Add comments to all the pi-related stuff.

src/main/java/org/nwapw/abacus/Abacus.java

@@ -1,12 +1,12 @@
 package org.nwapw.abacus;
 
 import org.nwapw.abacus.config.ConfigurationObject;
-import org.nwapw.abacus.number.NaiveNumber;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.parsing.LexerTokenizer;
 import org.nwapw.abacus.parsing.ShuntingYardParser;
 import org.nwapw.abacus.parsing.TreeBuilder;
 import org.nwapw.abacus.plugin.ClassFinder;
+import org.nwapw.abacus.plugin.NumberImplementation;
 import org.nwapw.abacus.plugin.PluginManager;
 import org.nwapw.abacus.plugin.StandardPlugin;
 import org.nwapw.abacus.tree.NumberReducer;
@@ -16,7 +16,6 @@ import org.nwapw.abacus.window.Window;
 import javax.swing.*;
 import java.io.File;
 import java.io.IOException;
-import java.lang.reflect.InvocationTargetException;
 
 /**
  * The main calculator class. This is responsible
@@ -25,10 +24,7 @@ import java.lang.reflect.InvocationTargetException;
  */
 public class Abacus {
 
-    /**
+    public static final NumberImplementation DEFAULT_IMPLEMENTATION = StandardPlugin.IMPLEMENTATION_NAIVE;
-     * The default implementation to use for the number representation.
-     */
-    public static final Class<? extends NumberInterface> DEFAULT_NUMBER = NaiveNumber.class;
     /**
      * The file used for saving and loading configuration.
      */
@@ -154,15 +150,10 @@ public class Abacus {
      * @return the resulting number.
      */
     public NumberInterface numberFromString(String numberString) {
-        Class<? extends NumberInterface> toInstantiate =
+        NumberImplementation toInstantiate =
-                pluginManager.numberFor(configuration.getNumberImplementation());
+                pluginManager.numberImplementationFor(configuration.getNumberImplementation());
-        if (toInstantiate == null) toInstantiate = DEFAULT_NUMBER;
+        if (toInstantiate == null) toInstantiate = DEFAULT_IMPLEMENTATION;
 
-        try {
+        return toInstantiate.instanceForString(numberString);
-            return toInstantiate.getConstructor(String.class).newInstance(numberString);
-        } catch (InstantiationException | IllegalAccessException | NoSuchMethodException | InvocationTargetException e) {
-            e.printStackTrace();
-        }
-        return null;
     }
 }

src/main/java/org/nwapw/abacus/function/Function.java

@@ -1,10 +1,6 @@
 package org.nwapw.abacus.function;
 
-import org.nwapw.abacus.number.NaiveNumber;
 import org.nwapw.abacus.number.NumberInterface;
-import org.nwapw.abacus.number.PreciseNumber;
-
-import java.util.HashMap;
 
 /**
  * A function that operates on one or more
@@ -12,15 +8,6 @@ import java.util.HashMap;
  */
 public abstract class Function {
 
-    /**
-     * A map to correctly promote different number implementations to each other.
-     */
-    private static final HashMap<Class<? extends NumberInterface>, Integer> priorityMap =
-            new HashMap<Class<? extends NumberInterface>, Integer>() {{
-                put(NaiveNumber.class, 0);
-                put(PreciseNumber.class, 1);
-            }};
-
     /**
      * Checks whether the given params will work for the given function.
      *

src/main/java/org/nwapw/abacus/number/NaiveNumber.java

@@ -93,6 +93,26 @@ public class NaiveNumber implements NumberInterface {
         return this.compareTo(ZERO);
     }
 
+    @Override
+    public NumberInterface ceiling() {
+        return new NaiveNumber(Math.ceil(value));
+    }
+
+    @Override
+    public NumberInterface floor() {
+        return new NaiveNumber(Math.floor(value));
+    }
+
+    @Override
+    public NumberInterface fractionalPart() {
+        return new NaiveNumber(value - Math.floor(value));
+    }
+
+    @Override
+    public int intValue() {
+        return (int)value;
+    }
+
     @Override
     public NumberInterface promoteTo(Class<? extends NumberInterface> toClass) {
         if (toClass == this.getClass()) return this;

src/main/java/org/nwapw/abacus/number/NumberInterface.java

@@ -79,6 +79,31 @@ public interface NumberInterface {
      */
     int signum();
 
