Also note that we see the same thing in Ruby:
irb(main):001:0> 100*(23/40)
=> 0
irb(main):002:0> 100.0*(23.0/40.0)
=> 57.49999999999999
irb(main):003:0> (100.0*23.0)/40.0
=> 57.5
and in C:
hpages@latitude:~$ cat test.c
#include <stdio.h>
main() {
printf("%.15f\n", 100.0 * (23.0 / 40.0));
printf("%.15f\n", (100.0 * 23.0) / 40.0);
}
hpages@latitude:~$ gcc test.c
hpages@latitude:~$ ./a.out
57.499999999999993
57.500000000000000
These rounding errors are intrinsically related to how computers
do floating point arithmetic.
H.
On 04/20/2017 03:34 PM, Michael Hannon wrote:
I might add that things that *look* like integers in R are not really
integers, unless you explicitly label them as such:
str(20)
num 20
str(20.5)
num 20.5
str(20L)
int 20
I think that Python 2 will do integer arithmetic on things that look
like integers:
$ python2
.
.
.
30 / 20
1
But that behavior has changed in Python 3:
$ python3
.
.
.
30 / 20
1.5
-- Mike
On Thu, Apr 20, 2017 at 3:20 PM, Nordlund, Dan (DSHS/RDA)
<nord...@dshs.wa.gov> wrote:
This is FAQ 7.31. It is not a bug, it is the unavoidable problem of accurately
representing floating point numbers with a finite number of bits of precision.
Look at the following:
a <- 100*(23/40)
b <- (100*23)/40
print(a,digits=20)
[1] 57.499999999999993
print(b,digits=20)
[1] 57.5
Your example with all.equal evaluates TRUE because all.equal uses a 'fuzz
factor'. From the all.equal man page
"all.equal(x, y) is a utility to compare R objects x and y testing 'near
equality'."
Hope this is helpful,
Dan
Daniel Nordlund, PhD
Research and Data Analysis Division
Services & Enterprise Support Administration
Washington State Department of Social and Health Services
-----Original Message-----
From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Paul
Johnson
Sent: Thursday, April 20, 2017 2:56 PM
To: R-help
Subject: [R] Interesting quirk with fractions and rounding
Hello, R friends
My student unearthed this quirk that might interest you.
I wondered if this might be a bug in the R interpreter. If not a bug,
it certainly stands as a good example of the dangers of floating point
numbers in computing.
What do you think?
100*(23/40)
[1] 57.5
(100*23)/40
[1] 57.5
round(100*(23/40))
[1] 57
round((100*23)/40)
[1] 58
The result in the 2 rounds should be the same, I think. Clearly some
digital number devil is at work. I *guess* that when you put in whole
numbers and group them like this (100*23), the interpreter does
integer math, but if you group (23/40), you force a fractional
division and a floating point number. The results from the first 2
calculations are not actually 57.5, they just appear that way.
Before you close the books, look at this:
aa <- 100*(23/40)
bb <- (100*23)/40
all.equal(aa,bb)
[1] TRUE
round(aa)
[1] 57
round(bb)
[1] 58
I'm putting this one in my collection of "difficult to understand"
numerical calculations.
If you have seen this before, I'm sorry to waste your time.
pj
--
Paul E. Johnson
https://urldefense.proofpoint.com/v2/url?u=http-3A__pj.freefaculty.org&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=mCvk8xBulYqnlArSRFzabdeCvvmH9UFJ0kxrxsNC0SE&e=
Director, Center for Research Methods and Data Analysis
https://urldefense.proofpoint.com/v2/url?u=http-3A__crmda.ku.edu&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=rtQq4X4vty_dsRAWEsD_-ZZh7UDdnlLKyBllAl3i5eY&e=
To write to me directly, please address me at pauljohn at ku.edu.
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
PLEASE do read the posting guide
https://urldefense.proofpoint.com/v2/url?u=http-3A__www.R-2Dproject.org_posting-2D&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=ZmY65_nfgCDuDwZFHVL0QcFn1ttVyyj8UY4XADgtDm0&e=
guide.html
and provide commented, minimal, self-contained, reproducible code.
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
PLEASE do read the posting guide
https://urldefense.proofpoint.com/v2/url?u=http-3A__www.R-2Dproject.org_posting-2Dguide.html&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=0CaeomvoF9oO4LmfDFSjbfMQn4TufgUA-mqqIP7VFno&e=
and provide commented, minimal, self-contained, reproducible code.
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://urldefense.proofpoint.com/v2/url?u=https-3A__stat.ethz.ch_mailman_listinfo_r-2Dhelp&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=efyHNH41uiy_mo_2RYV1aQU3sMi2yKoAfK7LMdoK5eM&e=
PLEASE do read the posting guide
https://urldefense.proofpoint.com/v2/url?u=http-3A__www.R-2Dproject.org_posting-2Dguide.html&d=DwICAg&c=eRAMFD45gAfqt84VtBcfhQ&r=BK7q3XeAvimeWdGbWY_wJYbW0WYiZvSXAJJKaaPhzWA&m=h2uDuHofumYjJ48NvOaART10-esHowpTtp37cGtD3yQ&s=0CaeomvoF9oO4LmfDFSjbfMQn4TufgUA-mqqIP7VFno&e=
and provide commented, minimal, self-contained, reproducible code.
--
Hervé Pagès
Program in Computational Biology
Division of Public Health Sciences
Fred Hutchinson Cancer Research Center
1100 Fairview Ave. N, M1-B514
P.O. Box 19024
Seattle, WA 98109-1024
E-mail: hpa...@fredhutch.org
Phone: (206) 667-5791
Fax: (206) 667-1319
______________________________________________
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
