Change precision to getMaxPrecision, as precision can be configured.

This prevents infinite loops, as Link nodes do not follow regular
addInto behavior.

.gitignore

@@ -20,3 +20,12 @@
 
 # virtual machine crash logs, see http://www.java.com/en/download/help/error_hotspot.xml
 hs_err_pid*
+
+# Custom Stuff
+# Gradle
+.gradle/*
+build/*
+
+# IntelliJ
+.idea/*
+abacus.iml

RESOURCES.md

@@ -8,3 +8,5 @@
 * Rembulan(5.3) - https://github.com/mjanicek/rembulan
 * LuaJava - https://github.com/jasonsantos/luajava
 * jnlua - https://code.google.com/archive/p/jnlua/ 
+## Gist
+* https://gist.github.com/rileyJones/1c18338821b88e92a477bfa270344db3

build.gradle

@@ -0,0 +1,23 @@
+apply plugin: 'java'
+apply plugin: 'application'
+
+sourceSets {
+  main {
+    java {
+      srcDirs = ['src']
+    }
+  }
+}
+
+repositories {
+  mavenCentral()
+}
+
+dependencies {
+    compile 'com.moandjiezana.toml:toml4j:0.7.1'
+    testCompile 'junit:junit:4.12'
+}
+
+// Define the main class for the application
+mainClassName = 'org.nwapw.abacus.Abacus'
+

gradle/wrapper/gradle-wrapper.properties

@@ -0,0 +1,6 @@
+#Fri Jul 28 17:18:51 PDT 2017
+distributionBase=GRADLE_USER_HOME
+distributionPath=wrapper/dists
+zipStoreBase=GRADLE_USER_HOME
+zipStorePath=wrapper/dists
+distributionUrl=https\://services.gradle.org/distributions/gradle-3.3-bin.zip

gradlew

@@ -0,0 +1,172 @@
+#!/usr/bin/env sh
+
+##############################################################################
+##
+##  Gradle start up script for UN*X
+##
+##############################################################################
+
+# Attempt to set APP_HOME
+# Resolve links: $0 may be a link
+PRG="$0"
+# Need this for relative symlinks.
+while [ -h "$PRG" ] ; do
+    ls=`ls -ld "$PRG"`
+    link=`expr "$ls" : '.*-> \(.*\)$'`
+    if expr "$link" : '/.*' > /dev/null; then
+        PRG="$link"
+    else
+        PRG=`dirname "$PRG"`"/$link"
+    fi
+done
+SAVED="`pwd`"
+cd "`dirname \"$PRG\"`/" >/dev/null
+APP_HOME="`pwd -P`"
+cd "$SAVED" >/dev/null
+
+APP_NAME="Gradle"
+APP_BASE_NAME=`basename "$0"`
+
+# Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+DEFAULT_JVM_OPTS=""
+
+# Use the maximum available, or set MAX_FD != -1 to use that value.
+MAX_FD="maximum"
+
+warn ( ) {
+    echo "$*"
+}
+
+die ( ) {
+    echo
+    echo "$*"
+    echo
+    exit 1
+}
+
+# OS specific support (must be 'true' or 'false').
+cygwin=false
+msys=false
+darwin=false
+nonstop=false
+case "`uname`" in
+  CYGWIN* )
+    cygwin=true
+    ;;
+  Darwin* )
+    darwin=true
+    ;;
+  MINGW* )
+    msys=true
+    ;;
+  NONSTOP* )
+    nonstop=true
+    ;;
+esac
+
+CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar
+
+# Determine the Java command to use to start the JVM.
+if [ -n "$JAVA_HOME" ] ; then
+    if [ -x "$JAVA_HOME/jre/sh/java" ] ; then
+        # IBM's JDK on AIX uses strange locations for the executables
+        JAVACMD="$JAVA_HOME/jre/sh/java"
+    else
+        JAVACMD="$JAVA_HOME/bin/java"
+    fi
+    if [ ! -x "$JAVACMD" ] ; then
+        die "ERROR: JAVA_HOME is set to an invalid directory: $JAVA_HOME
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+    fi
+else
+    JAVACMD="java"
+    which java >/dev/null 2>&1 || die "ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+
+Please set the JAVA_HOME variable in your environment to match the
+location of your Java installation."
+fi
+
+# Increase the maximum file descriptors if we can.
+if [ "$cygwin" = "false" -a "$darwin" = "false" -a "$nonstop" = "false" ] ; then
+    MAX_FD_LIMIT=`ulimit -H -n`
+    if [ $? -eq 0 ] ; then
+        if [ "$MAX_FD" = "maximum" -o "$MAX_FD" = "max" ] ; then
+            MAX_FD="$MAX_FD_LIMIT"
+        fi
+        ulimit -n $MAX_FD
+        if [ $? -ne 0 ] ; then
+            warn "Could not set maximum file descriptor limit: $MAX_FD"
+        fi
+    else
+        warn "Could not query maximum file descriptor limit: $MAX_FD_LIMIT"
+    fi
+fi
+
+# For Darwin, add options to specify how the application appears in the dock
+if $darwin; then
+    GRADLE_OPTS="$GRADLE_OPTS \"-Xdock:name=$APP_NAME\" \"-Xdock:icon=$APP_HOME/media/gradle.icns\""
+fi
+
+# For Cygwin, switch paths to Windows format before running java
+if $cygwin ; then
+    APP_HOME=`cygpath --path --mixed "$APP_HOME"`
+    CLASSPATH=`cygpath --path --mixed "$CLASSPATH"`
+    JAVACMD=`cygpath --unix "$JAVACMD"`
+
+    # We build the pattern for arguments to be converted via cygpath
+    ROOTDIRSRAW=`find -L / -maxdepth 1 -mindepth 1 -type d 2>/dev/null`
+    SEP=""
+    for dir in $ROOTDIRSRAW ; do
+        ROOTDIRS="$ROOTDIRS$SEP$dir"
+        SEP="|"
+    done
+    OURCYGPATTERN="(^($ROOTDIRS))"
+    # Add a user-defined pattern to the cygpath arguments
+    if [ "$GRADLE_CYGPATTERN" != "" ] ; then
+        OURCYGPATTERN="$OURCYGPATTERN|($GRADLE_CYGPATTERN)"
+    fi
+    # Now convert the arguments - kludge to limit ourselves to /bin/sh
+    i=0
+    for arg in "$@" ; do
+        CHECK=`echo "$arg"|egrep -c "$OURCYGPATTERN" -`
+        CHECK2=`echo "$arg"|egrep -c "^-"`                                 ### Determine if an option
+
+        if [ $CHECK -ne 0 ] && [ $CHECK2 -eq 0 ] ; then                    ### Added a condition
+            eval `echo args$i`=`cygpath --path --ignore --mixed "$arg"`
+        else
+            eval `echo args$i`="\"$arg\""
+        fi
+        i=$((i+1))
+    done
+    case $i in
+        (0) set -- ;;
+        (1) set -- "$args0" ;;
+        (2) set -- "$args0" "$args1" ;;
+        (3) set -- "$args0" "$args1" "$args2" ;;
+        (4) set -- "$args0" "$args1" "$args2" "$args3" ;;
+        (5) set -- "$args0" "$args1" "$args2" "$args3" "$args4" ;;
+        (6) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" ;;
+        (7) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" ;;
+        (8) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" ;;
+        (9) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" "$args8" ;;
+    esac
+fi
+
+# Escape application args
+save ( ) {
+    for i do printf %s\\n "$i" | sed "s/'/'\\\\''/g;1s/^/'/;\$s/\$/' \\\\/" ; done
+    echo " "
+}
+APP_ARGS=$(save "$@")
+
+# Collect all arguments for the java command, following the shell quoting and substitution rules
+eval set -- $DEFAULT_JVM_OPTS $JAVA_OPTS $GRADLE_OPTS "\"-Dorg.gradle.appname=$APP_BASE_NAME\"" -classpath "\"$CLASSPATH\"" org.gradle.wrapper.GradleWrapperMain "$APP_ARGS"
+
+# by default we should be in the correct project dir, but when run from Finder on Mac, the cwd is wrong
+if [ "$(uname)" = "Darwin" ] && [ "$HOME" = "$PWD" ]; then
+  cd "$(dirname "$0")"
+fi
+
+exec "$JAVACMD" "$@"

gradlew.bat

@@ -0,0 +1,84 @@
+@if "%DEBUG%" == "" @echo off
+@rem ##########################################################################
+@rem
+@rem  Gradle startup script for Windows
+@rem
+@rem ##########################################################################
+
+@rem Set local scope for the variables with windows NT shell
+if "%OS%"=="Windows_NT" setlocal
+
+set DIRNAME=%~dp0
+if "%DIRNAME%" == "" set DIRNAME=.
+set APP_BASE_NAME=%~n0
+set APP_HOME=%DIRNAME%
+
+@rem Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script.
+set DEFAULT_JVM_OPTS=
+
+@rem Find java.exe
+if defined JAVA_HOME goto findJavaFromJavaHome
+
+set JAVA_EXE=java.exe
+%JAVA_EXE% -version >NUL 2>&1
+if "%ERRORLEVEL%" == "0" goto init
+
+echo.
+echo ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH.
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:findJavaFromJavaHome
+set JAVA_HOME=%JAVA_HOME:"=%
+set JAVA_EXE=%JAVA_HOME%/bin/java.exe
+
+if exist "%JAVA_EXE%" goto init
+
+echo.
+echo ERROR: JAVA_HOME is set to an invalid directory: %JAVA_HOME%
+echo.
+echo Please set the JAVA_HOME variable in your environment to match the
+echo location of your Java installation.
+
+goto fail
+
+:init
+@rem Get command-line arguments, handling Windows variants
+
+if not "%OS%" == "Windows_NT" goto win9xME_args
+
+:win9xME_args
+@rem Slurp the command line arguments.
+set CMD_LINE_ARGS=
+set _SKIP=2
+
+:win9xME_args_slurp
+if "x%~1" == "x" goto execute
+
+set CMD_LINE_ARGS=%*
+
+:execute
+@rem Setup the command line
+
+set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar
+
+@rem Execute Gradle
+"%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %CMD_LINE_ARGS%
+
+:end
+@rem End local scope for the variables with windows NT shell
+if "%ERRORLEVEL%"=="0" goto mainEnd
+
+:fail
+rem Set variable GRADLE_EXIT_CONSOLE if you need the _script_ return code instead of
+rem the _cmd.exe /c_ return code!
+if  not "" == "%GRADLE_EXIT_CONSOLE%" exit 1
+exit /b 1
+
+:mainEnd
+if "%OS%"=="Windows_NT" endlocal
+
+:omega

settings.gradle

@@ -0,0 +1 @@
+rootProject.name = 'abacus'

src/org/nwapw/abacus/Abacus.java

@@ -1,9 +1,46 @@
 package org.nwapw.abacus;
 
+import org.nwapw.abacus.plugin.PluginManager;
+//import org.nwapw.abacus.plugin.StandardPlugin;
+import org.nwapw.abacus.plugin.StandardPlugin;
+import org.nwapw.abacus.window.Window;
+import org.nwapw.abacus.plugin.ClassFinder;
+
+import javax.swing.*;
+import java.io.IOException;
+import java.util.ArrayList;
+
 public class Abacus {
 
+    private Window mainUi;
+    private PluginManager manager;
+
+    public Abacus(){
+        init();
+    }
+
+    private void init() {
+        try {
+            UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
+        } catch (ClassNotFoundException | InstantiationException | UnsupportedLookAndFeelException | IllegalAccessException e) {
+            e.printStackTrace();
+        }
+        manager = new PluginManager();
+        manager.addInstantiated(new StandardPlugin(manager));
+        try {
+            ClassFinder.loadJars("plugins")
+                    .forEach(plugin -> manager.addClass(plugin));
+        } catch (IOException | ClassNotFoundException e) {
+            e.printStackTrace();
+        }
+        mainUi = new Window(manager);
+        mainUi.setVisible(true);
+        manager.load();
+
+    }
+
     public static void main(String[] args){
-        System.out.println("Hello world!");
+        new Abacus();
     }
 
