Python math accuracy

Question

I have try this simple math operation in python

>>> math.floor(8.2-0.21)
7.0
>>> math.floor(8.21-0.2)
8.0
>>> math.floor(8.2-0.2)
7.0

The third one should return 8 but it is return 7?!

UPDATE

i have try it in PHP, ruby and JAVA and i have got the same results.

Update 2 i don't know why the question get many votes down !!

You edited it in after everyone answered you, but your third example is floating-point error. — roippi, Oct 21 '13 at 21:11
[Read this](http://docs.python.org/2/tutorial/floatingpoint.html) and use the `decimal` module instead if you want to avoid these shallow surprises. — Tim Peters, Oct 21 '13 at 21:17
You're using `round()` instead of `floor()` in your Java/Ruby tests... — arshajii, Oct 21 '13 at 21:26
All the down votes are kinda harsh IMHO. +1 from me (even tho this is a common question...) — the wolf, Oct 22 '13 at 00:32

score 8 · Accepted Answer · answered Oct 21 '13 at 21:42

The languages you cite use either IEEE-754 64-bit binary floating-point or use the floating-point of the underlying hardware, which is likely IEEE-754 binary floating-point.

In IEEE-754 64-bit binary floating-point, the nearest representable value to 8.2 is 8.199999999999999289457264239899814128875732421875, and the nearest representable value to .2 is 0.200000000000000011102230246251565404236316680908203125.

So, when you write 8.2 - 0.2, what actually happens is that 0.200000000000000011102230246251565404236316680908203125 is subtracted from 8.199999999999999289457264239899814128875732421875. The result is a value slightly under 8, and the floor of a value slightly under 8 is 7.

The lesson here is that floating-point arithmetic is generally approximate, so you must be careful when evaluating functions with discontinuities (like floor) or steep slopes. You must either design your code to accept results that may cross the discontinuities or you must design your calculations to avoid errors that cross the discontinuities.

arshajii · Answer 2 · 2013-10-21T21:53:24.957

Your first two examples are to be expected:

8.2 - 0.21 is 7.99. Floor of 7.99 is 7, and that's what is returned. Remember that floor(x) is the greatest integer less than or equal to x. 8 is greater than 7.99, so it can't possibly be returned. 7, on the other hand, meets this requirement.
8.21 - 0.2 is 8.01. Floor of 8.01 is 8 -- no magic here.

>>> math.floor(8.2-0.2)
7.0

Now this is more interesting. It has to do with the fact that 8.2 and 0.2 cannot be exactly represented with floats, so the result of the computation is perhaps not what you might have thought:

>>> 8.2 - 0.2
7.999999999999999

Again, floor() is working as documented.

You can see this for yourself using decimal:

>> from decimal import Decimal
>>> Decimal(0.2)
Decimal('0.200000000000000011102230246251565404236316680908203125')
>>> Decimal(8.2)
Decimal('8.199999999999999289457264239899814128875732421875')

Relevant: What Every Computer Scientist Should Know About Floating-Point Arithmetic

@EricPostpischil Nevermind, you are correct -- I was thinking of 0.8. The error stems from `8.2` and `0.2` themselves. I'll update the answer. — arshajii, Oct 21 '13 at 21:51

score 0 · Answer 3 · answered Oct 21 '13 at 21:09

0

Why should it be 8? Floor functions return the nearest integer rounded down, so those two examples are correct.

8.2 - 0.21 = 7.99, which rounded down is 7.

8.21 - 0.2 = 8.01, which rounded down is 8.

answered Oct 21 '13 at 21:09

zo7

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score 0 · Answer 4 · answered Oct 21 '13 at 21:40

0

>>> a=0.2
>>> a
0.20000000000000001
>>> b = 8.2
>>> b
8.1999999999999993
>>> b-a
7.9999999999999991
>>> math.floor(b-a)
7.0

Due to floating point inaccuracies

answered Oct 21 '13 at 21:40

Steve Barnes

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Python math accuracy

4 Answers4