+    /**
+     * Returns the least integer greater than or equal to the number.
+     * @return the least integer >= the number, if int can hold the value.
+     */
+    NumberInterface ceiling();
+
+    /**
+     * Return the greatest integer less than or equal to the number.
+     * @return the greatest int >= the number, if int can hold the value.
+     */
+    NumberInterface floor();
+
+    /**
+     * Returns the fractional part of the number.
+     * @return the fractional part of the number.
+     */
+    NumberInterface fractionalPart();
+
+    /**
+     * Returns the integer representation of this number, discarding any fractional part,
+     * if int can hold the value.
+     * @return
+     */
+    int intValue();
+
     /**
      * Promotes this class to another number class.
      *

src/main/java/org/nwapw/abacus/number/PreciseNumber.java

@@ -8,15 +8,15 @@ public class PreciseNumber implements NumberInterface {
     /**
      * The number one.
      */
-    static final PreciseNumber ONE = new PreciseNumber(BigDecimal.ONE);
+    public static final PreciseNumber ONE = new PreciseNumber(BigDecimal.ONE);
     /**
      * The number zero.
      */
-    static final PreciseNumber ZERO = new PreciseNumber(BigDecimal.ZERO);
+    public static final PreciseNumber ZERO = new PreciseNumber(BigDecimal.ZERO);
     /**
      * The number ten.
      */
-    static final PreciseNumber TEN = new PreciseNumber(BigDecimal.TEN);
+    public static final PreciseNumber TEN = new PreciseNumber(BigDecimal.TEN);
 
     /**
      * The value of the PreciseNumber.
@@ -44,12 +44,12 @@ public class PreciseNumber implements NumberInterface {
 
     @Override
     public int getMaxPrecision() {
-        return 54;
+        return 65;
     }
 
     @Override
     public NumberInterface multiply(NumberInterface multiplier) {
-        return new PreciseNumber(value.multiply(((PreciseNumber) multiplier).value));
+        return new PreciseNumber(this.value.multiply(((PreciseNumber) multiplier).value));
     }
 
     @Override
@@ -94,6 +94,41 @@ public class PreciseNumber implements NumberInterface {
         return value.signum();
     }
 
+    @Override
+    public NumberInterface ceiling() {
+        String str = value.toPlainString();
+        int decimalIndex = str.indexOf('.');
+        if(decimalIndex != -1){
+            return this.floor().add(ONE);
+        }
+        return this;
+    }
+
+    @Override
+    public NumberInterface floor() {
+        String str = value.toPlainString();
+        int decimalIndex = str.indexOf('.');
+        if(decimalIndex != -1){
+            return new PreciseNumber(str.substring(0, decimalIndex));
+        }
+        return this;
+    }
+
+    @Override
+    public NumberInterface fractionalPart() {
+        String str = value.toPlainString();
+        int decimalIndex = str.indexOf('.');
+        if(decimalIndex != -1){
+            return new PreciseNumber(str.substring(decimalIndex + 1));
+        }
+        return ZERO;
+    }
+
+    @Override
+    public int intValue() {
+        return value.intValue();
+    }
+
     @Override
     public NumberInterface negate() {
         return new PreciseNumber(value.negate());
@@ -109,7 +144,7 @@ public class PreciseNumber implements NumberInterface {
 
     @Override
     public String toString() {
-        BigDecimal rounded = value.setScale(getMaxPrecision() - 4, RoundingMode.HALF_UP);
+        BigDecimal rounded = value.setScale(getMaxPrecision() - 15, RoundingMode.HALF_UP);
         return rounded.stripTrailingZeros().toPlainString();
     }
 }

src/main/java/org/nwapw/abacus/plugin/NumberImplementation.java

@@ -0,0 +1,75 @@
+package org.nwapw.abacus.plugin;
+
+import org.nwapw.abacus.number.NumberInterface;
+
+import java.util.HashMap;
+import java.util.Map;
+import java.util.function.Function;
+
+/**
+ * A class that holds data about a number implementation.
+ */
+public abstract class NumberImplementation {
+
+    /**
+     * The list of paths through which this implementation can be promoted.
+     */
+    protected Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> promotionPaths;
+    /**
+     * The implementation class for this implementation.
+     */
+    private Class<? extends NumberInterface> implementation;
+    /**
+     * The priority of converting into this number implementation.
+     */
+    private int priority;
+
+    /**
+     * 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.
+     */
+    public NumberImplementation(Class<? extends NumberInterface> implementation, int priority){
+        this.implementation = implementation;
+        this.priority = priority;
+        promotionPaths = new HashMap<>();
+    }
+
+    /**
+     * 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(){
+        return promotionPaths;
+    }
+
+    /**
+     * Gets the implementation class used by this implementation.
+     * @return the implementation class.
+     */
+    public final Class<? extends NumberInterface> getImplementation(){
+        return implementation;
+    }
+
+    /**
+     * Gets the priority of this number implementation.
+     * @return the priority.
+     */
+    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.
+     */
+    public abstract NumberInterface instanceForString(String string);
+
+    /**
+     * Get the instance of pi with the given implementation.
+     * @return pi
+     */
+    public abstract NumberInterface instanceForPi();
+
+}