 }

src/org/nwapw/abacus/config/Configuration.java

@@ -0,0 +1,18 @@
+package org.nwapw.abacus.config;
+
+/**
+ * Serializable class that will be used to load TOML
+ * configurations.
+ */
+public class Configuration {
+
+    /**
+     * The precision to which the calculator should operator.
+     */
+    public int decimalPrecision;
+    /**
+     * The type of number this calculator should use.
+     */
+    public String numberType;
+
+}

src/org/nwapw/abacus/config/ConfigurationObject.java

@@ -0,0 +1,146 @@
+package org.nwapw.abacus.config;
+
+import com.moandjiezana.toml.Toml;
+import com.moandjiezana.toml.TomlWriter;
+import org.nwapw.abacus.number.NaiveNumber;
+
+import java.io.File;
+import java.io.IOException;
+import java.lang.reflect.InvocationTargetException;
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * A configuration object, which essentially
+ * manages saving, loading, and getting values
+ * from the configuration. While Configuration is
+ * the data model, this is the interface with it.
+ */
+public class ConfigurationObject {
+
+    /**
+     * The default implementation to use for instantiating numbers.
+     */
+    private static final Class<? extends NaiveNumber> DEFAULT_IMPLEMENTATION = NaiveNumber.class;
+    /**
+     * The writer used to store the configuration.
+     */
+    private static final TomlWriter TOML_WRITER = new TomlWriter();
+    /**
+     * The configuration instance being modeled.
+     */
+    private Configuration configuration;
+    /**
+     * A map of number names to their implementations, which
+     * will be provided by plugins.
+     */
+    private Map<String, Class<? extends NaiveNumber>> numberImplementations;
+
+    /**
+     * Sets up the ConfigurationObject.
+     * different constructors do different things,
+     * but they all lead here.
+     * @param configuration the configuration to set up with.
+     */
+    private void setup(Configuration configuration){
+        this.configuration = configuration;
+        numberImplementations = new HashMap<>();
+    }
+
+    /**
+     * Creates a default configuration.
+     * @return the newly created default configuration.
+     */
+    private Configuration getDefaultConfig(){
+        configuration = new Configuration();
+        configuration.decimalPrecision = -1;
+        configuration.numberType = "naive";
+        return configuration;
+    }
+
+    /**
+     * Register a number implementation.
+     * @param name the name of the number implementation to register the class as.
+     * @param newClass the class that will be used to instantiate the new number.
+     *                 It is required that this class provides a Number(String) constructor.
+     */
+    public void registerImplementation(String name, Class<? extends NaiveNumber> newClass){
+        numberImplementations.put(name, newClass);
+    }
+
+    /**
+     * Creates a new number with the configured type, passing
+     * it the given string.
+     * @param string the string from which the number should be parsed.
+     * @return the resulting number, or null if an error occurred.
+     */
+    public NaiveNumber numberFromString(String string)  {
+        Class<? extends NaiveNumber> toLoad =
+                numberImplementations.getOrDefault(configuration.numberType, DEFAULT_IMPLEMENTATION);
+        try {
+            return toLoad.getConstructor(String.class).newInstance(string);
+        } catch (InstantiationException | IllegalAccessException | InvocationTargetException | NoSuchMethodException e) {
+            e.printStackTrace();
+        }
+        return null;
+    }
+
+    /**
+     * Returns the configured, user-requested precision.
+     * @return the precision.
+     */
+    public int getPrecision(){
+        return configuration.decimalPrecision;
+    }
+
+    /**
+     * Saves the ConfigurationObject to the given file.
+     * @param toFile the file to save ot.
+     * @return true if the save succeed, false if otherwise.
+     */
+    public boolean save(File toFile){
+        if(toFile.getParentFile() != null) toFile.getParentFile().mkdirs();
+        try {
+            TOML_WRITER.write(configuration, toFile);
+            return true;
+        } catch (IOException e) {
+            e.printStackTrace();
+        }
+        return false;
+    }
+
+    /**
+     * Creates a new configuration object with the given config.
+     * @param config the config to use.
+     */
+    public ConfigurationObject(Configuration config){
+        setup(config);
+    }
+
+    /**
+     * Create a configuration object by attempting to
+     * load a config from the given path, using the
+     * default configuration otherwise.
+     * @param path the path to attempt to load.
+     */
+    public ConfigurationObject(File path){
+        Configuration config;
+        if(!path.exists()) {
+            config = getDefaultConfig();
+        } else {
+            Toml parse = new Toml();
+            parse.read(path);
+            config = parse.to(Configuration.class);
+        }
+        setup(config);
+    }
+
+    /**
+     * Creates a new configuration object with the
+     * default configuration.
+     */
+    public ConfigurationObject(){
+        setup(getDefaultConfig());
+    }
+
+}

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

@@ -0,0 +1,49 @@
+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
+ * inputs and returns a single number.
+ */
+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.
+     * @param params the given params
+     * @return true if the params can be used with this function.
+     */
+    protected abstract boolean matchesParams(NumberInterface[] params);
+
+    /**
+     * Internal apply implementation, which already receives appropriately promoted
+     * parameters that have bee run through matchesParams
+     * @param params the promoted parameters.
+     * @return the return value of the function.
+     */
+    protected abstract NumberInterface applyInternal(NumberInterface[] params);
+
+    /**
+     * Function to check, promote arguments and run the function.
+     * @param params the raw input parameters.
+     * @return the return value of the function, or null if an error occurred.
+     */
+    public NumberInterface apply(NumberInterface...params) {
+        if(!matchesParams(params)) return null;
+        return applyInternal(params);
+    }
+
+}

src/org/nwapw/abacus/function/Operator.java

@@ -0,0 +1,70 @@
+package org.nwapw.abacus.function;
+
+/**
+ * A class that represents a single infix operator.
+ */
+public class Operator {
+
+    /**
+     * The associativity of the operator.
+     */
+    private OperatorAssociativity associativity;
+    /**
+     * The type of this operator.
+     */
+    private OperatorType type;
+    /**
+     * The precedence of the operator.
+     */
+    private int precedence;
+    /**
+     * The function that is called by this operator.
+     */
+    private Function function;
+
+    /**
+     * Creates a new operator with the given parameters.
+     * @param associativity the associativity of the operator.
+     * @param precedence the precedence of the operator.
+     * @param function the function that the operator calls.
+     */
+    public Operator(OperatorAssociativity associativity, OperatorType operatorType, int precedence, Function function){
+        this.associativity = associativity;
+        this.type = operatorType;
+        this.precedence = precedence;
+        this.function = function;
+    }
+
+    /**
+     * Gets the operator's associativity.
+     * @return the associativity.
+     */
+    public OperatorAssociativity getAssociativity() {
+        return associativity;
+    }
+
+    /**
+     * Gets the operator's type.
+     * @return the type.
+     */
+    public OperatorType getType() {
+        return type;
+    }
+
+    /**
+     * Gets the operator's precedence.
+     * @return the precedence.
+     */
+    public int getPrecedence() {
+        return precedence;
+    }
+
+    /**
+     * Gets the operator's function.
+     * @return the function.
+     */
+    public Function getFunction() {
+        return function;
+    }
+
+}

src/org/nwapw/abacus/function/OperatorAssociativity.java

@@ -0,0 +1,8 @@
+package org.nwapw.abacus.function;
+
+/**
+ * Enum to represent the associativity of an operator.
+ */
+public enum OperatorAssociativity {
+    LEFT, RIGHT
+}

src/org/nwapw/abacus/function/OperatorType.java

@@ -0,0 +1,8 @@
+package org.nwapw.abacus.function;
+
+/**
+ * The type of an operator, describing how it should behave.
+ */
+public enum OperatorType {
+    BINARY_INFIX, UNARY_POSTFIX
+}

src/org/nwapw/abacus/lexing/Lexer.java

@@ -5,29 +5,96 @@ import org.nwapw.abacus.lexing.pattern.Match;
 import org.nwapw.abacus.lexing.pattern.Pattern;
 import org.nwapw.abacus.lexing.pattern.PatternNode;
 
-import java.util.ArrayList;
-import java.util.Comparator;
-import java.util.HashSet;
+import java.util.*;
 
+/**
+ * A lexer that can generate tokens of a given type given a list of regular expressions
+ * to operate on.
+ * @param <T> the type used to identify which match belongs to which pattern.
+ */
 public class Lexer<T> {
 
-    private ArrayList<Pattern<T>> patterns;
+    /**
+     * An entry that represents a pattern that has been registered with the lexer.
+     * @param <T> the type used to identify the pattern.
+     */
+    private static class PatternEntry<T>{
+        /**
+         * The name of the entry.
+         */
+        public String name;
+        /**
+         * The id of the entry.
+         */
+        public T id;
 
-    public Lexer(){
-        patterns = new ArrayList<>();
+        /**
+         * Creates a new pattern entry with the given name and id.
+         * @param name the name of the pattern entry.
+         * @param id the id of the pattern entry.
+         */
+        public PatternEntry(String name, T id){
+            this.name = name;
+            this.id = id;
+        }
+
+        @Override
+        public int hashCode() {
+            return Objects.hash(name, id);
+        }
+
+        @Override
+        public boolean equals(Object obj) {
+            return obj instanceof PatternEntry &&
+                    ((PatternEntry) obj).name.equals(name) &&
+                    ((PatternEntry) obj).id.equals(id);
+        }
     }
 
+    /**
+     * The registered patterns.
+     */
+    private Map<PatternEntry<T>, Pattern<T>> patterns;
+
+    /**
+     * Creates a new lexer with no registered patterns.
+     */
+    public Lexer(){
+        patterns = new HashMap<>();
+    }
+
+    /**
+     * Registers a single pattern.
+     * @param pattern the pattern regex
+     * @param id the ID by which to identify the pattern.
+     */
     public void register(String pattern, T id){
         Pattern<T> compiledPattern = new Pattern<>(pattern, id);
-        if(compiledPattern.getHead() != null) patterns.add(compiledPattern);
+        if(compiledPattern.getHead() != null) patterns.put(new PatternEntry<>(pattern, id), compiledPattern);
     }
 
+    /**
+     * Unregisters a pattern.
+     * @param pattern the pattern to unregister
+     * @param id the ID by which to identify the pattern.
+     */
+    public void unregister(String pattern, T id){
+        patterns.remove(new PatternEntry<>(pattern, id));
+    }
+
+    /**
+     * Reads one token from the given string.
+     * @param from the string to read from
+     * @param startAt the index to start at
+     * @param compare the comparator used to sort tokens by their ID.
+     * @return the best match.
+     */
     public Match<T> lexOne(String from, int startAt, Comparator<T> compare){
         ArrayList<Match<T>> matches = new ArrayList<>();
         HashSet<PatternNode<T>> currentSet = new HashSet<>();
         HashSet<PatternNode<T>> futureSet = new HashSet<>();
         int index = startAt;
-        for(Pattern<T> pattern : patterns){
+        for(Pattern<T> pattern : patterns.values()){
             pattern.getHead().addInto(currentSet);
         }
         while(!currentSet.isEmpty()){
@@ -53,15 +120,23 @@ public class Lexer<T> {
         return matches.isEmpty() ? null : matches.get(matches.size() - 1);
     }
 
-    public ArrayList<Match<T>> lexAll(String from, int startAt, Comparator<T> compare){
+    /**
+     * Reads all tokens from a string.
+     * @param from the string to start from.
+     * @param startAt the index to start at.
+     * @param compare the comparator used to sort matches by their IDs.
+     * @return the resulting list of matches, in order, or null on error.
+     */
+    public List<Match<T>> lexAll(String from, int startAt, Comparator<T> compare){
         int index = startAt;
         ArrayList<Match<T>> matches = new ArrayList<>();
         Match<T> lastMatch = null;
-        while((lastMatch = lexOne(from, index, compare)) != null && index < from.length()){
+        while(index < from.length() && (lastMatch = lexOne(from, index, compare)) != null){
             if(lastMatch.getTo() == lastMatch.getFrom()) return null;
             matches.add(lastMatch);
             index += lastMatch.getTo() - lastMatch.getFrom();
         }
+        if(lastMatch == null) return null;
         return matches;
     }
 

src/org/nwapw/abacus/lexing/pattern/AnyNode.java

@@ -1,5 +1,9 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A pattern node that matches any character.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class AnyNode<T> extends PatternNode<T> {
 
     @Override

src/org/nwapw/abacus/lexing/pattern/EndNode.java

@@ -1,13 +1,28 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A node that represents a successful match.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class EndNode<T> extends PatternNode<T> {
 
+    /**
+     * The ID of the pattenr that has been matched.
+     */
     private T patternId;
 
+    /**
+     * Creates a new end node with the given ID.
+     * @param patternId the pattern ID.
+     */
     public EndNode(T patternId){
         this.patternId = patternId;
     }
 
+    /**
+     * Gets the pattern ID.
+     * @return the pattern ID.
+     */
     public T getPatternId(){
         return patternId;
     }

src/org/nwapw/abacus/lexing/pattern/LinkNode.java

@@ -3,11 +3,18 @@ package org.nwapw.abacus.lexing.pattern;
 import java.util.ArrayList;
 import java.util.Collection;
 
+/**
+ * A node that is used as structural glue in pattern compilation.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class LinkNode<T> extends PatternNode<T> {
 
     @Override
     public void addInto(Collection<PatternNode<T>> into) {
-        addOutputsInto(into);
+        if(!into.contains(this)) {
+            into.add(this);
+            addOutputsInto(into);
+        }
     }
 
 }

src/org/nwapw/abacus/lexing/pattern/Match.java

@@ -1,25 +1,56 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A match that has been generated by the lexer.
+ * @param <T> the type used to represent the ID of the pattern this match belongs to.
+ */
 public class Match<T> {
 
+    /**
+     * The bottom range of the string, inclusive.
+     */
     private int from;
+    /**
+     * The top range of the string, exclusive.
+     */
     private int to;
+    /**
+     * The pattern type this match matched.
+     */
     private T type;
 
+    /**
+     * Creates a new match with the given parameters.
+     * @param from the bottom range of the string.
+     * @param to the top range of the string.
+     * @param type the type of the match.
+     */
     public Match(int from, int to, T type){
         this.from = from;
         this.to = to;
         this.type = type;
     }
 
