Little useless-useful R functions – Finding substrings in number Pi

They say that number Pi holds all infinite possibilities, all the words, all the combinations. Well, easier said to be done. So let’s put this to a test.

This is my translational table.

We will do this in the following steps (for the word “eggs”):

1. Encode the word EGGS to numbers. E = 5, G = 7, G = 7 and S = 19. Together concatenated we get the string of 57719.
2. We store a veeery long string of PI number.
3. Start looking in PI number for substring of “57719”.

Well, let’s create a function to do just that

library(Rmpfr)

encode_a1z26 <- function(s) {
  s_clean <- gsub("[^A-Za-z]", "", toupper(s))
  if (nchar(s_clean) == 0) stop("No letters found in input.")
  letters_vec <- strsplit(s_clean, "", fixed = TRUE)[[1]]
  nums <- match(letters_vec, LETTERS)          
  paste0(nums, collapse = "")
}


pi_fraction_digits <- function(n_digits) {
  # bits of precison ~ n_digits * log2(10)
  precBits <- ceiling(n_digits * log2(10)) + 32L
  pi_mpfr <- Const("pi", precBits)                        
  s <- formatMpfr(pi_mpfr, digits = n_digits + 2L, scientific = FALSE, base = 10L)
  s <- gsub("\\.", "", s, fixed = FALSE)
  frac <- substr(s, 2L, n_digits + 1L)
  if (nchar(frac) < n_digits) {
    stop("To low precision; did not get requested number of digits")
  }
  frac
}

find_in_pi <- function(pattern, n_digits) {
  if (!grepl("^[0-9]+$", pattern)) stop("Pattern must be digits!")
  t0 <- proc.time()[["elapsed"]]
  frac <- pi_fraction_digits(n_digits)
  loc <- regexpr(pattern, frac, fixed = TRUE)
  elapsed <- proc.time()[["elapsed"]] - t0
  
  #getting the positions
  if (loc[1] != -1) {
    start_pos <- as.integer(loc[1])                
    end_pos   <- start_pos + nchar(pattern) - 1L
    list(found = TRUE,
         start = start_pos,
         end   = end_pos,
         digits_scanned = n_digits,
         seconds = elapsed)
  } else {
    list(found = FALSE,
         start = NA_integer_,
         end   = NA_integer_,
         digits_scanned = n_digits,
         seconds = elapsed)
  }
}

find_phrase_in_pi <- function(phrase, n_digits) {
  pat <- encode_a1z26(phrase)
  res <- find_in_pi(pat, n_digits)
  res$pattern <- pat
  res$phrase  <- phrase
  res
}

and finally, to run the function(s):

## Run functions
word <- "eggs"
encoded_word <- encode_a1z26(word)
cat("Encoded ",word," ->", encoded_word, "\n")  
result_today <- find_in_pi(encoded_word, 1e5)
print(result_today)

And see that the word “EGGS” as the number 57719, appears on Pi Number on 6026th till 6030th position. Pretty useless

As always, the complete code is available on GitHub in  Useless_R_function repository. The first version is here (filename: Find_substring_in_Pi.r).

Check the repository for future updates!

Stay healthy and happy R-coding!