Print a number in any base without help

write sends bytes. A register holding 12345 contains no bytes that a terminal would recognise as 1, 2, 3, 4 and 5, so a program that wants to print a number has to manufacture those five characters itself.

The method is repeated division, and it produces the digits in the wrong order. Divide 12345 by ten and the remainder is 5, which is the last digit. Divide the quotient by ten and the remainder is 4, the one before it. Keep going and the digits come out backwards, which is why this program fills its buffer from the far end and works towards the front.

The console reads 12345, then 3039, then 11000000111001. One number, three bases, one subroutine, and the only thing that changed between the three calls was rsi.

Walk the buffer. rcx starts at buffer + 64, one byte past the end, and every digit produced moves it down by one and writes there. So the first digit produced, the last digit of the number, ends up at the highest address; the last one produced ends up at the lowest; and when the loop finishes, rcx is pointing at the first character of the answer with the rest of them in order in front of it. Nothing has to be reversed afterwards. buffer + 64 minus rcx is then the length, which is precisely what write wants next.

 buffer                                        buffer + 64
   |                                                |
   |                             [ 1 2 3 4 5 ]      |
                                 ^
                                rcx when the loop stops

div rsi produces both halves of what the loop needs from one instruction: the quotient in rax to go round again with, the remainder in rdx to turn into a character. The xor rdx, rdx at the top of each pass is not optional, because rdx is still holding the remainder that pass produced, and leaving it there makes the next dividend astronomically large and ends the program on a divide error.

digits is what turns a remainder into a character. Remainder 5 picks up the byte at digits + 5, which is '5'. Remainder 11 picks up 'b'. Having all thirty six of them there is the only reason the base can be an argument instead of a constant. Ask for base 36 with the number 1295 and the answer is zz, which is the largest two digit number that base has.