+    /**
+     * Gets the bottom range bound of the string.
+     * @return the bottom range bound of the string.
+     */
     public int getFrom() {
         return from;
     }
 
+    /**
+     * Gets the top range bound of the string.
+     * @return the top range bound of the string.
+     */
     public int getTo() {
         return to;
     }
 
+    /**
+     * Gets the pattern type of the node.
+     * @return the ID of the pattern that this match matched.
+     */
     public T getType() {
         return type;
     }

src/org/nwapw/abacus/lexing/pattern/Pattern.java

@@ -2,28 +2,61 @@ package org.nwapw.abacus.lexing.pattern;
 
 import java.util.Collection;
 import java.util.HashMap;
+import java.util.Map;
 import java.util.Stack;
 import java.util.function.Function;
 
+/**
+ * A pattern that can be compiled from a string and used in lexing.
+ * @param <T> the type that is used to identify and sort this pattern.
+ */
 public class Pattern<T> {
 
+    /**
+     * The ID of this pattern.
+     */
     private T id;
+    /**
+     * The head of this pattern.
+     */
     private PatternNode<T> head;
+    /**
+     * The source string of this pattern.
+     */
     private String source;
+    /**
+     * The index at which the compilation has stopped.
+     */
     private int index;
 
-    private HashMap<Character, Function<PatternChain<T>, PatternChain<T>>> operations =
+    /**
+     * A map of regex operator to functions that modify a PatternChain
+     * with the appropriate operation.
+     */
+    private Map<Character, Function<PatternChain<T>, PatternChain<T>>> operations =
             new HashMap<Character, Function<PatternChain<T>, PatternChain<T>>>() {{
                 put('+', Pattern.this::transformPlus);
                 put('*', Pattern.this::transformStar);
                 put('?', Pattern.this::transformQuestion);
             }};
 
+    /**
+     * A regex operator function that turns the chain
+     * into a one-or-more chain.
+     * @param chain the chain to transform.
+     * @return the modified chain.
+     */
     private PatternChain<T> transformPlus(PatternChain<T> chain){
         chain.tail.outputStates.add(chain.head);
         return chain;
     }
 
+    /**
+     * A regex operator function that turns the chain
+     * into a zero-or-more chain.
+     * @param chain the chain to transform.
+     * @return the modified chain.
+     */
     private PatternChain<T> transformStar(PatternChain<T> chain){
         LinkNode<T> newTail = new LinkNode<>();
         LinkNode<T> newHead = new LinkNode<>();
@@ -36,6 +69,12 @@ public class Pattern<T> {
         return chain;
     }
 
+    /**
+     * A regex operator function that turns the chain
+     * into a zero-or-one chain.
+     * @param chain the chain to transform.
+     * @return the modified chain.
+     */
     private PatternChain<T> transformQuestion(PatternChain<T> chain){
         LinkNode<T> newTail = new LinkNode<>();
         LinkNode<T> newHead = new LinkNode<>();
@@ -47,6 +86,11 @@ public class Pattern<T> {
         return chain;
     }
 
+    /**
+     * Combines a collection of chains into one OR chain.
+     * @param collection the collection of chains to combine.
+     * @return the resulting OR chain.
+     */
     private PatternChain<T> combineChains(Collection<PatternChain<T>> collection){
         LinkNode<T> head = new LinkNode<>();
         LinkNode<T> tail = new LinkNode<>();
@@ -58,6 +102,10 @@ public class Pattern<T> {
         return newChain;
     }
 
+    /**
+     * Parses a single value from the input into a chain.
+     * @return the resulting chain, or null on error.
+     */
     private PatternChain<T> parseValue(){
         if(index >= source.length()) return null;
         if(source.charAt(index) == '\\'){
@@ -66,6 +114,10 @@ public class Pattern<T> {
         return new PatternChain<>(new ValueNode<>(source.charAt(index++)));
     }
 
+    /**
+     * Parses a [] range from the input into a chain.
+     * @return the resulting chain, or null on error.
+     */
     private PatternChain<T> parseOr(){
         Stack<PatternChain<T>> orStack = new Stack<>();
         index++;
@@ -88,6 +140,12 @@ public class Pattern<T> {
         return (orStack.size() == 1) ? orStack.pop() : combineChains(orStack);
     }
 
+    /**
+     * Parses a repeatable segment from the input into a chain
+     * @param isSubsegment whether the segment is a sub-expression "()", and therefore
+     *                     whether to expect a closing brace.
+     * @return the resulting chain, or null on error.
+     */
     private PatternChain<T> parseSegment(boolean isSubsegment){
         if(index >= source.length() || ((source.charAt(index) != '(') && isSubsegment)) return null;
         if(isSubsegment) index++;
@@ -152,6 +210,11 @@ public class Pattern<T> {
         return fullChain;
     }
 
+    /**
+     * Creates / compiles a new pattern with the given id from the given string.
+     * @param from the string to compile a pattern from.
+     * @param id the ID to use.
+     */
     public Pattern(String from, T id){
         this.id = id;
         index = 0;
@@ -166,7 +229,29 @@ public class Pattern<T> {
         }
     }
 
+    /**
+     * Gets the head PatternNode, for use in matching
+     * @return the pattern node.
+     */
     public PatternNode<T> getHead() {
         return head;
     }
+
+    /**
+     * Removes all characters that are considered "special" from
+     * the given string.
+     * @param from the string to sanitize.
+     * @return the resulting string.
+     */
+    public static String sanitize(String from){
+        Pattern<Integer> pattern = new Pattern<>("", 0);
+        from = from.replace(".", "\\.");
+        from = from.replace("|", "\\|");
+        from = from.replace("(", "\\(");
+        from = from.replace(")", "\\)");
+        for(Character key : pattern.operations.keySet()){
+            from = from.replace("" + key, "\\" + key);
+        }
+        return from;
+    }
 }

src/org/nwapw/abacus/lexing/pattern/PatternChain.java

@@ -1,23 +1,52 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A chain of nodes that can be treated as a single unit.
+ * Used during pattern compilation.
+ * @param <T> the type used to identify which pattern has been matched.
+ */
 public class PatternChain<T> {
 
+    /**
+     * The head node of the chain.
+     */
     public PatternNode<T> head;
+    /**
+     * The tail node of the chain.
+     */
     public PatternNode<T> tail;
 
+    /**
+     * Creates a new chain with the given start and end.
+     * @param head the start of the chain.
+     * @param tail the end of the chain.
+     */
     public PatternChain(PatternNode<T> head, PatternNode<T> tail){
         this.head = head;
         this.tail = tail;
     }
 
+    /**
+     * Creates a chain that starts and ends with the same node.
+     * @param node the node to use.
+     */
     public PatternChain(PatternNode<T> node){
         this(node, node);
     }
 
+    /**
+     * Creates an empty chain.
+     */
     public PatternChain(){
         this(null);
     }
 
+    /**
+     * Appends the other chain to this one. This modifies
+     * the nodes, as well.
+     * If this chain is empty, it is set to the other.
+     * @param other the other chain to append.
+     */
     public void append(PatternChain<T> other){
         if(other.head == null || tail == null) {
             this.head = other.head;
@@ -28,6 +57,12 @@ public class PatternChain<T> {
         }
     }
 
+    /**
+     * Appends a single node to this chain. This modifies
+     * the nodes, as well.
+     * If this chain is empty, it is set to the node.
+     * @param node the node to append to this chain.
+     */
     public void append(PatternNode<T> node){
         if(tail == null){
             head = tail = node;

src/org/nwapw/abacus/lexing/pattern/PatternNode.java

@@ -3,27 +3,60 @@ package org.nwapw.abacus.lexing.pattern;
 import java.util.ArrayList;
 import java.util.Collection;
 import java.util.HashSet;
+import java.util.Set;
 
+/**
+ * A base class for a pattern node. Provides all functions
+ * necessary for matching, and is constructed by a Pattern instance
+ * from a string.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class PatternNode<T> {
 
-    protected HashSet<PatternNode<T>> outputStates;
+    /**
+     * The set of states to which the lexer should continue
+     * should this node be correctly matched.
+     */
+    protected Set<PatternNode<T>> outputStates;
 
+    /**
+     * Creates a new pattern node.
+     */
     public PatternNode(){
         outputStates = new HashSet<>();
     }
 
+    /**
+     * Determines whether the current input character can
+     * be matched by this node.
+     * @param other the character being matched.
+     * @return true if the character can be matched, false otherwise.
+     */
     public boolean matches(char other){
         return false;
     }
 
+    /**
+     * If this node can be used as part of a range, returns that value.
+     * @return a NULL terminator if this character cannot be converted
+     * into a range bound, or the appropriate range bound if it can.
+     */
     public char range(){
         return '\0';
     }
 
+    /**
+     * Adds this node in a collection of other nodes.
+     * @param into the collection to add into.
+     */
     public void addInto(Collection<PatternNode<T>> into){
         into.add(this);
     }
 
+    /**
+     * Adds the node's children into a collection of other nodes.
+     * @param into the collection to add into.
+     */
     public void addOutputsInto(Collection<PatternNode<T>> into){
         outputStates.forEach(e -> e.addInto(into));
     }

src/org/nwapw/abacus/lexing/pattern/RangeNode.java

@@ -1,10 +1,25 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A node that matches a range of characters.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class RangeNode<T> extends PatternNode<T> {
 
+    /**
+     * The bottom bound of the range, inclusive.
+     */
     private char from;
+    /**
+     * The top bound of the range, inclusive.
+     */
     private char to;
 
+    /**
+     * Creates a new range node from the given range.
+     * @param from the bottom bound of the range.
+     * @param to the top bound of hte range.
+     */
     public RangeNode(char from, char to){
         this.from = from;
         this.to = to;

src/org/nwapw/abacus/lexing/pattern/ValueNode.java

@@ -1,9 +1,20 @@
 package org.nwapw.abacus.lexing.pattern;
 
+/**
+ * A node that matches a single value.
+ * @param <T> the type that's used to tell which pattern this node belongs to.
+ */
 public class ValueNode<T> extends PatternNode<T> {
 
+    /**
+     * The value this node matches.
+     */
     private char value;
 
+    /**
+     * Creates a new node that matches the given character.
+     * @param value
+     */
     public ValueNode(char value){
         this.value = value;
     }

src/org/nwapw/abacus/number/Function.java

@@ -1,20 +0,0 @@
-package org.nwapw.abacus.number;
-
-import java.util.HashMap;
-
-public abstract class Function {
-
-    private static final HashMap<Class<? extends Number>, Integer> priorityMap =
-            new HashMap<Class<? extends Number>, Integer>() {{
-                put(NaiveNumber.class, 0);
-            }};
-
-    protected abstract boolean matchesParams(Number[] params);
-    protected abstract Number applyInternal(Number[] params);
-
-    public Number apply(Number...params) {
-        if(!matchesParams(params)) return null;
-        return applyInternal(params);
-    }
-
-}

src/org/nwapw/abacus/number/FunctionDatabase.java

@@ -1,77 +0,0 @@
-package org.nwapw.abacus.number;
-
-import java.util.HashMap;
-
-public class FunctionDatabase {
-
-    private HashMap<String, Function> functions;
-
-    private void registerDefault(){
-
-        functions.put("+", new Function() {
-            @Override
-            protected boolean matchesParams(Number[] params) {
-                return params.length >= 1;
-            }
-
-            @Override
-            protected Number applyInternal(Number[] params) {
-                Number sum = params[0];
-                for(int i = 1; i < params.length; i++){
-                    sum = sum.add(params[i]);
-                }
-                return sum;
-            }
-        });
-
-        functions.put("-", new Function() {
-            @Override
-            protected boolean matchesParams(Number[] params) {
-                return params.length == 2;
-            }
-
-            @Override
-            protected Number applyInternal(Number[] params) {
-                return params[0].subtract(params[1]);
-            }
-        });
-
-        functions.put("*", new Function() {
-            @Override
-            protected boolean matchesParams(Number[] params) {
-                return params.length >= 1;
-            }
-
-            @Override
-            protected Number applyInternal(Number[] params) {
-                Number product = params[1];
-                for(int i = 1; i < params.length; i++){
-                    product = product.multiply(params[i]);
-                }
-                return product;
-            }
-        });
-
-        functions.put("/", new Function() {
-            @Override
-            protected boolean matchesParams(Number[] params) {
-                return params.length == 2;
-            }
-
-            @Override
-            protected Number applyInternal(Number[] params) {
-                return params[0].divide(params[1]);
-            }
-        });
-    }
-
-    public FunctionDatabase(){
-        functions = new HashMap<>();
-        registerDefault();
-    }
-
-    public Function getFunction(String name){
-        return functions.get(name);
-    }
-
-}

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

@@ -1,57 +1,110 @@
 package org.nwapw.abacus.number;
 
-public class NaiveNumber implements Number {
+/**
+ * An implementation of NumberInterface using a double.
+ */
+public class NaiveNumber implements NumberInterface {
 
+    /**
+     * The value of this number.
+     */
     private double value;
 
