Simple addition exposes Javascript engine floating point error

Question

While working on measurement.js, the joys of TDD helped me stumble upon a really strange (at least as i occurs to me) behaviour exposed in the javascript engines.

No matter if entered into the console or performed inside a script, this is what happens:

-1 + 0.85     --> -0.85               ✓  
-1 + 1        --> 0                   ✓   
-1 + 1 + -.15 --> 0.15                ✓
-1 + 1.15     --> 0.1499999999999999  ?!?

This is tested and reproduced exactly under following Browsers / OS's:

FF 24.0 (Debian 3.10)
Chrome 30.0.1599.114 (Debian 3.10)
Chrome 30.0.1599.101m (Win7SP1)
Internet Explorer 10.0.9200.16721 (Win7SP1)

As this is consistent throughout different vendors, i assume there must be a specific reason for this, so:

What is the reason for this?
What is the best practice to circumvent this behaviour, as it poses a problem for exact calculations with JS

Update:
Best lay-comprehensible explanation incl. answers and workarounds for multiple programming languages so far found at
http://floating-point-gui.de/ (thanx @RocketHazmat)

Not sure this is a duplicate as the OP is also asking the best practice to circumvent this behavior (however it should probably be worded differently then). — Jack, Oct 24 '13 at 20:56

score 0 · Answer 1 · answered Oct 24 '13 at 19:04

0

No duh. You try doing the math in base two.

Short answer: you can't do it. It's like trying to add 1/3 in decimal repeatedly. You get 0.333333, then 0.666666, then 0.99999... but shouldn't that last one be 3/3, in other words 1?

To avoid this problem, just use integers for everything, as much as possible.

answered Oct 24 '13 at 19:04

Niet the Dark Absol

320,036
81
464
592

+1, but `just use integers for everything, as much as possible` - was that a joke? Isn't the solution to use toFixed before presenting the results to the client? – Adam Rackis Oct 24 '13 at 19:06
1

"No duh. you try doing the math" - unhelpul, now i feel more stupid than before. "just use integers for everything" - so what you'd suggest as an integer representation of 1.15 ? – Philzen Oct 24 '13 at 19:07
1

@AdamRackis: That wasn't a joke. With money for example, do the math in "cents". Instead of doing `0.1+0.2`, do `10+20`, then convert to dollars later. `(10+20)/100 => 0.3` – gen_Eric Oct 24 '13 at 19:07
2

@Philzen: Times it by 100, do the math, then divide by 100. `(-100 + 115)/100 => 1.5`. Or use `toFixed`: `(-1 + 1.15).toFixed(2)`. – gen_Eric Oct 24 '13 at 19:11
@RocketHazmat - thx, that's heaps better and actually answers half of my question. I'll try to read through the referenced links and see if i can grasp why this isn't done internally anyway (i mean any cheap desktop calculator gets this addition right, shouldn't JS do it as well?) – Philzen Oct 24 '13 at 19:15
2

@Philzen: Check out this page: http://floating-point-gui.de/ It should explain it. – gen_Eric Oct 24 '13 at 19:16

score 0 · Answer 2 · answered Oct 24 '13 at 19:04

I think this is because of the problems inherent in representing some floating point numbers in binary.

Read this:- What Every Computer Scientist Should Know About Floating-Point Arithmetic.

Try to use toFixed to avoid your problem

Formats a number using fixed-point notation.

Simple addition exposes Javascript engine floating point error

2 Answers2