Calculating the value of e: Difference between revisions

<p>

This is can be in Java using the the <code>BigDecimal</code> and <code>BigInteger</code> classes.<br />

Each which offer the ability to compute values beyond the constraints of both <code>double</code> and <code>long</code>, respectively.

</p>

<p>

I used a <kbd>rounding-mode</kbd> of "half-up", which rounds 0.5 to 1, and -0.5 to -1.

</p>

<p>

You can set the amount of terms with the <kbd>epsilon</kbd> argument.

And you can set the scale with the <kbd>scale</kbd> argument, which will ultimately be the <code>int</code> maximum, which is 2,147,483,647.

</p>

<syntaxhighlight lang="java">

import static java.math.RoundingMode.HALF_UP;

import java.math.BigDecimal;

import java.math.BigInteger;

</syntaxhighlight>

<syntaxhighlight lang="java">

BigDecimal e(BigInteger epsilon, int scale) {

BigDecimal e = BigDecimal.ONE.setScale(scale, HALF_UP);

BigDecimal n;

BigInteger index = BigInteger.ONE;

while (index.compareTo(epsilon) < 0) {

n = new BigDecimal(String.valueOf(factorial(index)));

e = e.add(BigDecimal.ONE.divide(n, scale, HALF_UP));

index = index.add(BigInteger.ONE);

}

return e;

}

BigInteger factorial(BigInteger value) {

if (value.compareTo(BigInteger.ONE) > 0) {

return value.multiply(factorial(value.subtract(BigInteger.ONE)));

} else {

return BigInteger.ONE;

}

}

</syntaxhighlight>

<p>

Here is a execution using 100 terms, and a scale of 1000.

</p>

<syntaxhighlight lang="java">

BigDecimal e = e(BigInteger.valueOf(100), 1000);

</syntaxhighlight>

<pre>

2.718281828459045235360287471352662497757247093699959574966967627724076630353547

59457138217852516642742746639193200305992181741359662904357290033429526059563072

73100853237805275106368648701695314186552748459082449550453392864976427741366416

59646366325087360915841343970999831703538233800921168146554153749305420222461709

32123094916776349931113070302925698934206764391913665038487357884661077572557630

79218988673537904194120433774064949070738630790492489764370698362973668621984292

50767700214157406500293826954406871877954270969766247465243666295138572019208303

17726923409770165674539225777914734160368493572310330448576142902663326352937973

44504000613119416470868982597552087347829370853870094341780806567997280704595039

17013351431243873005220184059659629058572148124084211850064775039817941961218573

36935973323362272606025181783889270251361949206078243869370233748144842017157072

21499854656151809995508987059685112005970217969141325866928660231731022979729068

783220835224413915990618593145821470347881

</pre>

<br />

Anternately, you could use the following implementation.