Controlling number of decimal digits in print output in R

Question

There is an option in R to get control over digit display. For example:

options(digits=10)

is supposed to give the calculation results in 10 digits till the end of R session. In the help file of R, the definition for digits parameter is as follows:

digits: controls the number of digits to print when printing numeric values. It is a suggestion only. Valid values are 1...22 with default 7

So, it says this is a suggestion only. What if I like to always display 10 digits, not more or less?

My second question is, what if I like to display more than 22 digits, i.e. for more precise calculations like 100 digits? Is it possible with base R, or do I need an additional package/function for that?

Edit: Thanks to jmoy's suggestion, I tried sprintf("%.100f",pi) and it gave

[1] "3.1415926535897931159979634685441851615905761718750000000000000000000000000000000000000000000000000000"

which has 48 decimals. Is this the maximum limit R can handle?

Answer 1

The reason it is only a suggestion is that you could quite easily write a print function that ignored the options value. The built-in printing and formatting functions do use the options value as a default.

As to the second question, since R uses finite precision arithmetic, your answers aren't accurate beyond 15 or 16 decimal places, so in general, more aren't required. The gmp and rcdd packages deal with multiple precision arithmetic (via an interace to the gmp library), but this is mostly related to big integers rather than more decimal places for your doubles.

Mathematica or Maple will allow you to give as many decimal places as your heart desires.

EDIT:
It might be useful to think about the difference between decimal places and significant figures. If you are doing statistical tests that rely on differences beyond the 15th significant figure, then your analysis is almost certainly junk.

On the other hand, if you are just dealing with very small numbers, that is less of a problem, since R can handle number as small as .Machine$double.xmin (usually 2e-308).

Compare these two analyses.

x1 <- rnorm(50, 1, 1e-15)
y1 <- rnorm(50, 1 + 1e-15, 1e-15)
t.test(x1, y1)  #Should throw an error

x2 <- rnorm(50, 0, 1e-15)
y2 <- rnorm(50, 1e-15, 1e-15)
t.test(x2, y2)  #ok

In the first case, differences between numbers only occur after many significant figures, so the data are "nearly constant". In the second case, Although the size of the differences between numbers are the same, compared to the magnitude of the numbers themselves they are large.

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As mentioned by e3bo, you can use multiple-precision floating point numbers using the Rmpfr package.

mpfr("3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825")

These are slower and more memory intensive to use than regular (double precision) numeric vectors, but can be useful if you have a poorly conditioned problem or unstable algorithm.

Answer 2

If you are producing the entire output yourself, you can use sprintf(), e.g.

> sprintf("%.10f",0.25)
[1] "0.2500000000"

specifies that you want to format a floating point number with ten decimal points (in %.10f the f is for float and the .10 specifies ten decimal points).

I don't know of any way of forcing R's higher level functions to print an exact number of digits.

Displaying 100 digits does not make sense if you are printing R's usual numbers, since the best accuracy you can get using 64-bit doubles is around 16 decimal digits (look at .Machine$double.eps on your system). The remaining digits will just be junk.