp").apply(StandardPlugin.this.getFunction("ln").apply(params[0]).multiply(params[1]));
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}
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}));
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registerOperator("!", new Operator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0, new Function() {
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//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
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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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if(params[0].signum() == 0){
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return (new NaiveNumber(1)).promoteTo(params[0].getClass());
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}
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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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factorial = factorial.multiply(multiplier);
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}
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return factorial;
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/*if(!storedList.containsKey(params[0].getClass())){
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storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
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storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
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storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
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}*/
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}
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}));
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registerFunction("abs", 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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return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
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}
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});
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registerFunction("exp", 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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boolean takeReciprocal = params[0].signum() == -1;
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params[0] = StandardPlugin.this.getFunction("abs").apply(params[0]);
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NumberInterface sum = sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
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if(takeReciprocal){
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sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
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}
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return sum;
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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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registerFunction("sqrt", 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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return StandardPlugin.this.getOperator("^").getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
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}
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});
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registerFunction("abs", FUNCTION_ABS);
|
||||
registerFunction("exp", FUNCTION_EXP);
|
||||
registerFunction("ln", FUNCTION_LN);
|
||||
registerFunction("sqrt",FUNCTION_SQRT);
|
||||
}
|
||||
|
||||
@Override
|
||||
|
|
@ -249,8 +256,8 @@ public class StandardPlugin extends Plugin {
|
|||
* @param x the real number at which the series is evaluated.
|
||||
* @return the nth term of the series.
|
||||
*/
|
||||
private NumberInterface getExpSeriesTerm(int n, NumberInterface x){
|
||||
return x.intPow(n).divide(this.getOperator("!").getFunction().apply((new NaiveNumber(n)).promoteTo(x.getClass())));
|
||||
private static NumberInterface getExpSeriesTerm(int n, NumberInterface x){
|
||||
return x.intPow(n).divide(OP_FACTORIAL.getFunction().apply((new NaiveNumber(n)).promoteTo(x.getClass())));
|
||||
}
|
||||
|
||||
/**
|
||||
|
|
@ -260,11 +267,11 @@ public class StandardPlugin extends Plugin {
|
|||
* @param x where the function is evaluated.
|
||||
* @return the number of terms needed to evaluated the exponential function.
|
||||
*/
|
||||
private int getNTermsExp(NumberInterface maxError, NumberInterface x) {
|
||||
private static 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);
|
||||
x = FUNCTION_ABS.apply(x);
|
||||
NumberInterface LHS = x, RHS = maxError;
|
||||
while (LHS.compareTo(RHS) > 0) {
|
||||
n++;
|
||||
|
|
@ -282,7 +289,7 @@ public class StandardPlugin extends Plugin {
|
|||
* @param n the number of terms in the partial sum.
|
||||
* @return the value of the partial sum that has the same class as x.
|
||||
*/
|
||||
private NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n){
|
||||
private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n){
|
||||
NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
|
||||
for(int i = 0; i <= n; i++){
|
||||
sum = sum.add(nthTermFunction.apply(i, x));
|
||||
|
|
@ -295,7 +302,7 @@ public class StandardPlugin extends Plugin {
|
|||
* @param number Any instance of the NumberInterface in question (should return an appropriate precision).
|
||||
* @return the maximum error.
|
||||
*/
|
||||
private NumberInterface getMaxError(NumberInterface number){
|
||||
private static NumberInterface getMaxError(NumberInterface number){
|
||||
return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision());
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user