Write a RationalNumber class.

build.gradle

@@ -11,6 +11,7 @@ repositories {
 }
 
 dependencies {
+    compile group: 'org.apache.commons', name: 'commons-math3', version: '3.6.1'
     compile 'com.moandjiezana.toml:toml4j:0.7.1'
     compile "org.jetbrains.kotlin:kotlin-stdlib-jre8"
     testCompile 'junit:junit:4.12'

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

@@ -1,6 +1,7 @@
 package org.nwapw.abacus.number;
 
 import java.math.BigDecimal;
+import java.math.BigInteger;
 import java.math.MathContext;
 
 /**
@@ -61,6 +62,15 @@ public class PreciseNumber extends NumberInterface {
         this.value = value;
     }
 
+    /**
+     * Constructs a precise number from the given BigInteger.
+     *
+     * @param value a BigInteger object representing the value of the number.
+     */
+    public PreciseNumber(BigInteger value) {
+        this.value = new BigDecimal(value);
+    }
+
     @Override
     public int getMaxPrecision() {
         return internalContext.getPrecision();

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

@@ -0,0 +1,115 @@
+package org.nwapw.abacus.number;
+
+import org.apache.commons.math3.fraction.BigFraction;
+import org.apache.commons.math3.fraction.Fraction;
+
+import java.math.BigInteger;
+
+public class RationalNumber extends NumberInterface{
+
+    static final RationalNumber ONE = new RationalNumber(BigFraction.ONE);
+
+    /**
+     * The value of the number.
+     */
+    private BigFraction value;
+
+    /**
+     * Constructs a new instance with the given value.
+     * @param value
+     */
+    public RationalNumber(BigFraction value){
+        this.value = value;
+    }
+
+    @Override
+    public int getMaxPrecision() {
+        return 0;
+    }
+
+    @Override
+    protected NumberInterface multiplyInternal(NumberInterface multiplier) {
+        return new RationalNumber(value.multiply(((RationalNumber)multiplier).value));
+    }
+
+    @Override
+    protected NumberInterface divideInternal(NumberInterface divisor) {
+        return new RationalNumber(value.divide(((RationalNumber)divisor).value));
+    }
+
+    @Override
+    protected NumberInterface addInternal(NumberInterface summand) {
+        return new RationalNumber(value.add(((RationalNumber)summand).value));
+    }
+
+    @Override
+    protected NumberInterface subtractInternal(NumberInterface subtrahend) {
+        return new RationalNumber(value.subtract(((RationalNumber)subtrahend).value));
+    }
+
+    @Override
+    protected NumberInterface negateInternal() {
+        return new RationalNumber(value.negate());
+    }
+
+    @Override
+    protected NumberInterface intPowInternal(int exponent) {
+        return new RationalNumber(value.pow(exponent));
+    }
+
+    @Override
+    public int compareTo(NumberInterface number) {
+        return value.compareTo(((RationalNumber)number).value);
+    }
+
+    @Override
+    public int signum() {
+        return value.getNumerator().signum();
+    }
+
+    @Override
+    protected NumberInterface ceilingInternal() {
+        if(value.getNumeratorAsInt() != 1){
+            return floorInternal().add(ONE);
+        }
+        return this;
+    }
+
+    @Override
+    protected NumberInterface floorInternal() {
+        BigInteger floor = value.bigDecimalValue().toBigInteger();
+        if(value.compareTo(BigFraction.ZERO) < 0 && value.getDenominatorAsInt() != 1){
+            floor = floor.subtract(BigInteger.ONE);
+        }
+        return new RationalNumber(new BigFraction(floor));
+    }
+
+    @Override
+    protected NumberInterface fractionalPartInternal() {
+        return this.subtractInternal(floorInternal());
+    }
+
+    @Override
+    public int intValue() {
+        return 0;
+    }
+
+    @Override
+    protected NumberInterface promoteToInternal(Class<? extends NumberInterface> toClass) {
+        return null;
+    }
+
+    @Override
+    public NumberInterface getMaxError() {
+        return toPreciseNumber().getMaxError();
+    }
+
+    @Override
+    public String toString(){
+        return toPreciseNumber().toString();
+    }
+
+    PreciseNumber toPreciseNumber(){
+        return (PreciseNumber) new PreciseNumber(value.getNumerator()).divideInternal(new PreciseNumber(value.getDenominator()));
+    }
+}

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

@@ -451,144 +451,6 @@ public class StandardPlugin extends Plugin {
         }
     };
 
