Optimize pow for integer bases.

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

@@ -182,7 +182,7 @@ public abstract class NumberInterface {
      * Also, checks if the thread has been interrupted, and if so, throws
      * an exception.
      *
-     * @return the least integer bigger or equal to the number, if int can hold the value.
+     * @return the least integer bigger or equal to the number.
      */
     public final NumberInterface ceiling(){
         checkInterrupted();
@@ -192,7 +192,7 @@ public abstract class NumberInterface {
     /**
      * Return the greatest integer less than or equal to the number.
      *
-     * @return the greatest integer smaller or equal the number, if int can hold the value.
+     * @return the greatest integer smaller or equal the number.
      */
     protected abstract NumberInterface floorInternal();
 
@@ -201,7 +201,7 @@ public abstract class NumberInterface {
      * Also, checks if the thread has been interrupted, and if so, throws
      * an exception.
      *
-     * @return the greatest int >= the number, if int can hold the value.
+     * @return the greatest int greater than or equal to the number.
      */
     public final NumberInterface floor(){
         checkInterrupted();
@@ -216,7 +216,7 @@ public abstract class NumberInterface {
     protected abstract NumberInterface fractionalPartInternal();
 
     /**
-     * Returns the fractional part of the number.
+     * Returns the fractional part of the number, specifically x - floor(x).
      * Also, checks if the thread has been interrupted,
      * and if so, throws an exception.
      * @return the fractional part of the number.

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

@@ -113,19 +113,18 @@ public class PreciseNumber extends NumberInterface {
         String str = value.toPlainString();
         int decimalIndex = str.indexOf('.');
         if (decimalIndex != -1) {
-            return new PreciseNumber(str.substring(0, decimalIndex));
+            NumberInterface floor = new PreciseNumber(str.substring(0, decimalIndex));
+            if(signum() == -1){
+                floor = floor.subtract(ONE);
+            }
+            return floor;
         }
         return this;
     }
 
     @Override
     public NumberInterface fractionalPartInternal() {
-        String str = value.toPlainString();
+        return this.subtractInternal(floorInternal());
-        int decimalIndex = str.indexOf('.');
-        if (decimalIndex != -1) {
-            return new PreciseNumber(str.substring(decimalIndex + 1));
-        }
-        return ZERO;
     }
 
     @Override

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

@@ -17,6 +17,18 @@ import java.util.Set;
  */
 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 map of the number implementations this plugin provides.
+     */
+    private Map<String, NumberImplementation> numberImplementations;
     /**
      * The plugin manager in which to search for functions
      * not inside this package,
@@ -37,9 +49,69 @@ public abstract class Plugin {
      */
     public Plugin(PluginManager manager) {
         this.manager = manager;
+        functions = new HashMap<>();
+        operators = new HashMap<>();
+        numberImplementations = 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 the list of number implementations provided by this plugin.
+     *
+     * @return the list of registered number implementations.
+     */
+    public final Set<String> providedNumberImplementations() {
+        return numberImplementations.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);
+    }
+
+    /**
+     * Gets the number implementation under the given name.
+     *
+     * @param name the name of the number implementation to look up.
+     * @return the number implementation associated with that name, or null if the plugin doesn't provide it.
+     */
+    public final NumberImplementation getNumberImplementation(String name) {
+        return numberImplementations.get(name);
+    }
+
     /**
      * Enables the function, loading the necessary instances
      * of functions.
@@ -57,6 +129,8 @@ public abstract class Plugin {
     public final void disable() {
         if (!enabled) return;
         onDisable();
+        functions.clear();
+        operators.clear();
         enabled = false;
     }
 
@@ -68,7 +142,7 @@ public abstract class Plugin {
      * @param toRegister the function implementation.
      */
     protected final void registerFunction(String name, Function toRegister) {
-        manager.registerFunction(name, toRegister);
+        functions.put(name, toRegister);
     }
 
     /**
@@ -80,7 +154,7 @@ public abstract class Plugin {
      * @param operator the operator to register.
      */
     protected final void registerOperator(String name, Operator operator) {
-        manager.registerOperator(name, operator);
+        operators.put(name, operator);
     }
 
     /**
@@ -91,7 +165,7 @@ public abstract class Plugin {
      * @param implementation the actual implementation class to register.
      */
     protected final void registerNumberImplementation(String name, NumberImplementation implementation) {
-        manager.registerNumberImplementation(name, implementation);
+        numberImplementations.put(name, implementation);
     }
 
