#Convert from base n with a list of numbers greater than n

CJam converts a list to a number with this formula: A₀*n^l + A₁*n^l-1 + A₂*n^l-2 + A_l*n⁰ (with nonnegative n). n is the base and l is the list length. This means A_i can be any integer, which doesn't have to be in the range of [0,n).

Some examples:

• 0b extracts the last item and cast it to integer. Works like W=i and saves a byte if it wasn't integer. But everything else in the list must also be able to cast into integer.

• 1b returns the sum. Works like :i:+ and saves two bytes if they aren't integer. It also works with empty list while :+ doesn't.

• [i{_1&9 32?_@\m2/}16*;]W%:c converts a character to a string of line endings and tabs, which can be converted back with 2bc. The encoding function isn't easy to be golfed in a code-golf program, though. But you don't usually need that.

• You can use the following code to convert a string to Unicode characters not in 16 bit, which can be converted back with 2A#b128b:c. (Explanations will be added later. Or perhaps I'll write a new version later.)

    128b2A#b         " Convert to base 1024. ";
    W%2/)W%\:+       " Convert to two base 1024 digit groups. ";
    [0X@
    {
      _54+
      @I+_Am>@\-
      _Am<@+ 0@-@1^
    }fI
    ]);)
    @\+[~+]2A#b_2G#<!{2A#b}*
    \W%+:c
  

The similar method works with any set of n integers which have different values mod n.

#Convert from base n with a list of numbers greater than n

CJam converts a list to a number with this formula: A₀*n^l + A₁*n^l-1 + A₂*n^l-2 + A_l*n⁰ (with nonnegative n). n is the base and l is the list length. This means A_i can be any integer, which doesn't have to be in the range of [0,n).

Some examples:

• 0b extracts the last item and cast it to integer. Works like W=i and saves a byte if it wasn't integer. But everything else in the list must also be able to cast into integer.

• 1b returns the sum. Works like :i:+ and saves two bytes if they weren't integers. It also works with empty lists while :+ doesn't.

• [i{_1&9 32?_@\m2/}16*;]W%:c converts a character to a string of line endings and tabs, which can be converted back with 2bc. The encoding function isn't easy to be golfed in a code-golf program, though. But you don't usually need that.

• You can use the following code to convert a string to Unicode characters not in 16 bit, which can be converted back with 2A#b128b:c. (Explanations will be added later. Or perhaps I'll write a new version later.)

    128b2A#b         " Convert to base 1024. ";
    W%2/)W%\:+       " Convert to two base 1024 digit groups. ";
    [0X@
    {
      _54+
      @I+_Am>@\-
      _Am<@+ 0@-@1^
    }fI
    ]);)
    @\+[~+]2A#b_2G#<!{2A#b}*
    \W%+:c
  

The similar method works with any set of n integers which have different values mod n, if you can find some way to get rid of the most significant digit.