# [R] Log plus one transformation in R

John Sorkin jsorkin at grecc.umaryland.edu
Tue Dec 13 18:18:49 CET 2016

```Duncan,
Thank you. You are correct no one answered my question , despite the fact that several people reply to my email, until you replied. Your exclamation is quite clear and I thank you for your kindness. I did not pursue my question any further as I was concerned that I would be flamed.
John

> John David Sorkin M.D., Ph.D.
> Professor of Medicine
> Chief, Biostatistics and Informatics
> University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine
> Baltimore VA Medical Center
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> (Phone) 410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)

> On Dec 13, 2016, at 12:12 PM, Duncan Murdoch <murdoch.duncan at gmail.com> wrote:
>
>> On 12/12/2016 12:26 PM, John Sorkin wrote:
>> David,
>>
>> I did read the help page. All it says is
>> log1p(x) computes log(1+x) accurately also for |x| << 1 (and less
>> accurately when x is approximately -1).
>> This gives me pause. Does it mean that log(x) does not give accurate
>> results? If log1p gives more accurate values than log, why is the log
>> function not written to use the more accurate computation performed by
>> log1p.
>
> I don't think anyone has directly answered these questions.  The problem
> isn't with log(), it's with the representation of floating point numbers
> in R.  The log of 1 + 10^(-100) is very close to 10^(-100), but since 1
> + 1e-100 evaluates to 1 (we only keep 15 or 16 digits of precision),
> log(1 + 1e-100) will come out as zero.  On the other hand, log1p(1e-100)
> evaluates correctly to 1e-100.
>
>>  I don't believe I can look directly at the code for log and
>> log1p,
>
> R is open source, so you could, but those are likely coming from system
> libraries, so it isn't easy to see how the approximations are being done.
>
> Duncan Murdoch
>>  so I need to rely on the kindness of others to explain the
>> differences between the computations performed by the functions. I guess
>> the test I ran, log1p(0.000001)/log(0.000001+1), did not have enough
>> precision to demonstrate a difference between the two functions.
>> John
>>
>>
>>
>> John David Sorkin M.D., Ph.D.
>> Professor of Medicine
>> Chief, Biostatistics and Informatics
>> University of Maryland School of Medicine Division of Gerontology and
>> Geriatric Medicine
>> Baltimore VA Medical Center
>> 10 North Greene Street
>> GRECC (BT/18/GR)
>> Baltimore, MD 21201-1524
>> (Phone) 410-605-7119
>> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>>>>> David Winsemius <dwinsemius at comcast.net> 12/12/16 12:05 PM >>>
>>
>>> On Dec 12, 2016, at 8:53 AM, John Sorkin <jsorkin at grecc.umaryland.edu>
>> wrote:
>>>
>>> At the risk of being flamed . . .
>>> What is the difference between log1p(x) and log(x+1)?
>>> The two methods appear to give the same results:
>>>> log1p(0.000001)/log(0.000001+1)
>>> [1] 1
>>> John
>>
>> Read the help page more carefully.
>>
>

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