src/main/java/org/nwapw/abacus/plugin/Plugin.java

@@ -26,9 +26,9 @@ public abstract class Plugin {
      */
     private Map<String, Operator> operators;
     /**
-     * A hash map of operators mapped to their string names.
+     * The map of the number implementations this plugin provides.
      */
-    private Map<String, Class<? extends NumberInterface>> numbers;
+    private Map<String, NumberImplementation> numberImplementations;
     /**
      * The plugin manager in which to search for functions
      * not inside this package,
@@ -51,7 +51,7 @@ public abstract class Plugin {
         this.manager = manager;
         functions = new HashMap<>();
         operators = new HashMap<>();
-        numbers = new HashMap<>();
+        numberImplementations = new HashMap<>();
         enabled = false;
     }
 
@@ -74,12 +74,12 @@ public abstract class Plugin {
     }
 
     /**
-     * Gets the list of all numbers provided by this plugin.
+     * Gets the list of number implementations provided by this plugin.
      *
-     * @return the list of registered numbers.
+     * @return the list of registered number implementations.
      */
-    public final Set<String> providedNumbers() {
+    public final Set<String> providedNumberImplementations(){
-        return numbers.keySet();
+        return numberImplementations.keySet();
     }
 
     /**
@@ -103,13 +103,13 @@ public abstract class Plugin {
     }
 
     /**
-     * Gets the class under the given name.
+     * Gets the number implementation under the given name.
      *
-     * @param numberName the name of the class.
+     * @param name the name of the number implementation to look up.
-     * @return the class, or null if the plugin doesn't provide it.
+     * @return the number implementation associated with that name, or null if the plugin doesn't provide it.
      */
-    public final Class<? extends NumberInterface> getNumber(String numberName) {
+    public final NumberImplementation getNumberImplementation(String name){
-        return numbers.get(numberName);
+        return numberImplementations.get(name);
     }
 
     /**
@@ -158,16 +158,13 @@ public abstract class Plugin {
     }
 
     /**
-     * To be used in load(). Registers a number class
+     * To be used in load(). Registers a new number implementation with the plugin.
-     * with the plugin internally, which makes it possible
+     * This makes it accessible to the plugin manager.
-     * for the user to select it as an "implementation" for the
+     * @param name the name of the implementation.
-     * number that they would like to use.
+     * @param implementation the actual implementation class to register.
-     *
-     * @param name       the name to register it under.
-     * @param toRegister the class to register.
      */
-    protected final void registerNumber(String name, Class<? extends NumberInterface> toRegister) {
+    protected final void registerNumberImplementation(String name, NumberImplementation implementation){
-        numbers.put(name, toRegister);
+        numberImplementations.put(name, implementation);
     }
 
     /**
@@ -194,6 +191,30 @@ public abstract class Plugin {
         return manager.operatorFor(name);
     }
 
+    /**
+     * Searches the PluginManager for the given number implementation
+     * name. This can be used by the plugins internally in order to find
+     * implementations that they do not provide.
+     *
+     * @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){
+        return manager.numberImplementationFor(name);
+    }
+
+    /**
+     * Searches the plugin manager for a Pi value for the given number implementation.
+     * 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){
+        return manager.piFor(forClass);
+    }
+
     /**
      * Abstract method to be overridden by plugin implementation, in which the plugins
      * are supposed to register the functions they provide and do any other