+    /**
+     * Creates a new NaiveNumber with the given string.
+     * @param value the value, which will be parsed as a double.
+     */
+    public NaiveNumber(String value) {
+        this(Double.parseDouble(value));
+    }
+    /**
+     * Creates a new NaiveNumber with the given value.
+     * @param value the value to use.
+     */
     public NaiveNumber(double value) {
         this.value = value;
     }
 
+    /**
+     * The number zero.
+     */
+    public static final NaiveNumber ZERO = new NaiveNumber(0);
+    /**
+     * The number one.
+     */
+    public static final NaiveNumber ONE = new NaiveNumber(1);
+
     @Override
-    public int precision() {
-        return 4;
+    public int getMaxPrecision() {
+        return 18;
     }
 
     @Override
-    public Number multiply(Number multiplier) {
+    public NumberInterface multiply(NumberInterface multiplier) {
         return new NaiveNumber(value * ((NaiveNumber)multiplier).value);
     }
 
     @Override
-    public Number divide(Number divisor) {
+    public NumberInterface divide(NumberInterface divisor) {
         return new NaiveNumber(value / ((NaiveNumber)divisor).value);
     }
 
     @Override
-    public Number add(Number summand) {
+    public NumberInterface add(NumberInterface summand) {
         return new NaiveNumber(value + ((NaiveNumber)summand).value);
     }
 
     @Override
-    public Number subtract(Number subtrahend) {
+    public NumberInterface subtract(NumberInterface subtrahend) {
         return new NaiveNumber(value - ((NaiveNumber)subtrahend).value);
     }
 
     @Override
-    public Number negate() {
+    public NumberInterface negate() {
         return new NaiveNumber(-value);
     }
 
     @Override
-    public Number zero() {
-        return new NaiveNumber(0);
+    public NumberInterface intPow(int exponent) {
+        if(exponent == 0){
+            return NaiveNumber.ONE;
+        }
+        boolean takeReciprocal = exponent < 0;
+        exponent = Math.abs(exponent);
+        NumberInterface power = this;
+        for(int currentExponent = 1; currentExponent < exponent; currentExponent++){
+            power = power.multiply(this);
+        }
+        if(takeReciprocal){
+            power = NaiveNumber.ONE.divide(power);
+        }
+        return power;
     }
 
     @Override
-    public Number one() {
-        return new NaiveNumber(1);
+    public int compareTo(NumberInterface number) {
+        NaiveNumber num = (NaiveNumber) number;
+        return Double.compare(value, num.value);
     }
 
     @Override
-    public Number promoteTo(Class<? extends Number> toClass) {
+    public int signum() {
+        return this.compareTo(ZERO);
+    }
+
+    @Override
+    public NumberInterface promoteTo(Class<? extends NumberInterface> toClass) {
         if(toClass == this.getClass()) return this;
+        else if(toClass == PreciseNumber.class){
+            return new PreciseNumber(Double.toString(value));
+        }
         return null;
     }
+
+    public String toString(){
+        double shiftBy = Math.pow(10, 10);
+        return Double.toString(Math.round(value * shiftBy) / shiftBy);
+    }
+
 }
 

src/org/nwapw/abacus/number/Number.java

@@ -1,17 +0,0 @@
-package org.nwapw.abacus.number;
-
-public interface Number {
-
-    int precision();
-    Number multiply(Number multiplier);
-    Number divide(Number divisor);
-    Number add(Number summand);
-    Number subtract(Number subtrahend);
-    Number negate();
-
-    Number zero();
-    Number one();
-
-    Number promoteTo(Class<? extends Number> toClass);
-
-}

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

@@ -0,0 +1,77 @@
+package org.nwapw.abacus.number;
+
+/**
+ * An interface used to represent a number.
+ */
+public interface NumberInterface {
+
+    /**
+     * The maximum precision to which this number operates.
+     * @return the precision.
+     */
+    int getMaxPrecision();
+
+    /**
+     * Multiplies this number by another, returning
+     * a new number instance.
+     * @param multiplier the multiplier
+     * @return the result of the multiplication.
+     */
+    NumberInterface multiply(NumberInterface multiplier);
+    /**
+     * Divides this number by another, returning
+     * a new number instance.
+     * @param divisor the divisor
+     * @return the result of the division.
+     */
+    NumberInterface divide(NumberInterface divisor);
+    /**
+     * Adds this number to another, returning
+     * a new number instance.
+     * @param summand the summand
+     * @return the result of the summation.
+     */
+    NumberInterface add(NumberInterface summand);
+    /**
+     * Subtracts another number from this number,
+     * a new number instance.
+     * @param subtrahend the subtrahend.
+     * @return the result of the subtraction.
+     */
+    NumberInterface subtract(NumberInterface subtrahend);
+
+    /**
+     * Returns a new instance of this number with
+     * the sign flipped.
+     * @return the new instance.
+     */
+    NumberInterface negate();
+
+    /**
+     * Raises this number to an integer power.
+     * @param exponent the exponent to which to take the number.
+     * @return the resulting value.
+     */
+    NumberInterface intPow(int exponent);
+
+    /**
+     * Compares this number to another.
+     * @param number the number to compare to.
+     * @return same as Integer.compare();
+     */
+    int compareTo(NumberInterface number);
+
+    /**
+     * Same as Math.signum().
+     * @return 1 if this number is positive, -1 if this number is negative, 0 if this number is 0.
+     */
+    int signum();
+
+    /**
+     * Promotes this class to another number class.
+     * @param toClass the class to promote to.
+     * @return the resulting new instance.
+     */
+    NumberInterface promoteTo(Class<? extends NumberInterface> toClass);
+
+}

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

@@ -0,0 +1,113 @@
+package org.nwapw.abacus.number;
+
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+
+public class PreciseNumber implements NumberInterface{
+
+    /**
+     * The number one.
+     */
+    static final PreciseNumber ONE = new PreciseNumber(BigDecimal.ONE);
+    /**
+     * The number zero.
+     */
+    static final PreciseNumber ZERO = new PreciseNumber(BigDecimal.ZERO);
+    /**
+     * The number ten.
+     */
+    static final PreciseNumber TEN = new PreciseNumber(BigDecimal.TEN);
+
+    /**
+     * The value of the PreciseNumber.
+     */
+    BigDecimal value;
+
+    /**
+     * Constructs a precise number from the given string.
+     * @param string a string representation of the number meeting the same conditions
+     *               as the BidDecimal(String) constructor.
+     */
+    public PreciseNumber(String string){
+        value = new BigDecimal(string);
+    }
+
+    /**
+     * Constructs a precise number from the given BigDecimal.
+     * @param value a BigDecimal object representing the value of the number.
+     */
+    public PreciseNumber(BigDecimal value){
+        this.value = value;
+    }
+
+    @Override
+    public int getMaxPrecision() {
+        return 54;
+    }
+
+    @Override
+    public NumberInterface multiply(NumberInterface multiplier) {
+        return new PreciseNumber(value.multiply(((PreciseNumber) multiplier).value));
+    }
+
+    @Override
+    public NumberInterface divide(NumberInterface divisor) {
+        return new PreciseNumber(value.divide(((PreciseNumber) divisor).value, this.getMaxPrecision(), RoundingMode.HALF_UP));
+    }
+
+    @Override
+    public NumberInterface add(NumberInterface summand) {
+        return new PreciseNumber(value.add(((PreciseNumber) summand).value));
+    }
+
+    @Override
+    public NumberInterface subtract(NumberInterface subtrahend) {
+        return new PreciseNumber(value.subtract(((PreciseNumber) subtrahend).value));
+    }
+
+    @Override
+    public NumberInterface intPow(int exponent) {
+        if(exponent == 0){
+            return PreciseNumber.ONE;
+        }
+        boolean takeReciprocal = exponent < 0;
+        exponent = Math.abs(exponent);
+        NumberInterface power = this;
+        for(int currentExponent = 1; currentExponent < exponent; currentExponent++){
+            power = power.multiply(this);
+        }
+        if(takeReciprocal){
+            power = PreciseNumber.ONE.divide(power);
+        }
+        return power;
+    }
+
+    @Override
+    public int compareTo(NumberInterface number) {
+        return value.compareTo(((PreciseNumber) number).value);
+    }
+
+    @Override
+    public int signum() {
+        return value.signum();
+    }
+
+    @Override
+    public NumberInterface negate(){
+        return new PreciseNumber(value.negate());
+    }
+
+    @Override
+    public NumberInterface promoteTo(Class<? extends NumberInterface> toClass) {
+        if(toClass == this.getClass()){
+            return this;
+        }
+        return null;
+    }
+
+    @Override
+    public String toString() {
+        BigDecimal rounded = value.setScale(getMaxPrecision() - 4, RoundingMode.HALF_UP);
+        return rounded.stripTrailingZeros().toPlainString();
+    }
+}

src/org/nwapw/abacus/plugin/ClassFinder.java

@@ -0,0 +1,76 @@
+package org.nwapw.abacus.plugin;
+
+import java.io.File;
+import java.io.IOException;
+import java.net.URL;
+import java.net.URLClassLoader;
+import java.nio.file.Files;
+import java.nio.file.Path;
+import java.util.ArrayList;
+import java.util.Enumeration;
+import java.util.jar.JarEntry;
+import java.util.jar.JarFile;
+import java.util.stream.Collectors;
+
+/**
+ * Class that loads plugin classes from their jars.
+ */
+public class ClassFinder {
+
+    /**
+     * Loads all the plugin classes from the given plugin folder.
+     * @param filePath the path for the plugin folder.
+     * @return the list of all loaded classes.
+     * @throws IOException thrown if an error occurred scanning the plugin folder.
+     * @throws ClassNotFoundException thrown if the class listed in the file doesn't get loaded.
+     */
+    public static ArrayList<Class<?>> loadJars(String filePath) throws IOException, ClassNotFoundException {
+        return loadJars(new File(filePath));
+    }
+
+    /**
+     * Loads all the plugin classes from the given plugin folder.
+     * @param pluginFolderPath the folder in which to look for plugins.
+     * @return the list of all loaded classes.
+     * @throws IOException thrown if an error occurred scanning the plugin folder.
+     * @throws ClassNotFoundException thrown if the class listed in the file doesn't get loaded.
+     */
+    public static ArrayList<Class<?>> loadJars(File pluginFolderPath) throws IOException, ClassNotFoundException {
+        ArrayList<Class<?>> toReturn = new ArrayList<>();
+        if(!pluginFolderPath.exists()) return toReturn;
+        ArrayList<File> files = Files.walk(pluginFolderPath.toPath())
+                .map(Path::toFile)
+                .filter(f -> f.getName().endsWith(".jar"))
+                .collect(Collectors.toCollection(ArrayList::new));
+        for (File file : files){
+            toReturn.addAll(loadJar(file));
+        }
+        return toReturn;
+    }
+
+    /**
+     * Loads the classes from a single path, given by the file.
+     * @param jarLocation the location of the jar to load.
+     * @return the list of loaded classes loaded from the jar.
+     * @throws IOException thrown if there was an error reading the file
+     * @throws ClassNotFoundException thrown if the class could not be loaded.
+     */
+    public static ArrayList<Class<?>> loadJar(File jarLocation) throws IOException, ClassNotFoundException {
+        ArrayList<Class<?>> loadedClasses = new ArrayList<>();
+        String path = jarLocation.getPath();
+        URL[] urls = new URL[]{new URL("jar:file:" + path + "!/")};
+
+        URLClassLoader classLoader = URLClassLoader.newInstance(urls);
+        JarFile jarFolder = new JarFile(jarLocation);
+        Enumeration jarEntityList = jarFolder.entries();
+
+        while (jarEntityList.hasMoreElements()) {
+            JarEntry jarEntity = (JarEntry) jarEntityList.nextElement();
+            if (jarEntity.getName().endsWith(".class")) {
+                loadedClasses.add(classLoader.loadClass(jarEntity.getName().replace('/', '.').substring(0, jarEntity.getName().length() - 6)));
+            }
+        }
+        return loadedClasses;
+    }
+
+}

