Inverse trig documentation.

build.gradle

@@ -16,6 +16,5 @@ dependencies {
     testCompile 'junit:junit:4.12'
 }
 
-// Define the main class for the application
 mainClassName = 'org.nwapw.abacus.Abacus'
 

src/main/java/org/nwapw/abacus/fx/AbacusController.java

@@ -222,7 +222,7 @@ public class AbacusController implements PluginListener {
         Callback<TableColumn<HistoryModel, String>, TableCell<HistoryModel, String>> cellFactory =
                 param -> new CopyableCell<>();
         Callback<ListView<ToggleablePlugin>, ListCell<ToggleablePlugin>> pluginCellFactory =
-                param -> new CheckBoxListCell<>(ToggleablePlugin::enabledProperty, new StringConverter<ToggleablePlugin>() {
+                param -> new CheckBoxListCell<>(ToggleablePlugin::getEnabledProperty, new StringConverter<ToggleablePlugin>() {
                     @Override
                     public String toString(ToggleablePlugin object) {
                         return object.getClassName().substring(object.getClassName().lastIndexOf('.') + 1);
@@ -230,7 +230,7 @@ public class AbacusController implements PluginListener {
 
                     @Override
                     public ToggleablePlugin fromString(String string) {
-                        return new ToggleablePlugin(true, string);
+                        return new ToggleablePlugin(string, true);
                     }
                 });
         functionList = FXCollections.observableArrayList();
@@ -249,11 +249,11 @@ public class AbacusController implements PluginListener {
         enabledPluginView.setItems(enabledPlugins);
         enabledPluginView.setCellFactory(pluginCellFactory);
         inputColumn.setCellFactory(cellFactory);
-        inputColumn.setCellValueFactory(cell -> cell.getValue().inputProperty());
+        inputColumn.setCellValueFactory(cell -> cell.getValue().getInputProperty());
         parsedColumn.setCellFactory(cellFactory);
-        parsedColumn.setCellValueFactory(cell -> cell.getValue().parsedProperty());
+        parsedColumn.setCellValueFactory(cell -> cell.getValue().getParsedProperty());
         outputColumn.setCellFactory(cellFactory);
-        outputColumn.setCellValueFactory(cell -> cell.getValue().outputProperty());
+        outputColumn.setCellValueFactory(cell -> cell.getValue().getOutputProperty());
         coreTabPane.getSelectionModel().selectedItemProperty().addListener((observable, oldValue, newValue) -> {
             if (oldValue.equals(settingsTab)) alertIfApplyNeeded(true);
         });
@@ -261,13 +261,7 @@ public class AbacusController implements PluginListener {
         abacus = new Abacus(new Configuration(CONFIG_FILE));
         PluginManager abacusPluginManager = abacus.getPluginManager();
         abacusPluginManager.addListener(this);
-        abacusPluginManager.addInstantiated(new StandardPlugin(abacus.getPluginManager()));
-        try {
-            ClassFinder.loadJars("plugins").forEach(abacusPluginManager::addClass);
-        } catch (IOException | ClassNotFoundException e) {
-            e.printStackTrace();
-        }
-        abacusPluginManager.reload();
+        performScan();
 
         computationLimitField.setText(Double.toString(abacus.getConfiguration().getComputationDelay()));
         computationLimitField.textProperty().addListener((observable, oldValue, newValue) -> {
@@ -317,6 +311,19 @@ public class AbacusController implements PluginListener {
         reloadAlertShown = false;
     }
 
+    @FXML
+    public void performScan(){
+        PluginManager abacusPluginManager = abacus.getPluginManager();
+        abacusPluginManager.removeAll();
+        abacusPluginManager.addInstantiated(new StandardPlugin(abacus.getPluginManager()));
+        try {
+            ClassFinder.loadJars("plugins").forEach(abacusPluginManager::addClass);
+        } catch (IOException | ClassNotFoundException e) {
+            e.printStackTrace();
+        }
+        abacusPluginManager.reload();
+    }
+
     @FXML
     public void performReload() {
         alertIfApplyNeeded(true);
@@ -349,8 +356,8 @@ public class AbacusController implements PluginListener {
         numberImplementationBox.getSelectionModel().select(toSelect);
         for (Class<?> pluginClass : abacus.getPluginManager().getLoadedPluginClasses()) {
             String fullName = pluginClass.getName();
-            ToggleablePlugin plugin = new ToggleablePlugin(!disabledPlugins.contains(fullName), fullName);
-            plugin.enabledProperty().addListener(e -> changesMade = true);
+            ToggleablePlugin plugin = new ToggleablePlugin(fullName, !disabledPlugins.contains(fullName));
+            plugin.getEnabledProperty().addListener(e -> changesMade = true);
             enabledPlugins.add(plugin);
         }
         PluginManager pluginManager = abacus.getPluginManager();

