## Floating point arithmetic, again [Software]

❝ A colleague recently pointed to a strange behaviour in Excel (I have 2013, he has 2016, both give the same result here.

And I have 2000 (don’t laugh).

❝ Type =0.5-0.4-0.1: you'll get the expected result, 0.

Yep.

❝ Now type =(0.5-0.4-0.1): you'll get -2,77556E-17. What ? Ain't that supposed to be the same calculation ?

In principle, yes. Unless we could inspect the source code by M$, difficult to tell what happens with the brackets.

❝ Trying =0=0.5-0.4-0.1: the answer I got was FALSE. WTF, if the answer you get is 0 ? It's not a matter of number of decimals displayed: I tried to add more to the first result, or to switch to scientific notation, but still got 0.

OK, write in

`=0.5-0.4-0.1`

and in `=A1=0`

- What do you expect?

- What do you get?

Try in

`=16-8-4-2-2`

, in `=(16-8-4-2-2)`

, and in `=A1=B1`

. I bet it “works” as expected, since *these*numbers can be converted to binary digits without error.

What about ?

`options("digits" = 16)`

a <- 0.5-0.4-0.1

b <- (0.5-0.4-0.1)

a; b

[1] -2.775557561562891e-17

[1] -2.775557561562891e-17

identical(a, b)

[1] TRUE

c <- 16-8-4-2-2

d <- (16-8-4-2-2)

c; d

[1] 0

[1] 0

identical(c, d)

[1] TRUE

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮

Science Quotes

### Complete thread:

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- Nasty beast Ohlbe 2019-07-18 17:30
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- To round or not to round… ElMaestro 2019-07-20 19:59
- floating-point math is always more complex than you think it is mittyri 2019-07-20 22:43

- To round or not to round… ElMaestro 2019-07-20 19:59

- To round or not to round… Helmut 2019-07-20 12:53

- As designed ☺ ElMaestro 2019-07-20 09:08

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- Spreadsheet addiction Helmut 2019-07-18 16:12
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- Floating point arithmetic, again Ohlbe 2020-12-10 21:46
- Floating point arithmetic, again ElMaestro 2020-12-10 22:05

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- Float is float PharmCat 2020-12-18 20:53

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