Best approximation of e using Java

Question

I would like to bring the value of e closer to any desired accuracy. What is the best way to do this? The most that I could get is e = 2.7182818284590455. Any examples of modifications to the following code will be appreciated.

public static long fact(int x){
    long prod = 1;
    for(int i = 1; i <= x; i++)
        prod = prod * i;
    return prod;
}//fact

public static void main(String[] args) {
    double e = 1;
    for(int i = 1; i < 50; i++)
        e = e + 1/(double)(fact(i));
    System.out.print("e = " + e);
}//main

Answer 1

Use BigDecimal instead of double.

BigDecimal e = BigDecimal.ONE;
BigDecimal fact = BigDecimal.ONE;

for(int i=1;i<100;i++) {
  fact = fact.multiply(new BigDecimal(i));

  e = e.add(BigDecimal.ONE.divide(fact, new MathContext(10000, RoundingMode.HALF_UP)));
}

Answer 2

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Answer 3

java.util.BigDecimal?

import java.math.BigDecimal;
import java.math.MathContext;
public class BigExp {
  public static void main(String[] args) {
BigDecimal FIFTY =new BigDecimal("50");
BigDecimal e = BigDecimal.ZERO;
BigDecimal f = BigDecimal.ONE;
MathContext context = new MathContext(1000);

for (BigDecimal i=BigDecimal.ONE; i.compareTo(FIFTY)<0; i=i.add(BigDecimal.ONE)) {
  f = f.multiply(i, context);
  e = e.add(i.divide(f,context),context);

  System.out.println("e = " + e);
}
  }
}

Answer 4

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Answer 5

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public static BigDecimal factorial(int x){
    BigDecimal prod = new BigDecimal("1");
    for(int i = x; i > 1; i--)
        prod = prod.multiply(new BigDecimal(i));
    return prod;
}//fact

public static void main(String[] args) {
    MathContext mc = new MathContext(1000);
    BigDecimal e = new BigDecimal("1", mc);
    for(int i = 1; i < 1000; i++)
        e = e.add(BigDecimal.ONE.divide(factorial(i), mc));
    System.out.print("e = " + e);
}//main 

Answer 6

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Answer 7

, " " double, :

Please note that this is a pretty technical document. For more information on how floating point numbers work, see this Wikipedia article: Double-precision floating-point format