Reducing Precision in Doubles in R

Question

I\'m looking for a way to consistently ignore small differences between floating point numbers in R (these are double precision floating points as per IEC 60559), by using b

Answer 1

There is no general answer for how much a result computed with floating-point may differ from the exact mathematical result. In general, the final error of a sequence of computations can range from zero to infinity (and may also produce Not-a-Number results when there is an exactly mathematical result or may produce a numeric result when there is no defined mathematical result). Therefore, determining what tolerance to use to classify whether two computed results are equal or not requires a problem-specific solution: One must analyze the calculations and numbers involved in the specific problem and determine bounds on the possible error or weigh the specific advantages and disadvantages of accepting incorrect classifications.

The study of errors that result in numerical computation is numerical analysis. It is a broad field addressed by many books. No simple answer exists.

In simple situations, it may be possible to determine bounds on the errors and to show that these bounds are less than the differences between results that are known to be different. In other words, given a computation that ideally would produce results a and b but actually produces a and b, it might be possible to show that there is some bound E on the error such that |a − b| < E if and only if a equals b. However, it is not possible to answer this question without knowing what computations are performed and, possibly, knowing what the domain of input values is.

Answer 2

One possible solution is to use signif, a function related to round and included in the same help file. The help file from ?signif, says

signif rounds the values in its first argument to the specified number of significant digits.

Whereas

round rounds the values in its first argument to the specified number of decimal places (default 0).

So it appears that signif may be more closely related to your problem.

Answer 3

Warning: this is not an direct answer to the question.

I find the following two functions useful. They allow me to compare doubles to a given degree of precision.

are.equal <- function(x, y, tol = .Machine$double.eps^0.5) abs(x - y) < tol
is.zero <- function(x, tol = .Machine$double.eps^0.5) abs(x) < tol

are.equal(1.45 - 0.55, 2.45 - 1.55)
#[1] TRUE

is.zero(1.45 - 0.55 - (2.45 - 1.55))
#[1] TRUE