mirror of
https://github.com/DanilaFe/abacus
synced 2026-01-23 07:15:19 +00:00
Format code.
This commit is contained in:
@@ -18,8 +18,6 @@ import java.util.function.BiFunction;
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*/
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public class StandardPlugin extends Plugin {
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private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
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/**
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* The addition operator, +
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*/
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@@ -129,20 +127,6 @@ public class StandardPlugin extends Plugin {
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}*/
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}
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});
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/**
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* The caret / pow operator, ^
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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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/**
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* The absolute value function, abs(-3) = 3
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*/
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@@ -157,49 +141,6 @@ public class StandardPlugin extends Plugin {
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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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/**
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* The exponential function, exp(1) = e^1 = 2.71...
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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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NumberInterface maxError = getMaxError(params[0]);
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int n = 0;
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if(params[0].signum() <= 0){
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NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
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while(FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0){
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n++;
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currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
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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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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 nextNumerator = params[0];
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NumberInterface left = params[0].multiply((new NaiveNumber(3)).promoteTo(params[0].getClass()).intPow(params[0].ceiling().intValue())), right = maxError;
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do{
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sum = sum.add(nextNumerator.divide(factorial(params[0].getClass(), n+1)));
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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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right = right.multiply(nextN);
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//System.out.println(left + ", " + right);
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}
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while(left.compareTo(right) > 0);
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//System.out.println(n+1);
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return sum;
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}
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}
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};
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/**
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* The natural log function.
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*/
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@@ -291,109 +232,6 @@ public class StandardPlugin extends Plugin {
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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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/**
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* The sine function (the argument is interpreted in radians).
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*/
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public final Function functionSin = 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 pi = getPi(params[0].getClass());
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NumberInterface twoPi = pi.multiply(new NaiveNumber(2).promoteTo(pi.getClass()));
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NumberInterface theta = getSmallAngle(params[0], pi);
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//System.out.println(theta);
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if(theta.compareTo(pi.multiply(new NaiveNumber(1.5).promoteTo(twoPi.getClass()))) >= 0){
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theta = theta.subtract(twoPi);
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}
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else if(theta.compareTo(pi.divide(new NaiveNumber(2).promoteTo(pi.getClass()))) > 0){
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theta = pi.subtract(theta);
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}
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//System.out.println(theta);
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return sinTaylor(theta);
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}
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};
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/**
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* The cosine function (the argument is in radians).
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*/
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public final Function functionCos = 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 functionSin.apply(getPi(params[0].getClass()).divide(new NaiveNumber(2).promoteTo(params[0].getClass()))
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.subtract(params[0]));
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}
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};
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/**
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* The tangent function (the argument is in radians).
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*/
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public final Function functionTan = 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 functionSin.apply(params[0]).divide(functionCos.apply(params[0]));
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}
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};
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/**
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* The secant function (the argument is in radians).
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*/
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public final Function functionSec = 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 NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionCos.apply(params[0]));
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}
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};
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/**
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* The cosecant function (the argument is in radians).
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*/
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public final Function functionCsc = 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 NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionSin.apply(params[0]));
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}
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};
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/**
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* The cotangent function (the argument is in radians).
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*/
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public final Function functionCot = 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 functionCos.apply(params[0]).divide(functionCos.apply(params[0]));
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}
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};
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/**
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* The implementation for double-based naive numbers.
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*/
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@@ -408,7 +246,6 @@ public class StandardPlugin extends Plugin {
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return new NaiveNumber(Math.PI);
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}
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};
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/**
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* The implementation for the infinite-precision BigDecimal.
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*/
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@@ -425,19 +262,19 @@ public class StandardPlugin extends Plugin {
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NumberInterface L = new PreciseNumber("13591409");
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NumberInterface X = M;
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NumberInterface sum = L;
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int termsNeeded = C.getMaxPrecision()/13 + 1;
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int termsNeeded = C.getMaxPrecision() / 13 + 1;
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NumberInterface lSummand = new PreciseNumber("545140134");
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NumberInterface xMultiplier = new PreciseNumber("262537412")
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.multiply(new PreciseNumber("1000000000"))
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.add(new PreciseNumber("640768000"))
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.negate();
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for(int i = 0; i < termsNeeded; i++){
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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 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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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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@@ -445,6 +282,158 @@ public class StandardPlugin extends Plugin {
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return C.divide(sum);
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}
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};
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private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
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/**
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* The exponential function, exp(1) = e^1 = 2.71...
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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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NumberInterface maxError = getMaxError(params[0]);
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int n = 0;
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if (params[0].signum() <= 0) {
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NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
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while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
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n++;
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currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
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sum = sum.add(currentTerm);
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}
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return sum;
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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 nextNumerator = params[0];
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NumberInterface left = params[0].multiply((new NaiveNumber(3)).promoteTo(params[0].getClass()).intPow(params[0].ceiling().intValue())), right = maxError;
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do {
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sum = sum.add(nextNumerator.divide(factorial(params[0].getClass(), n + 1)));
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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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right = right.multiply(nextN);
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//System.out.println(left + ", " + right);
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}
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while (left.compareTo(right) > 0);
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//System.out.println(n+1);
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return sum;
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}
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}
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};
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/**
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* The caret / pow operator, ^
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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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/**
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* The sine function (the argument is interpreted in radians).
