nafill new type: approx

Start with the existing nafill entry point and its current types, then review how the examples use approx() and zoo::na.approx() for comparison. Define the expected behavior for the proposed approx type, including the missing-value runs shown in the issue, and validate the result against the supplied examples and performance benchmark.

This is a FR. Also I apologize ahead of time if this is not an appropriate post for here.

From this StackOverflow post:

library(data.table)
dt <- data.table(dist = c(31091.33, NA, 31100.00, 31103.27, NA, NA, NA, NA, 31124.98))
dt[, time := .I]

##       dist time
##1: 31091.33    1
##2:       NA    2
##3: 31100.00    3
##4: 31103.27    4
##5:       NA    5
##6:       NA    6
##7:       NA    7
##8:       NA    8
##9: 31124.98    9

OP wants to do a linear interpolation to fill in the NA values. The most simple solution is to use base approx() or zoo:na.approx() per user dww:

copy(dt)[, dist := zoo::na.approx(dist)][]
copy(dt)[, dist := approx(.I, dist, .I)$y][]

#       dist time
#1: 31091.33    1
#2: 31095.67    2
#3: 31100.00    3
#4: 31103.27    4
#5: 31107.61    5
#6: 31111.95    6
#7: 31116.30    7
#8: 31120.64    8
#9: 31124.98    9

The current nafill types are: c("const", "locf", "nocb") - an "approx" type would be helpful. I wrote an Rcpp implementation to show that there is room for improvement as it's ~10 times faster than the base method which is already a C based method:

#data per @chinsoon12
nr <- 1e7
nNA <- nr/2
DT <- data.table(time=1:nr, dist=replace(rnorm(nr), sample(1:nr, nNA), NA_real_))

bench::mark(
  rcpp_appr = rcpp_approx(DT[['dist']]),
  base_approx = DT[, approx(.I, dist, .I)$y],
  zoo_approx = zoo::na.approx(DT[['dist']]),
  time_unit = 's'
)

# A tibble: 3 x 13 (in seconds)
  expression    min median `itr/sec` mem_alloc
  <bch:expr>  <dbl>  <dbl>     <dbl> <bch:byt>
1 rcpp_appr   0.126  0.132     7.08       76MB
2 base_approx 1.34   1.34      0.745     617MB
3 zoo_approx  2.22   2.22      0.450    1630MB ##manually changed from GB to MB

# this is the rcpp code
Rcpp::sourceCpp(code = '
#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
NumericVector rcpp_approx(NumericVector y) {
  double start = 0, slope = 0;
  int count = 0;

  NumericVector y1 = clone(y); //added to not update-by-reference

  for(int i = 0; i < y1.size(); ++i){
    if (NumericVector::is_na(y1[i])){
      count++;
    } else {
      if (count != 0) {
        start = y1[i - (count+1)];
        slope = (y1[i] - start) / (count + 1);
        for (int j = 0; j < count; j++){
          y1[i-(count-j)] = start + slope * (j + 1);
        }
      count = 0;
      } 
    }
  }
return(y1);
}
')

Thank you for your consideration.