birthday_probability.sh

# $1: items power of 10 (e.g. 3=kilo, 6=mega)
# $2: entropy bits (80=2^80 values)
# Requires `brew install bc` (GNU bc)
birthday_probability() {
  function bc() {
    declare fmt="$1"
    shift
    printf 'scale=256\n'"$fmt"'\n' ${1+"$@"} | BC_LINE_LENGTH=0 /usr/local/opt/bc/bin/bc -l
  }
  declare exact="$(bc '1-e(-((10^%s)^2)/((2^%s)*2))' "$1" "$2")"
  declare one_in="$(bc '1/%s' "$exact")"
  declare log10="$(bc 'l(%s)/l(10)' "$exact")"
  declare exp="$(( ${log10%%.*} - 1))"
  declare dec="$(bc '%s/(10^%s)' "$exact" "$exp")"
  declare prob="${dec::8}E$exp"
  [[ "$prob" != '10.00000E-1' ]] || prob='1'
  echo "Collision probability: $prob, or 1 in ${one_in%.*}"
}