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

@@ -0,0 +1,162 @@
+package org.nwapw.abacus.plugin;
+
+import org.nwapw.abacus.function.Function;
+import org.nwapw.abacus.function.Operator;
+
+import java.util.HashMap;
+import java.util.Map;
+import java.util.Set;
+
+/**
+ * A plugin class that can be externally implemented and loaded via the
+ * plugin manager. Plugins provide functionality to the calculator
+ * with the "hasFunction" and "getFunction" functions,
+ * and can use "registerFunction" and "functionFor" for
+ * loading internally.
+ */
+public abstract class Plugin {
+
+    /**
+     * A hash map of functions mapped to their string names.
+     */
+    private Map<String, Function> functions;
+    /**
+     * A hash map of operators mapped to their string names.
+     */
+    private Map<String, Operator> operators;
+    /**
+     * The plugin manager in which to search for functions
+     * not inside this package,
+     */
+    private PluginManager manager;
+    /**
+     * Whether this plugin has been loaded.
+     */
+    private boolean enabled;
+
+    private Plugin(){ }
+
+    /**
+     * Creates a new plugin with the given PluginManager.
+     * @param manager the manager controlling this plugin.
+     */
+    public Plugin(PluginManager manager) {
+        this.manager = manager;
+        functions = new HashMap<>();
+        operators = new HashMap<>();
+        enabled = false;
+    }
+
+    /**
+     * Gets the list of functions provided by this plugin.
+     * @return the list of registered functions.
+     */
+    public final Set<String> providedFunctions(){
+        return functions.keySet();
+    }
+
+    /**
+     * Gets the list of functions provided by this plugin.
+     * @return the list of registered functions.
+     */
+    public final Set<String> providedOperators(){
+        return operators.keySet();
+    }
+
+    /**
+     * Gets a function under the given function name.
+     * @param functionName the name of the function to get
+     * @return the function, or null if this plugin doesn't provide it.
+     */
+    public final Function getFunction(String functionName) {
+        return functions.get(functionName);
+    }
+
+    /**
+     * Gets an operator under the given operator name.
+     * @param operatorName the name of the operator to get.
+     * @return the operator, or null if this plugin doesn't provide it.
+     */
+    public final Operator getOperator(String operatorName) {
+        return operators.get(operatorName);
+    }
+
+    /**
+     * Enables the function, loading the necessary instances
+     * of functions.
+     */
+    public final void enable(){
+        if(enabled) return;
+        onEnable();
+        enabled = true;
+    }
+
+    /**
+     * Disables the plugin, clearing loaded data store by default
+     * and calling its disable() method.
+     */
+    public final void disable(){
+        if(!enabled) return;
+        onDisable();
+        functions.clear();
+        operators.clear();
+        enabled = false;
+    }
+
+    /**
+     * To be used in load(). Registers a function abstract class with the
+     * plugin internally, which makes it accessible to the plugin manager.
+     * @param name the name to register by.
+     * @param toRegister the function implementation.
+     */
+    protected final void registerFunction(String name, Function toRegister) {
+        functions.put(name, toRegister);
+    }
+
+    /**
+     * To be used in load(). Registers an operator abstract class
+     * with the plugin internally, which makes it accessible to
+     * the plugin manager.
+     * @param name the name of the operator.
+     * @param operator the operator to register.
+     */
+    protected final void registerOperator(String name, Operator operator) {
+        operators.put(name, operator);
+    }
+
+    /**
+     * Searches the PluginManager for the given function name.
+     * This can be used by the plugins internally in order to call functions
+     * they do not provide.
+     * @param name the name for which to search
+     * @return the resulting function, or null if none was found for that name.
+     */
+    protected final Function functionFor(String name) {
+        return manager.functionFor(name);
+    }
+
+    /**
+     * Searches the PluginManager for the given operator name.
+     * This can be used by the plugins internally in order to call
+     * operations they do not provide.
+     * @param name the name for which to search
+     * @return the resulting operator, or null if none was found for that name.
+     */
+    protected final Operator operatorFor(String name) {
+        return manager.operatorFor(name);
+    }
+
+    /**
+     * Abstract method to be overridden by plugin implementation, in which the plugins
+     * are supposed to register the functions they provide and do any other
+     * necessary setup.
+     */
+    public abstract void onEnable();
+
+    /**
+     * Abstract method overridden by the plugin implementation, in which the plugins
+     * are supposed to dispose of loaded functions, operators, and macros.
+     */
+    public abstract void onDisable();
+
+}

src/org/nwapw/abacus/plugin/PluginListener.java

@@ -0,0 +1,20 @@
+package org.nwapw.abacus.plugin;
+
+/**
+ * A listener that responds to changes in the PluginManager.
+ */
+public interface PluginListener {
+
+    /**
+     * Called when the PluginManager loads plugins.
+     * @param manager the manager that fired the event.
+     */
+    public void onLoad(PluginManager manager);
+
+    /**
+     * Called when the PluginManager unloads all its plugins.
+     * @param manager the manager that fired the event.
+     */
+    public void onUnload(PluginManager manager);
+
+}

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

@@ -0,0 +1,193 @@
+package org.nwapw.abacus.plugin;
+
+import org.nwapw.abacus.function.Function;
+import org.nwapw.abacus.function.Operator;
+
+import java.lang.reflect.InvocationTargetException;
+import java.util.*;
+
+/**
+ * A class that controls instances of plugins, allowing for them
+ * to interact with each other and the calculator.
+ */
+public class PluginManager {
+
+    /**
+     * List of classes loaded by this manager.
+     */
+    private Set<Class<?>> loadedPluginClasses;
+    /**
+     * A list of loaded plugins.
+     */
+    private Set<Plugin> plugins;
+    /**
+     * List of functions that have been cached,
+     * that is, found in a plugin and returned.
+     */
+    private Map<String, Function> cachedFunctions;
+    /**
+     * List of operators tha have been cached,
+     * that is, found in a plugin and returned.
+     */
+    private Map<String, Operator> cachedOperators;
+    /**
+     * List of all functions loaded by the plugins.
+     */
+    private Set<String> allFunctions;
+    /**
+     * List of all operators loaded by the plugins.
+     */
+    private Set<String> allOperators;
+    /**
+     * The list of plugin listeners attached to this instance.
+     */
+    private Set<PluginListener> listeners;
+
+    /**
+     * Creates a new plugin manager.
+     */
+    public PluginManager(){
+        loadedPluginClasses = new HashSet<>();
+        plugins = new HashSet<>();
+        cachedFunctions = new HashMap<>();
+        cachedOperators = new HashMap<>();
+        allFunctions = new HashSet<>();
+        allOperators = new HashSet<>();
+        listeners = new HashSet<>();
+    }
+
+    /**
+     * Searches the plugin list for a certain value, retrieving the Plugin's
+     * list of items of the type using the setFunction and getting the value
+     * of it is available via getFunction. If the value is contained
+     * in the cache, it returns the cached value instead.
+     * @param plugins the plugin list to search.
+     * @param cache the cache to use
+     * @param setFunction the function to retrieve a set of available T's from the plugin
+     * @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
+     * @return the retrieved element, or null if it was not found.
+     */
+    private static <T> T searchCached(Collection<Plugin> plugins, Map<String, T> cache,
+                                      java.util.function.Function<Plugin, Set<String>> setFunction,
+                                      java.util.function.BiFunction<Plugin, String, T> getFunction,
+                                      String name){
+        if(cache.containsKey(name)) return cache.get(name);
+
+        T loadedValue = null;
+        for(Plugin plugin : plugins){
+            if(setFunction.apply(plugin).contains(name)){
+                loadedValue = getFunction.apply(plugin, name);
+                break;
+            }
+        }
+
+        cache.put(name, loadedValue);
+        return loadedValue;
+    }
+    /**
+     * Gets a function under the given name.
+     * @param name the name of the function
+     * @return the function under the given name.
+     */
+    public Function functionFor(String name){
+        return searchCached(plugins, cachedFunctions, Plugin::providedFunctions, Plugin::getFunction, name);
+    }
+
+    /**
+     * Gets an operator under the given name.
+     * @param name the name of the operator.
+     * @return the operator under the given name.
+     */
+    public Operator operatorFor(String name){
+        return searchCached(plugins, cachedOperators, Plugin::providedOperators, Plugin::getOperator, name);
+    }
+
+    /**
+     * Adds an instance of Plugin that already has been instantiated.
+     * @param plugin the plugin to add.
+     */
+    public void addInstantiated(Plugin plugin){
+        if(loadedPluginClasses.contains(plugin.getClass())) return;
+        plugins.add(plugin);
+        loadedPluginClasses.add(plugin.getClass());
+    }
+
+    /**
+     * Instantiates a class of plugin, and adds it to this
+     * plugin manager.
+     * @param newClass the new class to instantiate.
+     */
+    public void addClass(Class<?> newClass){
+        if(!Plugin.class.isAssignableFrom(newClass) || newClass == Plugin.class) return;
+        try {
+            addInstantiated((Plugin) newClass.getConstructor(PluginManager.class).newInstance(this));
+        } catch (InstantiationException | IllegalAccessException | NoSuchMethodException | InvocationTargetException e) {
+            e.printStackTrace();
+        }
+    }
+
+    /**
+     * Loads all the plugins in the PluginManager.
+     */
+    public void load(){
+        for(Plugin plugin : plugins) plugin.enable();
+        for(Plugin plugin : plugins){
+            allFunctions.addAll(plugin.providedFunctions());
+            allOperators.addAll(plugin.providedOperators());
+        }
+        listeners.forEach(e -> e.onLoad(this));
+    }
+
+    /**
+     * Unloads all the plugins in the PluginManager.
+     */
+    public void unload(){
+        for(Plugin plugin : plugins) plugin.disable();
+        allFunctions.clear();
+        allOperators.clear();
+        listeners.forEach(e -> e.onUnload(this));
+    }
+
+    /**
+     * Reloads all the plugins in the PluginManager.
+     */
+    public void reload(){
+        unload();
+        reload();
+    }
+
+    /**
+     * Gets all the functions loaded by the Plugin Manager.
+     * @return the set of all functions that were loaded.
+     */
+    public Set<String> getAllFunctions() {
+        return allFunctions;
+    }
+
+    /**
+     * Gets all the operators loaded by the Plugin Manager.
+     * @return the set of all operators that were loaded.
+     */
+    public Set<String> getAllOperators() {
+        return allOperators;
+    }
+
+    /**
+     * Adds a plugin change listener to this plugin manager.
+     * @param listener the listener to add.
+     */
+    public void addListener(PluginListener listener){
+        listeners.add(listener);
+    }
+
+    /**
+     * Remove the plugin change listener from this plugin manager.
+     * @param listener the listener to remove.
+     */
+    public void removeListener(PluginListener listener){
+        listeners.remove(listener);
+    }
+    
+}

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

@@ -0,0 +1,298 @@
+package org.nwapw.abacus.plugin;
+
+import org.nwapw.abacus.function.Function;
+import org.nwapw.abacus.function.Operator;
+import org.nwapw.abacus.function.OperatorAssociativity;
+import org.nwapw.abacus.function.OperatorType;
+import org.nwapw.abacus.number.NaiveNumber;
+import org.nwapw.abacus.number.NumberInterface;
+
+import java.util.function.BiFunction;
+
+/**
+ * The plugin providing standard functions such as addition and subtraction to
+ * the calculator.
+ */
+public class StandardPlugin extends Plugin {
+
+    public StandardPlugin(PluginManager manager) {
+        super(manager);
+    }
+
+    @Override
+    public void onEnable() {
+        registerOperator("+", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length >= 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                NumberInterface sum = params[0];
+                for(int i = 1; i < params.length; i++){
+                    sum = sum.add(params[i]);
+                }
+                return sum;
+            }
+        }));
+
+        registerOperator("-", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 2;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                return params[0].subtract(params[1]);
+            }
+        }));
+
+        registerOperator("*", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length >= 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                NumberInterface product = params[0];
+                for(int i = 1; i < params.length; i++){
+                    product = product.multiply(params[i]);
+                }
+                return product;
+            }
+        }));
+
+        registerOperator("/", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 2;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                return params[0].divide(params[1]);
+            }
+        }));
+
+        registerOperator("^", 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 StandardPlugin.this.getFunction("exp").apply(StandardPlugin.this.getFunction("ln").apply(params[0]).multiply(params[1]));
+            }
+        }));
+
+        registerOperator("!", new Operator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0, new Function() {
+            //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;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                if(params[0].signum() == 0){
+                    return (new NaiveNumber(1)).promoteTo(params[0].getClass());
+                }
+                NumberInterface factorial = params[0];
+                NumberInterface multiplier = params[0];
+                //It is necessary to later prevent calls of factorial on anything but non-negative integers.
+                while((multiplier = multiplier.subtract(NaiveNumber.ONE.promoteTo(multiplier.getClass()))).signum() == 1){
+                    factorial = factorial.multiply(multiplier);
+                }
+                return factorial;
+                /*if(!storedList.containsKey(params[0].getClass())){
+                    storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
+                    storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
+                    storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
+                }*/
+            }
+        }));
+
+        registerFunction("abs", new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
+            }
+        });
+
+        registerFunction("exp", new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                boolean takeReciprocal = params[0].signum() == -1;
+                params[0] = StandardPlugin.this.getFunction("abs").apply(params[0]);
+                NumberInterface sum = sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
+                if(takeReciprocal){
+                    sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
+                }
+                return sum;
+            }
+        });
+
+        registerFunction("ln", new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                NumberInterface param = params[0];
+                int powersOf2 = 0;
+                while(StandardPlugin.this.getFunction("abs").apply(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass()))).compareTo((new NaiveNumber(0.1)).promoteTo(param.getClass())) >= 0){
+                    if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() == 1) {
+                        param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
+                        powersOf2++;
+                        if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
+                            break;
+                            //No infinite loop for you.
+                        }
+                    }
+                    else {
+                        param = param.multiply(new NaiveNumber(2).promoteTo(param.getClass()));
+                        powersOf2--;
+                        if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
+                            break;
+                            //No infinite loop for you.
+                        }
+                    }
+                }
+                return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
+            }
+
+            /**
+             * Returns the partial sum of the Taylor series for logx (around x=1).
+             * Automatically determines the number of terms needed based on the precision of x.
+             * @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
+             * @return the partial sum.
+             */
+            private NumberInterface getLogPartialSum(NumberInterface x){
+                NumberInterface maxError = StandardPlugin.this.getMaxError(x);
+                x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
+                NumberInterface currentTerm = x, sum = x;
+                int n = 1;
+                while(StandardPlugin.this.getFunction("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();
+                    sum = sum.add(currentTerm);
+                }
+                return sum;
+            }
+
+            /**
+             * Returns natural log of 2 to the required precision of the class of number.
+             * @param number a number of the same type as the return type. (Used for precision.)
+             * @return the value of log(2) with the appropriate precision.
+             */
+            private NumberInterface getLog2(NumberInterface number){
+                NumberInterface maxError = StandardPlugin.this.getMaxError(number);
+                //NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
+                //We'll use the series \sigma_{n >= 1) ((1/3^n + 1/4^n) * 1/n)
+                //In the following, a=1/3^n, b=1/4^n, c = 1/n.
+                //a is also an error bound.
+                NumberInterface a = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
+                NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
+                int n = 0;
+                while(a.compareTo(maxError) >= 1){
+                    n++;
+                    a = a.divide((new NaiveNumber(3)).promoteTo(number.getClass()));
+                    b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
+                    c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
+                    sum = sum.add(a.add(b).multiply(c));
+                }
+                return sum;
+            }
+        });
+
+        registerFunction("sqrt", new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                return StandardPlugin.this.getOperator("^").getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
+            }
+        });
+    }
+
+    @Override
+    public void onDisable() {
+
+    }
+
+    /**
+     * 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 NumberInterface getExpSeriesTerm(int n, NumberInterface x){
+        return x.intPow(n).divide(this.getOperator("!").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 int getNTermsExp(NumberInterface maxError, NumberInterface x) {
+        //We need n such that |x^(n+1)| <= (n+1)! * maxError
+        //The variables LHS and RHS refer to the above inequality.
+        int n = 0;
+        x = this.getFunction("abs").apply(x);
+        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.
+     * @param x the value at which the series is evaluated.
+     * @param nthTermFunction the function that returns the nth term of the series, in the format term(x, n).
+     * @param n the number of terms in the partial sum.
+     * @return the value of the partial sum that has the same class as x.
+     */
+    private NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n){
+        NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
+        for(int i = 0; i <= n; i++){
+            sum = sum.add(nthTermFunction.apply(i, x));
+        }
+        return sum;
+    }
+
+    /**
+     * Returns the maximum error based on the precision of the class of number.
+     * @param number Any instance of the NumberInterface in question (should return an appropriate precision).
+     * @return the maximum error.
+     */
+    private NumberInterface getMaxError(NumberInterface number){
+        return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision());
+    }
+
+}

