Math in Java - different results with different objects

Question

I'm getting some strange results doing a calculation for the application I'm working on and I thought someone on here might be able to help figure out what's going on.

The requirements for this particular calculation state that the calculation should look like this:

A and B are known

A * B = C

For this particular calculation

A = 0.0410
B = 123456789010

Here are the results I'm seeing:

Calculator:

0.0410 * 123456789010 = 5061728349.41

Java:

B is a double:

0.0410f * 123456789010d = 5.061728489223363E9 = 5061728489.223363

B is a long:

0.0410f * 123456789010l = 5.0617288E9 

The loss of precision is of less importance to me (I only need 9 digits of precision anyway) than the difference in the 10s and 1s spot. Why does doing the calculation using the double give me the "wrong" result?

Incidentally, I tried doing the calculation using BigDecimal and got the same result as I did using a double.

Answer 1

The various type conversions that happen are specified by the JLS #5.6.2. In your case (extract):

• If either operand is of type double, the other is converted to double.
• Otherwise, if either operand is of type float, the other is converted to float.

In 0.0410f * 123456789010d = 506172848.9223363, 0.0410f is first converted to a double which is not necessarily equal to 0.0410d. Actually you can try it and see that is is not:

    double d1 = 0.041d;
    double d2 = 0.041f;
    System.out.println(new BigDecimal(d1));
    System.out.println(new BigDecimal(d2));

outputs:

0.041000000000000001720845688168992637656629085540771484375
0.041000001132488250732421875

In your next example:

0.0410f * 123456789010L = 506172832

the long is converted to a float, which you can verify with this example:

    float f1 = 0.0410f;
    float f2 = 123456789010L;
    System.out.println(new BigDecimal(f1)); // 0.041000001132488250732421875
    System.out.println(new BigDecimal(f2)); // 123456790528
    System.out.println(new BigDecimal(0.0410f * 123456789010L)); // 5061728768
    System.out.println(new BigDecimal(f1 * f2)); // 5061728768

As for the precision of float / double operations in general, check this question.

Finally, if you use a BigDecimal, you get the correct answer:

    BigDecimal a = new BigDecimal("0.041");
    BigDecimal b = new BigDecimal("123456789010");
    System.out.println(a.multiply(b)); // outputs 5061728349.410