src/main/java/org/nwapw/abacus/fx/DocumentationCell.java

@@ -33,7 +33,7 @@ public class DocumentationCell extends ListCell<Documentation> {
         titledPane.textProperty().bindBidirectional(codeNameLabel.textProperty());
         titledPane.setContent(vbox);
         titledPane.setExpanded(false);
-        titledPane.prefWidthProperty().bind(widthProperty());
+        titledPane.prefWidthProperty().bind(widthProperty().subtract(32));
 
         visibleProperty().addListener((a, b, c) -> titledPane.setExpanded(false));
     }
@@ -54,5 +54,6 @@ public class DocumentationCell extends ListCell<Documentation> {
             longDescription.setText(item.getLongDescription());
             setGraphic(titledPane);
         }
+        titledPane.setExpanded(false);
     }
 }

src/main/java/org/nwapw/abacus/fx/HistoryModel.java

@@ -1,97 +0,0 @@
-package org.nwapw.abacus.fx;
-
-import javafx.beans.property.SimpleStringProperty;
-import javafx.beans.property.StringProperty;
-
-/**
- * The data model used for storing history entries.
- */
-public class HistoryModel {
-
-    /**
-     * The property used for displaying the column
-     * for the user input.
-     */
-    private final StringProperty input;
-    /**
-     * The property used for displaying the column
-     * that contains the parsed input.
-     */
-    private final StringProperty parsed;
-    /**
-     * The property used for displaying the column
-     * that contains the program output.
-     */
-    private final StringProperty output;
-
-    /**
-     * Creates a new history model with the given variables.
-     *
-     * @param input  the user input
-     * @param parsed the parsed input
-     * @param output the program output.
-     */
-    public HistoryModel(String input, String parsed, String output) {
-        this.input = new SimpleStringProperty();
-        this.parsed = new SimpleStringProperty();
-        this.output = new SimpleStringProperty();
-        this.input.setValue(input);
-        this.parsed.setValue(parsed);
-        this.output.setValue(output);
-    }
-
-    /**
-     * Gets the input property.
-     *
-     * @return the input property.
-     */
-    public StringProperty inputProperty() {
-        return input;
-    }
-
-    /**
-     * Gets the input.
-     *
-     * @return the input.
-     */
-    public String getInput() {
-        return input.get();
-    }
-
-    /**
-     * Gets the parsed input property.
-     *
-     * @return the parsed input property.
-     */
-    public StringProperty parsedProperty() {
-        return parsed;
-    }
-
-    /**
-     * Gets the parsed input.
-     *
-     * @return the parsed input.
-     */
-    public String getParsed() {
-        return parsed.get();
-    }
-
-    /**
-     * Gets the output property.
-     *
-     * @return the output property.
-     */
-    public StringProperty outputProperty() {
-        return output;
-    }
-
-    /**
-     * Gets the program output.
-     *
-     * @return the output.
-     */
-    public String getOutput() {
-        return output.get();
-    }
-
-}

src/main/java/org/nwapw/abacus/fx/ToggleablePlugin.java

@@ -1,60 +0,0 @@
-package org.nwapw.abacus.fx;
-
-import javafx.beans.property.BooleanProperty;
-import javafx.beans.property.SimpleBooleanProperty;
-
-/**
- * Class that represents an entry in the plugin check box list.
- * The changes from this property are written to the config on application.
- */
-public class ToggleablePlugin {
-
-    /**
-     * The property that determines whether the plugin will be enabled.
-     */
-    private final BooleanProperty enabled;
-    /**
-     * The name of the class this entry toggles.
-     */
-    private final String className;
-
-    /**
-     * Creates a new toggleable plugin with the given properties.
-     *
-     * @param enabled   the enabled / disabled state at the beginning.
-     * @param className the name of the class this plugin toggles.
-     */
-    public ToggleablePlugin(boolean enabled, String className) {
-        this.enabled = new SimpleBooleanProperty();
-        this.enabled.setValue(enabled);
-        this.className = className;
-    }
-
-    /**
-     * Gets the enabled property of this plugin.
-     *
-     * @return the enabled property.
-     */
-    public BooleanProperty enabledProperty() {
-        return enabled;
-    }
-
-    /**
-     * Checks if this plugin entry should be enabled.
-     *
-     * @return whether this plugin will be enabled.
-     */
-    public boolean isEnabled() {
-        return enabled.get();
-    }
-
-    /**
-     * Gets the class name this plugin toggles.
-     *
-     * @return the class name that should be disabled.
-     */
-    public String getClassName() {
-        return className;
-    }
-
-}

