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Code Issues Releases Wiki Activity

Format code.

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This commit is contained in:
Danila Fedorin
2017-08-04 13:20:57 -07:00
parent ce484cfd43
commit b78707a0f4
14 changed files with 317 additions and 286 deletions
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16
src/main/java/org/nwapw/abacus/plugin/NumberImplementation.java
View File

@@ -26,10 +26,11 @@ public abstract class NumberImplementation {
/**
* Creates a new number implementation with the given data.
*
* @param implementation the implementation class.
* @param priority the priority, higher -> more likely to be converted into.
* @param priority the priority, higher -> more likely to be converted into.
*/
public NumberImplementation(Class<? extends NumberInterface> implementation, int priority){
public NumberImplementation(Class<? extends NumberInterface> implementation, int priority) {
this.implementation = implementation;
this.priority = priority;
promotionPaths = new HashMap<>();
@@ -37,30 +38,34 @@ public abstract class NumberImplementation {
/**
* Gets the list of all promotion paths this implementation can take.
*
* @return the map of documentation paths.
*/
public final Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> getPromotionPaths(){
public final Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> getPromotionPaths() {
return promotionPaths;
}
/**
* Gets the implementation class used by this implementation.
*
* @return the implementation class.
*/
public final Class<? extends NumberInterface> getImplementation(){
public final Class<? extends NumberInterface> getImplementation() {
return implementation;
}
/**
* Gets the priority of this number implementation.
*
* @return the priority.
*/
public final int getPriority(){
public final int getPriority() {
return priority;
}
/**
* Abstract function to create a new instance from a string.
*
* @param string the string to create a number from.
* @return the resulting number.
*/
@@ -68,6 +73,7 @@ public abstract class NumberImplementation {
/**
* Get the instance of pi with the given implementation.
*
* @return pi
*/
public abstract NumberInterface instanceForPi();

14
src/main/java/org/nwapw/abacus/plugin/Plugin.java
View File

@@ -78,7 +78,7 @@ public abstract class Plugin {
*
* @return the list of registered number implementations.
*/
public final Set<String> providedNumberImplementations(){
public final Set<String> providedNumberImplementations() {
return numberImplementations.keySet();
}
@@ -108,7 +108,7 @@ public abstract class Plugin {
* @param name the name of the number implementation to look up.
* @return the number implementation associated with that name, or null if the plugin doesn't provide it.
*/
public final NumberImplementation getNumberImplementation(String name){
public final NumberImplementation getNumberImplementation(String name) {
return numberImplementations.get(name);
}
@@ -160,10 +160,11 @@ public abstract class Plugin {
/**
* To be used in load(). Registers a new number implementation with the plugin.
* This makes it accessible to the plugin manager.
* @param name the name of the implementation.
*
* @param name the name of the implementation.
* @param implementation the actual implementation class to register.
*/
protected final void registerNumberImplementation(String name, NumberImplementation implementation){
protected final void registerNumberImplementation(String name, NumberImplementation implementation) {
numberImplementations.put(name, implementation);
}
@@ -199,7 +200,7 @@ public abstract class Plugin {
* @param name the name for which to search.
* @return the resulting number implementation, or null if none was found.
*/
protected final NumberImplementation numberImplementationFor(String name){
protected final NumberImplementation numberImplementationFor(String name) {
return manager.numberImplementationFor(name);
}
@@ -208,10 +209,11 @@ public abstract class Plugin {
* This is done so that number implementations with various degrees of precision
* can provide their own pi values, without losing said precision by
* promoting NaiveNumbers.
*
* @param forClass the class to which to find the pi instance.
* @return the pi value for the given class.
*/
protected final NumberInterface getPi(Class<? extends NumberInterface> forClass){
protected final NumberInterface getPi(Class<? extends NumberInterface> forClass) {
return manager.piFor(forClass);
}