src/org/nwapw/abacus/tree/BinaryInfixNode.java

@@ -0,0 +1,100 @@
+package org.nwapw.abacus.tree;
+
+/**
+ * A tree node that represents an operation being applied to two operands.
+ */
+public class BinaryInfixNode extends TreeNode {
+
+    /**
+     * The operation being applied.
+     */
+    private String operation;
+    /**
+     * The left node of the operation.
+     */
+    private TreeNode left;
+    /**
+     * The right node of the operation.
+     */
+    private TreeNode right;
+
+    private BinaryInfixNode() {}
+
+    /**
+     * Creates a new operation node with the given operation
+     * and no child nodes.
+     * @param operation the operation.
+     */
+    public BinaryInfixNode(String operation){
+        this(operation, null, null);
+    }
+
+    /**
+     * Creates a new operation node with the given operation
+     * and child nodes.
+     * @param operation the operation.
+     * @param left the left node of the expression.
+     * @param right the right node of the expression.
+     */
+    public BinaryInfixNode(String operation, TreeNode left, TreeNode right){
+        this.operation = operation;
+        this.left = left;
+        this.right = right;
+    }
+
+    /**
+     * Gets the operation in this node.
+     * @return the operation in this node.
+     */
+    public String getOperation() {
+        return operation;
+    }
+
+    /**
+     * Gets the left sub-expression of this node.
+     * @return the left node.
+     */
+    public TreeNode getLeft() {
+        return left;
+    }
+
+    /**
+     * Sets the left sub-expression of this node.
+     * @param left the sub-expression to apply.
+     */
+    public void setLeft(TreeNode left) {
+        this.left = left;
+    }
+
+    /**
+     * Gets the right sub-expression of this node.
+     * @return the right node.
+     */
+    public TreeNode getRight() {
+        return right;
+    }
+
+    /**
+     * Sets the right sub-expression of this node.
+     * @param right the sub-expression to apply.
+     */
+    public void setRight(TreeNode right) {
+        this.right = right;
+    }
+
+    @Override
+    public <T> T reduce(Reducer<T> reducer) {
+        T leftReduce = left.reduce(reducer);
+        T rightReduce = right.reduce(reducer);
+        if(leftReduce == null || rightReduce == null) return null;
+        return reducer.reduceNode(this, leftReduce, rightReduce);
+    }
+
+    @Override
+    public String toString() {
+        String leftString = left != null ? left.toString() : "null";
+        String rightString = right != null ? right.toString() : "null";
+
+        return "(" + leftString + operation + rightString + ")";
+    }
+}

src/org/nwapw/abacus/tree/FunctionNode.java

@@ -0,0 +1,80 @@
+package org.nwapw.abacus.tree;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * A node that represents a function call.
+ */
+public class FunctionNode extends TreeNode {
+
+    /**
+     * The name of the function being called
+     */
+    private String function;
+    /**
+     * The list of arguments to the function.
+     */
+    private List<TreeNode> children;
+
+    /**
+     * Creates a function node with no function.
+     */
+    private FunctionNode() { }
+
+    /**
+     * Creates a new function node with the given function name.
+     * @param function the function name.
+     */
+    public FunctionNode(String function){
+        this.function = function;
+        children = new ArrayList<>();
+    }
+
+    /**
+     * Gets the function name for this node.
+     * @return the function name.
+     */
+    public String getFunction() {
+        return function;
+    }
+
+    /**
+     * Adds a child to the end of this node's child list.
+     * @param node the child to add.
+     */
+    public void appendChild(TreeNode node){
+        children.add(node);
+    }
+
+    /**
+     * Adds a new child to the beginning of this node's child list.
+     * @param node the node to add.
+     */
+    public void prependChild(TreeNode node) {
+        children.add(0, node);
+    }
+
+    @Override
+    public <T> T reduce(Reducer<T> reducer) {
+        Object[] reducedChildren = new Object[children.size()];
+        for(int i = 0; i < reducedChildren.length; i++){
+            reducedChildren[i] = children.get(i).reduce(reducer);
+            if(reducedChildren[i] == null) return null;
+        }
+        return reducer.reduceNode(this, reducedChildren);
+    }
+
+    @Override
+    public String toString() {
+        StringBuilder buffer = new StringBuilder();
+        buffer.append(function);
+        buffer.append("(");
+        for(int i = 0; i < children.size(); i++){
+            buffer.append(children.get(i));
+            buffer.append(i == children.size() - 1 ? "" : ", ");
+        }
+        buffer.append(")");
+        return buffer.toString();
+    }
+}

src/org/nwapw/abacus/tree/NumberNode.java

@@ -1,25 +1,48 @@
 package org.nwapw.abacus.tree;
 
 import org.nwapw.abacus.number.NaiveNumber;
-import org.nwapw.abacus.number.Number;
+import org.nwapw.abacus.number.NumberInterface;
 
+/**
+ * A node implementation that represents a single number.
+ */
 public class NumberNode extends TreeNode {
 
-    private Number number;
+    /**
+     * The number that is represented by this number node.
+     */
+    private NumberInterface number;
 
+    /**
+     * Creates a number node with no number.
+     */
     public NumberNode(){
         number = null;
     }
 
-    public NumberNode(double value){
-        number = new NaiveNumber(value);
+    /**
+     * Creates a new number node with the given double value.
+     * @param newNumber the number for which to create a number node.
+     */
+    public NumberNode(NumberInterface newNumber){
+        this.number = newNumber;
     }
 
-    public NumberNode(String value){
-        this(Double.parseDouble(value));
-    }
-
-    public Number getNumber() {
+    /**
+     * Gets the number value of this node.
+     * @return the number value of this node.
+     */
+    public NumberInterface getNumber() {
         return number;
     }
+
+    @Override
+    public <T> T reduce(Reducer<T> reducer) {
+        return reducer.reduceNode(this);
+    }
+
+    @Override
+    public String toString() {
+        return number != null ? number.toString() : "null";
+    }
 }

src/org/nwapw/abacus/tree/NumberReducer.java

@@ -0,0 +1,53 @@
+package org.nwapw.abacus.tree;
+
+import org.nwapw.abacus.function.Function;
+import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.plugin.PluginManager;
+
+/**
+ * A reducer implementation that turns a tree into a single number.
+ * This is not always guaranteed to work.
+ */
+public class NumberReducer implements Reducer<NumberInterface> {
+
+    /**
+     * The plugin manager from which to draw the functions.
+     */
+    private PluginManager manager;
+
+    /**
+     * Creates a new number reducer with the given plugin manager.
+     * @param manager the plugin manager.
+     */
+    public NumberReducer(PluginManager manager){
+        this.manager = manager;
+    }
+
+    @Override
+    public NumberInterface reduceNode(TreeNode node, Object... children) {
+        if(node instanceof NumberNode) {
+            return ((NumberNode) node).getNumber();
+        } else if(node instanceof BinaryInfixNode){
+            NumberInterface left = (NumberInterface) children[0];
+            NumberInterface right = (NumberInterface) children[1];
+            Function function = manager.operatorFor(((BinaryInfixNode) node).getOperation()).getFunction();
+            if(function == null) return null;
+            return function.apply(left, right);
+        } else if(node instanceof UnaryPrefixNode) {
+            NumberInterface child = (NumberInterface) children[0];
+            Function functionn = manager.operatorFor(((UnaryPrefixNode) node).getOperation()).getFunction();
+            if(functionn == null) return null;
+            return functionn.apply(child);
+        } else if(node instanceof FunctionNode){
+            NumberInterface[] convertedChildren = new NumberInterface[children.length];
+            for(int i = 0; i < convertedChildren.length; i++){
+                convertedChildren[i] = (NumberInterface) children[i];
+            }
+            Function function = manager.functionFor(((FunctionNode) node).getFunction());
+            if(function == null) return null;
+            return function.apply(convertedChildren);
+        }
+        return null;
+    }
+
+}

src/org/nwapw/abacus/tree/OpNode.java

@@ -1,38 +0,0 @@
-package org.nwapw.abacus.tree;
-
-public class OpNode extends TreeNode {
-
-    private String operation;
-    private TreeNode left;
-    private TreeNode right;
-
-    public OpNode(String operation){
-        this(operation, null, null);
-    }
-
-    public OpNode(String operation, TreeNode left, TreeNode right){
-        this.operation = operation;
-        this.left = left;
-        this.right = right;
-    }
-
-    public String getOperation() {
-        return operation;
-    }
-
-    public TreeNode getLeft() {
-        return left;
-    }
-
-    public void setLeft(TreeNode left) {
-        this.left = left;
-    }
-
-    public TreeNode getRight() {
-        return right;
-    }
-
-    public void setRight(TreeNode right) {
-        this.right = right;
-    }
-}

src/org/nwapw/abacus/tree/OperatorAssociativity.java

@@ -1,5 +0,0 @@
-package org.nwapw.abacus.tree;
-
-public enum OperatorAssociativity {
-    LEFT, RIGHT
-}

src/org/nwapw/abacus/tree/Reducer.java

@@ -0,0 +1,17 @@
+package org.nwapw.abacus.tree;
+
+/**
+ * Interface used to reduce a tree into a single value.
+ * @param <T> the value to reduce into.
+ */
+public interface Reducer<T> {
+
+    /**
+     * Reduces the given tree into a single value of type T.
+     * @param node the node being passed in to be reduced.
+     * @param children the already-reduced children of this node.
+     * @return the resulting value from the reduce.
+     */
+    public T reduceNode(TreeNode node, Object...children);
+
+}

src/org/nwapw/abacus/tree/TokenType.java

@@ -1,11 +1,23 @@
 package org.nwapw.abacus.tree;
 
+/**
+ * Enum to represent the type of the token that has been matched
+ * by the lexer.
+ */
 public enum TokenType {
 
-    ANY(0), OP(1), NUM(2), WORD(3), OPEN_PARENTH(4), CLOSE_PARENTH(5);
+    INTERNAL_FUNCTION_END(-1),
+    ANY(0), WHITESPACE(1), COMMA(2), OP(3), NUM(4), FUNCTION(5), OPEN_PARENTH(6), CLOSE_PARENTH(7);
 
+    /**
+     * The priority by which this token gets sorted.
+     */
     public final int priority;
 
