Question

How could I speed up the following while loop?

count <- function(start, stepsize, threshold) {
  i <- 1;
  while ( start <= threshold ) {
    start <- stepsize*i+start;
    i <- i+1;
  }
  return( i-1 );
}

system.time(count(1, 0.004, 1e10))

Answer 1

Working out the sums as in the comment above:

## start + S*n*(n-1)/2 = T
## (T-start)*2/S = n*(n-1)
## n*(n-1) - (T-start)*2/S = 0

A function to solve this quadratic equation:

ff <- function(start,stepsize,threshold) {
  C <- (threshold-start)*2/stepsize
  ceiling((-1 + sqrt(1+4*C))/2)
}

This solution takes essentially no time …

> system.time(cc <- count(1, 0.004, 1e10))
   user  system elapsed 
  5.372   0.056   5.642 
> system.time(cc2 <- ff(1, 0.004, 1e10))
   user  system elapsed 
      0       0       0 
> cc2
[1] 2236068
> cc
[1] 2236068

The question is whether this generalizes to the exact problem you need to solve.