     /**
@@ -139,7 +213,7 @@ public abstract class Plugin {
      * @param forClass the class to which to find the pi instance.
      * @return the pi value for the given class.
      */
-    protected final NumberInterface piFor(Class<? extends NumberInterface> forClass) {
+    protected final NumberInterface getPi(Class<? extends NumberInterface> forClass) {
         return manager.piFor(forClass);
     }
 

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

@@ -23,17 +23,20 @@ public class PluginManager {
      */
     private Set<Plugin> plugins;
     /**
-     * The map of functions registered by the plugins.
+     * List of functions that have been cached,
+     * that is, found in a plugin and returned.
      */
-    private Map<String, Function> registeredFunctions;
+    private Map<String, Function> cachedFunctions;
     /**
-     * The map of operators registered by the plugins
+     * List of operators that have been cached,
+     * that is, found in a plugin and returned.
      */
-    private Map<String, Operator> registeredOperators;
+    private Map<String, Operator> cachedOperators;
     /**
-     * The map of number implementations registered by the plugins.
+     * The list of number implementations that have
+     * been cached, that is, found in a plugin and returned.
      */
-    private Map<String, NumberImplementation> registeredNumberImplementations;
+    private Map<String, NumberImplementation> cachedNumberImplementations;
     /**
      * The list of number implementations that have been
      * found by their implementation class.
@@ -43,6 +46,18 @@ public class PluginManager {
      * The pi values for each implementation class that have already been computer.
      */
     private Map<Class<? extends NumberInterface>, NumberInterface> cachedPi;
+    /**
+     * List of all functions loaded by the plugins.
+     */
+    private Set<String> allFunctions;
+    /**
+     * List of all operators loaded by the plugins.
+     */
+    private Set<String> allOperators;
+    /**
+     * List of all the number implementations loaded by the plugins.
+     */
+    private Set<String> allNumberImplementations;
     /**
      * The list of plugin listeners attached to this instance.
      */
@@ -62,66 +77,79 @@ public class PluginManager {
         this.abacus = abacus;
         loadedPluginClasses = new HashSet<>();
         plugins = new HashSet<>();
-        registeredFunctions = new HashMap<>();
+        cachedFunctions = new HashMap<>();
-        registeredOperators = new HashMap<>();
+        cachedOperators = new HashMap<>();
-        registeredNumberImplementations = new HashMap<>();
+        cachedNumberImplementations = new HashMap<>();
         cachedInterfaceImplementations = new HashMap<>();
         cachedPi = new HashMap<>();
+        allFunctions = new HashSet<>();
+        allOperators = new HashSet<>();
+        allNumberImplementations = new HashSet<>();
         listeners = new HashSet<>();
     }
 
     /**
-     * Registers a function under the given name.
+     * Searches the plugin list for a certain value, retrieving the Plugin's
-     * @param name the name of the function.
+     * list of items of the type using the setFunction and getting the value
-     * @param function the function to register.
+     * 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
+     * @param <K>         the type of key that the cache is indexed by.
+     * @return the retrieved element, or null if it was not found.
      */
-    public void registerFunction(String name, Function function){
+    private static <T, K> T searchCached(Collection<Plugin> plugins, Map<K, T> cache,
-        registeredFunctions.put(name, function);
+                                         java.util.function.Function<Plugin, Set<K>> setFunction,
+                                         java.util.function.BiFunction<Plugin, K, T> getFunction,
+                                         K name) {
+        if (cache.containsKey(name)) return cache.get(name);
+
+        T loadedValue = null;
+        for (Plugin plugin : plugins) {
+            if (setFunction.apply(plugin).contains(name)) {
+                loadedValue = getFunction.apply(plugin, name);
+                break;
+            }
+        }
+
+        cache.put(name, loadedValue);
+        return loadedValue;
     }
 
     /**
-     * Registers an operator under the given name.
+     * 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.
-     * @param operator the operator to register.
+     * @return the operator under the given name.
      */
-    public void registerOperator(String name, Operator operator){
+    public Operator operatorFor(String name) {
-        registeredOperators.put(name, operator);
+        return searchCached(plugins, cachedOperators, Plugin::providedOperators, Plugin::getOperator, name);
     }
 