src/main/java/org/nwapw/abacus/plugin/PluginManager.java

@@ -32,10 +32,19 @@ public class PluginManager {
      */
     private Map<String, Operator> cachedOperators;
     /**
-     * List of registered number implementations that have
+     * The list of number implementations that have
      * been cached, that is, found in a plugin and returned.
      */
-    private Map<String, Class<? extends NumberInterface>> cachedNumbers;
+    private Map<String, NumberImplementation> cachedNumberImplementations;
+    /**
+     * The list of number implementations that have been
+     * found by their implementation class.
+     */
+    private Map<Class<? extends NumberInterface>, NumberImplementation> cachedInterfaceImplementations;
+    /**
+     * The pi values for each implementation class that have already been computer.
+     */
+    private Map<Class<? extends NumberInterface>, NumberInterface> cachedPi;
     /**
      * List of all functions loaded by the plugins.
      */
@@ -45,9 +54,9 @@ public class PluginManager {
      */
     private Set<String> allOperators;
     /**
-     * List of all numbers loaded by the plugins.
+     * List of all the number implementations loaded by the plugins.
      */
-    private Set<String> allNumbers;
+    private Set<String> allNumberImplementations;
     /**
      * The list of plugin listeners attached to this instance.
      */
@@ -61,10 +70,12 @@ public class PluginManager {
         plugins = new HashSet<>();
         cachedFunctions = new HashMap<>();
         cachedOperators = new HashMap<>();
-        cachedNumbers = new HashMap<>();
+        cachedNumberImplementations = new HashMap<>();
+        cachedInterfaceImplementations = new HashMap<>();
+        cachedPi = new HashMap<>();
         allFunctions = new HashSet<>();
         allOperators = new HashSet<>();
-        allNumbers = new HashSet<>();
+        allNumberImplementations = new HashSet<>();
         listeners = new HashSet<>();
     }
 
@@ -80,12 +91,13 @@ public class PluginManager {
      * @param getFunction the function to get the T value under the given name
      * @param name        the name to search for
      * @param <T>         the type of element being search
+     * @param <K>         the type of key that the cache is indexed by.
      * @return the retrieved element, or null if it was not found.
      */
-    private static <T> T searchCached(Collection<Plugin> plugins, Map<String, T> cache,
+    private static <T, K> T searchCached(Collection<Plugin> plugins, Map<K, T> cache,
-                                      java.util.function.Function<Plugin, Set<String>> setFunction,
+                                      java.util.function.Function<Plugin, Set<K>> setFunction,
-                                      java.util.function.BiFunction<Plugin, String, T> getFunction,
+                                      java.util.function.BiFunction<Plugin, K, T> getFunction,
-                                      String name) {
+                                      K name) {
         if (cache.containsKey(name)) return cache.get(name);
 
         T loadedValue = null;
@@ -121,13 +133,51 @@ public class PluginManager {
     }
 
     /**
-     * Gets a numer implementation under the given name.
+     * Gets the number implementation under the given name.
-     *
      * @param name the name of the implementation.
-     * @return the implementation class
+     * @return the implementation.
      */
-    public Class<? extends NumberInterface> numberFor(String name) {
+    public NumberImplementation numberImplementationFor(String name){
-        return searchCached(plugins, cachedNumbers, Plugin::providedNumbers, Plugin::getNumber, 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);
+        NumberImplementation toReturn = null;
+        outside:
+        for(Plugin plugin : plugins){
+            for(String implementationName : plugin.providedNumberImplementations()){
+                NumberImplementation implementation = plugin.getNumberImplementation(implementationName);
+                if(implementation.getImplementation().equals(name)) {
+                    toReturn = implementation;
+                    break outside;
+                }
+            }
+        }
+        cachedInterfaceImplementations.put(name, toReturn);
+        return toReturn;
+    }
+
+    /**
+     * 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);
+        NumberImplementation implementation = interfaceImplementationFor(forClass);
+        NumberInterface generatedPi = null;
+        if(implementation != null){
+            generatedPi = implementation.instanceForPi();
+        }
+        cachedPi.put(forClass, generatedPi);
+        return generatedPi;
     }
 
     /**
@@ -164,7 +214,7 @@ public class PluginManager {
         for (Plugin plugin : plugins) {
             allFunctions.addAll(plugin.providedFunctions());
             allOperators.addAll(plugin.providedOperators());
-            allNumbers.addAll(plugin.providedNumbers());
+            allNumberImplementations.addAll(plugin.providedNumberImplementations());
         }
         listeners.forEach(e -> e.onLoad(this));
     }
@@ -176,7 +226,7 @@ public class PluginManager {
         for (Plugin plugin : plugins) plugin.disable();
         allFunctions.clear();
         allOperators.clear();
-        allNumbers.clear();
+        allNumberImplementations.clear();
         listeners.forEach(e -> e.onUnload(this));
     }
 
@@ -207,12 +257,12 @@ public class PluginManager {
     }
 
     /**
-     * Gets all the number implementations loaded by the Plugin Manager
+     * Gets all the number implementations loaded by the Plugin Manager.
      *
-     * @return the set of all implementations that were loaded
+     * @return the set of all implementations that were loaded.
      */
-    public Set<String> getAllNumbers() {
+    public Set<String> getAllNumberImplementations(){
-        return allNumbers;
+        return allNumberImplementations;
     }
 