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

@@ -128,5 +128,9 @@ public class NaiveNumber extends NumberInterface {
         return Double.toString(Math.round(value * shiftBy) / shiftBy);
     }
 
+    @Override
+    public NumberInterface getMaxError(){
+        return new NaiveNumber(Math.pow(10, -18));
+    }
 }
 

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

@@ -240,6 +240,7 @@ public abstract class NumberInterface {
      * @param toClass the class to promote to.
      * @return the resulting new instance.
      */
+    @Deprecated
     protected abstract NumberInterface promoteToInternal(Class<? extends NumberInterface> toClass);
 
     /**
@@ -250,9 +251,17 @@ public abstract class NumberInterface {
      * @param toClass the class to promote to.
      * @return the resulting new instance.
      */
+    @Deprecated
     public final NumberInterface promoteTo(Class<? extends NumberInterface> toClass) {
         checkInterrupted();
         return promoteToInternal(toClass);
     }
 
+    /**
+     * Returns the smallest error this instance can tolerate depending
+     * on its precision and value.
+     * @return the smallest error that should be permitted in calculations.
+     */
+    public abstract NumberInterface getMaxError();
+
 }

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

@@ -1,7 +1,7 @@
 package org.nwapw.abacus.number;
 
 import java.math.BigDecimal;
-import java.math.RoundingMode;
+import java.math.MathContext;
 
 /**
  * A number that uses a BigDecimal to store its value,
@@ -22,6 +22,21 @@ public class PreciseNumber extends NumberInterface {
      */
     public static final PreciseNumber TEN = new PreciseNumber(BigDecimal.TEN);
 
+    /**
+     * The number of extra significant figures kept in calculations before rounding for output.
+     */
+    private static int numExtraInternalSigFigs = 15;
+
+    /**
+     * MathContext that is used when rounding a number prior to output.
+     */
+    private static MathContext outputContext = new MathContext(50);
+
+    /**
+     * MathContext that is actually used in calculations.
+     */
+    private static MathContext internalContext = new MathContext(outputContext.getPrecision()+numExtraInternalSigFigs);
+
     /**
      * The value of the PreciseNumber.
      */
@@ -48,7 +63,7 @@ public class PreciseNumber extends NumberInterface {
 
     @Override
     public int getMaxPrecision() {
-        return 65;
+        return internalContext.getPrecision();
     }
 
     @Override
@@ -58,7 +73,7 @@ public class PreciseNumber extends NumberInterface {
 
     @Override
     public NumberInterface divideInternal(NumberInterface divisor) {
-        return new PreciseNumber(value.divide(((PreciseNumber) divisor).value, this.getMaxPrecision(), RoundingMode.HALF_UP));
+        return new PreciseNumber(value.divide(((PreciseNumber) divisor).value, internalContext));
     }
 
     @Override
@@ -147,7 +162,11 @@ public class PreciseNumber extends NumberInterface {
 
     @Override
     public String toString() {
-        BigDecimal rounded = value.setScale(getMaxPrecision() - 15, RoundingMode.HALF_UP);
-        return rounded.stripTrailingZeros().toPlainString();
+        return value.round(outputContext).toString();
+    }
+
+    @Override
+    public NumberInterface getMaxError(){
+        return new PreciseNumber(value.ulp()).multiplyInternal(TEN.intPowInternal(value.precision()-internalContext.getPrecision()));
     }
 }

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

@@ -14,7 +14,7 @@ public abstract class NumberImplementation {
     /**
      * The list of paths through which this implementation can be promoted.
      */
-    protected Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> promotionPaths;
+    private Map<Class<? extends NumberInterface>, Function<NumberInterface, NumberInterface>> promotionPaths;
     /**
      * The implementation class for this implementation.
      */

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

@@ -224,6 +224,24 @@ public class PluginManager {
         }
     }
 
+    /**
+     * Removes the plugin with the given class from the manager.
+     * @param toRemove the plugin to remove.
+     */
+    public void removeClass(Class<? extends Plugin> toRemove){
+        if(!loadedPluginClasses.contains(toRemove)) return;
+        plugins.removeIf(plugin -> plugin.getClass() == toRemove);
+        loadedPluginClasses.remove(toRemove);
+    }
+
+    /**
+     * Removes all plugins from this plugin manager.
+     */
+    public void removeAll(){
+        loadedPluginClasses.clear();
+        plugins.clear();
+    }
+
     /**
      * Loads all the plugins in the PluginManager.
      */

