# [R] Exponentiate very large numbers

Albyn Jones jones at reed.edu
Tue Feb 5 19:48:35 CET 2013

```I stayed out of this one thinking it was probably a homework exercise.
After others have responded, I'll go ahead with my gloss on
Bill's function...

The specific problem is really of the form

exp(a) - exp(a+eps) = exp(a)*(1-exp(eps))

So even though we can't compute exp(1347), we can
compute 1-exp(eps) for eps of the desired size.
The given eps was

> 1351+log(.1) -1347
[1] 1.697415

and as Bill noted, you can compute the log
of the absolute value of that quantity...

> 1347 + log(abs(1-exp(1.697415)))
[1] 1348.495

albyn

On 2013-02-05 10:01, William Dunlap wrote:
>> Are there any tricks I can use to get a real result
>> for exp( ln(a) ) - exp( ln(0.1) + ln(b) ), either in logarithm or
>> exponential form?
>
>   log.a <- 1347
>   log.b <- 1351
>   f0 <- function(log.a, log.b) exp(log.a) - exp(log(0.1) + log.b)
>
> will not work because f0(1347,1351) is too big to represent as
> a double precision number (abs(result)>10^308)).
> If you are satisfied with computing log(result) you can do it
> with some helper function:
>    addOnLogScale <- function (e1, e2)
>    {
>        # log(exp(e1) + exp(e2))
>        small <- pmin(e1, e2)
>        big <- pmax(e1, e2)
>        log1p(exp(small - big)) + big
>    }
>    subtractOnLogScale <- function (e1, e2)
>    {
>       # log(abs(exp(e1) - exp(e2)))
>        small <- pmin(e1, e2)
>        big <- pmax(e1, e2)
>        structure(log1p(-exp(small - big)) + big, isPositive = e1 >
> e2)
>    }
>
> as
>
>    f1 <- function(log.a, log.b)  {
>         # log(abs(exp(log.a) - exp( log(0.1) + log.b))), avoiding
> overflow
>         subtractOnLogScale( log.a, log(0.1) + log.b )
>    }
>
> E.g.,
>   > f0(7,3)
>   [1] 1094.625
>   > exp(f1(7,3))
>   [1] 1094.625
>   attr(,"isPositive")
>   [1] TRUE
>
> With your log.a and log.b we get
>   > f1(1347, 1351)
>   [1] 1348.495
>   attr(,"isPositive")
>   [1] FALSE
>
> You can use the Rmpfr package to compute the results to any desired
> precision.
>
> Bill Dunlap
> Spotfire, TIBCO Software
> wdunlap tibco.com
>
>
>> -----Original Message-----
>> From: r-help-bounces at r-project.org
>> [mailto:r-help-bounces at r-project.org] On Behalf
>> Of francesca casalino
>> Sent: Monday, February 04, 2013 8:00 AM
>> To: r-help at r-project.org
>> Subject: Re: [R] Exponentiate very large numbers
>>
>> I am sorry I have confused you, the logs are all base e:
>>
>> ln(a) = 1347
>> ln(b) = 1351
>>
>> And I am trying to solve this expression:
>>
>> exp( ln(a) ) - exp( ln(0.1) + ln(b) )
>>
>>
>> Thank you.
>>
>> 2013/2/4 francesca casalino <francy.casalino at gmail.com>:
>> > Dear R experts,
>> >
>> > I have the logarithms of 2 values:
>> >
>> > log(a) = 1347
>> > log(b) = 1351
>> >
>> > And I am trying to solve this expression:
>> >
>> > exp( ln(a) ) - exp( ln(0.1) + ln(b) )
>> >
>> > But of course every time I try to exponentiate the log(a) or
>> log(b)
>> > values I get Inf. Are there any tricks I can use to get a real
>> result
>> > for exp( ln(a) ) - exp( ln(0.1) + ln(b) ), either in logarithm or
>> > exponential form?
>> >
>> >
>> > Thank you very much for the help
>>
>> ______________________________________________
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>
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