# [R] How to handle large numbers?

Thomas Lumley tlumley at u.washington.edu
Wed Feb 11 12:05:20 CET 2009

```On Wed, 11 Feb 2009, Feng Li wrote:

> 1, Why both R and Matlab give 0*Inf==NaN? To my knowledge, it should be zero
> mathematically. Am I right?

No.  0*Inf is NaN according to the floating point arithmetic standards that R depends on.

It's true that 0*x==0 for all finite x, but it's also true that x*Inf==Inf for all non-zero x, and you can't preserve both of these with 0*Inf.

> 2, I need to calculate e.g. exp(a)/(exp(b)+c), where both a and b are very
> large numbers (>>1000, e.g a=1000, b=1007, and c=5). R gives me NaN when I
> use the following command:
>
>> exp(1000)/(exp(1007)+5)
>  NaN
>
> I am pretty sure this should be close to zero.

No. It should be close to 1. Try  1000/(1000+5) for a simpler example.

> My question is whether there
> is a general way to solve this kind of question or should I do some settings
> before computing?
>

exp(1000)/(exp(1007)+5) is 1/(exp(7)+5*exp(-1000)), which is the same as 1/exp(7) to more than 400 digits accuracy.

-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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