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

@@ -11,6 +11,7 @@ import org.nwapw.abacus.tree.TokenType;
 import org.nwapw.abacus.tree.TreeNode;
 
 import java.util.ArrayList;
+import java.util.Date;
 import java.util.HashMap;
 import java.util.List;
 import java.util.function.BiFunction;
@@ -97,7 +98,7 @@ public class StandardPlugin extends Plugin {
     public static final Operator OP_DIVIDE = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 1, new Function() {
         @Override
         protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 2 && params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0;
+            return params.length == 2 && params[1].compareTo(fromInt(params[0].getClass(), 0)) != 0;
         }
 
         @Override
@@ -113,7 +114,7 @@ public class StandardPlugin extends Plugin {
         @Override
         protected boolean matchesParams(NumberInterface[] params) {
             return params.length == 1
-                    && params[0].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
+                    && params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
                     && params[0].signum() >= 0;
         }
 
@@ -122,10 +123,11 @@ public class StandardPlugin extends Plugin {
             if (params[0].signum() == 0) {
                 return fromInt(params[0].getClass(), 1);
             }
+            NumberInterface one = fromInt(params[0].getClass(), 1);
             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) {
+            while ((multiplier = multiplier.subtract(one)).signum() == 1) {
                 factorial = factorial.multiply(multiplier);
             }
             return factorial;
@@ -136,6 +138,51 @@ public class StandardPlugin extends Plugin {
                 }*/
         }
     });
+    /**
+     * The permutation operator.
+     */
+    public static final Operator OP_NPR = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0, new Function() {
+        @Override
+        protected boolean matchesParams(NumberInterface[] params) {
+            return params.length == 2 && params[0].fractionalPart().signum() == 0
+                    && params[1].fractionalPart().signum() == 0;
+        }
+
+        @Override
+        protected NumberInterface applyInternal(NumberInterface[] params) {
+            if(params[0].compareTo(params[1]) < 0 ||
+                    params[0].signum() < 0 ||
+                    (params[0].signum() == 0 && params[1].signum() != 0)) return fromInt(params[0].getClass(), 0);
+            NumberInterface total = fromInt(params[0].getClass(), 1);
+            NumberInterface multiplyBy = params[0];
+            NumberInterface remainingMultiplications = params[1];
+            NumberInterface halfway = params[0].divide(fromInt(params[0].getClass(), 2));
+            if(remainingMultiplications.compareTo(halfway) > 0){
+                remainingMultiplications = params[0].subtract(remainingMultiplications);
+            }
+            while(remainingMultiplications.signum() > 0){
+                total = total.multiply(multiplyBy);
+                remainingMultiplications = remainingMultiplications.subtract(fromInt(params[0].getClass(), 1));
+                multiplyBy = multiplyBy.subtract(fromInt(params[0].getClass(), 1));
+            }
+            return total;
+        }
+    });
+    /**
+     * The combination operator.
+     */
+    public static final Operator OP_NCR = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 0, new Function() {
+        @Override
+        protected boolean matchesParams(NumberInterface[] params) {
+            return params.length == 2 && params[0].fractionalPart().signum() == 0
+                    && params[1].fractionalPart().signum() == 0;
+        }
+
+        @Override
+        protected NumberInterface applyInternal(NumberInterface[] params) {
+            return OP_NPR.getFunction().apply(params).divide(OP_FACTORIAL.getFunction().apply(params[1]));
+        }
+    });
     /**
      * The absolute value function, abs(-3) = 3
      */
@@ -147,7 +194,7 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
+            return params[0].multiply(fromInt(params[0].getClass(), params[0].signum()));
         }
     };
     /**
@@ -156,31 +203,32 @@ public class StandardPlugin extends Plugin {
     public static final Function FUNCTION_LN = new Function() {
         @Override
         protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) > 0;
+            return params.length == 1 && params[0].compareTo(fromInt(params[0].getClass(), 0)) > 0;
         }
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
             NumberInterface param = params[0];
+            NumberInterface one = fromInt(param.getClass(), 1);
             int powersOf2 = 0;
-            while (FUNCTION_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) {
+            while (FUNCTION_ABS.apply(param.subtract(one)).compareTo(new NaiveNumber(0.1).promoteTo(param.getClass())) >= 0) {
+                if (param.subtract(one).signum() == 1) {
                     param = param.divide(fromInt(param.getClass(), 2));
                     powersOf2++;
-                    if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
+                    if (param.subtract(one).signum() != 1) {
                         break;
                         //No infinite loop for you.
                     }
                 } else {
                     param = param.multiply(fromInt(param.getClass(), 2));
                     powersOf2--;
-                    if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != -1) {
+                    if (param.subtract(one).signum() != -1) {
                         break;
                         //No infinite loop for you.
                     }
                 }
             }
-            return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
+            return getLog2(param).multiply(fromInt(param.getClass(), powersOf2)).add(getLogPartialSum(param));
         }
 