+    /**
+     * Creates a new token type with the given priority.
+     * @param priority the priority of this token type.
+     */
     TokenType(int priority){
         this.priority = priority;
     }

src/org/nwapw/abacus/tree/TreeBuilder.java

@@ -0,0 +1,207 @@
+package org.nwapw.abacus.tree;
+
+import org.nwapw.abacus.function.OperatorAssociativity;
+import org.nwapw.abacus.function.OperatorType;
+import org.nwapw.abacus.lexing.Lexer;
+import org.nwapw.abacus.lexing.pattern.Match;
+import org.nwapw.abacus.lexing.pattern.Pattern;
+import org.nwapw.abacus.number.NaiveNumber;
+import org.nwapw.abacus.number.PreciseNumber;
+
+import java.util.*;
+
+/**
+ * The builder responsible for turning strings into trees.
+ */
+public class TreeBuilder {
+
+    /**
+     * The lexer used to get the input tokens.
+     */
+    private Lexer<TokenType> lexer;
+    /**
+     * The map of operator precedences.
+     */
+    private Map<String, Integer> precedenceMap;
+    /**
+     * The map of operator associativity.
+     */
+    private Map<String, OperatorAssociativity> associativityMap;
+    /**
+     * The map of operator types.
+     */
+    private Map<String, OperatorType> typeMap;
+
+    /**
+     * Comparator used to sort token types.
+     */
+    protected static Comparator<TokenType> tokenSorter = Comparator.comparingInt(e -> e.priority);
+
+    /**
+     * Creates a new TreeBuilder.
+     */
+    public TreeBuilder(){
+        lexer = new Lexer<TokenType>(){{
+            register(" ", TokenType.WHITESPACE);
+            register(",", TokenType.COMMA);
+            register("[0-9]*(\\.[0-9]+)?", TokenType.NUM);
+            register("\\(", TokenType.OPEN_PARENTH);
+            register("\\)", TokenType.CLOSE_PARENTH);
+        }};
+        precedenceMap = new HashMap<>();
+        associativityMap = new HashMap<>();
+        typeMap = new HashMap<>();
+    }
+
+    /**
+     * Registers a function with the TreeBuilder.
+     * @param function the function to register.
+     */
+    public void registerFunction(String function){
+        lexer.register(Pattern.sanitize(function), TokenType.FUNCTION);
+    }
+
+    /**
+     * Registers an operator with the TreeBuilder.
+     * @param operator the operator to register.
+     * @param precedence the precedence of the operator.
+     * @param associativity the associativity of the operator.
+     */
+    public void registerOperator(String operator, OperatorAssociativity associativity,
+                                 OperatorType operatorType, int precedence){
+        lexer.register(Pattern.sanitize(operator), TokenType.OP);
+        precedenceMap.put(operator, precedence);
+        associativityMap.put(operator, associativity);
+        typeMap.put(operator, operatorType);
+    }
+
+    /**
+     * Tokenizes a string, converting it into matches
+     * @param string the string to tokenize.
+     * @return the list of tokens produced.
+     */
+    public List<Match<TokenType>> tokenize(String string){
+        return lexer.lexAll(string, 0, tokenSorter);
+    }
+
+    /**
+     * Rearranges tokens into a postfix list, using Shunting Yard.
+     * @param source the source string.
+     * @param from the tokens to be rearranged.
+     * @return the resulting list of rearranged tokens.
+     */
+    public List<Match<TokenType>> intoPostfix(String source, List<Match<TokenType>> from){
+        ArrayList<Match<TokenType>> output = new ArrayList<>();
+        Stack<Match<TokenType>> tokenStack = new Stack<>();
+        while(!from.isEmpty()){
+            Match<TokenType> match = from.remove(0);
+            TokenType matchType = match.getType();
+            if(matchType == TokenType.NUM) {
+                output.add(match);
+            } else if(matchType == TokenType.FUNCTION) {
+                output.add(new Match<>(0, 0, TokenType.INTERNAL_FUNCTION_END));
+                tokenStack.push(match);
+            } else if(matchType == TokenType.OP){
+                String tokenString = source.substring(match.getFrom(), match.getTo());
+                OperatorType type = typeMap.get(tokenString);
+                int precedence = precedenceMap.get(tokenString);
+                OperatorAssociativity associativity = associativityMap.get(tokenString);
+
+                if(type == OperatorType.UNARY_POSTFIX){
+                    output.add(match);
+                    continue;
+                }
+
+                while(!tokenStack.empty()) {
+                    Match<TokenType> otherMatch = tokenStack.peek();
+                    TokenType otherMatchType = otherMatch.getType();
+                    if(!(otherMatchType == TokenType.OP || otherMatchType == TokenType.FUNCTION)) break;
+
+                    if(otherMatchType == TokenType.OP){
+                        int otherPrecedence = precedenceMap.get(source.substring(otherMatch.getFrom(), otherMatch.getTo()));
+                        if(otherPrecedence < precedence ||
+                                (associativity == OperatorAssociativity.RIGHT && otherPrecedence == precedence)) {
+                            break;
+                        }
+                    }
+                    output.add(tokenStack.pop());
+                }
+                tokenStack.push(match);
+            } else if(matchType == TokenType.OPEN_PARENTH){
+                tokenStack.push(match);
+            } else if(matchType == TokenType.CLOSE_PARENTH || matchType == TokenType.COMMA){
+                while(!tokenStack.empty() && tokenStack.peek().getType() != TokenType.OPEN_PARENTH){
+                    output.add(tokenStack.pop());
+                }
+                if(tokenStack.empty()) return null;
+                if(matchType == TokenType.CLOSE_PARENTH){
+                    tokenStack.pop();
+                }
+            }
+        }
+        while(!tokenStack.empty()){
+            Match<TokenType> match = tokenStack.peek();
+            TokenType matchType = match.getType();
+            if(!(matchType == TokenType.OP || matchType == TokenType.FUNCTION)) return null;
+            output.add(tokenStack.pop());
+        }
+        return output;
+    }
+
+    /**
+     * Constructs a tree recursively from a list of tokens.
+     * @param source the source string.
+     * @param matches the list of tokens from the source string.
+     * @return the construct tree expression.
+     */
+    public TreeNode fromStringRecursive(String source, List<Match<TokenType>> matches){
+        if(matches.size() == 0) return null;
+        Match<TokenType> match = matches.remove(0);
+        TokenType matchType = match.getType();
+        if(matchType == TokenType.OP){
+            String operator = source.substring(match.getFrom(), match.getTo());
+            OperatorType type = typeMap.get(operator);
+            if(type == OperatorType.BINARY_INFIX){
+                TreeNode right = fromStringRecursive(source, matches);
+                TreeNode left = fromStringRecursive(source, matches);
+                if(left == null || right == null) return null;
+                else return new BinaryInfixNode(operator, left, right);
+            } else {
+                TreeNode applyTo = fromStringRecursive(source, matches);
+                if(applyTo == null) return null;
+                else return new UnaryPrefixNode(operator, applyTo);
+            }
+        } else if(matchType == TokenType.NUM){
+            return new NumberNode(new NaiveNumber(Double.parseDouble(source.substring(match.getFrom(), match.getTo()))));
+        } else if(matchType == TokenType.FUNCTION){
+            String functionName = source.substring(match.getFrom(), match.getTo());
+            FunctionNode node = new FunctionNode(functionName);
+            while(!matches.isEmpty() && matches.get(0).getType() != TokenType.INTERNAL_FUNCTION_END){
+                TreeNode argument = fromStringRecursive(source, matches);
+                if(argument == null) return null;
+                node.prependChild(argument);
+            }
+            if(matches.isEmpty()) return null;
+            matches.remove(0);
+            return node;
+        }
+        return null;
+    }
+
+    /**
+     * Creates a tree node from a string.
+     * @param string the string to create a node from.
+     * @return the resulting tree.
+     */
+    public TreeNode fromString(String string){
+        List<Match<TokenType>> matches = tokenize(string);
+        if(matches == null) return null;
+        matches.removeIf(m -> m.getType() == TokenType.WHITESPACE);
+        matches = intoPostfix(string, matches);
+        if(matches == null) return null;
+
+        Collections.reverse(matches);
+        return fromStringRecursive(string, matches);
+    }
+
+}

src/org/nwapw/abacus/tree/TreeNode.java

@@ -1,103 +1,22 @@
 package org.nwapw.abacus.tree;
 
+import org.nwapw.abacus.function.OperatorAssociativity;
 import org.nwapw.abacus.lexing.Lexer;
 import org.nwapw.abacus.lexing.pattern.Match;
 
 import java.util.*;
 
+/**
+ * An abstract class that represents an expression tree node.
+ */
 public abstract class TreeNode {
 
-    private static Lexer<TokenType> lexer = new Lexer<TokenType>(){{
-        register(".", TokenType.ANY);
-        register("\\+|-|\\*|/|^", TokenType.OP);
-        register("[0-9]+(\\.[0-9]+)?", TokenType.NUM);
-        register("[a-zA-Z]+", TokenType.WORD);
-        register("\\(", TokenType.OPEN_PARENTH);
-        register("\\)", TokenType.CLOSE_PARENTH);
-    }};
-    private static HashMap<String, Integer> precedenceMap = new HashMap<String, Integer>(){{
-        put("+", 0);
-        put("-", 0);
-        put("*", 1);
-        put("/", 1);
-        put("^", 2);
-    }};
-    private static HashMap<String, OperatorAssociativity> associativityMap =
-            new HashMap<String, OperatorAssociativity>() {{
-                put("+", OperatorAssociativity.LEFT);
-                put("-", OperatorAssociativity.LEFT);
-                put("*", OperatorAssociativity.LEFT);
-                put("/", OperatorAssociativity.LEFT);
-                put("^", OperatorAssociativity.RIGHT);
-            }};
-
-    private static Comparator<TokenType> tokenSorter = Comparator.comparingInt(e -> e.priority);
-
-    public static ArrayList<Match<TokenType>> tokenize(String string){
-        return lexer.lexAll(string, 0, tokenSorter);
-    }
-
-    public static ArrayList<Match<TokenType>> intoPostfix(String source, ArrayList<Match<TokenType>> from){
-        ArrayList<Match<TokenType>> output = new ArrayList<>();
-        Stack<Match<TokenType>> tokenStack = new Stack<>();
-        while(!from.isEmpty()){
-            Match<TokenType> match = from.remove(0);
-            if(match.getType() == TokenType.NUM) {
-                output.add(match);
-            } else if(match.getType() == TokenType.OP){
-                String tokenString = source.substring(match.getFrom(), match.getTo());
-                int precedence = precedenceMap.get(tokenString);
-                OperatorAssociativity associativity = associativityMap.get(tokenString);
-
-                while(!tokenStack.empty()) {
-                    Match<TokenType> otherMatch = tokenStack.peek();
-                    if(otherMatch.getType() != TokenType.OP) break;
-
-                    int otherPrecdence = precedenceMap.get(source.substring(otherMatch.getFrom(), otherMatch.getTo()));
-                    if(otherPrecdence < precedence ||
-                            (associativity == OperatorAssociativity.RIGHT && otherPrecdence == precedence)) {
-                        break;
-                    }
-                    output.add(tokenStack.pop());
-                }
-                tokenStack.push(match);
-            } else if(match.getType() == TokenType.OPEN_PARENTH){
-                tokenStack.push(match);
-            } else if(match.getType() == TokenType.CLOSE_PARENTH){
-                while(!tokenStack.empty() && tokenStack.peek().getType() != TokenType.OPEN_PARENTH){
-                    output.add(tokenStack.pop());
-                }
-                if(tokenStack.empty()) return null;
-                tokenStack.pop();
-            }
-        }
-        while(!tokenStack.empty()){
-            if(!(tokenStack.peek().getType() == TokenType.OP)) return null;
-            output.add(tokenStack.pop());
-        }
-        return output;
-    }
-
-    public static TreeNode fromStringRecursive(String source, ArrayList<Match<TokenType>> matches){
-        if(matches.size() == 0) return null;
-        Match<TokenType> match = matches.remove(0);
-        if(match.getType() == TokenType.OP){
-            TreeNode right = fromStringRecursive(source, matches);
-            TreeNode left = fromStringRecursive(source, matches);
-            if(left == null || right == null) return null;
-            else return new OpNode(source.substring(match.getFrom(), match.getTo()), left, right);
-        } else if(match.getType() == TokenType.NUM){
-            return new NumberNode(Double.parseDouble(source.substring(match.getFrom(), match.getTo())));
-        }
-        return null;
-    }
-
-    public static TreeNode fromString(String string){
-        ArrayList<Match<TokenType>> matches = intoPostfix(string, tokenize(string));
-        if(matches == null) return null;
-
-        Collections.reverse(matches);
-        return fromStringRecursive(string, matches);
-    }
+    /**
+     * The function that reduces a tree to a single vale.
+     * @param reducer the reducer used to reduce the tree.
+     * @param <T> the type the reducer produces.
+     * @return the result of the reduction, or null on error.
+     */
+    public abstract <T> T reduce(Reducer<T> reducer);
 