36
src/main/java/org/nwapw/abacus/plugin/PluginManager.java
View File

@@ -102,9 +102,9 @@ public class PluginManager {
* @return the retrieved element, or null if it was not found.
*/
private static <T, K> T searchCached(Collection<Plugin> plugins, Map<K, T> cache,
java.util.function.Function<Plugin, Set<K>> setFunction,
java.util.function.BiFunction<Plugin, K, T> getFunction,
K name) {
java.util.function.Function<Plugin, Set<K>> setFunction,
java.util.function.BiFunction<Plugin, K, T> getFunction,
K name) {
if (cache.containsKey(name)) return cache.get(name);
T loadedValue = null;
@@ -141,27 +141,29 @@ public class PluginManager {
/**
* Gets the number implementation under the given name.
*
* @param name the name of the implementation.
* @return the implementation.
*/
public NumberImplementation numberImplementationFor(String name){
public NumberImplementation numberImplementationFor(String name) {
return searchCached(plugins, cachedNumberImplementations, Plugin::providedNumberImplementations,
Plugin::getNumberImplementation, name);
}
/**
* Gets the number implementation for the given implementation class.
*
* @param name the class for which to find the implementation.
* @return the implementation.
*/
public NumberImplementation interfaceImplementationFor(Class<? extends NumberInterface> name){
if(cachedInterfaceImplementations.containsKey(name)) return cachedInterfaceImplementations.get(name);
public NumberImplementation interfaceImplementationFor(Class<? extends NumberInterface> name) {
if (cachedInterfaceImplementations.containsKey(name)) return cachedInterfaceImplementations.get(name);
NumberImplementation toReturn = null;
outside:
for(Plugin plugin : plugins){
for(String implementationName : plugin.providedNumberImplementations()){
for (Plugin plugin : plugins) {
for (String implementationName : plugin.providedNumberImplementations()) {
NumberImplementation implementation = plugin.getNumberImplementation(implementationName);
if(implementation.getImplementation().equals(name)) {
if (implementation.getImplementation().equals(name)) {
toReturn = implementation;
break outside;
}
@@ -173,14 +175,15 @@ public class PluginManager {
/**
* Gets the mathematical constant pi for the given implementation class.
*
* @param forClass the class for which to find pi.
* @return pi
*/
public NumberInterface piFor(Class<? extends NumberInterface> forClass){
if(cachedPi.containsKey(forClass)) return cachedPi.get(forClass);
public NumberInterface piFor(Class<? extends NumberInterface> forClass) {
if (cachedPi.containsKey(forClass)) return cachedPi.get(forClass);
NumberImplementation implementation = interfaceImplementationFor(forClass);
NumberInterface generatedPi = null;
if(implementation != null){
if (implementation != null) {
generatedPi = implementation.instanceForPi();
}
cachedPi.put(forClass, generatedPi);
@@ -219,11 +222,11 @@ public class PluginManager {
public void load() {
Set<String> disabledPlugins = abacus.getConfiguration().getDisabledPlugins();
for (Plugin plugin : plugins) {
if(disabledPlugins.contains(plugin.getClass().getName())) continue;
if (disabledPlugins.contains(plugin.getClass().getName())) continue;
plugin.enable();
}
for (Plugin plugin : plugins) {
if(disabledPlugins.contains(plugin.getClass().getName())) continue;
if (disabledPlugins.contains(plugin.getClass().getName())) continue;
allFunctions.addAll(plugin.providedFunctions());
allOperators.addAll(plugin.providedOperators());
allNumberImplementations.addAll(plugin.providedNumberImplementations());
@@ -238,7 +241,7 @@ public class PluginManager {
listeners.forEach(e -> e.onUnload(this));
Set<String> disabledPlugins = abacus.getConfiguration().getDisabledPlugins();
for (Plugin plugin : plugins) {
if(disabledPlugins.contains(plugin.getClass().getName())) continue;
if (disabledPlugins.contains(plugin.getClass().getName())) continue;
plugin.disable();
}
cachedFunctions.clear();
@@ -283,7 +286,7 @@ public class PluginManager {
*
* @return the set of all implementations that were loaded.
*/
public Set<String> getAllNumberImplementations(){
public Set<String> getAllNumberImplementations() {
return allNumberImplementations;
}
@@ -308,6 +311,7 @@ public class PluginManager {
/**
* Gets a list of all the plugin class files that have been
* added to the plugin manager.
*
* @return the list of all the added plugin classes.
*/
public Set<Class<?>> getLoadedPluginClasses() {

