# in pseudo-code:
for each element
  calculate the sorting value for that element
  put the original element and the sorting value into a 2-element list
pass these 2-element lists to your sorting routine, which
  sorts based on the sorting value of each element
for each element in the sorted list of 2-element lists
  pull out the original element

# in perl, an example using the typical map/sort/map layout 
# to sort a list of numbers based on the return value of a 
# complex subroutine that calculates the number of primes
# less than each number's 25th power:

my @newarray = map { $_->[0] } 
               sort { $a->[1] <=> $b->[1] }
               map { [ $_ => n_primes_less_than_25th_power($_) ] }
             @oldarray;