Java: Dealing with Exponentiation

Question

I have a problem with this program where I have to calculate the value of base^expo, and the base is a real number whereas the exponent is an integer. With (95.123)^12 I'm expecting 548815620517731830194541.899025343415715973535967221869852721, but my program produces 548815620517732160000000.000000, which is wrong. Please suggest a better approach.

// declare variables and read values
double myBase = scan.nextDouble(); 
int myExponent = scan.nextInt();

// display result
System.out.printf("%f", Math.pow(myBase, myExponent));

I recommend you having a look at "What Every Computer Scientist Should Know About Floating-Point Arithmetic" http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html — ale64bit, Jan 02 '15 at 19:13
As others say, use `BigDecimal`. If you have many such operations to perform and you seek better performance, you may want to have a look at apfloat as well. — fge, Jan 02 '15 at 19:21

Pierfrancesco Soffritti · Answer 1 · 2015-01-02T19:22:28.113

5

try to use BigDecimal

example:

BigDecimal base = new BigDecimal("some number");
int exponent = ..;

BigDecimal result = base.pow(exponent);

edited Jan 02 '15 at 19:22

answered Jan 02 '15 at 19:09

Pierfrancesco Soffritti

1,678
1
18
22

score 1 · Answer 2 · answered Jan 02 '15 at 19:18

The double type in Java is a IEEE double and has only 53 bits of precision. Because of this, you will get the closest double value possible to the true answer.

Because of the large magnitude of the result, the closest double values are quite a bit more than 1 apart. You can verify this by calling the Math.ulp method (unit in the last place).

System.out.println(Math.ulp(Math.pow(myBase, myExponent)));

This outputs:

6.7108864E7

Even with the precision, consecutive double values are 67 million apart.

As an alternative, you can use BigDecimals instead, e.g.

BigDecimal myBase= new BigDecimal(scan.next());
int myExponent= scan.nextInt();

//displays result
System.out.println(myBase.pow(myExponent));

Output:

548815620517731830194541.899025343415715973535967221869852721

Note that pow here takes an int, not another BigDecimal.

Java: Dealing with Exponentiation

2 Answers2