     /**
-     * Registers a number implementation under the given name.
+     * Gets the number implementation under the given name.
-     * @param name the name of the number implementation.
+     *
-     * @param implementation the number implementation to register.
+     * @param name the name of the implementation.
+     * @return the implementation.
      */
-    public void registerNumberImplementation(String name, NumberImplementation implementation){
+    public NumberImplementation numberImplementationFor(String name) {
-        registeredNumberImplementations.put(name, implementation);
+        return searchCached(plugins, cachedNumberImplementations, Plugin::providedNumberImplementations,
-    }
+                Plugin::getNumberImplementation, name);
-
-    /**
-     * Gets the function registered under the given name.
-     * @param name the name of the function.
-     * @return the function, or null if it was not found.
-     */
-    public Function functionFor(String name){
-        return registeredFunctions.get(name);
-    }
-
-    /**
-     * Gets the operator registered under the given name.
-     * @param name the name of the operator.
-     * @return the operator, or null if it was not found.
-     */
-    public Operator operatorFor(String name){
-        return registeredOperators.get(name);
-    }
-
-    /**
-     * Gets the number implementation registered under the given name.
-     * @param name the name of the number implementation.
-     * @return the number implementation, or null if it was not found.
-     */
-    public NumberImplementation numberImplementationFor(String name){
-        return registeredNumberImplementations.get(name);
     }
 
     /**
@@ -133,11 +161,14 @@ public class PluginManager {
     public NumberImplementation interfaceImplementationFor(Class<? extends NumberInterface> name) {
         if (cachedInterfaceImplementations.containsKey(name)) return cachedInterfaceImplementations.get(name);
         NumberImplementation toReturn = null;
-        for(String key : registeredNumberImplementations.keySet()){
+        outside:
-            NumberImplementation implementation = registeredNumberImplementations.get(key);
+        for (Plugin plugin : plugins) {
-            if(implementation.getImplementation() == name) {
+            for (String implementationName : plugin.providedNumberImplementations()) {
-                toReturn = implementation;
+                NumberImplementation implementation = plugin.getNumberImplementation(implementationName);
-                break;
+                if (implementation.getImplementation().equals(name)) {
+                    toReturn = implementation;
+                    break outside;
+                }
             }
         }
         cachedInterfaceImplementations.put(name, toReturn);
@@ -196,6 +227,12 @@ public class PluginManager {
             if (disabledPlugins.contains(plugin.getClass().getName())) continue;
             plugin.enable();
         }
+        for (Plugin plugin : plugins) {
+            if (disabledPlugins.contains(plugin.getClass().getName())) continue;
+            allFunctions.addAll(plugin.providedFunctions());
+            allOperators.addAll(plugin.providedOperators());
+            allNumberImplementations.addAll(plugin.providedNumberImplementations());
+        }
         listeners.forEach(e -> e.onLoad(this));
     }
 
@@ -209,8 +246,14 @@ public class PluginManager {
             if (disabledPlugins.contains(plugin.getClass().getName())) continue;
             plugin.disable();
         }
+        cachedFunctions.clear();
+        cachedOperators.clear();
+        cachedNumberImplementations.clear();
         cachedInterfaceImplementations.clear();
         cachedPi.clear();
+        allFunctions.clear();
+        allOperators.clear();
+        allNumberImplementations.clear();
         listeners.forEach(e -> e.onUnload(this));
     }
 
@@ -228,7 +271,7 @@ public class PluginManager {
      * @return the set of all functions that were loaded.
      */
     public Set<String> getAllFunctions() {
-        return registeredFunctions.keySet();
+        return allFunctions;
     }
 
     /**
@@ -237,7 +280,7 @@ public class PluginManager {
      * @return the set of all operators that were loaded.
      */
     public Set<String> getAllOperators() {
-        return registeredOperators.keySet();
+        return allOperators;
     }
 
     /**
@@ -246,7 +289,7 @@ public class PluginManager {
      * @return the set of all implementations that were loaded.
      */
     public Set<String> getAllNumberImplementations() {
-        return registeredNumberImplementations.keySet();
+        return allNumberImplementations;
     }
 
     /**

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

@@ -18,6 +18,11 @@ import java.util.function.BiFunction;
  */
 public class StandardPlugin extends Plugin {
 
