DanilaFe/Abacus
1
0
Fork 0
mirror of https://github.com/DanilaFe/abacus synced 2026-01-23 07:15:19 +00:00
Code Issues Releases Wiki Activity

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

Browse Source
This commit is contained in:
Arthur Drobot
2017-08-04 13:30:05 -07:00
parent e4a45c0ec4 b036b6c242
commit d7ae1a80f1
12 changed files with 594 additions and 103 deletions
Download Patch File Download Diff File Expand all files Collapse all files

221
src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java
View File

@@ -19,7 +19,7 @@ import java.util.function.BiFunction;
*/
public class StandardPlugin extends Plugin {
private static HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> factorialLists = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
/**
* The addition operator, +
@@ -106,7 +106,9 @@ public class StandardPlugin extends Plugin {
//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
return params.length == 1
&& params[0].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
&& params[0].signum() >= 0;
}
@Override
@@ -191,7 +193,7 @@ public class StandardPlugin extends Plugin {
//right and left refer to lhs and rhs in the above inequality.
NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
NumberInterface nextNumerator = params[0];
NumberInterface left = params[0].multiply((new NaiveNumber(3)).promoteTo(params[0].getClass()).intPow(params[0].ceiling())), right = maxError;
NumberInterface left = params[0].multiply((new NaiveNumber(3)).promoteTo(params[0].getClass()).intPow(params[0].ceiling().intValue())), right = maxError;
do{
sum = sum.add(nextNumerator.divide(factorial(params[0].getClass(), n+1)));
n++;
@@ -299,6 +301,160 @@ public class StandardPlugin extends Plugin {
}
};
/**
* The sine function (the argument is interpreted in radians).
*/
public final Function functionSin = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface pi = getPi(params[0].getClass());
NumberInterface twoPi = pi.multiply(new NaiveNumber(2).promoteTo(pi.getClass()));
NumberInterface theta = getSmallAngle(params[0], pi);
//System.out.println(theta);
if(theta.compareTo(pi.multiply(new NaiveNumber(1.5).promoteTo(twoPi.getClass()))) >= 0){
theta = theta.subtract(twoPi);
}
else if(theta.compareTo(pi.divide(new NaiveNumber(2).promoteTo(pi.getClass()))) > 0){
theta = pi.subtract(theta);
}
//System.out.println(theta);
return sinTaylor(theta);
}
};
/**
* The cosine function (the argument is in radians).
*/
public final Function functionCos = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return functionSin.apply(getPi(params[0].getClass()).divide(new NaiveNumber(2).promoteTo(params[0].getClass()))
.subtract(params[0]));
}
};
/**
* The tangent function (the argument is in radians).
*/
public final Function functionTan = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return functionSin.apply(params[0]).divide(functionCos.apply(params[0]));
}
};
/**
* The secant function (the argument is in radians).
*/
public final Function functionSec = 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(functionCos.apply(params[0]));
}
};
/**
* 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]));
}
};
/**
* The implementation for double-based naive numbers.
*/
public static final NumberImplementation IMPLEMENTATION_NAIVE = new NumberImplementation(NaiveNumber.class, 0) {
@Override
public NumberInterface instanceForString(String string) {
return new NaiveNumber(string);
}
@Override
public NumberInterface instanceForPi() {
return new NaiveNumber(Math.PI);
}
};
/**
* The implementation for the infinite-precision BigDecimal.
*/
public static final NumberImplementation IMPLEMENTATION_PRECISE = new NumberImplementation(PreciseNumber.class, 0) {
@Override
public NumberInterface instanceForString(String string) {
return new PreciseNumber(string);
}
@Override
public NumberInterface instanceForPi() {
NumberInterface C = FUNCTION_SQRT.apply(new PreciseNumber("10005")).multiply(new PreciseNumber("426880"));
NumberInterface M = PreciseNumber.ONE;
NumberInterface L = new PreciseNumber("13591409");
NumberInterface X = M;
NumberInterface sum = L;
int termsNeeded = C.getMaxPrecision()/13 + 1;
NumberInterface lSummand = new PreciseNumber("545140134");
NumberInterface xMultiplier = new PreciseNumber("262537412")
.multiply(new PreciseNumber("1000000000"))
.add(new PreciseNumber("640768000"))
.negate();
for(int i = 0; i < termsNeeded; i++){
M = M
.multiply(new NaiveNumber(12*i+2).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12*i+6).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12*i+10).promoteTo(PreciseNumber.class))
.divide(new NaiveNumber(Math.pow(i+1,3)).promoteTo(PreciseNumber.class));
L = L.add(lSummand);
X = X.multiply(xMultiplier);
sum = sum.add(M.multiply(L).divide(X));
}
return C.divide(sum);
}
};
public StandardPlugin(PluginManager manager) {
super(manager);
}
@@ -331,8 +487,8 @@ public class StandardPlugin extends Plugin {
@Override
public void onEnable() {
registerNumber("naive", NaiveNumber.class);
registerNumber("precise", PreciseNumber.class);
registerNumberImplementation("naive", IMPLEMENTATION_NAIVE);
registerNumberImplementation("precise", IMPLEMENTATION_PRECISE);
registerOperator("+", OP_ADD);
registerOperator("-", OP_SUBTRACT);
@@ -346,6 +502,12 @@ public class StandardPlugin extends Plugin {
registerFunction("exp", FUNCTION_EXP);
registerFunction("ln", FUNCTION_LN);
registerFunction("sqrt", FUNCTION_SQRT);
registerFunction("sin", functionSin);
registerFunction("cos", functionCos);
registerFunction("tan", functionTan);
registerFunction("sec", functionSec);
registerFunction("csc", functionCsc);
registerFunction("cot", functionCot);
}
@Override
@@ -353,13 +515,20 @@ public class StandardPlugin extends Plugin {
}
/**
* 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(!factorialLists.containsKey(numberClass)){
factorialLists.put(numberClass, new ArrayList<>());
factorialLists.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
factorialLists.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
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 = factorialLists.get(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)));
@@ -368,4 +537,36 @@ public class StandardPlugin extends Plugin {
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;
}
}