         /**
@@ -191,14 +239,14 @@ public class StandardPlugin extends Plugin {
          */
         private NumberInterface getLogPartialSum(NumberInterface x) {
 
-            NumberInterface maxError = getMaxError(x);
-            x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
+            NumberInterface maxError = x.getMaxError();
+            x = x.subtract(fromInt(x.getClass(), 1)); //Terms used are for log(x+1).
             NumberInterface currentNumerator = x, currentTerm = x, sum = x;
             int n = 1;
             while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
                 n++;
                 currentNumerator = currentNumerator.multiply(x).negate();
-                currentTerm = currentNumerator.divide(new NaiveNumber(n).promoteTo(x.getClass()));
+                currentTerm = currentNumerator.divide(fromInt(x.getClass(), n));
                 sum = sum.add(currentTerm);
             }
             return sum;
@@ -210,19 +258,20 @@ public class StandardPlugin extends Plugin {
          * @return the value of log(2) with the appropriate precision.
          */
         private NumberInterface getLog2(NumberInterface number) {
-            NumberInterface maxError = getMaxError(number);
+            NumberInterface maxError = number.getMaxError();
             //NumberInterface errorBound = fromInt(number.getClass(), 1);
             //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 = fromInt(number.getClass(), 1), b = a, c = a;
-            NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
+            NumberInterface sum = fromInt(number.getClass(), 0);
+            NumberInterface one = fromInt(number.getClass(), 1);
             int n = 0;
             while (a.compareTo(maxError) >= 1) {
                 n++;
                 a = a.divide(fromInt(number.getClass(), 3));
                 b = b.divide(fromInt(number.getClass(), 4));
-                c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
+                c = one.divide(fromInt(number.getClass(), n));
                 sum = sum.add(a.add(b).multiply(c));
             }
             return sum;
@@ -242,6 +291,20 @@ public class StandardPlugin extends Plugin {
             return OP_CARET.getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
         }
     };
+    /**
+     * Gets a random number smaller or equal to the given number's integer value.
+     */
+    public static final Function FUNCTION_RAND_INT = new Function() {
+        @Override
+        protected boolean matchesParams(NumberInterface[] params) {
+            return params.length == 1;
+        }
+
+        @Override
+        protected NumberInterface applyInternal(NumberInterface[] params) {
+            return fromInt(params[0].getClass(), (int) Math.round(Math.random() * params[0].floor().intValue()));
+        }
+    };
     /**
      * The implementation for double-based naive numbers.
      */
@@ -281,10 +344,10 @@ public class StandardPlugin extends Plugin {
                     .negate();
             for (int i = 0; i < termsNeeded; i++) {
                 M = M
-                        .multiply(new NaiveNumber(12 * i + 2).promoteTo(PreciseNumber.class))
-                        .multiply(new NaiveNumber(12 * i + 6).promoteTo(PreciseNumber.class))
-                        .multiply(new NaiveNumber(12 * i + 10).promoteTo(PreciseNumber.class))
-                        .divide(new NaiveNumber(Math.pow(i + 1, 3)).promoteTo(PreciseNumber.class));
+                        .multiply(new PreciseNumber((12 * i + 2) + ""))
+                        .multiply(new PreciseNumber((12 * i + 6) + ""))
+                        .multiply(new PreciseNumber((12 * i + 10) + ""))
+                        .divide(new PreciseNumber(Math.pow(i + 1, 3) + ""));
                 L = L.add(lSummand);
                 X = X.multiply(xMultiplier);
                 sum = sum.add(M.multiply(L).divide(X));
@@ -304,20 +367,15 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface maxError = getMaxError(params[0]);
+            NumberInterface maxError = params[0].getMaxError();
             int n = 0;
-            if (params[0].signum() <= 0) {
-                NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
-                while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
-                    n++;
-                    currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
-                    sum = sum.add(currentTerm);
-                }
-                return sum;
+            if (params[0].signum() < 0) {
+                NumberInterface[] negatedParams = {params[0].negate()};
+               return fromInt(params[0].getClass(), 1).divide(applyInternal(negatedParams));
             } else {
                 //We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
                 //right and left refer to lhs and rhs in the above inequality.
-                NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
+                NumberInterface sum = fromInt(params[0].getClass(), 1);
                 NumberInterface nextNumerator = params[0];
                 NumberInterface left = params[0].multiply(fromInt(params[0].getClass(), 3).intPow(params[0].ceiling().intValue())), right = maxError;
                 do {
@@ -325,7 +383,7 @@ public class StandardPlugin extends Plugin {
                     n++;
                     nextNumerator = nextNumerator.multiply(params[0]);
                     left = left.multiply(params[0]);
-                    NumberInterface nextN = (new NaiveNumber(n + 1)).promoteTo(params[0].getClass());