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*/
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public final Function functionSin = 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 pi = getPi(params[0].getClass());
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NumberInterface twoPi = pi.multiply(new NaiveNumber(2).promoteTo(pi.getClass()));
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NumberInterface theta = getSmallAngle(params[0], pi);
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//System.out.println(theta);
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if (theta.compareTo(pi.multiply(new NaiveNumber(1.5).promoteTo(twoPi.getClass()))) >= 0) {
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theta = theta.subtract(twoPi);
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} else if (theta.compareTo(pi.divide(new NaiveNumber(2).promoteTo(pi.getClass()))) > 0) {
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theta = pi.subtract(theta);
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}
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//System.out.println(theta);
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return sinTaylor(theta);
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}
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};
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/**
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* The cosine function (the argument is in radians).
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*/
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public final Function functionCos = 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 functionSin.apply(getPi(params[0].getClass()).divide(new NaiveNumber(2).promoteTo(params[0].getClass()))
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.subtract(params[0]));
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}
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};
|
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/**
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* The tangent function (the argument is in radians).
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*/
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public final Function functionTan = 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 functionSin.apply(params[0]).divide(functionCos.apply(params[0]));
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}
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};
|
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/**
|
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* The secant function (the argument is in radians).
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*/
|
||||
public final Function functionSec = 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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|
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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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* The cosecant function (the argument is in radians).
|
||||
*/
|
||||
public final Function functionCsc = new Function() {
|
||||
@Override
|
||||
protected boolean matchesParams(NumberInterface[] params) {
|
||||
return params.length == 1;
|
||||
}
|
||||
|
||||
@Override
|
||||
protected NumberInterface applyInternal(NumberInterface[] params) {
|
||||
return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionSin.apply(params[0]));
|
||||
}
|
||||
};
|
||||
/**
|
||||
* The cotangent function (the argument is in radians).
|
||||
*/
|
||||
public final Function functionCot = new Function() {
|
||||
@Override
|
||||
protected boolean matchesParams(NumberInterface[] params) {
|
||||
return params.length == 1;
|
||||
}
|
||||
|
||||
@Override
|
||||
protected NumberInterface applyInternal(NumberInterface[] params) {
|
||||
return functionCos.apply(params[0]).divide(functionCos.apply(params[0]));
|
||||
}
|
||||
};
|
||||
|
||||
public StandardPlugin(PluginManager manager) {
|
||||
super(manager);
|
||||
@@ -476,6 +465,64 @@ public class StandardPlugin extends Plugin {
|
||||
return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision());
|
||||
}
|
||||
|
||||
/**
|
||||
* A factorial function that uses memoization for each number class; it efficiently
|
||||
* computes factorials of non-negative integers.
|
||||
*
|
||||
* @param numberClass type of number to return.
|
||||
* @param n non-negative integer.
|
||||
* @return a number of numClass with value n factorial.
|
||||
*/
|
||||
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));
|
||||
}
|
||||
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)));
|
||||
}
|
||||
}
|
||||
return list.get(n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the value of the Taylor series for sin (centered at 0) at x.
|
||||
*
|
||||
* @param x where the series is evaluated.
|
||||
* @return the value of the series
|
||||
*/
|
||||
private static NumberInterface sinTaylor(NumberInterface x) {
|
||||
NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
|
||||
NumberInterface maxError = getMaxError(x);
|
||||
int n = 1;
|
||||
do {
|
||||
n += 2;
|
||||
power = power.multiply(multiplier);
|
||||
currentTerm = power.divide(factorial(x.getClass(), n));
|
||||
sum = sum.add(currentTerm);
|
||||
} while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0);
|
||||
return sum;
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns an equivalent angle in the interval [0, 2pi)
|
||||
*
|
||||
* @param phi an angle (in radians).
|
||||
* @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 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) {
|
||||
theta = twoPi.subtract(theta);
|
||||
}
|
||||
return theta;
|
||||
}
|
||||
|
||||
@Override
|
||||
public void onEnable() {
|
||||
registerNumberImplementation("naive", IMPLEMENTATION_NAIVE);
|
||||
@@ -505,59 +552,4 @@ public class StandardPlugin extends Plugin {
|
||||
public void onDisable() {
|
||||
|
||||
}
|
||||
|
||||
/**
|
||||
* A factorial function that uses memoization for each number class; it efficiently
|
||||
* computes factorials of non-negative integers.
|
||||
* @param numberClass type of number to return.
|
||||
* @param n non-negative integer.
|
||||
* @return a number of numClass with value n factorial.
|
||||
*/
|
||||
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));
|
||||
}
|
||||
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)));
|
||||
}
|
||||
}
|
||||
return list.get(n);
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the value of the Taylor series for sin (centered at 0) at x.
|
||||
* @param x where the series is evaluated.
|
||||
* @return the value of the series
|
||||
*/
|
||||
private static NumberInterface sinTaylor(NumberInterface x){
|
||||
NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
|
||||
NumberInterface maxError = getMaxError(x);
|
||||
int n = 1;
|
||||
do{
|
||||
n += 2;
|
||||
power = power.multiply(multiplier);
|
||||
currentTerm = power.divide(factorial(x.getClass(), n));
|
||||
sum = sum.add(currentTerm);
|
||||
} while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0);
|
||||
return sum;
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns an equivalent angle in the interval [0, 2pi)
|
||||
* @param phi an angle (in radians).
|
||||
* @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 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){
|
||||
theta = twoPi.subtract(theta);
|
||||
}
|
||||
return theta;
|
||||
}
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user