440
src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java
View File

@@ -18,8 +18,6 @@ import java.util.function.BiFunction;
*/
public class StandardPlugin extends Plugin {
private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
/**
* The addition operator, +
*/
@@ -129,20 +127,6 @@ public class StandardPlugin extends Plugin {
}*/
}
});
/**
* The caret / pow operator, ^
*/
public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return FUNCTION_EXP.apply(FUNCTION_LN.apply(params[0]).multiply(params[1]));
}
});
/**
* The absolute value function, abs(-3) = 3
*/
@@ -157,49 +141,6 @@ public class StandardPlugin extends Plugin {
return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
}
};
/**
* The exponential function, exp(1) = e^1 = 2.71...
*/
public static final Function FUNCTION_EXP = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface maxError = getMaxError(params[0]);
int n = 0;
if(params[0].signum() <= 0){
NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
while(FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0){
n++;
currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
sum = sum.add(currentTerm);
}
return sum;
}
else{
//We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
//right and left refer to lhs and rhs in the above inequality.
NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
NumberInterface nextNumerator = params[0];
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++;
nextNumerator = nextNumerator.multiply(params[0]);
left = left.multiply(params[0]);
NumberInterface nextN = (new NaiveNumber(n+1)).promoteTo(params[0].getClass());
right = right.multiply(nextN);
//System.out.println(left + ", " + right);
}
while(left.compareTo(right) > 0);
//System.out.println(n+1);
return sum;
}
}
};
/**
* The natural log function.
*/
@@ -291,109 +232,6 @@ public class StandardPlugin extends Plugin {
return OP_CARET.getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
}
};
/**
* 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.
*/
@@ -408,7 +246,6 @@ public class StandardPlugin extends Plugin {
return new NaiveNumber(Math.PI);
}
};
/**
* The implementation for the infinite-precision BigDecimal.
*/
@@ -425,19 +262,19 @@ public class StandardPlugin extends Plugin {
NumberInterface L = new PreciseNumber("13591409");
NumberInterface X = M;
NumberInterface sum = L;
int termsNeeded = C.getMaxPrecision()/13 + 1;
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++){
for (int i = 0; i < termsNeeded; i++) {
M = M
.multiply(new NaiveNumber(12*i+2).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12*i+6).promoteTo(PreciseNumber.class))
.multiply(new NaiveNumber(12*i+10).promoteTo(PreciseNumber.class))
.divide(new NaiveNumber(Math.pow(i+1,3)).promoteTo(PreciseNumber.class));
.multiply(new 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));
@@ -445,6 +282,158 @@ public class StandardPlugin extends Plugin {
return C.divide(sum);
}
};
private static final HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> FACTORIAL_LISTS = new HashMap<>();
/**
* The exponential function, exp(1) = e^1 = 2.71...
*/
public static final Function FUNCTION_EXP = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface maxError = getMaxError(params[0]);
int n = 0;
if (params[0].signum() <= 0) {
NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
n++;
currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
sum = sum.add(currentTerm);
}
return sum;
} else {
//We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
//right and left refer to lhs and rhs in the above inequality.
NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
NumberInterface nextNumerator = params[0];
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++;
nextNumerator = nextNumerator.multiply(params[0]);
left = left.multiply(params[0]);
NumberInterface nextN = (new NaiveNumber(n + 1)).promoteTo(params[0].getClass());
right = right.multiply(nextN);
//System.out.println(left + ", " + right);
}
while (left.compareTo(right) > 0);
//System.out.println(n+1);
return sum;
}
}
};
/**
* The caret / pow operator, ^
*/
public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return FUNCTION_EXP.apply(FUNCTION_LN.apply(params[0]).multiply(params[1]));
}
});
/**
* 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]));
}
};
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;
}
}