gsub speed vs pattern length

Question

I've been using gsub extensively lately, and I noticed that short patterns run faster than long ones, which is not surprising. Here's a fully reproducible code:

library(microbenchmark)
set.seed(12345)
n = 0
rpt = seq(20, 1461, 20)
msecFF = numeric(length(rpt))
msecFT = numeric(length(rpt))
inp = rep("aaaaaaaaaa",15000)

for (i in rpt) {
  n = n + 1
  print(n)
  patt = paste(rep("a", rpt[n]), collapse = "")
  #time = microbenchmark(func(count[1:10000,12], patt, "b"), times = 10)
  timeFF = microbenchmark(gsub(patt, "b", inp, fixed=F), times = 10)
  msecFF[n] = mean(timeFF$time)/1000000.

  timeFT = microbenchmark(gsub(patt, "b", inp, fixed=T), times = 10)
  msecFT[n] = mean(timeFT$time)/1000000.
}

library(ggplot2)
library(grid)
library(gridExtra)

axis(1,at=seq(0,1000,200),labels=T)

p1 = qplot(rpt, msecFT, xlab="pattern length, characters", ylab="time, msec",main="fixed = TRUE" )
p2 = qplot(rpt, msecFF, xlab="pattern length, characters", ylab="time, msec",main="fixed = FALSE")
grid.arrange(p1, p2, nrow = 2)

As you see, I'm looking for a pattern that contains a replicated rpt[n] times. The slope is positive, as expected. However, I noticed a kink at 300 characters with fixed=T and 600 characters with fixed=F and then the slope seems to be approximately as before (see plot below). I suppose, it is due to memory, object size, etc. I also noticed that the longest allowed pattern is 1463 symbols, with object size of 1552 bytes.

Can someone explain the kink better and why at 300 and 600 characters?

Added: it is worth mentioning, that most of my patterns are 5-10 characters long, which gives me on my real data (not the mock-up inp in the example above) the following timing.

gsub, fixed = TRUE: ~50 msec per one pattern
gsub, fixed = FALSE: ~190 msec per one pattern
stringi, fixed = FALSE: ~55 msec per one pattern
gsub, fixed = FALSE, perl = TRUE: ~95 msec per one pattern

(I have 4k patterns, so total timing of my module is roughly 200 sec, which is exactly 0.05 x 4000 with gsub and fixed = TRUE. It is the fastest method for my data and patterns)

Answer 1

The kinks might be related to the bits required to hold patterns of that length.

There is another solution that scales much better, use the repetition operator {} to specify how many repeats you want to find. In order to find more than 255 (8 bit integer max) you'll have to specify perl = TRUE.

patt2 <- paste0('a{',rpt[n],'}')
timeRF <- microbenchmark(gsub(patt2, "b", inp, perl = T), times = 10)

I get speeds of around 2.1 ms per search with no penalty for pattern length. That's about 8x faster than fixed = FALSE for small pattern lengths and about 60x faster for large pattern lengths.