Floating Point Fun

surprise.md

Floating point unexpected results demo

Save for the last case (a poor try at showing floating point equality isn't reflexive), these examples seem specially surprising due to the base-conversion involved (since input is decimal and the floating point numbers used are binary), which hides the actual number of significant digits involved in each case.

Python

python
>>> 0.1 + 0.2 == 0.3
False
>>> 1E19*1E-20 == 1E-1
False
>>> 0.1+(0.2+0.3) == (0.1+0.2)+0.3
False
>>> 0.1+0.2+0.3 == 0.3+0.2+0.1
False
>>> 100*(0.1 + 0.2) == 100*0.1 + 100*0.2
False

>>> import numpy
>>> numpy.float64(0.0)/numpy.float64(0.0) == numpy.float64(0.0)/numpy.float64(0.0)
False

Ruby

irb
irb(main):001:0> 0.1 + 0.2 == 0.3
=> false
irb(main):002:0> 1E19*1E-20 == 1E-1
=> false
irb(main):003:0> 0.1+(0.2+0.3) == (0.1+0.2)+0.3
=> false
irb(main):004:0> 0.1+0.2+0.3 == 0.3+0.2+0.1
=> false
irb(main):005:0> 100*(0.1 + 0.2) == 100*0.1 + 100*0.2
=> false
irb(main):006:0> 0.0/0 == 0.0/0
=> false

Julia

julia> 0.1 + 0.2 == 0.3
false

julia> 1E19*1E-20 == 1E-1
false

julia> 0.1+(0.2+0.3) == (0.1+0.2)+0.3
false

julia> 0.1+0.2+0.3 == 0.3+0.2+0.1
false

julia> 100*(0.1 + 0.2) == 100*0.1 + 100*0.2
false

julia> 0.0/0 == 0.0/0
false

JavaScript (Node)

>  0.1 + 0.2 == 0.3
false
>  1E19*1E-20 == 1E-1
false
>  0.1+(0.2+0.3) == (0.1+0.2)+0.3
false
>  0.1+0.2+0.3 == 0.3+0.2+0.1
false
> 100*(0.1 + 0.2) == 100*0.1 + 100*0.2
false
> 0/0 == 0/0
false

R

> 0.1 + 0.2 == 0.3
[1] FALSE
> 1E19*1E-20 == 1E-1
[1] FALSE
> 0.1+(0.2+0.3) == (0.1+0.2)+0.3
[1] FALSE
> 0.1+0.2+0.3 == 0.3+0.2+0.1
[1] FALSE
> 100*(0.1 + 0.2) == 100*0.1 + 100*0.2
[1] FALSE
> 0.0/0 == 0.0/0
[1] NA
>