From 6673771ca9a37afbf19f915debf246179a87ada1 Mon Sep 17 00:00:00 2001
From: Arthur Drobot <drobotarthur@gmail.com>
Date: Wed, 26 Jul 2017 15:26:06 -0700
Subject: [PATCH] Add exp and helper functions for Taylor Series etc.

---
 .../nwapw/abacus/plugin/StandardPlugin.java   | 59 ++++++++++++++++++-
 1 file changed, 58 insertions(+), 1 deletion(-)

diff --git a/src/org/nwapw/abacus/plugin/StandardPlugin.java b/src/org/nwapw/abacus/plugin/StandardPlugin.java
index f7a2363..9881ff2 100755
--- a/src/org/nwapw/abacus/plugin/StandardPlugin.java
+++ b/src/org/nwapw/abacus/plugin/StandardPlugin.java
@@ -4,6 +4,8 @@ import org.nwapw.abacus.function.Function;
 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.
@@ -93,7 +95,17 @@ public class StandardPlugin extends Plugin {
             }
         });
 
-        System.out.println(getExpSeriesTerm(4, new NaiveNumber(3)));
+        registerFunction("exp", new Function() {
+            @Override
+            protected boolean matchesParams(NumberInterface[] params) {
+                return params.length == 1;
+            }
+
+            @Override
+            protected NumberInterface applyInternal(NumberInterface[] params) {
+                return sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
+            }
+        });
     }
 
     /**
@@ -106,4 +118,49 @@ public class StandardPlugin extends Plugin {
         return x.intPow(n).divide(this.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
+     */
+    private int getNTermsExp(NumberInterface maxError, NumberInterface x){
+        //We need n such that x^(n+2) <= (n+1)! * maxError
+        //The variables LHS and RHS refer to the above inequality.
+        int n = 0;
+        NumberInterface LHS = x.intPow(2), RHS = maxError;
+        while(LHS.compareTo(RHS) > 0){
+            n++;
+            LHS = LHS.multiply(x);
+            RHS = RHS.multiply(new NaiveNumber(n).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
+     */
+    private NumberInterface getMaxError(NumberInterface number){
+        return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.precision());
+    }
+
 }