Re: [R] Exponentiate very large numbers

Albyn Jones Tue, 05 Feb 2013 10:50:33 -0800

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

So the answer is exp(1347)*(1-exp(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))), avoidingoverflow

        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-boun...@r-project.org[mailto:r-help-boun...@r-project.org] On Behalf

Of francesca casalino
Sent: Monday, February 04, 2013 8:00 AM
To: r-help@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.casal...@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) orlog(b)> values I get Inf. Are there any tricks I can use to get a realresult

> 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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and provide commented, minimal, self-contained, reproducible code.


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Re: [R] Exponentiate very large numbers

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