+    /**
+     * Stores objects of NumberInterface with integer values for reuse.
+     */
+    private final static HashMap<Class<? extends NumberInterface>, HashMap<Integer, NumberInterface>> integerValues = new HashMap<>();
+
     /**
      * The addition operator, +
      */
@@ -112,7 +117,7 @@ public class StandardPlugin extends Plugin {
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
             if (params[0].signum() == 0) {
-                return (new NaiveNumber(1)).promoteTo(params[0].getClass());
+                return fromInt(params[0].getClass(), 1);
             }
             NumberInterface factorial = params[0];
             NumberInterface multiplier = params[0];
@@ -157,14 +162,14 @@ public class StandardPlugin extends Plugin {
             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) {
-                    param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
+                    param = param.divide(fromInt(param.getClass(), 2));
                     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()));
+                    param = param.multiply(fromInt(param.getClass(), 2));
                     powersOf2--;
                     if (param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != -1) {
                         break;
@@ -203,17 +208,17 @@ public class StandardPlugin extends Plugin {
          */
         private NumberInterface getLog2(NumberInterface number) {
             NumberInterface maxError = getMaxError(number);
-            //NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
+            //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 = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
+            NumberInterface a = fromInt(number.getClass(), 1), 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()));
+                a = a.divide(fromInt(number.getClass(), 3));
-                b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
+                b = b.divide(fromInt(number.getClass(), 4));
                 c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
                 sum = sum.add(a.add(b).multiply(c));
             }
@@ -311,7 +316,7 @@ public class StandardPlugin extends Plugin {
                 //right and left refer to lhs and rhs in the above inequality.
                 NumberInterface sum = NaiveNumber.ONE.promoteTo(params[0].getClass());
                 NumberInterface nextNumerator = params[0];
-                NumberInterface left = params[0].multiply((new NaiveNumber(3)).promoteTo(params[0].getClass()).intPow(params[0].ceiling().intValue())), right = maxError;
+                NumberInterface left = params[0].multiply(fromInt(params[0].getClass(), 3).intPow(params[0].ceiling().intValue())), right = maxError;
                 do {
                     sum = sum.add(nextNumerator.divide(factorial(params[0].getClass(), n + 1)));
                     n++;
@@ -344,6 +349,13 @@ public class StandardPlugin extends Plugin {
                 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());
+            //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[1].getClass(), 1)) >= 0){
+                NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
+                return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(newParams));
+            }
             return FUNCTION_EXP.apply(FUNCTION_LN.apply(FUNCTION_ABS.apply(params[0])).multiply(params[1]));
         }
     });
@@ -358,13 +370,13 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface pi = piFor(params[0].getClass());
+            NumberInterface pi = getPi(params[0].getClass());
-            NumberInterface twoPi = pi.multiply(new NaiveNumber(2).promoteTo(pi.getClass()));
+            NumberInterface twoPi = pi.multiply(fromInt(pi.getClass(), 2));
             NumberInterface theta = getSmallAngle(params[0], pi);
             //System.out.println(theta);
             if (theta.compareTo(pi.multiply(new NaiveNumber(1.5).promoteTo(twoPi.getClass()))) >= 0) {
                 theta = theta.subtract(twoPi);
-            } else if (theta.compareTo(pi.divide(new NaiveNumber(2).promoteTo(pi.getClass()))) > 0) {
+            } else if (theta.compareTo(pi.divide(fromInt(pi.getClass(), 2))) > 0) {
                 theta = pi.subtract(theta);
             }
             //System.out.println(theta);
@@ -382,7 +394,7 @@ public class StandardPlugin extends Plugin {
 
         @Override
         protected NumberInterface applyInternal(NumberInterface[] params) {
-            return functionSin.apply(piFor(params[0].getClass()).divide(new NaiveNumber(2).promoteTo(params[0].getClass()))
+            return functionSin.apply(getPi(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
                     .subtract(params[0]));
         }
     };
@@ -470,7 +482,7 @@ public class StandardPlugin extends Plugin {
      * @return the maximum error.
      */
     private static NumberInterface getMaxError(NumberInterface number) {
-        return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision());
+        return fromInt(number.getClass(), 10).intPow(-number.getMaxPrecision());
     }
 
     /**
@@ -531,6 +543,22 @@ public class StandardPlugin extends Plugin {
         return theta;
     }
 
+    /**
+     * Returns a number of class numType with value n.
+     * @param numType class of number to return.
+     * @param n value of returned number.
+     * @return numClass instance with value n.
+     */
+    private static NumberInterface fromInt(Class<? extends NumberInterface> numType, int n){
+        if(!integerValues.containsKey(numType)){
+            integerValues.put(numType, new HashMap<>());
+        }
+        if(!integerValues.get(numType).containsKey(n)){
+            integerValues.get(numType).put(n, new NaiveNumber(n).promoteTo(numType));
+        }
+        return integerValues.get(numType).get(n);
+    }
+
     @Override
     public void onEnable() {
         registerNumberImplementation("naive", IMPLEMENTATION_NAIVE);