     /**

src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java

@@ -8,6 +8,8 @@ import org.nwapw.abacus.number.NaiveNumber;
 import org.nwapw.abacus.number.NumberInterface;
 import org.nwapw.abacus.number.PreciseNumber;
 
+import java.util.ArrayList;
+import java.util.HashMap;
 import java.util.function.BiFunction;
 
 /**
@@ -16,6 +18,8 @@ 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>>();
+
     /**
      * The addition operator, +
      */
@@ -152,17 +156,40 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            boolean takeReciprocal = params[0].signum() == -1;
+            NumberInterface maxError = getMaxError(params[0]);
-            params[0] = FUNCTION_ABS.apply(params[0]);
+            int n = 0;
-            NumberInterface sum = sumSeries(params[0], StandardPlugin::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
+            if(params[0].signum() <= 0){
-            if (takeReciprocal) {
+                NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
-                sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
+                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;
             }
-            return sum;
         }
     };
     /**
-     * The natural log function, ln(exp(1)) = 1
+     * The natural log function.
      */
     public static final Function FUNCTION_LN = new Function() {
         @Override
@@ -203,11 +230,12 @@ public class StandardPlugin extends Plugin {
         private NumberInterface getLogPartialSum(NumberInterface x) {
             NumberInterface maxError = getMaxError(x);
             x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
-            NumberInterface currentTerm = x, sum = x;
+            NumberInterface currentNumerator = x, currentTerm = x, sum = x;
             int n = 1;
             while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
                 n++;
-                currentTerm = currentTerm.multiply(x).multiply((new NaiveNumber(n - 1)).promoteTo(x.getClass())).divide((new NaiveNumber(n)).promoteTo(x.getClass())).negate();
+                currentNumerator = currentNumerator.multiply(x).negate();
+                currentTerm = currentNumerator.divide(new NaiveNumber(n).promoteTo(x.getClass()));
                 sum = sum.add(currentTerm);
             }
             return sum;
@@ -238,7 +266,7 @@ public class StandardPlugin extends Plugin {
         }
     };
     /**
-     * The square root function, sqrt(4) = 2
+     * The square root function.
      */
     public static final Function FUNCTION_SQRT = new Function() {
         @Override
@@ -252,43 +280,88 @@ 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 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);
     }
 
-    /**
-     * Returns the nth term of the Taylor series (centered at 0) of e^x
-     *
-     * @param n the term required (n >= 0).
-     * @param x the real number at which the series is evaluated.
-     * @return the nth term of the series.
-     */
-    private static NumberInterface getExpSeriesTerm(int n, NumberInterface x) {
-        return x.intPow(n).divide(OP_FACTORIAL.getFunction().apply((new NaiveNumber(n)).promoteTo(x.getClass())));
-    }
-
-    /**
-     * Returns the number of terms needed to evaluate the exponential function (at x)
-     * such that the error is at most maxError.
-     *
-     * @param maxError Maximum error permissible (This should probably be positive.)
-     * @param x        where the function is evaluated.
-     * @return the number of terms needed to evaluated the exponential function.
-     */
-    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 = FUNCTION_ABS.apply(x);
-        NumberInterface LHS = x, RHS = maxError;
-        while (LHS.compareTo(RHS) > 0) {
-            n++;
-            LHS = LHS.multiply(x);
-            RHS = RHS.multiply(new NaiveNumber(n + 1).promoteTo(RHS.getClass()));
-        }
-        return n;
-    }
-
     /**
      * Returns a partial sum of a series whose terms are given by the nthTermFunction, evaluated at x.
      *
@@ -317,8 +390,8 @@ public class StandardPlugin extends Plugin {
 
     @Override
     public void onEnable() {
-        registerNumber("naive", NaiveNumber.class);
+        registerNumberImplementation("naive", IMPLEMENTATION_NAIVE);
-        registerNumber("precise", PreciseNumber.class);
+        registerNumberImplementation("precise", IMPLEMENTATION_PRECISE);
 
         registerOperator("+", OP_ADD);
         registerOperator("-", OP_SUBTRACT);
@@ -331,6 +404,7 @@ public class StandardPlugin extends Plugin {
         registerFunction("exp", FUNCTION_EXP);
         registerFunction("ln", FUNCTION_LN);
         registerFunction("sqrt", FUNCTION_SQRT);
+        registerFunction("sin", functionSin);
     }
 
     @Override
@@ -338,4 +412,58 @@ 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<NumberInterface>());
+            factorialLists.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
+            factorialLists.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
+        }
+        ArrayList<NumberInterface> list = factorialLists.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;
+    }
 }