CODEWITHSUNDEEP
javamathdoublerounding
tomoswizzard
tomoswizzard

Reputation: 65

How do I avoid rounding errors with doubles?

I'm using Math.sin to calculate trigonometry in Java with 3 decimal precision. However when I calculate values that should result in an Integer I get 1.0000000002 instead of 1.

I have tried using 

 System.out.printf(Locale.ROOT, "%.3f ", v);

which does solve the problem of 1.000000002 turning into 1.000.

However when I calculate numbers that should result in 0 and instead get -1.8369701987210297E-16 and use

  System.out.printf(Locale.ROOT, "%.3f ", v);

prints out -0.000 when I need it to be 0.000.

Any ideas on how to get rid of that negative sign?

Upvotes: 0

Views: 1338

Answers (2)

Stephen C
Stephen C

Reputation: 719576

Lets start with this:

How do I avoid rounding errors with doubles?

Basically, you can't. They are inherent to numerical calculations using floating point types. Trust me ... or take the time to read this article:

In this case, the other thing that comes into play is that trigonometric functions are implemented by computing a finite number of steps of an infinite series with finite precision (i.e. floating point) arithmetic. The javadoc for the Math class leaves some "wiggle room" on the accuracy of the math functions. It is worth reading the javadocs to understand the expected error bounds.

Finally, if you are computing (for example) sin π/2 you need to consider how accurate your representation of π/2 is.

So what you should really be asking is how to deal with the rounding error that unavoidably happens.

In this case, you are asking is how to make it look like the user of your program as if there isn't any rounding error. There are two approaches to this:

  • Leave it alone! The rounding errors occur, so we should not lie to the users about it. It is better to educate them. (Honestly, this is high school maths, and even "the pointy haired boss" should understand that arithmetic is inexact.)

    Routines like printf do a pretty good job. And the -0.000 displayed in this case is actually a truthful answer. It means that the computed answer rounds to zero to 3 decimal places but is actually negative. This is not actually hard for someone with high school maths to understand. If you explain it.

  • Lie. Fake it. Put in some special case code to explicitly convert numbers between -0.0005 and zero to exactly zero. The code suggested in a comment

      System.out.printf(Locale.ROOT, "%.3f ", Math.round(v * 1000d) / 1000d);

    is another way to do the job. But the risk of this is that the lie could be dangerous in some circumstances. On the other hand, you could say that real mistake problem is displaying the numbers to 3 decimal places.

Upvotes: 4

Antoniossss
Antoniossss

Reputation: 32535

Depends on accuracy you need, you can multiply by X and divide by X where X is X=10^y and y is required floating poing precision.

Upvotes: 0

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