Calculating how many increments larger one value is compared to another

I have some incremental numerical data that has a specific range of values, where all increments is the double of the previous value, e.g. 0.064, 0.128, 0.256, 0.512, 1.024 ...
I want to calculate how many increments higher a specific value is to another. Based on this value I want to define that if this incremental change is equal to or larger than 3, the test value is TRUE. I cannot base this directly on the numerical value, as this will not reflect the incremental changes, e.g. the value 64 here would be 8 increments higher than 0.25, and not 256, as it would be if the actual numeric value was used.

library(dplyr)

testdata <- data.frame(
  var1 = c(0.25, 0.5, 2, 64, 32),
  var2 = c(0.064, 64, 32, 16, 0.128)
)



testdata %>%
  mutate(
    test = case_when(
      var1/var2 >= 3 ~ TRUE,
      TRUE ~ FALSE
    )
  )

Any ideas on how this could be done?

>Solution :

What you want is the base 2 logarithm of the division between your two numbers. For instance, 64 / 0.25 = 256 = 2^8.
In R, you can use log to do that:

f <- function(x1, x2) log(x1 / x2, base = 2)
f(64, 0.25)
#[1] 8

With your data:

transform(testdata, test = f(var1, var2) >= 3)
#    var1   var2  test
# 1  0.25  0.064 FALSE
# 2  0.50 64.000 FALSE
# 3  2.00 32.000 FALSE
# 4 64.00 16.000 FALSE
# 5 32.00  0.128  TRUE