-    /**
-     * The arcsine function (return type in radians).
-     */
-    public final Function functionArcsin = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1
-                    && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) <= 0;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            if(FUNCTION_ABS.apply(params[0]).compareTo(new NaiveNumber(0.8).promoteTo(params[0].getClass())) >= 0){
-                NumberInterface[] newParams = {FUNCTION_SQRT.apply(fromInt(params[0].getClass(), 1).subtract(params[0].multiply(params[0])))};
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                        .subtract(applyInternal(newParams)).multiply(fromInt(params[0].getClass(), params[0].signum()));
-            }
-            NumberInterface currentTerm = params[0], sum = currentTerm,
-                    multiplier = currentTerm.multiply(currentTerm), summandBound = sum.getMaxError().multiply(fromInt(sum.getClass(), 1).subtract(multiplier)),
-                    power = currentTerm, coefficient = fromInt(params[0].getClass(), 1);
-            int exponent = 1;
-            while(FUNCTION_ABS.apply(currentTerm).compareTo(summandBound) > 0){
-                exponent += 2;
-                power = power.multiply(multiplier);
-                coefficient = coefficient.multiply(fromInt(params[0].getClass(), exponent-2))
-                        .divide(fromInt(params[0].getClass(), exponent - 1));
-                currentTerm = power.multiply(coefficient).divide(fromInt(power.getClass(), exponent));
-                sum = sum.add(currentTerm);
-            }
-            return sum;
-        }
-    };
-
-    /**
-     * The arccosine function.
-     */
-    public final Function functionArccos = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) <= 0;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                    .subtract(functionArcsin.apply(params));
-        }
-    };
-
-    /**
-     * The arccosecant function.
-     */
-    public final Function functionArccsc = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) >= 0;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface[] reciprocalParamArr = {fromInt(params[0].getClass(), 1).divide(params[0])};
-            return functionArcsin.apply(reciprocalParamArr);
-        }
-    };
-
-    /**
-     * The arcsecant function.
-     */
-    public final Function functionArcsec = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1 && FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), 1)) >= 0;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            NumberInterface[] reciprocalParamArr = {fromInt(params[0].getClass(), 1).divide(params[0])};
-            return functionArccos.apply(reciprocalParamArr);
-        }
-    };
-
-    /**
-     * The arctangent function.
-     */
-    public final Function functionArctan = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            if(params[0].signum() == -1){
-                NumberInterface[] negatedParams = {params[0].negate()};
-                return applyInternal(negatedParams).negate();
-            }
-            if(params[0].compareTo(fromInt(params[0].getClass(), 1)) > 0){
-                NumberInterface[] reciprocalParams = {fromInt(params[0].getClass(), 1).divide(params[0])};
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                        .subtract(applyInternal(reciprocalParams));
-            }
-            if(params[0].compareTo(fromInt(params[0].getClass(), 1)) == 0){
-                return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 4));
-            }
-            if(params[0].compareTo(new NaiveNumber(0.9).promoteTo(params[0].getClass())) >= 0){
-                NumberInterface[] newParams = {params[0].multiply(fromInt(params[0].getClass(),2 ))
-                .divide(fromInt(params[0].getClass(), 1).subtract(params[0].multiply(params[0])))};
-                return applyInternal(newParams).divide(fromInt(params[0].getClass(), 2));
-            }
-            NumberInterface currentPower = params[0], currentTerm = currentPower, sum = currentTerm,
-                    maxError = params[0].getMaxError(), multiplier = currentPower.multiply(currentPower).negate();
-            int n = 1;
-            while(FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0){
-                n += 2;
-                currentPower = currentPower.multiply(multiplier);
-                currentTerm = currentPower.divide(fromInt(currentPower.getClass(), n));
-                sum = sum.add(currentTerm);
-            }
-            return sum;
-        }
-    };
-
-    /**
-     * The arccotangent function. Range: (0, pi).
-     */
-    public final Function functionArccot = new Function() {
-        @Override
-        protected boolean matchesParams(NumberInterface[] params) {
-            return params.length == 1;
-        }
-
-        @Override
-        protected NumberInterface applyInternal(NumberInterface[] params) {
-            return piFor(params[0].getClass()).divide(fromInt(params[0].getClass(), 2))
-                    .subtract(functionArctan.apply(params));
-        }
-    };
-
     public StandardPlugin(PluginManager manager) {
         super(manager);
     }
@@ -706,12 +568,6 @@ public class StandardPlugin extends Plugin {
         registerFunction("sec", functionSec);
         registerFunction("csc", functionCsc);
         registerFunction("cot", functionCot);
-        registerFunction("arcsin", functionArcsin);
-        registerFunction("arccos", functionArccos);
-        registerFunction("arccsc", functionArccsc);
-        registerFunction("arcsec", functionArcsec);
-        registerFunction("arctan", functionArctan);
-        registerFunction("arccot", functionArccot);
     }
 
     @Override