+                    NumberInterface nextN = fromInt(params[0].getClass(), n + 1);
                     right = right.multiply(nextN);
                     //System.out.println(left + ", " + right);
                 }
@@ -341,21 +399,23 @@ public class StandardPlugin extends Plugin {
     public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
         @Override
         protected boolean matchesParams(NumberInterface[] params) {
+            NumberInterface zero = fromInt(params[0].getClass(), 0);
             return params.length == 2
-                    && !(params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0
-                    && params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) == 0)
-                    && !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(NaiveNumber.ZERO.promoteTo(params[1].getClass())) != 0);
+                    && !(params[0].compareTo(zero) == 0
+                    && params[1].compareTo(zero) == 0)
+                    && !(params[0].signum() == -1 && params[1].fractionalPart().compareTo(zero) != 0);
         }
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            if (params[0].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
-                return NaiveNumber.ZERO.promoteTo(params[0].getClass());
-            else if (params[1].compareTo(NaiveNumber.ZERO.promoteTo(params[0].getClass())) == 0)
-                return NaiveNumber.ONE.promoteTo(params[1].getClass());
+            NumberInterface zero = fromInt(params[0].getClass(), 0);
+            if (params[0].compareTo(zero) == 0)
+                return zero;
+            else if (params[1].compareTo(zero) == 0)
+                return fromInt(params[0].getClass(), 1);
             //Detect integer bases:
             if(params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
-                    && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
+                    && FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
                     && FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[1].getClass(), 1)) >= 0){
                 NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
                 return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(newParams));
@@ -427,7 +487,7 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionCos.apply(params[0]));
+            return fromInt(params[0].getClass(), 1).divide(functionCos.apply(params[0]));
         }
     };
     /**
@@ -441,7 +501,7 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            return NaiveNumber.ONE.promoteTo(params[0].getClass()).divide(functionSin.apply(params[0]));
+            return fromInt(params[0].getClass(), 1).divide(functionSin.apply(params[0]));
         }
     };
     /**
@@ -472,23 +532,13 @@ public class StandardPlugin extends Plugin {
      * @return the value of the partial sum that has the same class as x.
      */
     private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n) {
-        NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
+        NumberInterface sum = fromInt(x.getClass(), 0);
         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 static NumberInterface getMaxError(NumberInterface number) {
-        return fromInt(number.getClass(), 10).intPow(-number.getMaxPrecision());
-    }
-
     /**
      * A factorial function that uses memoization for each number class; it efficiently
      * computes factorials of non-negative integers.
@@ -500,13 +550,13 @@ public class StandardPlugin extends Plugin {
     public static NumberInterface factorial(Class<? extends NumberInterface> numberClass, int n) {
         if (!FACTORIAL_LISTS.containsKey(numberClass)) {
             FACTORIAL_LISTS.put(numberClass, new ArrayList<>());
-            FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
-            FACTORIAL_LISTS.get(numberClass).add(NaiveNumber.ONE.promoteTo(numberClass));
+            FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
+            FACTORIAL_LISTS.get(numberClass).add(fromInt(numberClass, 1));
         }
         ArrayList<NumberInterface> list = FACTORIAL_LISTS.get(numberClass);
         if (n >= list.size()) {
             while (list.size() < n + 16) {
-                list.add(list.get(list.size() - 1).multiply(new NaiveNumber(list.size()).promoteTo(numberClass)));
+                list.add(list.get(list.size() - 1).multiply(fromInt(numberClass, list.size())));
             }
         }
         return list.get(n);
@@ -520,7 +570,7 @@ public class StandardPlugin extends Plugin {
      */
     private static NumberInterface sinTaylor(NumberInterface x) {
         NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
-        NumberInterface maxError = getMaxError(x);
+        NumberInterface maxError = x.getMaxError();
         int n = 1;
         do {
             n += 2;
@@ -538,7 +588,7 @@ public class StandardPlugin extends Plugin {
      * @return theta in [0, 2pi) that differs from phi by a multiple of 2pi.
      */
     private static NumberInterface getSmallAngle(NumberInterface phi, NumberInterface pi) {
-        NumberInterface twoPi = pi.multiply(new NaiveNumber("2").promoteTo(phi.getClass()));
+        NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
         NumberInterface theta = FUNCTION_ABS.apply(phi).subtract(twoPi
                 .multiply(FUNCTION_ABS.apply(phi).divide(twoPi).floor())); //Now theta is in [0, 2pi).
         if (phi.signum() < 0) {
@@ -576,6 +626,9 @@ public class StandardPlugin extends Plugin {
         registerOperator("^", OP_CARET);
         registerOperator("!", OP_FACTORIAL);
 