 }

src/org/nwapw/abacus/tree/UnaryPrefixNode.java

@@ -0,0 +1,59 @@
+package org.nwapw.abacus.tree;
+
+public class UnaryPrefixNode extends TreeNode {
+
+    /**
+     * The operation this node will apply.
+     */
+    private String operation;
+    /**
+     * The tree node to apply the operation to.
+     */
+    private TreeNode applyTo;
+
+    /**
+     * Creates a new node with the given operation and no child.
+     * @param operation the operation for this node.
+     */
+    public UnaryPrefixNode(String operation){
+        this(operation, null);
+    }
+
+    /**
+     * Creates a new node with the given operation and child.
+     * @param operation the operation for this node.
+     * @param applyTo the node to apply the function to.
+     */
+    public UnaryPrefixNode(String operation, TreeNode applyTo){
+        this.operation = operation;
+        this.applyTo = applyTo;
+    }
+
+    @Override
+    public <T> T reduce(Reducer<T> reducer) {
+        Object reducedChild = applyTo.reduce(reducer);
+        if(reducedChild == null) return null;
+        return reducer.reduceNode(this, reducedChild);
+    }
+
+    /**
+     * Gets the operation of this node.
+     * @return the operation this node performs.
+     */
+    public String getOperation() {
+        return operation;
+    }
+
+    /**
+     * Gets the node to which this node's operation applies.
+     * @return the tree node to which the operation will be applied.
+     */
+    public TreeNode getApplyTo() {
+        return applyTo;
+    }
+
+    @Override
+    public String toString() {
+        return "(" + (applyTo == null ? "null" : applyTo.toString()) + ")" + operation;
+    }
+}

src/org/nwapw/abacus/window/HistoryTableModel.java

@@ -0,0 +1,108 @@
+package org.nwapw.abacus.window;
+
+import org.nwapw.abacus.tree.TreeNode;
+
+import javax.swing.event.TableModelListener;
+import javax.swing.table.AbstractTableModel;
+import javax.swing.table.TableModel;
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * A table model to store data about the history of inputs
+ * in the calculator.
+ */
+public class HistoryTableModel extends AbstractTableModel {
+
+    /**
+     * Static array used to get the column names.
+     */
+    public static final String[] COLUMN_NAMES = {
+            "Input",
+            "Parsed Input",
+            "Output"
+    };
+
+    /**
+     * Static array used to get the class of each column.
+     */
+    public static final Class[] CLASS_TYPES = {
+            String.class,
+            TreeNode.class,
+            String.class
+    };
+
+    /**
+     * Class used specifically to hold data about
+     * the previous entries into the calculator.
+     */
+    public static class HistoryEntry {
+        public String input;
+        public TreeNode parsedInput;
+        public String output;
+
+        public HistoryEntry(String input, TreeNode parsedInput, String output){
+            this.input = input;
+            this.parsedInput = parsedInput;
+            this.output = output;
+        }
+
+        Object nthValue(int n){
+            if(n == 0) return input;
+            if(n == 1) return parsedInput;
+            if(n == 2) return output;
+            return null;
+        }
+    }
+
+    /**
+     * The list of entries.
+     */
+    List<HistoryEntry> entries;
+
+    /**
+     * Creates a new empty history table model
+     */
+    public HistoryTableModel() {
+        entries = new ArrayList<>();
+    }
+
+    /**
+     * Adds an entry to the model.
+     * @param entry the entry to add.
+     */
+    public void addEntry(HistoryEntry entry){
+        entries.add(entry);
+    }
+
+    @Override
+    public int getRowCount() {
+        return entries.size();
+    }
+
+    @Override
+    public int getColumnCount() {
+        return 3;
+    }
+
+    @Override
+    public String getColumnName(int columnIndex) {
+        return COLUMN_NAMES[columnIndex];
+    }
+
+    @Override
+    public Class<?> getColumnClass(int columnIndex) {
+        return CLASS_TYPES[columnIndex];
+    }
+
+    @Override
+    public boolean isCellEditable(int rowIndex, int columnIndex) {
+        return false;
+    }
+
+    @Override
+    public Object getValueAt(int rowIndex, int columnIndex) {
+        return entries.get(rowIndex).nthValue(columnIndex);
+    }
+
+}

src/org/nwapw/abacus/window/Window.java

@@ -0,0 +1,283 @@
+package org.nwapw.abacus.window;
+
+import org.nwapw.abacus.function.Operator;
+import org.nwapw.abacus.number.NumberInterface;
+import org.nwapw.abacus.plugin.PluginListener;
+import org.nwapw.abacus.plugin.PluginManager;
+import org.nwapw.abacus.tree.NumberReducer;
+import org.nwapw.abacus.tree.TreeBuilder;
+import org.nwapw.abacus.tree.TreeNode;
+
+import javax.swing.*;
+import java.awt.*;
+import java.awt.datatransfer.StringSelection;
+import java.awt.event.ActionListener;
+import java.awt.event.MouseAdapter;
+import java.awt.event.MouseEvent;
+
+/**
+ * The main UI window for the calculator.
+ */
+public class Window extends JFrame implements PluginListener {
+
+    private static final String CALC_STRING = "Calculate";
+    private static final String SYNTAX_ERR_STRING = "Syntax Error";
+    private static final String EVAL_ERR_STRING = "Evaluation Error";
+    private static final String NUMBER_SYSTEM_LABEL = "Number Type:";
+    private static final String FUNCTION_LABEL = "Functions:";
+
+    /**
+     * Array of Strings to which the "calculate" button's text
+     * changes. For instance, in the graph tab, the name will
+     * be "Graph" and not "Calculate".
+     */
+    private static final String[] BUTTON_NAMES = {
+            CALC_STRING,
+            CALC_STRING
+    };
+
+    /**
+     * Array of booleans that determine whether the input
+     * field and the input button are enabled at a particular
+     * index.
+     */
+    private static boolean[] INPUT_ENABLED = {
+            true,
+            false
+    };
+
+    /**
+     * The plugin manager used to retrieve functions.
+     */
+    private PluginManager manager;
+    /**
+     * The builder used to construct the parse trees.
+     */
+    private TreeBuilder builder;
+    /**
+     * The reducer used to evaluate the tree.
+     */
+    private NumberReducer reducer;
+
+    /**
+     * The last output by the calculator.
+     */
+    private String lastOutput;
+
+    /**
+     * The tabbed pane that separates calculator contexts.
+     */
+    private JTabbedPane pane;
+
+    /**
+     * The panel where the output occurs.
+     */
+    private JPanel calculationPanel;
+    /**
+     * The text area reserved for the last output.
+     */
+    private JTextArea lastOutputArea;
+    /**
+     * The table used for storing history results.
+     */
+    private JTable historyTable;
+    /**
+     * The table model used for managing history.
+     */
+    private HistoryTableModel historyModel;
+    /**
+     * The scroll pane for the history area.
+     */
+    private JScrollPane historyScroll;
+
+    /**
+     * The panel where the input occurs.
+     */
+    private JPanel inputPanel;
+    /**
+     * The input text field.
+     */
+    private JTextField inputField;
+    /**
+     * The "submit" button.
+     */
+    private JButton inputEnterButton;
+
+    /**
+     * The side panel for separate configuration.
+     */
+    private JPanel settingsPanel;
+    /**
+     * Panel for elements relating to number
+     * system selection.
+     */
+    private JPanel numberSystemPanel;
+    /**
+     * The possible list of number systems.
+     */
+    private JComboBox<String> numberSystemList;
+    /**
+     * The panel for elements relating to
+     * function selection.
+     */
+    private JPanel functionSelectPanel;
+    /**
+     * The list of functions available to the user.
+     */
+    private JComboBox<String> functionList;
+
+    /**
+     * Action listener that causes the input to be evaluated.
+     */
+    private ActionListener evaluateListener = (event) -> {
+        if(builder == null) return;
+        TreeNode parsedExpression = builder.fromString(inputField.getText());
+        if(parsedExpression == null){
+            lastOutputArea.setText(SYNTAX_ERR_STRING);
+            return;
+        }
+        NumberInterface numberInterface = parsedExpression.reduce(reducer);
+        if(numberInterface == null){
+            lastOutputArea.setText(EVAL_ERR_STRING);;
+            return;
+        }
+        lastOutput = numberInterface.toString();
+        historyModel.addEntry(new HistoryTableModel.HistoryEntry(inputField.getText(), parsedExpression, lastOutput));
+        historyTable.invalidate();
+        lastOutputArea.setText(lastOutput);
+        inputField.setText("");
+    };
+
+    /**
+     * Array of listeners that tell the input button how to behave
+     * at a given input tab.
+     */
+    private ActionListener[] listeners = {
+            evaluateListener,
+            null
+    };
+
+    /**
+     * Creates a new window with the given manager.
+     * @param manager the manager to use.
+     */
+    public Window(PluginManager manager){
+        this();
+        this.manager = manager;
+        manager.addListener(this);
+        reducer = new NumberReducer(manager);
+    }
+
+    /**
+     * Creates a new window.
+     */
+    private Window() {
+        super();
+
+        lastOutput = "";
+
+        setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
+        setSize(320, 480);
+
+        inputField = new JTextField();
+        inputEnterButton = new JButton(CALC_STRING);
+
+        inputPanel = new JPanel();
+        inputPanel.setLayout(new BorderLayout());
+        inputPanel.add(inputField, BorderLayout.CENTER);
+        inputPanel.add(inputEnterButton, BorderLayout.SOUTH);
+
+        historyModel = new HistoryTableModel();
+        historyTable = new JTable(historyModel);
+        historyScroll = new JScrollPane(historyTable);
+        lastOutputArea = new JTextArea(lastOutput);
+        lastOutputArea.setEditable(false);
+
+        calculationPanel = new JPanel();
+        calculationPanel.setLayout(new BorderLayout());
+        calculationPanel.add(historyScroll, BorderLayout.CENTER);
+        calculationPanel.add(lastOutputArea, BorderLayout.SOUTH);
+
+        numberSystemList = new JComboBox<>();
+
+        numberSystemPanel = new JPanel();
+        numberSystemPanel.setAlignmentX(Component.LEFT_ALIGNMENT);
+        numberSystemPanel.setLayout(new FlowLayout());
+        numberSystemPanel.add(new JLabel(NUMBER_SYSTEM_LABEL));
+        numberSystemPanel.add(numberSystemList);
+        numberSystemPanel.setMaximumSize(numberSystemPanel.getPreferredSize());
+
+        functionList = new JComboBox<>();
+
+        functionSelectPanel = new JPanel();
+        functionSelectPanel.setAlignmentX(Component.LEFT_ALIGNMENT);
+        functionSelectPanel.setLayout(new FlowLayout());
+        functionSelectPanel.add(new JLabel(FUNCTION_LABEL));
+        functionSelectPanel.add(functionList);
+        functionSelectPanel.setMaximumSize(functionSelectPanel.getPreferredSize());
+
+        settingsPanel = new JPanel();
+        settingsPanel.setAlignmentX(Component.LEFT_ALIGNMENT);
+        settingsPanel.setLayout(new BoxLayout(settingsPanel, BoxLayout.PAGE_AXIS));
+        settingsPanel.add(numberSystemPanel);
+        settingsPanel.add(functionSelectPanel);
+
+        pane = new JTabbedPane();
+        pane.add("Calculator", calculationPanel);
+        pane.add("Settings", settingsPanel);
+        pane.addChangeListener(e -> {
+            int selectionIndex = pane.getSelectedIndex();
+            boolean enabled = INPUT_ENABLED[selectionIndex];
+            ActionListener listener = listeners[selectionIndex];
+            inputEnterButton.setText(BUTTON_NAMES[selectionIndex]);
+            inputField.setEnabled(enabled);
+            inputEnterButton.setEnabled(enabled);
+
+            for(ActionListener removingListener : inputEnterButton.getActionListeners()){
+                inputEnterButton.removeActionListener(removingListener);
+                inputField.removeActionListener(removingListener);
+            }
+            if(listener != null){
+                inputEnterButton.addActionListener(listener);
+                inputField.addActionListener(listener);
+            }
+        });
+        add(pane, BorderLayout.CENTER);
+        add(inputPanel, BorderLayout.SOUTH);
+
+        inputEnterButton.addActionListener(evaluateListener);
+        inputField.addActionListener(evaluateListener);
+        historyTable.addMouseListener(new MouseAdapter() {
+            @Override
+            public void mouseClicked(MouseEvent e) {
+                Point clickPoint = e.getPoint();
+                if(e.getClickCount() == 2){
+                    int row = historyTable.rowAtPoint(clickPoint);
+                    int column = historyTable.columnAtPoint(clickPoint);
+                    String toCopy = historyTable.getValueAt(row, column).toString();
+                    Toolkit.getDefaultToolkit().getSystemClipboard().setContents(new StringSelection(toCopy), null);
+                }
+            }
+        });
+    }
+
+    @Override
+    public void onLoad(PluginManager manager) {
+        builder = new TreeBuilder();
+        for(String function : manager.getAllFunctions()){
+            builder.registerFunction(function);
+        }
+        for(String operator : manager.getAllOperators()){
+            Operator operatorObject = manager.operatorFor(operator);
+            builder.registerOperator(operator,
+                    operatorObject.getAssociativity(),
+                    operatorObject.getType(),
+                    operatorObject.getPrecedence());
+        }
+    }
+
+    @Override
+    public void onUnload(PluginManager manager) {
+        builder = null;
+    }
+}