JS floating point causing incorrect rounding

Question

I have what may be an edge case scenario. When trying to round the value 4.015 to 2 decimal places, I always end up with 4.01 instead of the expected 4.02. This happens consistently for all numbers with .015 as the decimal portion.

I round using a fairly common method in JS:

val = Math.round(val * 100) / 100;

I think the problem starts when multiplying by 100. The floating point inaccuracy causes this value to be rounded down rather than up.

var a = 4.015,                // 4.015
    mult = a * 100,           // 401.49999999999994 (the issue)
    round = Math.round(mult), // 401
    result = round / 100;     // 4.01 (expected 4.02)

Fiddle: http://jsfiddle.net/eVXRL/

This problem does not happen if I try to round 4.025. The expected value of 4.03 does return; it's only an issue with .015 (so far).

Is there a way to elegantly resolve this? There is of course the hack of just looking for .015 and handling that case one-off, but that just seems wrong!

Answer 1

I ended up using math.js to do mathematical operations and that solved all my floating point issues.

The advantage of this lib was that there was no need to instantiate any sort of Big Decimal object (even though the lib does support BigDecimal). It was just as simple as replacing Math with math and passing the precision.

Answer 2

Floating point numbers are not real numbers, they are floating point numbers.

There are infinite number of real numbers, but only finite number of bits to represent them, thus sometimes, there must be some rounding error if the exact number you want cannot be represented in the floating point system.

Thus, when dealing with floating point numbers, you must take into consideration, that you won't have the exact same number you had in mind.
If you need an exact number, you should use a library that gives you better precision, usually it will be using a fixed point, and/or symblic representation

More information can be found in the wikipedia page, and in this (a bit complex, but important) article: What Every Computer Scientist Should Know About Floating-Point Arithmetic