+        registerOperator("nPr", OP_NPR);
+        registerOperator("nCr", OP_NCR);
+
         registerFunction("abs", FUNCTION_ABS);
         registerFunction("exp", FUNCTION_EXP);
         registerFunction("ln", FUNCTION_LN);
@@ -587,6 +640,8 @@ public class StandardPlugin extends Plugin {
         registerFunction("csc", functionCsc);
         registerFunction("cot", functionCot);
 
+        registerFunction("random_int", FUNCTION_RAND_INT);
+
         registerDocumentation(new Documentation("abs", "Absolute Value", "Finds the distance " +
                 "from zero of a number.", "Given a number, this function finds the distance form " +
                 "zero of a number, effectively turning negative numbers into positive ones.\n\n" +
@@ -600,21 +655,40 @@ public class StandardPlugin extends Plugin {
                 "the power that e has to be brought to to be equal to the number.\n\n" +
                 "Example: ln(2.718) -> 1", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("sqrt", "Square Root", "Finds the square root " +
-                "of the number.", "A square root a of a number is defined such that a times a is equal " +
+                "of the number.", "A square root a of a number is defined as the non-negative a such that a times a is equal " +
                 "to that number.\n\n" +
                 "Example: sqrt(4) -> 2", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("sin", "Sine", "Computes the sine of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: sin(pi/6) -> 0.5", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("cos", "Cosine", "Computes the cosine of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: cos(pi/6) -> 0.866... (the exact result is sqrt(3)/2)", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("tan", "Tangent", "Computes the tangent of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: tan(pi/6) -> 0.577... (the exact result is 1/sqrt(3))", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("sec", "Secant", "Computes the secant of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: sec(pi/6) -> 1.154... (the exact result is 2/sqrt(3))", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("csc", "Cosecant", "Computes the cosecant of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: csc(pi/6) -> 2", DocumentationType.FUNCTION));
         registerDocumentation(new Documentation("cot", "Cotangent", "Computes the cotangent of the given angle, " +
-                "in radians.", "", DocumentationType.FUNCTION));
+                "in radians.", "Example: cot(pi/6) -> 1.732... (the exact result is sqrt(3))", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("random_int", "Random Integer", "Generates a random integer [0, n].",
+                "Generates a pseudorandom number using the standard JVM random mechanism, keeping it less than or " +
+                        "equal to the given number.\n\n" +
+                        "Example: random_int(5) -> 4\n" +
+                        "random_int(5) -> 3\n" +
+                        "random_int(5) -> 3\n", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arcsin", "Arcsine", "Computes the arcsine of x. (The result is in radians.)",
+                "Example: arcsin(0.5) -> 0.523... (the exact result is pi/6)", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arccos", "Arccosine", "Computes the arccosine of x. (The result is in radians.)",
+                "Example: arccos(0.5) -> 1.047... (the exact result is pi/3)", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arctan", "Arctangent", "Computes the arctangent of x. (The result is in radians.)",
+                "Example: arctan(1) -> 0.785... (the exact result is pi/4)", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arcsec", "Arcsecant", "Computes the arcsecant of x. (The result is in radians.)",
+                "Example: arcsec(2) -> 1.047... (the exact result is pi/3)", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arccsc", "Arccosecant", "Computes the arcscosecant of x. (The result is in radians.)",
+                "Example: arccsc(2) -> 0.523... (the exact result is pi/6)", DocumentationType.FUNCTION));
+        registerDocumentation(new Documentation("arccot", "Arccotangent", "Computes the arccotangent of x. (The result is in radians," +
+                " in the range (0, pi).)",
+                "Example: arccot(0) -> 1.570... (the exact result is pi/2)", DocumentationType.FUNCTION));
     }
 
     @Override

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

@@ -1,19 +0,0 @@
-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/main/kotlin/org/nwapw/abacus/fx/HistoryModel.kt

