# [Rd] Floating point maths in R

From: Tom McCallum <tom.mccallum_at_levelelimited.com>
Date: Sat 09 Dec 2006 - 13:29:01 GMT

Hi,

> (2.34567 - 2.00000) == 0.34567 <------- should be true
[1] FALSE

> (2.23-2.00) == 0.23 <------- should be true
[1] FALSE

> 4-2==2
[1] TRUE

> (4-2)==2
[1] TRUE

> (4.0-2)==2
[1] TRUE

> (4.0-2.0)==2
[1] TRUE

> (4.0-2.0)==2.0
[1] TRUE

> (4.2-2.2)==2.0
[1] TRUE

> (4.20-2.20)==2.00
[1] TRUE

> (4.23-2.23)==2.00 <------- should be true
[1] FALSE

> (4.230-2.230)==2.000 <------- should be true
[1] FALSE

> (4.230-2.230)==2.00 <------- should be true
[1] FALSE

> (4.230-2.23)==2.00 <------- should be true
[1] FALSE
I have tried these on both 64 and 32-bit machines. Surely R should be able to do maths to 2 decimal places and be able to test these simple expressions? The problem occurs as in the 16th decimal place junk is being placed by the FPU it seems. I have also tried:

> (4.2300000000000000-2.230000000000000) == 2
[1] FALSE

> a <- (4.2300000000000000-2.230000000000000) > a == 2
[1] FALSE

```> (4.2300000000000000-2.230000000000000) == 2.0000000000000000
```

[1] FALSE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000004 <-- correct > when add 16th decimal place to 4
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.00000000000000043 <-- any > values after the 16th decimal place mean that the expression is true
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.000000000000000435
[1] TRUE
Also :

> (4.2300000000000000-2.230000000000000) == 2.0000000000000001
[1] FALSE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000003
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000004
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000005
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000006 <-- 3,5 I > can understand being true if rounding occurring, but 6?
[1] TRUE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000007
[1] FALSE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000008
[1] FALSE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000009
[1] FALSE

> (4.2300000000000000-2.230000000000000) == 2.0000000000000010

This is an example of junk being added in the FPU > formatC(a, digits=20)
[1] "2.0000000000000004441"

I don't know if this is just a formatC error when using more than 16 decimal places or if this junk is what is stopping the equality from being true:

> formatC(a, digits=16)
[1] " 2"

> formatC(a, digits=17) <-- 16 decimal places, 17 significant figures > shown
[1] "2.0000000000000004" <-- the problem is the 4 at the end

Obviously the bytes are divided between the exponent and mantissa in 16-16bit share it seems, but this doesn't account for the 16th decimal place behaviour does it?

If any one has a work around or reason why this should occur it would be useful to know.

what I would like is to be able to do sums such as (2.3456 - 2 ) == 0.3456 and get a sensible answer - any suggestions? Currently the only way is for formatC the expression to a known number of decimal places - is there a better way?

Many thanks

Tom

```--
Dr. Thomas McCallum
Systems Architect,
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Work  +44 (0) 131 472 4813
Fax:  +44 (0) 131 472 4719
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Email: tom@levelelimited.com

Level E is a limited company incorporated in Scotland. The c...{{dropped}}

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Received on Sun Dec 10 07:32:09 2006

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