using BigDecimal for very large numbers

Question

I have this code:

while (counter <= t)
{
   a = a * counter;
   c = c * r + a;
   counter++;
}

and I have t with the value 101835.

The output should be 7.1*10^438, but NetBeans shows the output as infinity.

Is there anything that will make the output as a decimal number?

Answer 1

A double as defined by IEEE-754 can't represent such a number, it's too large. The bounds are approximately between -10³⁰⁸ and 10³⁰⁸.

You need to use a BigDecimal to represent it: a number with an arbitrary number of bytes to represent numbers.

Better way to implement this:

double c = 0.0005d;//initialize c
double r = 0.01d;  //initialize r
double a = 0.0006d;//initialize a
BigDecimal abd = new BigDecimal(a); //BigDecimal for a
BigDecimal cbd = new BigDecimal(c); //BigDecimal for c
BigDecimal rbd = new BigDecimal(r); //BigDecimal for r
for (int counter = 1; counter <= t; counter++) {//perhaps other offset for counter?
   abd = abd.multiply(new BigDecimal(counter));
   cbd = cbd.multiply(rbd).add(abd);
}

A potential problem with this approach is that the precision is too high: Java will calculate all operations exactly resulting in numbers that have thousands of digits. Since every operation blows up the number of digits, within a few iterations, simple addition and multiplication operations become unfeasible.

You can solve this by defining a precision using the optional MathContext parameter: it determines on how precise the result should be. You can for instance use MathContext.DECIMAL128:

int t = 101835;
double c = 0.0005d;//initialize c
double r = 0.01d;  //initialize r
double a = 0.0006d;//initialize a
BigDecimal abd = new BigDecimal(a); //BigDecimal for a
BigDecimal cbd = new BigDecimal(c); //BigDecimal for c
BigDecimal rbd = new BigDecimal(r); //BigDecimal for r
for (int counter = 1; counter <= t; counter++) {//perhaps other offset for counter?
    abd = abd.multiply(new BigDecimal(counter),MathContext.DECIMAL128);
    cbd = cbd.multiply(rbd,MathContext.DECIMAL128).add(abd,MathContext.DECIMAL128);
}
System.out.println(abd);
System.out.println(cbd);

This gives:

abd = 3.166049846031012773846494375835059E+465752
cbd = 3.166050156931013454758413539958330E+465752

This is approximately correct, after all the result of a should be:

Which is approximately correct according to Wolfram Alpha.

Furthermore I would advice to use a for and not a while if it is a for loop. Since while tends to create another type of infinity: an infinite loop ;).

Answer 2

Yes, the only thing which you should use here is BigDecimal class. It'll easily handle that complex value without burdening you.

The maximum supported double value is only around 1.7 * 10^ 308 as given by Double.MAX_VALUE specified for Java.