@@ -0,0 +1,32 @@
+package org.nwapw.abacus.fx
+
+import javafx.beans.property.SimpleStringProperty
+
+/**
+ * A model representing an input / output in the calculator.
+ *
+ * The HistoryModel class stores a record of a single user-provided input,
+ * its parsed form as it was interpreted by the calculator, and the output
+ * that was provided by the calculator. These are represented as properties
+ * to allow easy access by JavaFX cells.
+ *
+ * @param input the user input
+ * @param parsed the parsed version of the input.
+ * @param output the output string.
+ */
+class HistoryModel(input: String, parsed: String, output: String){
+
+    /**
+     * The property that holds the input.
+     */
+    val inputProperty = SimpleStringProperty(input)
+    /**
+     * The property that holds the parsed input.
+     */
+    val parsedProperty = SimpleStringProperty(parsed)
+    /**
+     * The property that holds the output.
+     */
+    val outputProperty = SimpleStringProperty(output)
+
+}

src/main/kotlin/org/nwapw/abacus/fx/ToggleablePlugin.kt

@@ -0,0 +1,31 @@
+package org.nwapw.abacus.fx
+
+import javafx.beans.property.SimpleBooleanProperty
+
+/**
+ * A model representing a plugin that can be disabled or enabled.
+ *
+ * ToggleablePlugin is a model that is used to present to the user the option
+ * of disabling / enabling plugins. The class name in this plugin is stored if
+ * its "enabledPropery" is false, essentially blacklisting the plugin.
+ *
+ * @param className the name of the class that this model concerns.
+ * @param enabled whether or not the model should start enabled.
+ */
+class ToggleablePlugin (val className: String, enabled: Boolean) {
+
+    /**
+     * The property used to interact with JavaFX components.
+     */
+    val enabledProperty = SimpleBooleanProperty(enabled)
+
+    /**
+     * Checks whether this plugin is currently enabled or not.
+     *
+     * @return true if it is enabled, false otherwise.
+     */
+    fun isEnabled(): Boolean {
+        return enabledProperty.value
+    }
+
+}

src/main/kotlin/org/nwapw/abacus/tree/FunctionNode.kt

@@ -16,7 +16,7 @@ data class FunctionNode(val function: String) : TreeNode() {
     val children: MutableList<TreeNode> = mutableListOf()
 
     override fun <T : Any> reduce(reducer: Reducer<T>): T? {
-        val children = Array<Any?>(children.size, { children[it].reduce(reducer) ?: return null; })
+        val children = Array<Any>(children.size, { children[it].reduce(reducer) ?: return null; })
         return reducer.reduceNode(this, *children)
     }
 

src/main/kotlin/org/nwapw/abacus/tree/Reducer.kt

@@ -0,0 +1,19 @@
+package org.nwapw.abacus.tree
+
+/**
+ * Reducer interface that takes a tree and returns a single value.
+ *
+ * The reducer walks the tree, visiting the children first, converting them into
+ * a value, and then attempts to reduce the parent. Eventually, the single final value is returned.
+ */
+interface Reducer <out T> {
+
+    /**
+     * Reduces the given tree node, given its already reduced children.
+     *
+     * @param treeNode the tree node to reduce.
+     * @param children the list of children, of type T.
+     */
+    fun reduceNode(treeNode: TreeNode, vararg children: Any) : T?
+
+}

src/main/resources/abacus.fxml

@@ -57,6 +57,7 @@
                         <Button text="Apply" onAction="#performSave"/>
                         <Button text="Reload Plugins" onAction="#performReload"/>
                         <Button text="Apply and Reload" onAction="#performSaveAndReload"/>
+                        <Button text="Scan Plugins" onAction="#performScan"/>
                     </FlowPane>
                 </GridPane>
             </Tab>

src/test/java/org/nwapw/abacus/tests/CalculationTests.java

@@ -88,8 +88,8 @@ public class CalculationTests {
     public void testExp(){
         testOutput("exp0", "exp(0)", "1");
         testOutput("exp1", "exp(1)", "2.718281828459045235360287471352662497757247");
-        testOutput("exp300", "exp(300)", "19424263952412559365842088360176992193662086");
-        testOutput("exp300", "exp(300)", "19424263952412559365842088360176992193662086");
+        testOutput("exp300", "exp(300)", "1.9424263952412559365842088360176992193662086");
+        testOutput("exp(-500)", "exp((500)`)", "7.1245764067412855315491573771227552469277568");
     }
 
     @Test
@@ -99,6 +99,9 @@ public class CalculationTests {
         testOutput("2^1", "(2^1)", "2");
         testOutput("2^-1", "(2^(1)`)", "0.5");
         testOutput("2^50", "(2^50)", "112589990684262");
+        testOutput("7^(-sqrt2*17)", "(7^((sqrt(2)*17))`)", "4.81354609155297814551845300063563");
+        testEvalError("0^0", "(0^0)");
+        testEvalError("(-13)^.9999", "((13)`^0.9999)");
     }
 
 }